Physics of Solid Surfaces: Subvolume B (Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology - New Series, 45B) 3662539063, 9783662539064

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Landolt-Bo€rnstein: Numerical Data and Functional Relationships in Science and Technology – New Series Group III: Condensed Matter Volume 45B

Landolt-B€ornstein Numerical Data and Functional Relationships in Science and Technology

New Series

Units and Fundamental Constants in Physics and Chemistry Elementary Particles, Nuclei and Atoms (Group I) (Formerly: Nuclear and Particle Physics)

Molecules and Radicals (Group II) (Formerly: Atomic and Molecular Physics)

Condensed Matter (Group III) (Formerly: Solid State Physics)

Physical Chemistry (Group IV) (Formerly: Macroscopic Properties of Matter)

Geophysics (Group V) Astronomy and Astrophysics (Group VI) Biophysics (Group VII) Advanced Materials and Technologies (Group VIII) Some of the group names have been changed to provide a better description of their contents.

G. Chiarotti • P. Chiaradia Editors

Physics of Solid Surfaces Subvolume B

Editors G. Chiarotti Department of Physics University of Rome Tor Vergata Rome, Italy

P. Chiaradia Department of Physics University of Rome Tor Vergata Rome, Italy

ISSN 1615-1925 ISBN 978-3-662-53906-4 ISBN 978-3-662-53908-8 (eBook) https://doi.org/10.1007/978-3-662-53908-8 Library of Congress Control Number: 2017955702 © Springer-Verlag GmbH Germany 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer-Verlag GmbH Germany The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany

This volume is dedicated to the memory of Prof. G. Chiarotti, who passed away on the 12th October 2017 at the age of 89, soon after completing this editorial work. In mourning his passing, we recall his commitment and dedication as scientist and teacher, his outstanding legacy in surface science, and celebrate his moral standing and intellectual honesty. P. Chiaradia (Co-editor), the Authors of LB III/45A and B and the Editorial Staff of Springer Nature

Preface

Nowadays about two decades have elapsed since the publication of Volume III/24 of the LandoltB€ ornstein Series, a book presenting the main results obtained in the field of Physics of Solid Surfaces since its birth (~1970) up to mid-1990s. After such a considerable time, the need for updating Volume III/24 was widely recognized. Actually, the issue was not merely to write an update of single chapters of Volume III/24, but also to account for the numerous significant developments appeared in Surface Physics in the last 20 years. These were the ideas behind the present LB Volume III/45, which maintains the same title of Volume III/24: Physics of Solid Surfaces. Volume III/45 consists of 21 contributions (against 17 for Volume III/24), divided in two subvolumes, A and B. About one third of these contributions deal with entirely new topics or methods – some of which are still in a phase of rapid expansion. As in the case of Volume III/24, emphasis is given to clean solid surfaces, without neglecting adsorbatecovered surfaces, when required by a special interest or for the sake of completeness. Rome, March 2017

The Editors

vii

Contents

Part I

General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 General introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 G. Chiarotti and P. Chiaradia

Chapter 1

Part II

Theoretical Foundations and Simulation of Surface Structures . . . . . . . . . . . . . . . . . . . 1

Chapter 2

Introduction to basic principles of surface structure theoretical simulation . . . . . 1 A. Shkrebtii and M. Rohlfing

Chapter 3

Physics mechanisms of the surface structure formation . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii and M. Rohlfing

Chapter 4

Compilation of the theoretical frameworks for surface structure simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii and M. Rohlfing

Chapter 5

Determination of the total energy of a many-particle system . . . . . . . . . . . . . . . . 1 A. Shkrebtii and M. Rohlfing

Chapter 6

Basic numerical approaches for surface structure simulation . . . . . . . . . . . . . . . . 1 A. Shkrebtii and M. Rohlfing

Chapter 7

Comparing theoretically simulated and experimentally determined surface structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii and M. Rohlfing

Chapter 8

Application to prototypical homopolar semiconductor clean surfaces . . . . . . . . . . 1 A. Shkrebtii and M. Rohlfing

Chapter 9

Application to prototypical heteropolar semiconductor clean surfaces . . . . . . . . . 1 A. Shkrebtii and M. Rohlfing

Chapter 10

Application to prototypical metal clean surfaces: the Au(110) 1  2 missing-row structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii and M. Rohlfing

Chapter 11

Application to prototypical metal-oxide clean surfaces: the complex TiO2 (110) surface reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii and M. Rohlfing

Chapter 12

Conclusions about theoretical foundations and simulation of surface structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii and M. Rohlfing

Part III

Surface Reconstruction and Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 13

Introduction to surface reconstruction and relaxation . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 14

Clean surfaces of semiconductors: introductory remarks . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino ix

x

Contents

Chapter 15

Homopolar cubic semiconductors: clean diamond surfaces C(100), C(110), and C(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 16

Homopolar cubic semiconductors: clean silicon surfaces Si(100), Si(110), and Si(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 17

Homopolar cubic semiconductors: clean germanium surfaces Ge(100), Ge(110), and Ge(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 18

Heteropolar cubic semiconductors: low-index surfaces of zinc blend compound semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 19

Heteropolar Wurtzite type semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 20

Clean surfaces of oxides: introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 21

Clean surfaces of titanium dioxide TiO2 and other rutile structures . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 22

Clean surfaces of zinc oxide and other Wurtzite type structures . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 23

Clean surfaces of rock salt oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 24

Clean surfaces of perovskites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 25

Clean surfaces of corundum oxides and similar . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 26

Clean surfaces of calcite-form oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 27

Clean surfaces of metals: introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 28

Relaxation of the clean surfaces of metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Chapter 29

Reconstruction at the clean surfaces of metals . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A. Shkrebtii, F. Filippone, and A. Fasolino

Part IV

Structural Defects at Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 30

Introduction to structural defects at surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 31

Structure of domain boundaries: metals: Au . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 32

Structure of domain boundaries: metals: Fe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 33

Structure of domain boundaries: metals: Ga . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Contents

xi

Chapter 34

Structure of domain boundaries: metals: Ir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 35

Structure of domain boundaries: metals: Pt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 36

Structure of domain boundaries: metals: W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 37

Structure of domain boundaries: group IV elements and IV–IV compounds: diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 38

Structure of domain boundaries: group IV elements and IV–IV compounds: Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 39

Structure of domain boundaries: group IV elements and IV–IV compounds: Ge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 40

Structure of domain boundaries: group IV elements and IV–IV compounds: SiC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 41

Structure of domain boundaries: group III–V compounds: GaAs . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 42

Structure of domain boundaries: other III–V compounds: GaP, GaSb, InAs, InP, InSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 43

Structure of domain boundaries: II–VI compounds: CdTe, HgTe . . . . . . . . . . . . 1 J. Wollschläger

Chapter 44

Structure of domain boundaries: binary oxides: Al2O3 . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 45

Structure of domain boundaries: binary oxides: Al2O3 films . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 46

Structure of domain boundaries: binary oxides: Fe3O4 . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 47

Structure of domain boundaries: binary oxides: Fe3O4 films on MgO(001) . . . . . 1 J. Wollschläger

Chapter 48

Structure of domain boundaries: binary oxides: TiO2 (anatase) . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 49

Structure of domain boundaries: binary oxides: TiO2 (rutile) . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 50

Structure of domain boundaries: other binary oxides: SiO2, SnO2, and WO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 51

Structure of domain boundaries: ternary oxides: titanates (BaTiO3, SrTiO3) . . . . 1 J. Wollschläger

Chapter 52

Decoration of domain boundaries: metals: Au (decoration by metals) . . . . . . . . . 1 J. Wollschläger

xii

Contents

Chapter 53

Decoration of domain boundaries: metals: Au (decoration by molecules) . . . . . . . 1 J. Wollschläger

Chapter 54

Decoration of domain boundaries – group IV elements and IV–IV compounds – Si (001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 55

Decoration of domain boundaries: group IV elements and IV–IV compounds: Si(111) (decoration by elemental metals and semiconductors) . . . . . . 1 J. Wollschläger

Chapter 56

Decoration of domain boundaries: group IV elements and IV–IV compounds: Si(111) (decoration by compounds) . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 57

Decoration of domain boundaries: group IV elements and IV–IV compounds: Si(111) (decoration by molecules) . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 58

Decoration of domain boundaries: group IV elements and IV–IV compounds: other Si surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 59

Decoration of domain boundaries: group IV elements and IV–IV compounds: Ge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 60

Decoration of domain boundaries: group IV elements and IV–IV compounds: SiC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 61

Decoration of domain boundaries: group III–V compounds: InSb . . . . . . . . . . . . 1 J. Wollschläger

Chapter 62

Decoration of domain boundaries: binary oxides: Al2O3 . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 63

Decoration of domain boundaries: binary oxides: Al2O3 films . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 64

Decoration of domain boundaries: binary oxides: Fe3O4 . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 65

Decoration of domain boundaries: binary oxides: TiO2 . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 66

Decoration of domain boundaries: ternary oxides: SrTiO3 . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 67

Coexistence of domains: metals: Au . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 68

Coexistence of domains: metals: other metals (Ir, Pt, W) . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 69

Coexistence of domains: group IV elements and IV–IV compounds: diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 70

Coexistence of domains: group IV elements and IV–IV compounds: Si . . . . . . . . 1 J. Wollschläger

Contents

xiii

Chapter 71

Coexistence of domains: group IV elements and IV–IV compounds: Ge . . . . . . . . 1 J. Wollschläger

Chapter 72

Coexistence of domains: group III–V compounds: GaAs . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 73

Coexistence of domains: other III–V compounds and II–VI compounds (AlSb, GaP, GaSb, InAs, InP, InSb, CdTe) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 74

Coexistence of domains: binary oxides: Al2O3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 75

Coexistence of domains: binary oxides: TiO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 76

Coexistence of domains: other binary oxides (Ce7O11, Fe3O4, Fe3O4/MgO, SnO2, WO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 77

Coexistence of domains: ternary oxides: BaTiO3 . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 78

Coexistence of domains: ternary oxides: SrTiO3 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 79

Phase transition: metals: Au . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 80

Phase transition: metals: Ga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 81

Phase transition: metals: Ir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 82

Phase transition: metals: Mo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 83

Phase transition: metals: Pt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 84

Phase transition: metals: W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 85

Phase transition: group IV elements and IV–IV compounds: diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 86

Phase transition: group IV elements and IV–IV compounds: Si . . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 87

Phase transition: group IV elements and IV–IV compounds: Ge . . . . . . . . . . . . . 1 J. Wollschläger

Chapter 88

Phase transition: group IV elements and IV–IV compounds: SiC . . . . . . . . . . . . . 1 J. Wollschläger

Part V

Photoelectron Spectroscopies Applied to Condensed Matter Systems . . . . . . . . . . . . . . 1

Chapter 89

Historical remarks and introduction to photoemission . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

xiv

Contents

Chapter 90

The photoemission process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 91

Inverse photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 92

Spin-polarized photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 93

Two-photon photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 94

Core-level excitation and related resonant phenomena . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 95

Escape depth of the photoelectrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 96

Electronic structure in the surface region: bulk and surface states . . . . . . . . . . . 1 P. D. Johnson

Chapter 97

Electronic structure in the surface region: Shockley surface states and image states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 98

Electronic structure in the surface region: the Rashba effect and surface states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 99

Electronic structure in the surface region: quantum well states . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 100

Electronic structure in the surface region: electron-boson coupling in metallic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 101

The common crystal structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 102

Electronic structure studies of Be (beryllium) . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 103

Electronic structure studies of C (carbon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 104

Electronic structure studies of Mg (magnesium) . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 105

Electronic structure studies of Si (silicon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 106

Electronic structure studies of V (vanadium) . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 107

Electronic structure studies of Cr (chromium) . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 108

Electronic structure studies of Fe (iron) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 109

Electronic structure studies of Ni (nickel) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Contents

xv

Chapter 110

Electronic structure studies of Cu (copper) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 111

Electronic structure studies of Ga (gallium) and related compounds: the case of GaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 112

Electronic structure studies of Ge (germanium) . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 113

Electronic structure studies of Nb (niobium) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 114

Electronic structure studies of Mo (molybdenum) . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 115

Electronic structure studies of Pd (palladium) . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 116

Electronic structure studies of Ag (silver) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 117

Electronic structure studies of W (tungsten) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 118

Electronic structure studies of Ir (iridium) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 119

Electronic structure studies of Pt (platinum) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 120

Electronic structure studies of Au (gold) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 121

Electronic structure studies of Pb (lead) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 122

Electronic structure studies of Bi (bismuth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 123

Electronic structure studies of Ce (cerium) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 124

Electronic structure studies of Gd (gadolinium) . . . . . . . . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 125

Strongly correlated systems: high-Tc superconductors: cuprates . . . . . . . . . . . . 1 P. D. Johnson

Chapter 126

(strongly correlated systems): high Tc superconductors: Fe-based . . . . . . . . . . . 1 P. D. Johnson

Chapter 127

Dirac cones and topological states: topological insulators . . . . . . . . . . . . . . . . . . 1 P. D. Johnson

Chapter 128

Dirac cones and topological states: Dirac and Weyl semimetals . . . . . . . . . . . . . 1 P. D. Johnson

Part VI

Raman Scattering at Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 129

Introduction to Raman scattering at surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

xvi

Contents

Chapter 130

Fundamentals of surface Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 131

Raman selection rules and surface Raman tensor . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 132

Surface resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 133

Historical remarks on surface Raman scattering . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 134

Clean InP(110) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 135

Clean Ge(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 136

Clean Si(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 137

Sb monolayer-terminated III–V(110) surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 138

Sb-terminated Si(001) and Ge(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 139

As-terminated Si(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 140

In-terminated Si(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 141

Au-terminated Si(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 142

Au-terminated Si(553) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Chapter 143

Metal surfaces: Si nanoribbons on Ag(110) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 N. Esser and E. Speiser

Part VII

Field Electron and Ion Emission: Basic Formulae and Constants . . . . . . . . . . . . . . . . 1

Chapter 144

Introduction to field electron and ion emission and customary units . . . . . . . . . . 1 R. G. Forbes

Chapter 145

Basic terminology of Fowler-Nordheim electron transmission theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 146

Transmission probability for an exactly triangular barrier . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 147

Transmission probability for a general rounded barrier . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 148

The Schottky effect and related parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 149

Transmission probability for a Schottky-Nordheim barrier . . . . . . . . . . . . . . . . 1 R. G. Forbes

Contents

xvii

Chapter 150

Local emission current density regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 151

Local emission current densities for a Schottky-Nordheim barrier . . . . . . . . . . . 1 R. G. Forbes

Chapter 152

Energy distributions for the Schottky-Nordheim barrier . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 153

Basic auxiliary relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 154

Field electron emission measurement circuit theory . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 155

Basic theory of Fowler-Nordheim plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 156

Testing for lack of field emission orthodoxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 157

Theoretical introduction to field evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 158

The prediction of zero-barrier evaporation field . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 159

Post-field ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 160

The “changeover field” in thermal-field shaping . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 161

The position of the electrical surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 162

Physical properties of the noble operating gases . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Chapter 163

Field calibration issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 R. G. Forbes

Part VIII

Epigraphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 164

Introduction to epigraphene and overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Berger, E. H. Conrad, and W. A. de Heer

Chapter 165

The electronic band structure of graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Berger, E. H. Conrad, and W. A. de Heer

Chapter 166

Silicon carbide and epitaxial graphene on silicon carbide . . . . . . . . . . . . . . . . . . 1 C. Berger, E. H. Conrad, and W. A. de Heer

Chapter 167

Structure and band structure of epitaxial graphene on hexagonal silicon carbide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Berger, E. H. Conrad, and W. A. de Heer

Chapter 168

Electronic transport properties of epigraphene . . . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Berger, E. H. Conrad, and W. A. de Heer

Chapter 169

Transport properties of epigraphene in magnetic field . . . . . . . . . . . . . . . . . . . . 1 C. Berger, E. H. Conrad, and W. A. de Heer

xviii

Contents

Chapter 170

Towards electronic devices based on epigraphene . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Berger, E. H. Conrad, and W. A. de Heer

Chapter 171

Optical and plasmonic properties of epigraphene . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Berger, E. H. Conrad, and W. A. de Heer

Part IX

Fullerenes on Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 172

Introduction to fullerenes on surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Cepek and A. Goldoni

Chapter 173

Band dispersion of solid C60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Cepek and A. Goldoni

Chapter 174

Fullerenes on metals and semiconductors: interaction with the substrate . . . . . . 1 C. Cepek and A. Goldoni

Chapter 175

Ordered fullerenes on metal surfaces: monatomic steps on vicinal surfaces and reconstruction on metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Cepek and A. Goldoni

Chapter 176

C60 monolayer on semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Cepek and A. Goldoni

Chapter 177

Directing fullerene adsorption via supramolecular templates . . . . . . . . . . . . . . . 1 C. Cepek and A. Goldoni

Chapter 178

Co-adsorbed fullerene systems and the formation of heterojunction layers at a nanometer scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 C. Cepek and A. Goldoni

Part X

Surfaces at Metal-Electrolyte Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 179

Introduction to surfaces at metal-electrolyte interfaces . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 180

Anion interaction with copper surfaces: general properties of metal surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 181

Hydrohalic acid interaction with copper surfaces: adsorption of halide anions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 182

Hydrohalic acid interaction with copper surfaces: Cu(100) – chloride and bromide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 183

Hydrohalic acid interaction with copper surfaces: Cu(100) – iodide . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 184

Hydrohalic acid interaction with copper surfaces: XRD of chloride, bromide, and iodide on Cu(100) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 185

Hydrohalic acid interaction with copper surfaces: Cu(111) – chloride . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 186

Hydrohalic acid interaction with copper surfaces: Cu(111) – bromide . . . . . . . . 1 M. Nowicki and K. Wandelt

Contents

xix

Chapter 187

Hydrohalic acid interaction with copper surfaces: Cu(111) – iodide . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 188

Hydrohalic acid interaction with copper surfaces: Cu(110) – bromide . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 189

Hydrohalic acid interaction with copper surfaces: Cu(110) – chloride . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 190

Hydrohalic acids interaction with copper surfaces: CuI compound formation . . . . 1 M. Nowicki and K. Wandelt

Chapter 191

Hydrohalic acids interaction with copper surfaces: XPS of Cu(111) – iodide interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 192

Copper surfaces in perchloric acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 193

Copper surfaces in sulfuric acid: sulfate adsorption on Cu(100) and Cu(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 194

Copper surfaces in sulfuric acid: sulfate structure on Cu(111) . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 195

Copper surfaces in sulfuric acid: sulfate adsorption configuration . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 196

Copper surfaces in sulfuric acid: sulfate-induced surface morphology . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 197

Copper surfaces in sulfuric acid: sulfate adsorption/desorption kinetics . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 198

Hydrohalic acid anion interaction with silver surfaces: Ag(100) – chloride . . . . . 1 M. Nowicki and K. Wandelt

Chapter 199

Hydrohalic acid anion interaction with silver surfaces: Ag(100) – bromide . . . . 1 M. Nowicki and K. Wandelt

Chapter 200

Hydrohalic acid anion interaction with silver surfaces: Ag(100) – iodide . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 201

Hydrohalic acid anion interaction with silver surfaces: Ag(111) – chloride . . . . . 1 M. Nowicki and K. Wandelt

Chapter 202

Hydrohalic acid anion interaction with silver surfaces: Ag(111) – bromide . . . . 1 M. Nowicki and K. Wandelt

Chapter 203

Hydrohalic acid anion interaction with silver surfaces: Ag(111) – iodide . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 204

Hydrohalic acid anion interaction with silver surfaces: Ag(110) – chloride, bromide, and iodide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 205

Silver surfaces in perchloric acid: Ag(110) – perchlorate . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 206

Silver surfaces in sulfuric acid: Ag(100) – sulfate . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

xx

Contents

Chapter 207

Silver surfaces in sulfuric acid: Ag(111) – sulfate . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 208

Silver surfaces in sulfuric acid: Ag(110) – sulfate . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 209

Hydrohalic-acid anion interaction with gold surfaces: Au(100) – chloride . . . . . 1 M. Nowicki and K. Wandelt

Chapter 210

Hydrohalic-acid anion interaction with gold surfaces: Au(100) – bromide . . . . . 1 M. Nowicki and K. Wandelt

Chapter 211

Hydrohalic-acid anion interaction with gold surfaces: Au(100) – iodide . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 212

Hydrohalic-acid anion interaction with gold surfaces: Au(111) – chloride . . . . . 1 M. Nowicki and K. Wandelt

Chapter 213

Hydrohalic-acid anion interaction with gold surfaces: Au(111) – bromide . . . . . 1 M. Nowicki and K. Wandelt

Chapter 214

Hydrohalic acid anion interaction with gold surfaces: Au(111) – iodide . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 215

Hydrohalic acid anion interaction with gold surfaces: Au(110) – bromide . . . . . 1 M. Nowicki and K. Wandelt

Chapter 216

Hydrohalic acid anion interaction with gold surfaces: Au(110) – iodide . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 217

Gold surfaces in perchloric acid: Au(100) – perchlorate . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 218

Gold surfaces in perchloric acid: Au(111) – perchlorate . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 219

Gold surfaces in perchloric acid: Au(110) – perchlorate . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 220

Gold surfaces in sulfuric acid: Au(100) – sulfate . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 221

Gold surfaces in sulfuric acid: Au(111) – sulfate . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 222

Gold surfaces in sulfuric acid: Au(110) – sulfate . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 223

Hydrohalic-acid anion interaction with platinum surfaces: Pt(100) – bromide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 224

Hydrohalic acid anion interaction with platinum surfaces: Pt(100) – iodide . . . . . 1 M. Nowicki and K. Wandelt

Chapter 225

Hydrohalic acid anion interaction with platinum surfaces: Pt(111) – chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 226

Hydrohalic acid anion interaction with platinum surfaces: Pt(111) – bromide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Contents

xxi

Chapter 227

Hydrohalic acid anion interaction with platinum surfaces: Pt(111) – iodide . . . . 1 M. Nowicki and K. Wandelt

Chapter 228

Hydrohalic acid anion interaction with platinum surfaces: Pt(110) – bromide . . 1 M. Nowicki and K. Wandelt

Chapter 229

Hydrohalic acid anion interaction with platinum surfaces: Pt(110) – iodide . . . . 1 M. Nowicki and K. Wandelt

Chapter 230

Platinum surfaces in perchloric acid: Pt(111), Pt(100), Pt(110) – perchlorate . . . 1 M. Nowicki and K. Wandelt

Chapter 231

Platinum surfaces in sulfuric acid: general remarks . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 232

Platinum surfaces in sulfuric acid: Pt(100) – sulfate . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Chapter 233

Platinum surfaces in sulfuric acid: Pt(111) – sulfate . . . . . . . . . . . . . . . . . . . . . . 1 M. Nowicki and K. Wandelt

Contributors

Editors P. Chiaradia Department of Physics, University of Rome Tor Vergata, Rome, Italy G. Chiarotti Department of Physics, University of Rome Tor Vergata, Rome, Italy

Authors C. Berger School of Physics, Georgia Institute of Technology, Atlanta, GA, USA Institut Ne´el, CNRS - University Grenoble - Alpes, Grenoble, France C. Cepek CNR-IOM, Laboratorio Nazionale TASC, Trieste, Italy E. H. Conrad School of Physics, Georgia Institute of Technology, Atlanta, GA, USA N. Esser Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V., Interface Analytics Department, Berlin, Germany A. Fasolino Radboud Universiteit Nijmegen/Theory of Condensed Matter, Nijmegen, The Netherlands F. Filippone Institute of Structure of Matter (ISM) of CNR at Montelibretti, Monterotondo, RM, Italy R. G. Forbes Advanced Technology Institute, University of Surrey, Guildford, UK A. Goldoni Elettra Sincrotrone Trieste, Trieste, Italy W. A. de Heer School of Physics, Georgia Institute of Technology, Atlanta, GA, USA TICNN, Tianjin University, Tianjin, China P. D. Johnson Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA M. Nowicki Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland M. Rohlfing Institut für Festk€ orpertheorie, Universität Münster, Münster, Germany A. Shkrebtii Faculty of Science, University of Ontario Institute of Technology (UOIT), Oshawa, ON, Canada E. Speiser Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V., Interface Analytics Department, Berlin, Germany K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany J. Wollschläger Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany

xxiii

Part I

General Introduction

Chapter 1

General introduction G. Chiarotti and P. Chiaradia

1.1

Motivation

The present volume was initially thought as an updating of the volume “Physics of Solid Surfaces” LB III/24, edited by one of us (Gianfranco Chiarotti) in the years 1993–1996 and presenting data published until the early 1990s. However, in the last two decades, several new scientific topics have been developed. Examples are graphene, fullerenes, nanotubes, metal oxides, ab initio theoretical simulations, manipulation of surfaces with the methods of scanning probe microscopy, discovery of repulsive Casimir forces having potential interest for frictionless micromechanical devices, and recent developments in solid-electrolyte interfaces. Therefore, the present volume is only in part an updating of the old volume. It should rather be looked at as a reconsideration and expansion of the entire field of solid surfaces. Among the new contributions, Raman spectroscopy applied to surfaces is also included. In the early 1990s, this subject was still in its infancy and therefore did not appear in LB III/24. An interesting novelty is represented by topological insulators, whose surfaces behave as conductors. In the present volume, such a topic is not dealt with extensively, since the related literature is still rapidly evolving. However, the subject is addressed in two contributions. Firstly, in the contribution “Electronic Structure of Surfaces” (subvolume A), topological insulators are briefly discussed, and a few recent review articles are quoted. Secondly, in the contribution “Photoelectron spectroscopies applied to condensed matter systems” (subvolume B), after a clear and succinct introduction, the most important recent photoemission data on these materials are critically reviewed. By “updating” we actually meant covering the period of time from the previous LB volume to now, excluding the span of time already reviewed. However, a few exceptions to this rule were allowed, as specified below. In recent years, a great interest has been focused on surfaces covered with adsorbates and in general on more realistic systems than clean surfaces proper. The topic of surfaces with adsorbates was partially covered by the volume LB III/42A, edited by H.P. Bonzel more than a decade ago (2001). As already stated, the present volume deals essentially with clean surfaces. However, we have left freedom to the authors to extend their contributions to adsorbate-covered surfaces as well, where they have reckoned it useful for understanding the properties of clean surfaces or in cases of particular relevance. In the whole field of surface science, but especially when considering adsorbates, the boundary between physics and chemistry is ill defined. For this reason the reader should not be surprised to find a chemical point of view in treating some borderline topics. The volume is divided in two subvolumes, A and B. Warning: Due to a workflow change implemented by the Publisher after the publication of the first subvolume, the terminology is not fully standardized in the two subvolumes. In particular, while in subvolume A the various contributions are called “chapters,” in subvolume B the contributions become “parts” (one hierarchy higher), and the “sections” become “chapters.”

G. Chiarotti (*) • P. Chiaradia Department of Physics, University of Rome Tor Vergata, Rome, Italy e-mail: [email protected]; [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_1

1

2

G. Chiarotti and P. Chiaradia

As a rule, acronyms are defined in the text, the first time they appear. Furthermore, a comprehensive list of the most important acronyms, used throughout each subvolume, is provided at the end of the General Introduction, for the reader’s benefit. Outline of the Subvolumes A and B. Subvolume A contains the following 13 contributions: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

General introduction Scanning tunneling microscopy of metals and semiconductors Manipulation of surfaces by scanning probe microscopy X-ray diffraction of surface structures Elastic scattering and diffraction of electrons and positrons Elastic and inelastic scattering of ions Electronic structure of surfaces Optical properties of surfaces Inelastic scattering of electrons Interaction of atoms with surfaces and surface phonons Magnetic properties at surfaces Surface properties of nanotubes Casimir effect between solid surfaces

Subvolume B contains the following ten contributions: I. II. III. IV. V. VI. VII. VIII. IX. X.

General introduction Theoretical foundations and simulation of surface structures Surface reconstruction and relaxation Structural defects at surfaces Photoelectron spectroscopies applied to condensed matter systems Raman scattering at surfaces Field electron and ion emission: basic formulae and constants Epigraphene Fullerenes on surfaces Surfaces at metal-electrolyte interfaces

Each contribution is written by one or more authors of undiscussed authority in that specific field and generally consists of: 1. Introduction 2. Compilation of data in the form of tables and figures 3. Bibliography In each contribution the Introduction reviews in a succinct form the key aspects of the specific field and presents the relevant formulas, a hint to their derivation, a definition of the quantities reported in the Data Section. The scope of having such an Introduction is to offer a volume that is more “readable” than usual data handbooks so as to be used also by scientists working in a different area or approaching surface physics for the first time. In the Data Section, the results are ordered according to elements or compounds and, for each substance, according to specific surfaces, listed by increasing sum of Miller indices. In the following the single contributions of subvolume B are briefly introduced. Most of the Parts of this subvolume were finalized between the end of 2015 and the beginning of 2016, thereby setting the upper temporal limit of the references in these Parts.

1.2

Theoretical Foundations and Simulation of Surface Structures

After the seminal paper by Roberto Car and Michele Parrinello of 1985 that started the so-called “ab initio” calculations, opening the possibility of theoretically simulating the structure of surfaces, a number of papers have been published developing and improving the method. This is the subject of this contribution that starts explaining in words the various results and methods developed since 1985, leaving the complex

1 General introduction

3

mathematical formulation to a later part of the contribution. The authors individuate five basic principles that drive the relaxation and reconstruction of clean semiconductor surfaces: Principle 1. Reconstruction of semiconductor surfaces tends either to saturate surface dangling bonds (DBs) via re-hybridization or to convert them into nonbonding electronic states. Principle 2. In many cases even if DBs are saturated (as governed by principle 1), surfaces can lower their energies by further atomic relaxation leading to semiconducting (as opposed to metallic) surface state eigenvalue spectra. Principle 3. The surface structures observed will be the lowest free-energy structure kinetically accessible under the preparation conditions. Principle 4. Surfaces tend to be auto-compensated. Principle 5. For a given surface stoichiometry, the surface atomic geometry is determined primarily by a rehybridization-induced lowering of the surface state bonds associated with either surface bonds or (filled) anion dangling bonds. The contribution is divided in the following chapters: 2. 3. 4. 5.

6. 7. 8. 9.

10. 11. 12.

1.3

Introduction to basic principles of surface structure theoretical simulation Physics mechanisms of the surface structure formation Compilation of the theoretical frameworks for surface structure simulations Determination of the total energy of a many-particle system (including the following topics: parametrized force fields, empirical tight-binding methods, Hartree–Fock approximation, density functional theory, quantum Monte Carlo, random phase approximation total energy) Basic numerical approaches for surface structure simulation Comparing theoretically simulated and experimentally determined surface structures Application to prototypical homopolar semiconductor clean surfaces (Si(111) 2  1 Pandey reconstruction, Si(111) 7  7 DAS structure, and Ge(111) 2  1 and c (2  8) reconstructions) Application to prototypical heteropolar semiconductor clean surfaces (cleaved nonpolar surfaces of ionic semiconductors and oxides: GaAs(110) 1  1 bond rotation relaxation model as an example, polar surfaces of ionic materials; GaAs(100) surface stoichiometry and structure) Application to prototypical metal clean surfaces: the Au(110) 1  2 missing row structure Application to prototypical metal-oxide clean surfaces: the complex TiO2 (110) reconstruction Conclusions about theoretical foundations and simulation of surface structures

Surface Reconstruction and Relaxation

It is well known that the positions of surface atoms usually differ from those of the corresponding truncated bulk. Deviations from ideal positions may lead to reconstruction (mostly on semiconductors), relaxation (mostly on metals), and to a special case of inhomogeneous relaxation called rumpling (mostly on oxides). Accurate knowledge of the atomic structure of clean surfaces is fundamental for understanding a host of technologically important process. Among them are epitaxial growth, surface phase transitions, functionalization by adsorption of various molecules, development of sensors, catalysis, and fabrication of nanomaterials. The contribution illustrates the most important advances, which took place in the last two decades in the field of surface microscopic structure. Recent improvements of experimental techniques are described, as well as “computer experiments,” allowing one to theoretically simulate the results of certain experiments. As a matter of fact, just by comparing the results of real and simulated experiments, much progress was made. Since the atomic structure of low-index surfaces of most metals and semiconductors was already well known in the 1990s, at the time of the previous Landolt–B€ornstein data series, only an updating describing some relevant refinements is presented here. Speaking of metals, an open problem is represented by the lack of agreement between experimental and theoretical results on surface relaxation, which occurs in many cases. As far as the oxides are concerned, they represent a new field deserving special attention. The inherent complexity of oxide surfaces is discussed, starting from the difficulties encountered in obtaining high-quality stoichiometric, defect-free surfaces and including the charging problem and some ways of circumventing it.

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The contribution is divided into the following chapters: 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

1.4

Introduction to surface reconstruction and relaxation Clean surfaces of semiconductors: introductory remarks Homopolar cubic semiconductors: clean diamond surfaces C(100), C(110), and C(111) Homopolar cubic semiconductors: clean silicon surfaces Si(100), Si(110), and Si(111) Homopolar cubic semiconductors: clean germanium surfaces Ge(100), Ge(110), and Ge(111) Heteropolar cubic semiconductors: low-index surfaces of zinc-blend compound semiconductors Heteropolar wurtzite-type semiconductors Clean surfaces of oxides: introductory remarks Clean surfaces of titanium dioxide TiO2 and other rutile structures Clean surfaces of zinc oxide and other wurtzite-type structures Clean surfaces of rock salt oxides Clean surfaces of perovskites Clean surfaces of corundum oxides and similar Clean surfaces of calcite-form oxides Clean surfaces of metals: introductory remarks Relaxation of the clean surfaces of metals Reconstruction at the clean surfaces of metals

Structural Defects at Surfaces

This contribution is an updating of the earlier chapter published in 1993 in the LB volume III/24 edited by one of us (G.C.). In the last 23 years, several major improvements both in technical apparatuses and theoretical knowledge have taken place, calling for this updating. In this contribution a great emphasis is given to the morphology of surface defects (e.g., vacancies, interstitial adatoms, adatom-vacancy pairs, linear defects as atomic steps, domain boundaries, etc.). Surface defects can also be caused by defects in the underlying bulk, for example, linear dislocations emerging to the surface are truncated causing point defects. The author emphasizes that surface defects play an important role in different physical properties of surfaces. For instance, the diffusion of adatoms can be either enhanced or reduced by surface defects. Furthermore, defects may act as nucleation centers during epitaxy, and the morphology of the surface may depend drastically on the perfectness of the substrate. In addition, defects influence chemical reactions at surfaces, and these processes can be catalyzed by surface defects. The article is divided into an introduction and a data section. The latter is composed of: (i) Structure of domain boundary (metals, group IV elements and IV–IV compounds, group III–V compounds, II–VI compounds, binary oxides, ternary oxides), Chaps. 31–51 (ii) Decoration of domain boundary (metals, group IV elements and IV–IV compounds, group III–V compounds, binary oxides, ternary oxides), Chaps. 52–66 (iii) Coexisting domains (metals, group IV elements and IV–IV compounds, group III–V compounds, binary oxides, ternary oxides), Chaps. 67–78 (iv) Phase transitions (metals, group IV elements and IV–IV compounds), Chaps. 79–88

1.5

Photoelectron Spectroscopies Applied to Condensed Matter Systems

Photoemission has been one of the most popular tools for studying surface electronic states, since the birth of surface science. Besides updating the previous review which appeared in this series in the early 1990s, the present contribution presents the numerous novelties appeared in this field approximately in the last 20 years. On the instrumentation side, the advent of a new class of electron spectrometers, allowing measurements of both energy and momentum of photoelectrons, with high resolution, drastically changed the approach to this technique. Determination of electron lifetimes, of spin excitations, and of interaction of photoelectrons with collective excitations all became possible, paving the way to investigating new physical systems and phenomena. Another recent instrumental improvement consists in the use of new lasers, especially for two-photon processes (pump and probe), allowing one to study both occupied and

1 General introduction

5

unoccupied surface states. The latter can be investigated also with inverse photoemission, although with persisting severe limitations in the attainable energy resolution. The most relevant results obtained with photoemission on clean solid surfaces in the last two decades are critically reviewed, including a discussion on “old” and “new” high-Tc superconductors. An interesting chapter of the contribution is devoted to the emerging field of topological insulators, with tutorial introduction and critical presentation of a large amount of data. The contribution is divided into the following sections: (i) An introductory section (historical remarks and introduction to photoemission, photoemission process, inverse photoemission, spin-polarized photoemission, two-photon photoemission, core level excitation and related resonant phenomena, escape depth of the photoelectrons), Chaps. 89–95 (ii) Electronic structure in the surface region (bulk and surface states, Shockley surface states and image states, the Rashba effect and surface states, quantum well states, electron-boson coupling in metallic systems, the common crystal structures), Chaps. 96–101 (iii) A collection of electronic structure studies of elements (beryllium, carbon, magnesium, silicon, vanadium, chromium, iron, nickel, copper, gallium, gallium nitride, germanium, niobium, molybdenum, palladium, silver, tungsten, iridium, platinum, gold, lead, bismuth, cerium, gadolinium), Chaps. 102–125 (iv) Strongly correlated systems: high-Tc superconductors (cuprate- and Fe-based superconductors), Chaps. 126 and 127 (v) Dirac cones and topological states (topological insulators, Dirac and Weyl semimetals), Chaps. 128 and 129

1.6

Raman Scattering at Surfaces

Raman scattering was first demonstrated as a suitable tool for surface science in the early 1990s. Therefore it did not appear in the previous Landolt–B€ ornstein data series entitled Physics of Solid Surface, which was published in the same years. As discussed in this contribution, in normal conditions the Raman signal coming from a surface is expected to be very small, as compared to the bulk signal. However, surface sensitivity in Raman spectroscopy can be significantly enhanced by exploiting the resonance effect, i.e., with the energy of the excitation photon overlapping with (or being very close to) a surface electronic transition. After introducing the basic principles and the current understanding of surface Raman spectroscopy, the available data are critically reviewed. They concern mostly semiconductor surfaces, both clean and covered with adsorbates. The contribution is divided into an introductory part and a data section. The first comprises the following chapters: 130. 131. 132. 133. 134.

Introduction to Raman scattering at surfaces Fundamentals of surface Raman spectroscopy Raman selection rules and surface Raman tensor Surface resonance Historical remarks on surface Raman scattering

The data section comprises the following chapters: 135. 136. 137. 138. 139. 140. 141. 142.

Clean InP(110) Clean Ge(001) Clean Si(111) Sb monolayer-terminated III–V(110) surfaces (structure and electronic properties, surface phonons, selection rules, surface resonance) Sb-terminated Si(001) and Ge(001) As-terminated Si(111) In-terminated Si(111) (surface phonons, Raman selection rules, and surface resonance) Au-terminated Si(111)

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143. Au-terminated Si(553) 144. Pb-terminated Si(111) 145. Metal surfaces: Si nanoribbons on Ag(110)

1.7

Field Electron and Ion Emission: Basic Formulae and Constants

Emission of both electrons and ions from a surface can take place, even at normal temperatures, if a sufficiently strong electric field is applied to the surface, larger for ions than for electrons. A mandatory requirement for such a process to occur is that the sample is shaped as a sharp tip. These phenomena are interesting in themselves, since they are related to many relevant physical branches (especially condensed matter physics, electrostatics, electrodynamics, surface science). Nevertheless, they are also important in many applications concerning surface studies, since a large class of microscopes with near-atomic resolution is based on field electron or ion emission. Moreover, the combination of field ion emission and mass spectroscopy allows one to perform a chemical analysis at atomic level of the surface and even below the surface (atom-probe tomography). The reader may notice that this contribution differs from the standard ones in this series, in that emphasis is given – as the title says – on the definitions of relevant parameters and their use in working formulae, rather than on the available results. For instance, the original electron emission problem in terms of Sommerfeld model and Schottky–Nordheim barrier, with the wellknown Fowler–Nordheim equation as solution, is revisited according to modern views, by resorting to Airy functions. Basically, the need of reformulating an almost-a-century-old theory is due to the fact that nowadays very sharp and/or poorly conducting emitters are currently employed. Throughout the contribution, tables list useful parameters to be used in the appropriate formulae, making this presentation very profitable for people working in the field. The contribution is divided into the following chapters: 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165.

1.8

Introduction to field electron and ion emission and customary units Basic terminology of Fowler–Nordheim electron transmission theory Transmission probability for an exact triangular barrier Transmission probability for a general rounded barrier The Schottky effect and related parameters Transmission probability for a Schottky–Nordheim barrier Local emission current density regimes Local emission current densities for a Schottky–Nordheim barrier Energy distributions for the Schottky–Nordheim barrier Basic auxiliary relationships, related to the Schottky–Nordheim barrier Field electron emission measurement circuit theory Basic theory of Fowler–Nordheim plots Testing for lack of field emission orthodoxy Theoretical introduction to field evaporation The escape stage, with comments Post-field ionization The “changeover field” in thermal-field shaping The position of the electrical surface Physical properties of the noble operating gases Field calibration issues (introduction, the Sakurai–Müller approach, calibration via post-field ionization)

Epigraphene

In the article by Claire Berger, Edward H. Conrad, and Walt A. de Heer, the authors describe in great detail the difference between epigraphene, i.e., graphene epitaxially grown on a monocrystalline substrate (in general silicon carbide), and transferred graphene consisting on a leaf often obtained by the so-called Scotch tape method (i.e., exfoliated from a bulk graphite sample).

1 General introduction

7

The authors point out that only epigraphene can be used in the production of nanoelectronic devices that will have a great impact on the future electronics. The contribution is divided in the following chapters. 166. Introduction to epigraphene and overview It includes the definition of graphene; the distinction between epitaxial graphene and transferred graphene, as well as considerations on freely suspended graphene; and graphene isolated on substrates. 167. The electronic band structure of graphene Tight-binding and ab initio methods are presented, and the physics near the K point is briefly discussed. The role of the substrate is mentioned, and the issue of graphene nanostructures is also addressed. 168. Silicon carbide and epitaxial graphene on silicon carbide Starting from the discovery of silicon carbide by G.E. Acheson at the end of the nineteenth century, the growth of graphene on this material is discussed. 169. Structure and band structure of epitaxial graphene on hexagonal silicon carbide The growth mechanisms as well as the structural and electronic properties of graphene grown on both the Si and the C faces of hexagonal SiC are discussed. Results obtained on polymorphs, as, for instance, cubic SiC, are mentioned. Data on ribbons of graphene are also presented. 170. Electronic transport properties of epigraphene Charge density and mobility of both single layer and multilayer epigraphene are discussed, together with the role of substrate steps. 171. Transport properties of epigraphene in magnetic field Data on transport in magnetic field including Landau levels, Shubnikov–de Haas oscillation, and quantum Hall effect in graphene are presented. 172. Toward electronic devices based on epigraphene Open problems and potentialities of electronic devices based on epigraphene are discussed. Special attention is devoted to high-frequency transistors, spintronics, large-scale integration, band gaps, and sidewall ribbons. 173. Optical and plasmonic properties of epigraphene A brief discussion of the optical and plasmonic properties of graphene is presented, together with the few available data. In particular, the issues of ultrafast optical spectroscopy, THz generation, photocurrent, and plasmon properties in graphene are addressed.

1.9

Fullerenes on Surfaces

A fullerene is a molecule of carbon in the shape of a hollow sphere or ellipsoid, depending on the number of atoms. The most common fullerene is C60, discovered in 1985, exhibiting both hexagons (32) and pentagons (21) on the surface of a sphere, with 60 carbon atoms at the vertices of the polygons. Since their discovery, fullerenes have been attracting a great interest in the scientific community for their physical and chemical properties and also for potential applications in nanotechnology and medicine. Similar carbon-based materials, namely C-nanotubes and graphene, which have been drawing the attention of a great number of researchers in recently years, are the subjects of other contributions in this series. After a short introduction, a critical review is presented of recent results, mainly experimental but also theoretical, regarding fullerene adsorbed on different substrates. Emphasis is given to the physical properties of ordered arrangements obtained on metallic and semiconducting substrates, as well as on templates for two-dimensional supramolecular growth of fullerene networks. Also, the issue of chiral properties of fullerene-based layers, obtained either by co-adsorption with other molecules or by properly

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functionalizing fullerene, is discussed. Finally, recent results in the field of organic-organic heterojuntions involving fullerene molecules are presented. The contribution is divided into the following chapters: 174. 175. 176. 177.

Introduction to fullerenes on surfaces Band dispersion of solid C60 Fullerenes on metals and semiconductors: interaction with the substrate Ordered fullerenes on metal surfaces: monatomic steps on vicinal surfaces and reconstruction on metals 178. C60 monolayer on semiconductors 179. Directing fullerene adsorption via supramolecular templates 180. Coadsorbed fullerene systems and the formation of heterojunction layers at a nanometer scale

1.10

Surfaces at Metal-Electrolyte Interfaces

The investigation of surfaces immersed in liquids is much less common than that of surfaces in UHV. However, important technologies are based on solid–liquid interfaces like electro-catalysis, grafting, bio-functionalization of surfaces, electro-deposition, and electro-etching of metals at nanometer scale. Also biophysical and biochemical systems are commonly studied in aqueous solutions, and processes of scientific relevance take place at solid–liquid interfaces. The field is very broad. Electrified interfaces of metals, semiconductors, and even insulators have been investigated. Therefore a comprehensive review of all the available results would have been a formidable task. Here only metals are considered, which are the most studied and interesting materials. The field is further restricted to single-crystal electrodes and to anion adsorption. An important result is that by applying voltages to crystalline samples immersed in a solution, it is possible to obtain reconstructions similar to those obtained in UHV. In various parts of the present contribution, results obtained in UHV are compared with those of samples immersed in liquids. Also the various experimental apparatuses and methods (both physical and chemical) are presented and discussed. In general the approach is strictly chemical, though in various sections (e.g., 181.9, 181.10, and 181.11), the physical approach is also stressed. The contribution is divided into introductory and data sections. The first comprises: (i) Introductory text, at the beginning of Chap. 181 (ii) Concepts (properties of electrolytes, adsorption–desorption, electrochemical double-layer, structure of the metal surface), Sects. 181.1–181.4 (iii) Models (Helmholtz, Gouy–Chapman, Gouy–Chapman–Stern–Grahame [GCSG]), Sects. 181.5–181.7 (iv) Methods (general remarks on methods used for investigating solid–liquid interfaces, in situ and ex situ methods, theory and simulations, sample preparation by flame annealing, by electrochemical etching and annealing, by UHC-EC transfer), Sects. 181.8–181.14 (v) Concluding remarks, Sect. 181.15 In turn, the data section is divided into: (vi) Anion interaction with copper surfaces: general properties of copper surfaces (Chap. 182) (vii) Hydrohalic acid interaction with copper surfaces (adsorption of halide anions, chloride, bromide, and iodide on Cu(100); XPD of chloride, bromide, and iodide on Cu(100); chloride, bromide and iodide on Cu(111); bromide and chloride on Cu(110); CuI compound formation; XPS of Cu(111) – iodide interaction), Chaps. 183–193 (viii) Copper surfaces in perchloric acid (Chap. 194) (ix) Copper surfaces in sulfuric acid (general remarks, sulfate adsorption on Cu(100) and Cu(111), sulfate structure on Cu(111), sulfate adsorption configuration, sulfate-induced surface morphology, sulfate adsorption/desorption kinetics), Chaps. 195–200 (x) Hydrohalic-acid anions interaction with silver surfaces [chloride, bromide, and iodide on Ag(100), Ag(111), and Ag(110)], Chaps. 201–207 (xi) Silver surfaces in perchloric acid: Ag(110) – perchlorate (Chap. 208)

1 General introduction

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(xii) Silver surfaces [Ag(100), Ag(111), and Ag(110)] in sulfuric acid, Chaps. 209–211 (xiii) Hydrohalic-acid anion interaction with gold surfaces [chloride, bromide, and iodide on Au(100), Au(111), and Au(110)], Chaps. 212–219 (xiv) Gold surfaces in perchloric acid (Au(100), Au(111), and Au(110) – perchlorate), Chaps. 220–222 (xv) Gold surfaces [Au(100), Au(111), and Au(110)] in sulfuric acid, Chaps. 223–225 (xvi) Hydrohalic-acid anion interaction with platinum surfaces [bromide and iodide on Pt(100); chloride, bromide, and iodide on Pt(111); bromide and iodide on Pt(110)], Chaps. 226–232 (xvii) Platinum surfaces in perchloric acid: Pt(111), Pt(100), Pt(110) – perchlorate (Chap. 233) (xviii) Platinum surfaces in sulfuric acid (general remarks, Pt(100), Pt(111) – sulfate), Chaps. 234–236

List of Acronyms 1D 2D 2DEG 2DGF ABINIT ABS AC ACA AES AFM ALD ALICISS APDB APT APW AquaDAG™ ARPES ARUPS B3LYP BB bcc BCM BIF BIV BOMD BT BTE BV CCD CCS CDR CFE CMOS CPMD CRC CVD DAG DAS DB DB

One-dimensional Two-dimensional Two-dimensional electron gas Two-dimensional graphite film Ab initio simulation package Atom beam scattering Armchair Acridine-9-carboxylic acid Auger electron spectroscopy Atomic force microscopy Atomic layer deposition Alkali impact collision ion scattering spectroscopy Antiphase domain boundary Atom probe tomography Augmented plane waves Water suspension of deflocculated Acheson graphite Angle-resolved photoelectron spectroscopy Angle-resolved ultraviolet photoelectron spectroscopy Becke 3-parameter (exchange) Lee–Yang–Parr Bulk band Bulk-centered cubic Bond-charge model Best image field Best image voltage Born–Oppenheimer molecular dynamics Barrier top Barrier top electron emission Burgers vector Charge-coupled device Confinement controlled sublimation Copper dissolution reaction Cold field electron emission Complementary metal oxide semiconductor Car–Parrinello molecular dynamics Chemical rubber company (scientific reference publisher) Chemical vapor deposition Deflocculated Acheson graphite Dimer-adatom-stacking fault model [for Si (111)-(7  7)] Dangling bond Domain boundary

10

DEZn DFM DFPT DFT DFT+U DFTB DFT-LDA DH6T DMM DP DT DW EAM EC ECBM ECD ECLS ECP EC-STM EDC EELS EFM EMT Epigraphene ESD ESDI AD ESR ET ET ETB ETBM exTTF FC fcc FE FEF FePc FET FEV FF FFT FI FIM FI-STM FKM FM-AFM FM-DFM FN FOM FTIR FWHM GFIS GGA

G. Chiarotti and P. Chiaradia

Diethyl zinc Dynamic force microscopy Density functional perturbation theory Density functional theory Density functional theory with Hubbard U parameter for electron correlation Density functional tight binding Density functional theory with local density approximation α,ω-Dihexylsexithiophene Domain matrix method Deformation potential Deep tunneling Domain wall Embedded atom model Electrochemical cell Energy of the conduction band maximum Electrochemical deposition Epitaxial continued layer structure Electron channeling pattern Electrochemical scanning tunneling microscopy Energy distribution curve Electron energy-loss spectroscopy Electrostatic force microscopy Effective medium theory Epitaxial graphene grown on SiC Electron stimulated desorption Electron-stimulated desorption ion angular distribution Electron spin resonance Ethanethiol Exactly triangular Empirical tight binding Empirical tight binding method 2-[9-(1,3-Dithiol-2-ylidene)anthracen-10 (9H)ylidene]1,3-dithiole Franck-Condon Face-centered cubic Field electron emission Field enhancement factor Iron phthalocyanine Field effect transistor Field evaporation Fr€ oman and Fr€ oman Fast Fourier transform Field ion or field ionization Field ion microscopy Field ion – scanning tunneling microscopy Frenkel–Kontorova model Frequency modulation – atomic force microscopy Frequency modulation – dynamic force microscopy Fowler-Nordheim Figure of merit Fourier transform infrared spectrometer Full width half maximum Gas field ion source Generalized gradient approximation

1 General introduction

GISAXS GIXRD GIXS GW H2Pc HAS HCP HCP HDFT hdw HEFNS HER HF HF HF-CVD H-MnPc HOMO HOPG HR-EELS HR-LEED HR-TEM HTP HT-STM IAU ICISS IG-STM IPE IPES IR IRAS IS ISA ISQ ISS IUPAC JWKB KE KMC k-PEEM KRIPES LA LAFE LAO LB LCAO LDA LDA LDOS LECBD LECD LEED LEEM LEG

Grazing incidence small angle X-ray scattering Grazing incidence X-Ray diffraction Grazing incidence X-Ray scattering Green’s function of the Coulomb interaction W H2-phthalocyanine Helium atom scattering Hemisphere-on-cylindrical-post Hexagonal close packed Hybrid density functional theory Heavy-domain wall High electric field nanoscience Hydrogen evolution reaction Hartree-Fock High flyover Hot filament chemical vapor deposition Hydrogen manganese phthalocyanine Highest occupied molecular orbital Highly ordered (or oriented) pyrolytic graphite High-resolution electron energy-loss spectroscopy High-resolution low-energy electron diffraction High-resolution transmission electron microscopy High-temperature phase High-temperature scanning tunneling microscopy International Astronomical Union Impact collision ion scattering spectroscopy Ion gun (high temperature) scanning tunneling microscopy Inverse photoelectron emission Inverse photoelectron spectroscopy Infrared Infrared absorption spectroscopy Ion scattering Ion sputtering and annealing International System of Quantities Ion scattering spectroscopy International Union of Pure and Applied Chemistry Jeffreys-Wentzel-Kramers-Brillouin Kinetic energy Kinetic Monte Carlo simulation k-Resolved photoemission electron microscopy K- or momentum-resolved inverse photoemission Longitudinal acoustic Large-area field (electron) emitter Lanthanum aluminum oxide (LaAlO3) Landolt-Bornstein Linear combination of atomic orbitals Local density approximation Local dipole approximation Local density of states Low-energy cluster ion beam deposition Local emission current density Low-energy electron diffraction Low-energy electron microscopy Laser-modified epigraphene

11

12

LEIS LF LFM LL LL LMOKE LMTO LO LP-CVD LRO LT LTO LTP LT-STM LT-STS LUMO MBE MBE-STM MBPT MC MD MDB MDC MEAM MEE MEEM MEG MEIS MINDO ML MnPc MOCVD MOSFET MOVPE MPA-CVD μ-LEED μ -RHEED NC-AFM NC-SNDM NED NEXAFS NFE NICISS NIR NN NR OMBE OPA-MBE ORR PA-MBE PBC PBE PCA

G. Chiarotti and P. Chiaradia

Low-energy ion spectroscopy Low flyover Lateral force microscopy Landau and Lifschitz Landau level Longitudinal magneto-optical Kerr effect Linear muffin-tin orbital Longitudinal optical Low pressure chemical vapor deposition Long range order Low temperature Longitudinal and transverse optical Low-temperature phase Low-temperature scanning tunneling microscopy Low-temperature scanning tunneling spectroscopy Lowest unoccupied molecular orbital Molecular beam epitaxy Molecular beam epitaxy scanning tunneling microscopy Many-body perturbation theory Monte Carlo Molecular dynamics Mirrored domains boundary Momentum distribution curve Modified embedded atom method Migration-enhanced epitaxy Metastable electron emission microscopy Multilayer epitaxial graphene Medium-energy ion scattering Modified intermediate neglect of differential overlap Monolayer Manganese phthalocyanine Metal-organic chemical vapor deposition Metal-oxide semiconductor field-effect transistor Metal organic vapor phase epitaxy Microwave plasma-assisted chemical vapor deposition Micro-low-energy electron diffraction Micro-reflection high-energy electron diffraction Noncontact atomic force microscopy Noncontact scanning nonlinear dielectric microscopy Normal energy distribution Near-edge X-ray absorption fine structure Nearly free electron Noble gas impact collision ion scattering spectroscopy Near infrared 1-Nitronaphtalene Nanoribbon Organic molecular beam epitaxy Oxygen plasma-assisted molecular beam epitaxy Oxygen reduction reaction Plasma-assisted molecular beam epitaxy Periodic boundary conditions Perdew, Burke, and Ernzerhof Post-cleavage annealing

1 General introduction

PCBM PDA PDOS PE PED PEEM PES PFI PLA PMOKE POA PPW PSA PSV PT PTCDA PTCDI PVD PW91 QHE QM QMC QMS RA RAS RBS RDB RDS REM RHE RHEED RMBE RPA RPBE RPES RT SAM SAM SCE SEIRAS SEM SERS SESM SH shdw SI SIC SM SN SNIFTIRS SOC SOI SP

Phenyl-C60butyric acid methyl Post-deposition annealing Phonon density of states Potential energy Parallel energy distribution Photoemission electron microscopy Photoelectron spectroscopy Post-field ionization Pulsed laser annealing Polar magneto-optical Kerr effect Post-oxidation annealing Pseudopotential plane wave Post-sputter annealing Photo-surface voltage Phase transition 3,4,9,10-Perylene-tetracarboxylic-dianhydride Perylene tetracarboxylic diimide Physical vapor deposition Perdew and Wang 91 Quantum Hall effect Quantum mechanical Quantum Monte Carlo Quadrupole mass spectrometry Reflectance anisotropy Reflection anisotropy spectroscopy Rutherford backscattering Rotated domain boundary Reflectance difference spectroscopy Reflection electron microscopy Reference hydrogen electrode Reflection high-electron energy diffraction Reactive molecular beam epitaxy Random-phase approximation Revised PBE Resonant photoelectron spectroscopy Room temperature Scanning Auger electron microscopy Self-assembling monolayer Saturated calomel electrode Surface-enhanced infrared absorption spectroscopy Scanning electron microscopy Surface-enhanced Raman spectroscopy Scanning electron surface microscopy Shear horizontal Superheavy domain wall International System (of units) (French: Syste`me International d’unite´s) Striped incommensurate Sakurai and Müller Schottky-Nordheim Subtractively normalized interfacial Fourier transform IR spectroscopy Sphere-on-orthogonal-cone Silicon-on-insulator Sagittal plane

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SPA-LEED SPE SPELEEM SRO SR-PES SR-XRD SS STEM STFE STM STM/FM STS SXPS SXRD TA TBAs TBMD TBP TBT TC TCDB TCI TDS TE TEAS TED TEM TERS THT TI TMIn TO TOF TOF-SARS TPD TPP TPTC TR tr-ARPES TRI UC UHV UHV-HR-TEM UHV-SEM UHV-TEM UIC upd UPS UV VASP VDW VOPc VT-STM

G. Chiarotti and P. Chiaradia

Spot profile analysis of low-energy electron diffraction Solid-phase epitaxy Spectroscopic photoemission and low-energy electron microscopy Short-range order Synchrotron radiation photoelectron emission spectroscopy Synchrotron radiation X-ray diffraction Surface state Scanning transmission electron microscopy Single-tip field emitter Scanning tunneling microscopy Scanning tunneling microscopy/force microscopy Scanning tunneling spectroscopy Soft X-ray photoelectron spectroscopy Surface X-ray diffraction Transverse acoustic Tertiary butyl arsine Tight-binding molecular dynamics Tertiary butyl phosphine Tight-binding theory Critical temperature 1,3,5-Tris (10-carboxydecyloxy) benzene Topological crystalline insulator Thermal desorption spectroscopy Total energy Thermal energy atom scattering Transmission electron diffraction Transmission electron microscopy Tip-enhanced Raman spectroscopy Tersoff–Hamann theory Topological insulator Trimethyl indium Transverse optical Time of flight Time-of-flight scattering and recoiling spectrometry Temperature-programmed desorption Tetraphenylporphyrin p-Terphenyl-tetracarboxylic acid Roughening temperature Time–resolved angle–resolved photoemission spectroscopy Time reversal invariance Unit cell Ultrahigh vacuum Ultrahigh vacuum high-resolution transmission electron microscopy Ultrahigh vacuum scanning electron microscopy Ultrahigh vacuum transmission electron microscopy Uniaxially incommensurate Under-potential deposition Ultraviolet photoelectron spectroscopy Ultraviolet Vienna Ab initio simulation package Van der Waals Vanadyl phthalocyanine Variable temperature scanning tunneling microscopy

1 General introduction

XAS XMCD XPD XPEEM XPS XRD XSTM XSW XSW-XPS XTEM YRZ ZZ

X-ray absorption spectroscopy X-ray magnetic circular dichroism X-ray photoelectron diffraction X-ray photoemission electron microscopy X-ray photoelectron spectroscopy X-ray diffraction Cross-sectional scanning tunneling microscopy X-ray standing wave X-ray standing wave (enhanced)-X-ray photoemission spectroscopy Cross-sectional transmission electron microscopy Yang, Rice, and Zhang Zigzag

15

Part II

Theoretical Foundations and Simulation of Surface Structures

Chapter 2

Introduction to basic principles of surface structure theoretical simulation A. Shkrebtii and M. Rohlfing

Theoretical Foundations and Simulation of Surface Structures This contribution compiles the results on the main fundamental principles and theoretical formalisms used during the last four decades to simulate atomic structure of surfaces of metals, oxides, and semiconductors, and the formalisms applications. The selection of the surfaces under consideration corresponds to the choice of topics included in the Landolt Bo¨rnstein volume. Microscopic atomic arrangement on clean, solid surfaces rather than their morphology (i.e., macroscopic shape of surfaces, islands, steps) will be discussed. Several examples of the simulation of stable or metastable atomic geometries of prototypical ordered clean surfaces will be used to illustrate the application of the numerical methods described in Chaps. 8, 9, 10 and 11. This contribution demonstrates the maturity of modern theoretical formalisms and simulation tools in explaining, interpreting, and quantifying experimentally determined surface structures, including most complex ones. We also show the power of the theoretical approaches to predict new surface atomic geometries to be subsequently and successfully verified experimentally. It is important to stress that the theoretical and computational tools discussed in this contribution can also be directly applied to adsorbatemodified surfaces, various interfaces with crystalline solids, and 2D systems such as graphene and graphene-like materials. The above formalisms also allow treating surface defects, roughening or melting transitions, which occur at high temperatures, leading to the loss of 2D translational symmetry. Every solid object is terminated by surfaces, whose properties are very different from those of the bulk of the corresponding solid. Reduced top atom coordination number, modification of the atomic coordinates, and different periodicity of the atomic arrangement on the surface result in electronic structure, vibrational, optical, thermodynamical properties, among others, that differ from those of the bulk. In all such modifications, the microscopic atomic structure is the key parameter responsible for the properties of solid surfaces and their application. Simulations of the microscopic structures for solid surfaces have been carried out and extensively discussed in original papers, reviews, and monographs for over three decades due to the importance of surface-related applications in all areas of physical sciences and engineering. However, concise but comprehensive discussion from a general perspective has been lacking on the formalisms and numerical tools for all the main crystalline materials such as metals, semiconductors, and oxides with detailed structural results for prototypical systems. Experimentally, atomic structure, the most important surface property, can be accurately accessed through several quantitative structure-sensitive techniques, such as described in [97Duk, 03Our, 06Iba, 06Mar, 06Chi, 09Zan, 10Lüt, 12Wan]. Understanding of the surface microscopic structure is the first mandatory step in the calculation of the electronic, vibrational, chemical, and optical properties as well as scanning tunneling microscopy (STM) images of the surfaces [96Ned, 10Hou, 15Fee]. Knowledge of A. Shkrebtii (*) Faculty of Science, University of Ontario Institute of Technology (UOIT), Oshawa, ON, Canada e-mail: [email protected] M. Rohlfing Institut für Festk€orpertheorie, Universität Münster, Münster, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_2

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atomic geometry is also crucial to predict properties of surface- and nanostructure-based microelectronic devices. Despite the success of the above experimental techniques, the theoretical structure simulation tools and their extension to calculate, for instance, surface band structure, optical response, and vibrations, have become integral part of the solid surface physics field. Within the last three decades, computer-based simulations emerged as a powerful and accurate tool to predict materials properties [85Car, 92Pay, 02Car, 02Tuc, 06Fer, 08Haf, 09Gro, 09Gon, 09Gia, 12Mar]. Computer simulation has created a new interface between actual experiment and physics of surface processes. Computer surface structure simulation aims to accurately calculate the top atom rearrangement, which does not yield an analytic solution. Therefore computational numerical methods are used to simulate the surfaces modeled. In Chap. 3 of this contribution, we first discuss the key physics mechanisms that govern the process of solid surface structure formation. All these mechanisms reflect the tendency of any surface to reach the ground state, which corresponds to the global total energy minimum or local energy minimum. These mechanisms are explicitly or implicitly included in all the simulation formalisms. Chapters 4, 5 and 6 describes the basic theoretical approaches to quantitatively simulate the formation of surface structure and gives examples of numerical formalisms that implement the above approaches. Finally, in Chaps. 8, 9, 10 and 11 prototypical examples of different clean low-index surface structures, which illustrate applications of numerical approaches, will be presented. Some of these surfaces have attracted much attention during the last decades. They have been studied with particular care among a large number of researches, and large efforts have been directed toward convergence of the surface structure and numerical issues (e.g., basis-set expansion, reciprocal-space sampling, and similar details). As a consequence, the data for such surfaces can be considered conclusive. We restrict ourselves to several of these prototypical and well-defined relaxed or reconstructed structures that demonstrate a consensus between the structure simulation theory and surface-sensitive experiment. Fundamentally and technologically important, low-index planes of semiconductors, metals, and oxides will be discussed. The conclusion in Chap. 12 summarizes the main results, presented in the contribution, and indicates possible directions of further expanding the simulation approaches to treat more complex surface structure and related processes. Symbols and abbreviations Short form

Full form

STM

Scanning tunneling microscopy

References [85Car] [92Pay] [96Ned] [97Duk] [02Car] [02Tuc] [03Our]

Car, R., Parrinello, M.: Phys. Rev. Lett. 55, 2471 (1985) Payne, M.C., Teter, M.P., Allan, D.C., Arias, T.A., Joannopoulos, J.D.: Rev. Mod. Phys. 64, 1045 (1992) Neddermeyer, H. Reports on Progress in Physics 59, 701 (1996) Duke, C.B., Paton, A., Lazarides, A., Vasumathi, D., Canter, K.F.: Phys. Rev. B. 55, 7181 (1997) Car, R.: Quant. Struct.-Act. Relat. 21, 97 (2002) Tuckerman, M.E.: J. Phys. Condens. Matter. 14, R1297 (2002) Oura, K., Katayama, M., Zotov, A.V., Lifshits, V.G., Saranin, A.A.: Surface Science, p. 171. Springer Berlin Heidelberg (2003) [06Chi] Chiarotti, G.: The physics of solid surfaces. In: Springer Handbook of Condensed Matter and Materials Data, p. 979. Springer, Berlin/Heidelberg (2006) [06Fer] Ferrario, M., Ciccotti, G., Binder, K.: Computer Simulations in Condensed Matter: From Materials to Chemical Biology, vol. 1. Springer, New York (2006) [06Iba] Ibach, H.: Physics of Surfaces and Interfaces. Springer, Berlin (2006) [06Mar] Marini, A., Garcı´a-Gonza´lez, P., Rubio, A.: Phys. Rev. Lett. 96, 136404 (2006) [08Haf] Hafner, J.: J. Comput. Chem. 29, 2044 (2008) [09Gon] Gonze, X., Amadon, B., Anglade, P., Beuken, J., Bottin, F., Boulanger, P., Bruneval, F., Caliste, D., Caracas, R., Coˆte´, M., Deutsch, T., Genovese, L., Ghosez, P., Giantomassi, M., Goedecker, S., Hamann, D.R., Hermet, P., Jollet, F., Jomard, G., Leroux, S., et al.: Comput. Phys. Commun. 180, 2582 (2009)

2 Introduction to basic principles of surface structure theoretical simulation

[09Gia]

3

Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I., Corso, A.D., Gironcoli, S.D., Fabris, S., Fratesi, G., Gebauer, R., Gerstmann, U., Gougoussis, C., Kokalj, A., Lazzeri, M., Martin-Samos, L., et al.: J. Phys. Condens. Matter. 21, 395502 (2009) [09Gro] Gross, A.: Theoretical Surface Science. A Microscopic Perspective. Originally published in the series: Advanced Texts in Physics, 2nd ed. 342 p. 132 illus (2009) [09Zan] Zandvliet, H.J.W., van Houselt, A.: Annu. Rev. Anal. Chem. 2, 37 (2009) [10Hou] van Houselt, A., Zandvliet, H.J.W.: Rev. Mod. Phys. 82, 1593 (2010) [10Lüt] Lüth, H.: Solid Surfaces, Interfaces and Thin Films. Springer, New York (2010) [12Mar] Marx, D., Hutter, J.: Ab Initio Molecular Dynamics. Academic, Cambridge University press (2012) [12Wan] Wandelt, K.: Surface and Interface Science: Volume 1 and 2: Volume 1: Concepts and Methods/Volume 2: Properties of Elemental Surfaces. Wiley, Weinheim (2012) [15Fee] Feenstra, R.M., Hla, S.-H.: In: Chiaradia, P., Chiarotti, G. (eds.) Landolt-B€ ornstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Vol. III/45, Subvolume A, Scanning Tunneling Microscopy of Metals and Semiconductors, p. 15. Springer, Berlin/Heidelberg/New York (2015)

Chapter 3

Physics mechanisms of the surface structure formation A. Shkrebtii and M. Rohlfing

Creation of a solid surface (by cleaving, cutting of bulk material, or atomic deposition) produces asymmetry in atom coordination and electron charge distribution compared to their bulk values. To reach thermodynamic energy minimum, the surface atoms deviate from a simple bulk-termination structure, and such atomic geometry modification may take the form of relaxations or reconstruction. Relaxation involves top atom displacements, where interlayer and/or intralayer spacing is altered, but the surface symmetry remains the same as for the bulk-like-terminated atomic arrangement. Reconstruction involves large-scale atomic rearrangement across the surface often affecting several layers and radical changes in coordination of surface atom, periodicity, and of the surface symmetry. Generally, the structure of every solid surface can be described as an ensemble of ion cores (henceforth called ions or nuclei) in equilibrium positions {Ri}. The valence electrons (henceforth called electrons), which are responsible for the bonding at surfaces and the bulk beneath, are distributed among the ions. The valence electron distribution depends on the type of bonding: metallic, ionic, covalent, hydrogen, or van der Waals bonds are among the main types, and it is convenient to characterize the bonding in terms of the spatial distribution of the valence electrons using electron charge density n(r) (see, e.g., Chap. 3 from [03Bec]). Hydrogen bonds are not typical in solid crystals, and therefore we do not consider them in the contribution. Very weak van der Waals bonding will not be discussed as well. The bulk bonding type is one of the most important factors that define the solid surface atomic structure. Formation of a surface results in broken chemical bonds, initially present in a bulk environment, and this increases the system energy (see, e.g., discussion in [96Mol]). Minimizing this energy is the main driving force of solid surface relaxation or reconstruction, leading to upper atom rearrangement and modification of the charge density distribution n(r) as compared to the bulk. The main goal of simulation of the surface atomic structure is to find the total energy minima and corresponding top atom geometry. Some clean surfaces, depending on preparation, demonstrate multiple structures, and transition between them can be also simulated using molecular dynamics (MD) [94Tak, 95Shk, 01FuC, 03Kre, 03Som, 08Pan] or Monte Carlo (MC) methods [00Pet, 01Hea, 05Oht, 11Che]. The transitions between the different surface structures can be irreversible, such as the structural transitions at the clean Si(111) surface [87Han]: obtained by cleavage in ultrahigh vacuum at room temperature or below, 2
1 reconstruction is irreversibly transformed to 7
7 superstructure after heating the Si(111) 2
1 surface to T >900 K and following subsequent slow cooling. The standard preparation by cutting, followed by mechanical and/or chemical polishing of the Si(111) surface leads to the 7
7 reconstruction after heating T>1,100 K, following slow cooling. On the other hand, the Si(111) 7
7 reconstruction is stable up to 1,100 K and demonstrates reversible transition to a 1
1-like phase above 1,140 K [85McR, 87Han]. Concepts of thermodynamics (see, e.g., [96Wil] and [03Bec]) are useful to understand surface structure formation macroscopically and surface phase transitions, that is, transformations of one structure into another. The most general way to describe and microscopically understand the above structural phase A. Shkrebtii (*) Faculty of Science, University of Ontario Institute of Technology (UOIT), Oshawa, ON, Canada e-mail: [email protected] M. Rohlfing Institut für Festk€orpertheorie, Universität Münster, Münster, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_3

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A. Shkrebtii and M. Rohlfing

transitions is by combining thermodynamics and statistical physics [96Mol, 02Ste]. While thermodynamics uses macroscopic parameters to understand the surfaces, statistical physics deals with microscopic properties in terms of atomic motion [96Mol, 96Wil, 02Ste, 03Bec, 04Bon]. We will mostly focus here on microscopic statistical mechanics-based treatment of the surface structure formation and its simulation. From the point of view of thermodynamics, creating a surface always costs energy, and energetics of most solid surface systems can be accurately characterized by the free energy F. Following Chap. 2 from [03Bec], F ¼ U  ST,

ð3:1Þ

where U is the internal energy, S is the entropy of the system, and T is the absolute temperature. The surface internal energy U is the total energy contained by the system. Following the energy conservation law, an infinitesimal change of the internal energy for an open system can be written as dU ¼ TdS  pdV þ μdN,

ð3:2Þ

where p is the pressure, V is the volume, and dN is the variation of the number of particles N when particle exchange is allowed with a reservoir. The reservoir is characterized by the chemical potential μ of the particle. The pdV term can usually be ignored for the case of solid surfaces, while μdN term contributes to the energy and surface structure modification if there is an interchange with externally supplied atomic species, such as during the growth processes. If necessary, the surface structure simulation tools have to correctly include the μdN term to the energy. In equilibrium, F is a minimum with respect to the inner variables at constant T, V, and N. The surface free energy is dominated by the total energy Etot of the system, which corresponds to the internal energy U at zero temperature [03Bec]. In terms of the total energy, each stable or metastable surface structure can be associated with a minimum of total energy Emin, which corresponds to the specific surface atom arrangement {Ri}. Many !

Free energy F (a.u.)

surfaces exhibit multiple minima, differing in both composition and structural configurations R ¼ fRi g, as schematically shown in Fig. 3.1. Reaching the energy minima is the driving force of the surface relaxation or reconstruction. It can be a metastable energy minimum (such as for Si(111) 1
2 after cleavage in the vacuum [87Han, 89Han]) or global energy minimum (such as the Si(111) 7
7 structure that corresponds to the ground state of the surface [89Han, 97Yam]). Minimization of the surface free energy is the main way to simulate the surface geometry. In many cases, such as the above Si(111) example, the surface heating (annealing) leads to the structural phase transitions, and, if necessary, the sample temperature contribution to the formation of the structure has to also be included in the simulation formalisms.

ΔF Local minima

Global minimum

1

2

3

4

Configuraonal coordinate R Fig. 3.1 Schematic dependence of the free energy of solid surface F (not to scale) on possible structural configurations R. Configuration 1 corresponds to unstable bulk-terminated atomic structure, while 2 and 3 indicate local energy minima. Configuration 4 is the global minimum that corresponds to the ground state atomic structure. Following [90Anc, 91Tak] and [92Tak], configuration 1 can be, for instance, assigned to the ideal bulk-terminated unstable Si(111) 1
1 or Ge(111) 1
1 structure, 2 to a very shallow energy minimum for the Haneman-like-buckled Si(111) 2
1 or Ge(111) 2
1 structure, 3 to the Pandey Si(111) 2
1 or Ge(111) 2
1 phase, while 4 to the ground state Si(111) 7
7 or Ge(111) c(2
8) structures. The energy barrier between configurations 3 and 4 has to be overcome for the irreversible 2
1 ! c(2
8) or 2
1 ! 7
7 structural phase transitions, and ΔF corresponds approximately to the (thermal) activation energy, required for the transition

3 Physics mechanisms of the surface structure formation

3

From the point of view of the reconstruction/relaxation physics, when the surface structure is not in the total energy minimum configuration, this results in the nonzero microscopic forces. These forces are moving the atoms toward the equilibrium geometry with the total energy minimum. The general energy minimization mechanism acts differently, depending on the type of interatomic bonding in the bulk of material, from which the surface originates [96Une]. Dominant types of the bonding that determine the solid surface structure are metallic, covalent, and ionic. Although often there is no welldefined borderline between the bonding types due to substantial difference in the electron charge density distribution, in the literature surfaces of metals [96Cha, 10Kla, 12Mic] are usually considered separately from semiconductors [96Duk1, 96Duk2, 97Sri, 03Bec]. For most metals the charge density distribution is close to spherically symmetric around each atom (although d- or f-states in transition metals show some charge asymmetry [83Euc]). In contrast, covalent bonds of semiconductors demonstrate pronounced azimuthal dependence of the charge density. Although oxide surfaces are usually considered separately from semiconductors due to significant ionic character of their bonds [94LaF, 96LaF, 00Nog, 01Nog, 01Woo], heteropolar semiconductors, such as, e.g., GaAs, BN, etc., demonstrate noticeable ionic component in their covalent bonding. On the other hand, depending on the application, zinc oxide (ZnO) is considered both as semiconductor [09Jan] and oxide [10Die]. Finally, van der Waals forces are recently attracting a lot of attentions due to the discovery of graphene [07Gei, 09Cas] and graphene-like systems [12Nov, 12Gao]. Such two-dimensional (2D) materials demonstrate strong (predominantly covalent) bonding within each one-atom-thick layer and a weak van der Waals (VDW) interaction between the 2D layers or between a 2D layer and a solid surface, on which it is deposited [09Cas, 11Net]. Since the weak VDW interaction does not produce noticeable rearrangement of the atoms within a 2D layer, we will not consider the effect of van der Waals forces in this contribution. We discuss next the main mechanisms, responsible for driving atoms at the solid surfaces toward its stable structure(s). Currently used and dominating ab initio approaches to model surface atomic structure [85Car, 92Pay, 97Sri, 02Car, 03Bec, 08Haf, 09Gon, 09Gro, 09Gia, 12Mic] are very general, are parameter independent, and are not based on particular relaxation model or reconstruction mechanism. However, these mechanisms are still useful to understand the physics of the surface structure formation and can be explained, for instance, in terms of the charge density modification, surface band structure, vibrational spectra, etc. calculated from ab initio approaches. In metals the energetics of surface structure modification, compared to the bulk-terminated geometry, does not depend substantially on the bond angles: the electron charge density distribution is close to being spherical around the atoms not only for simple metals but for transitional and noble atoms as well [83Euc]. The distance between atoms, however, is important in the surface total energy. Examples include not only simple metals, such as Al, or alkali metals, as well as transitional and noble metals where d-shells are essentially filled: Au, Ag, Cu, Pt, Pd, and Ni [96Cha, 09Gro]. The great majority of the above metal surfaces demonstrate multilayer relaxation of the top layers, which is mostly driven by electrostatic screening of the external electric field that appears when a surface is created. Semiconductor and oxide crystals are characterized by directional bonding, and an ideal bulkterminated surface contains the so-called dangling bonds (DBs) [92LaF, 94LaF, 96LaF, 03Bec]. These are the unsaturated bonds which were used to bind surface atoms to their, now missing, bulk neighbors, and DB saturation process is dominant in lowering of the surface energy. Saturation of the DBs usually leads to a surface reconstruction, which changes the surface symmetry compared to the bulk-terminated geometry. (See discussion in previous Landolt–B€ ornstein chapter on surface reconstructions and relaxation [93Sel].) Additionally, if ionic component of the bonding is present, electrostatic energy contributes substantially to the formation of the surface structure [94LaF, 96Duk2, 96LaF, 03Bec]. This will be discussed in more detail later. Preparation of the solid surface plays a crucial role in the formation of the certain type of surface reconstruction. Three main preparation procedures can be identified as (i) cleavage, (ii) crystal cut followed by cleaning (e.g., ion bombardment and annealing), and (iii) growth using molecular beam epitaxy (MBE), metal-organic vapor phase epitaxy (MOVPE), or other deposition techniques [04Her, 07Kas, 10Lüt]. Theoretical structure simulation tools have to properly account for the role of a surface preparation, including high-temperature and chemically active environment, which is typical, for instance, in reactor chambers with a flux of different atoms, being deposited during the growth.

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A. Shkrebtii and M. Rohlfing

Cleavage in ultrahigh vacuum (UHV) is a simple way to prepare stoichiometric clean surface, which may often contain steps and various defects and is only possible along certain crystallographic directions. Only surfaces of brittle materials such as some oxides (ZnO, TiO2, SnO2, etc.) and semiconductors (Ge, Si, GaAs, etc.) can be prepared in this way. Cleavage planes are determined by the geometry of chemical bonding and their polarity (see, for instance, the discussion in Chap. 3 of [03Our] and Chap. 2 of [10Lüt]). Cleavage can produce good-quality surfaces for the case of homopolar group IV semiconductors, such as Si (111) and Ge(111) [87Han, 92LaF, 02Ste], and heteropolar, such as III–V (e.g., GaAs, InP, GaP, etc.) and II–VI (e.g., CdSe and CdS) compounds, semiconductors [93Mon, 02Ebe, 03Bec]. In the cases of Si(111) and Ge (111) surfaces, the cleavage is the only method to create a metastable 2
1 reconstruction, while such 2
1 structures cannot be formed using other surface preparation techniques. In principle, cleavage of the crystal could be numerically simulated, but this is too computationally expensive due to the vast configurational space involved. However, the path that the surface atoms follow after the cleavage to reach the ground state can be simulated, as it was done for Si(111) 2
1 [90Anc] or Ge(111) 2
1 [91Tak]. Cleavage, unfortunately, does not offer a variety of surface orientations, since only one cleavage plane for the cubic semiconductors exists. Homopolar Si, Ge, and diamond can only be cleaved along the (111) or equivalent plane, while for ionic heteropolar semiconductors, the (110) or equivalent plane

is the only   and 1120 , cleavage plane. For the wurtzite-type semiconductors, two cleavage planes, namely, 1010 exist [10Lüt]. For metals and oxides, however, cleavage generally leads to a poor quality of metal [10Lüt] or oxide [96LaF] surfaces. Compared to cleavage procedure, cutting the surface followed by ion bombardment and annealing has no limitation to a particular material or to a particular crystallographic surface plane [03Our, 10Lüt]. Noble gas ions are usually used to bombard and sputter off all contaminants (and frequently topmost atomic layers) from the surface. Ion bombardment is then followed by annealing of the surface to remove adsorbed noble gas atoms and to recover surface crystallography. Since annealing is done at high temperatures, metastable states, which can be formed, for instance, after low-temperature cleaving, can usually not be prepared this way. Annealing process (surface heating to a high temperature) and subsequent slow or rapid cooling can be simulated if necessary as well; see, for instance, [91Anc] for highly metastable Si(111) √3
√3 phase. Various crystalline surface growth techniques available do not have limitation on the surface orientation [03Our, 04Her, 07Kas, 10Lüt]. For instance, epitaxial growth refers to a deposition of an overlayer on a crystalline substrate using molecular beam (such as MBE, MOVPE, or chemical reaction in metal-organic chemical vapor deposition (MOCVD)). For most applications, it is desired that the deposited material forms a crystalline overlayer with well-defined orientation with respect to the substrate structure. Such procedure is called single-domain epitaxy. Monte Carlo or molecular dynamics methods are used to numerically simulate the growth and related surface atom diffusion, as it is done, for instance, for III–V semiconductors [99Ish, 02Kra] and for Si(111) [05Oht]. Homoepitaxy is an experimental technique used for growing a crystalline film on a substrate or film of the same material that is performed with only one material. It is important that a film, which is more pure than the substrate or has different doping levels, can be grown homoepitaxially. If only one material is used (e.g., Si grown on Si) and the initial substrate is reconstructed, homoepitaxial surface usually preserves the same surface structure. Due to low defect density and purity of the homoepitaxially grown surfaces, they are the best candidates to compare with the computer simulation results [96Ned]. More surface structure selection can be achieved using heteroepitaxy, which is the epitaxial growth of one material on a substrate given by another material. Furthermore, since the growth is performed in the presence of different gases, their pressure and temperatures, changing the temperature and pressure allows producing different surface structures. Heteroepitaxy is one of the main experimental methods for III–V compound growth, and one of the best known example is the GaAs(100) surface growth [04Her, 08Oht]. There is no fundamental limit to the number of components for the growth. For example, AlGaInPAs layers can be grown on GaAs. Each additional element adds an extra degree of freedom for tailoring the properties of the surface and thin films, although more detailed phase equilibria data or models are required to determine accurate compositions and temperatures [07Kas]. The above surface preparation methods include high temperature, presence of different foreign atomic species, and nonzero pressure, which have to be taken into account when simulating surface structure and will be discussed next.

3 Physics mechanisms of the surface structure formation

5

Additionally, the theoretical tools must account for the difference in the bonding type of the solids of interest. Overlayer growth processes can be simulated, and Monte Carlo techniques are the best fit for such numerical experiment [99Ish, 02Gro, 02Kra, 06Alf]. After crystalline surfaces are formed, to minimize their free energy, different mechanisms of relaxation or reconstruction are driving the process of the surface structure formation. This process can differ considerably for semiconductor, oxide, or metal surfaces. For instance, metallic bonding is nondirectional in character, that is, a simple metal surface lacks the localized dangling bonds, unlike the covalent bonding, which dominates elemental and compound semiconductors as well as some oxides. Formation of the metal surface usually leads to the subtle movements of the surface atoms relative to the bulk-termination positions. Such process is attributable to the effect of the changing valence charge density at the metal–vacuum interface. The outermost atoms change their positions to reduce the surface energy by smoothening this density [96Cha, 96Tit, 06Sil]. This usually leads to the contractive relaxation of the first atomic layer such that the spacing between the two outermost layers is smaller than in the bulk-terminated (unrelaxed) surface, which was found for the majority of simple and transition metal surfaces. A jellium (i.e., homogeneous electron gas) model was developed and applied in the past to quantitatively account for the contractive relaxation due to the surface charge smoothening [70Lan]. Although such a jellium model was not able to quantitatively predict metal surface relaxation, it was very useful when the first simulations of the clean metal surfaces started. Later, the model validity in explaining the contractive relaxation and its driving forces was confirmed by ab initio results [83Euc, 02Spe, 06Sil, 07Sfe]. Despite domination of the contractive relaxation for metal surfaces, an expansion of the upper relaxed layer was also found experimentally for some surfaces, such as in Be(0001) [92Dav, 96Fei, 06Sil]. To explain the outward relaxation, it was proposed in [96Fei] that existing consideration of “physical” picture of surface relaxation, based on smoothing of electronic charge density corrugation, has to be combined with a “chemical” picture based on promotion–hybridization ideas. It also implies the necessity of reexamining the idea that close-packed surfaces “always” manifest small relaxations. However, the modern first-principles calculations give mostly accurate prediction of the relaxed metal structures [06Sil, 07Sfe], including the expansion of the upper relaxed layer without the need to separate the chemical and physical pictures. Finally, certain clean fcc (110) metal surfaces undergo extensive reconstruction (rather than relaxation) [96Tit, 96Cha]. For many clean metal surfaces, the reconstruction was predicted numerically [93Ber, 96Tit]. In many cases this involves the missing-row reconstruction which has been simulated in [07Kag, 10Rei, 11Che, 13Zhu]. The creation of (111) microfacets has been cited as the driving force for the missingrow reconstruction, and the first-principles simulations were accurate in the prediction of the missing-row structures; see, for instance, [06Oli, 10Rei] for Au(110) 1
2 or [13Zhu] for Pt(110) 1
n (n ¼ 2–4). In contrast to the metal surfaces, it is possible to summarize well-defined principles that drive the relaxation and reconstruction of clean semiconductor surfaces. Duke [96Duk1] has summarized a set of five principles suitable to understand structure of the clean low-index faces of tetrahedrally coordinated elemental and compound semiconductors. The principles were used, for instance, in various review papers, such as [92LaF, 93Lan, 97Sri]. It is important to stress that these principles can also be successfully applied to understand oxide surface structures [96LaF]. Following the sequence from [96Duk1], these principles can be formulated as follows: Principle 1: Reconstructions of the semiconductor surfaces tend either to saturate surface dangling bonds (DBs) via rehybridization or to convert them into nonbonding electronic states. This principle applies to group IV semiconductors, e.g., Si(111) 2
1 [82Pan2, 90Anc] or Ge(111) 2
1 [91Tak], C(111) 2
1 [82Pan1, 96Sch, 06Squ, 14Pie], and many others. Principle 1 can also be extended to all tetrahedrally coordinated compound semiconductors (III–V, II–VI, and I–VII); its extension corresponds to principles 4 and 5, as discussed below. In the numerical simulation, the tendency of DB rehybridization is manifested through the forces, which move the surface atoms to saturate the bonds and minimize the total energy. The mechanism of principle 1 can be identified numerically through the simulated charge density of the modified or new bonds that are formed at the surface. Principle 2: In many cases, even if DBs are saturated (as governed by principle 1), surfaces can lower their energies by further atomic relaxations, leading to semiconducting (as opposed to metallic) surface state eigenvalue spectra. This mechanism is always accompanied by surface charge transfer. Perhaps the clearest example of its operation on tetrahedrally coordinated semiconductor surfaces is the tilting of the

6

A. Shkrebtii and M. Rohlfing

dimers on Si(100) and Ge(100) surfaces [79bCha, 95Shk, 96Roh, 05Nak]. In the above systems, the dimer tilting is accompanied by formation of sp3- and sp2-like bonding configurations of the topmost atoms, which opens the surface electron band gap. In the numerical simulation, the extra force component is due to charge transfer between the surface atoms and related change in the bond hybridization. Principle 3: The surface structure observed will be the lowest free-energy structure kinetically accessible under the preparation conditions. For instance, after the low-temperature cleavage, surfaces with multiple total energy minima can be trapped into one of the minima, which corresponds to a metastable structure. The standard total energy minimization techniques converge surface atom positions toward zerotemperature configuration without an indication whether this structure is metastable or not (as shown in Fig. 3.1). If a few of such configurations are known or can be suggested, the total energy minimization can indicate on the lowest-energy structure without guarantee; however, that this is the ground state of the surface. In laboratory experiment the surface, trapped into metastable configuration, can be transformed into the ground state global total energy minimum structure using, for instance, annealing [10Lüt] or keeping the surface at high temperature during deposition [04Her]. Experimentally this usually occurs if temperature-induced surface atom perturbation becomes sufficient to statistically overcome potential energy barriers between two atomic configurations (Fig.3.1), thus allowing the surface reaching the global minimum of the free energy. Theoretically, such dynamical process can be modeled directly using molecular dynamics (MD) [92Pay, 94Tak] or indirectly through the Monte Carlo simulations [92Pay, 00Pet, 05Reu]. Monte Carlo method is extensively used to model both microscopic atomic structure as well as the surface morphology during the growth [01Ito], investigating metastable structure formation and graphitization of C(111) surface [00Pet] or formation of the missing-row reconstructions at fcc (110) surfaces [11Che]. However, MD becomes too expensive numerically and is not typically used for finding the global energy minimum [92Pay, 05Reu]. Principle 3 also reflects surface structure dependence on the preparation. Two important examples have to be mentioned: the transition of the low-temperature cleavage Si(111) 2
1 reconstruction into the Si (111) 7
7 dimer-adatom-stacking fault (DAS) structure [85aTak, 85bTak, 86Qia, 92Sti, 92Bro] and the transition of the corresponding Ge(111) 2
1 reconstruction into the Ge(111) c(2
8) structure [81Cha, 92Tak, 94Tak, 95Tak]. In both cases such surface phase transitions occur experimentally after annealing of the 2
1 phases. Principles 1–3 are sufficient to explain driving forces of the surface structure of homopolar elemental semiconductors such as Si and Ge of diamond, and their validity is confirmed by computer simulations. For surfaces of compound heteropolar semiconductors, however, as well as for oxide surfaces, the ionicity contributes essentially to the total energy balance and correspondingly surface structure. In such a case, the surface atomic composition, that is, stoichiometry, may be different from that of the bulk, and large charge transfer routinely occurs at the surface from one atomic species to another. Two more principles have to be considered to understand the driving forces of the reconstruction in this case: Principle 4: Surfaces tend to be autocompensated. This constraint limits the possible stoichiometries of compound semiconductor surfaces to avoid charge accumulation at the surface and subsequent total energy increase due to electrostatics interaction. The charge neutrality constraint has been developed into a set of electron-counting rules, which can be applied directly to determine allowable surface compositions [89Pas, 99Mir]. In this limit, for instance, on surfaces of heteropolar semiconductors, DBs cannot be completely filled with electrons while simultaneously maintaining the local charge balance of the crystal. As a result, the DBs must be either partially or selectively filled. The above rules were generalized on the base of the first-principles total energy calculations for a large number of III–V semiconductor surfaces in order to establish a database that helps to isolate and predict the lowest-energy atomic surface geometries [99Mir]. This principle has to be applied when modeling the atomic structure of polar semiconductor and oxide surfaces. The most typical and important example is GaAs(100), for which numerous surface reconstructions exist, critically depending on the preparation conditions [04Her, 08Oht]. Its stoichiometrydependent geometries are extensively studied both in experiment and in theory and will be further discussed. Principle 4 is taken into account in theoretical modeling in terms of classical force fields that originate from the electrostatic dipole interaction and from surface charge transfer. Principle 5: For a given surface stoichiometry, the surface atomic geometry is determined primarily by a rehybridization-induced lowering of the surface state bands associated with either surface bonds or

3 Physics mechanisms of the surface structure formation

7

(filled) anion dangling bond states. Whereas for compound semiconductors principle 4 determines allowed surface stoichiometries, principle 5 determines their detailed atomic geometries. It is formulated as an extension to compound semiconductors of principle 1 which as articulated is most useful for the nonpolar surfaces of group IV and III–V semiconductors. Principle 5 is a generalization of principle 1 for both nonpolar and polar surfaces because it embodies a new notion not contained in principle 1: that of surface chemical bonding carried by the delocalized electronic surface states characteristic of a two-dimensional epitaxially constrained surface compound. This is an extension of traditional local bonding concepts characteristic of molecular bonding and bulk solid bonding, which is required to comprehend the similarities between the cleavage surface bonding of III–V, II–VI, and I–VII semiconductors. Thus, principle 5 can be applied to describe the relaxations of the cleavage faces of II–VI and I–VII semiconductors, whereas principle 1, while true, does not illuminate the origin of the resulting surface structures. Principle 5 is, moreover, subject to direct experimental verification in that the surface states which carry the surface chemical bonding can be observed directly by angle-resolved photoemission spectroscopy (ARPES). Thus, hypotheses about the character of this bonding can be tested by calculation of the surface band structure associated with the top atom geometry and comparing with the experimentally measured surface bands (see, e.g., [97Sch]). In the next chapters, we discuss the theoretical formalisms used to follow the above main principles in numerical simulations and their results with respect to the most typical and important crystalline solid surfaces. Symbols and abbreviations Short form

Full form

MD ARPES DAS MBE MOCVD MOVPE DB VDW UHV 2D MC

molecular dynamics angle-resolved photoemission spectroscopy dimer-adatom-stacking fault molecular beam epitaxy metal-organic chemical vapor deposition metal-organic vapor phase epitaxy dangling bond Van der Waals ultra high vacuum two-dimensional Monte Carlo

References [70Lan] [79bCha] [81Cha] [82Pan1] [82Pan2] [83Euc] [85McR] [85aTak] [85bTak] [85Car] [86Qia] [87Han] [89Han] [89Pas] [90Anc] [91Anc [91Tak] [92Bro]

Lang, N.D., Kohn, W.: Phys. Rev. B. 1, 4555 (1970) Chadi, D.J.: Phys. Rev. Lett. 43, 43 (1979b) Chadi, D.J., Chiang, C.: Phys. Rev. B. 23, 1843 (1981) Pandey, K.C.: Phys. Rev. B. 25, 4338 (1982) Pandey, K.C.: Phys. Rev. Lett. 49, 223 (1982) Euceda, A., Bylander, D.M., Kleinman, L.: Phys. Rev. B. 28, 528 (1983) McRae, E.G., Malic, R.A.: Surf. Sci. 161, 25 (1985) Takayanagi, K., Tanishiro, Y., Takahashi, M., Takahashi, S.: J. Vac. Sci. Technol. A. 3, 1502 (1985) Takayanagi, K., Tanishiro, Y., Takahashi, S., Takahashi, M.: Surf. Sci. 164, 367 (1985) Car, R., Parrinello, M.: Phys. Rev. Lett. 55, 2471 (1985) Qian, G., Chadi, D.J.: J. Vac. Sci. Technol. B: Microelectron. Nanometer Struct. 4, 1079 (1986) Haneman, D.: Rep. Prog. Phys. 50, 1045 (1987) Haneman, D., Rownd, J.J., Lagally, M.G.: Surf. Sci. Lett. 224, 965 (1989) Pashley, M.D.: Phys. Rev. B. 40, 10481 (1989) Ancilotto, F., Andreoni, W., Selloni, A., Car, R., Parrinello, M.: Phys. Rev. Lett. 65, 3148 (1990) ] Ancilotto, F., Selloni, A., Tosatti, E.: Phys. Rev. B. 43, 14726 (1991) Takeuchi, N., Selloni, A., Shkrebtii, A.I., Tosatti, E.: Phys. Rev. B. 44, 13611 (1991) Brommer, K.D., Needels, M., Larson, B., Joannopoulos, J.D.: Phys. Rev. Lett. 68, 1355 (1992)

8

[92LaF] [92Sti] [92Tak] [92Pay] [93Lan] [93Mon] [93Ber] [93Sel]

[94LaF] [94Tak] [95Shk] [95Tak] [96Cha] [96Duk1] [96Duk2] [96Fei] [96LaF] [96Mol] [96Ned] [96Roh] [96Sch] [96Wil] [96Tit] [96Une] [97Sch] [97Sri] [97Yam] [99Ish] [99Mir] [00Nog] [00Pet] [01FuC] [01Hea] [01Ito] [01Nog] [01Woo] [02Car] [02Ebe] [02Gro] [02Kra] [02Spe] [02Ste] [03Bec] [03Kre] [03Our] [03Som] [04Bon] [04Her] [05Nak] [05Oht] [05Reu] [06Alf] [06Oli] [06Sil]

A. Shkrebtii and M. Rohlfing

LaFemina, J.P.: Surf. Sci. Rep. 16, 137 (1992) Stich, I., Payne, M.C., King-Smith, R.D., Lin, J., Clarke, L.J.: Phys. Rev. Lett. 68, 1351 (1992) Takeuchi, N., Selloni, A., Tosatti, E.: Phys. Rev. Lett. 69, 648 (1992) Payne, M.C., Teter, M.P., Allan, D.C., Arias, T.A., Joannopoulos, J.D.: Rev. Mod. Phys. 64, 1045 (1992) Lannoo, M.: Mater. Sci. Eng. B. 22, 1 (1993) Monch, W.: Springer (1993), 438. Bernasconi, M., Tosatti, E.: Surf. Sci. Rep. 17, 363 (1993) Selloni, A., Fasolino, A., Shkrebtii, A.I.: Landolt-B€ ornstein: Numerical Data and Functional Relationships in Science and Technology – New Series, Subseries: Condensed Matter 1993 “Surface Reconstruction and Relaxation”. Springer, Berlin (1993) LaFemina, J.P.: Crit. Rev. Surf. Chem. 3, 297 (1994) Takeuchi, N., Selloni, A., Tosatti, E.: Phys. Rev. B. 49, 10757 (1994) Shkrebtii, A.I., Di Felice, R., Bertoni, C.M., Del Sole, R.: Phys. Rev. B. 51, 11201 (1995) Takeuchi, N., Selloni, A., Tosatti, E.: Phys. Rev. B. 51, 10844 (1995) Chan, C.T., Ho, K.M., Bohnen, K.P.: Physical Structure, p. 101. North-Holland (1996) Duke, C.B.: Chem. Rev. 96, 1237 (1996) Duke, C.B.: Physical Structure, p. 229. North-Holland (1996) Feibelman, P.J.: Phys. Rev. B. 53, 13740 (1996) LaFemina, J.P.: Physical Structure, p. 137. North-Holland (1996) Moll, N., Kley, A., Pehlke, E., Scheffler, M.: Phys. Rev. B. 54, 8844 (1996) Neddermeyer, H.: Reports on Progress in Physics 59, 701 (1996) Rohlfing, M., Krüger, P., Pollmann, J.: Phys. Rev. B. 54, 13759 (1996) Schmidt, W.G., Bechstedt, F.: Surf. Sci. 360, 473 (1996) Williams, E.D., Bartelt, N.C.: Physical Structure, p. 51. North-Holland (1996) Titmuss, S., Wander, A., King, D.A.: Chem. Rev. 96, 1291 (1996) Unertl, W.N.: Physical Structure, vol. 1, p. 3-884. Elsevier, Amsterdam/New York (1996). Series editors: Holloway, S., Richardson, N.V. Schmidt, W.G., Bechstedt, F.: Phys. Rev. B. 55, 13051 (1997) Srivastava, G.P.: Rep. Prog. Phys. 60, 561 (1997) Yamaguchi, K., Mitsui, H., Shigeta, Y.: J. Vac. Sci. Technol. A. 15, 2569 (1997) Ishii, A., Kawamura, T.: Surf. Sci. 436, 38 (1999) Mirbt, S., Moll, N., Kley, A., Joannopoulos, J.D.: Surf. Sci. 422, 177 (1999) Noguera, C.: J. Phys. Condens. Matter. 12, R367 (2000) Petukhov, A.V., Passerone, D., Ercolessi, F., Tosatti, E., Fasolino, A.: Phys. Rev. B. 61, R10590 (2000) Fu, C., Weissmann, M., Sau´l, A.: Surf. Sci. 494, 119 (2001) Healy, S.B., Filippi, C., Kratzer, P., Penev, E., Scheffler, M.: Phys. Rev. Lett. 87, 016105 (2001) Itoh, M.: Prog Surf Sci. 66, 53 (2001) Noguera, C.: Oxide surfaces. In: The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, vol. 9, p. 35. Elsevier, Amsterdam (2001) Woodruff, D.P.: The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, vol. 9. Elsevier, Amsterdam (2001) Car, R.: Quant. Struct.-Act. Relat. 21, 97 (2002) Ebert, P.: Appl. Phys. A. 75, 101 (2002) Grosse, F., Gyure, M.F.: Phys. Rev. B. 66, 075320 (2002) Kratzer, P., Penev, E., Scheffler, M.: Appl. Phys. A. 75, 79 (2002) Spencer, M.J.S., Hung, A., Snook, I.K., Yarovsky, I.: Surf. Sci. 513, 389 (2002) Stekolnikov, A.A., Furthmüller, J., Bechstedt, F.: Phys. Rev. B. 65, 115318 (2002) Bechstedt, F.: Principles of Surface Physics. Springer, Berlin (2003) Kresse, G., Bergermayer, W., Podloucky, R., Lundgren, E., Koller, R., Schmid, M., Varga, P.: Appl. Phys. A-Mater. Sci. Process. 76, 701 (2003) Oura, K., Katayama, M., Zotov, A.V., Lifshits, V.G., Saranin, A.A.: Surface Science, p. 171. Springer Berlin Heidelberg (2003) Somasi, S., Khomami, B., Lovett, R.: J. Chem. Phys. 119, 9783 (2003) Bonzel, H.P., Nowicki, M.: Phys. Rev. B. 70, 245430 (2004) Herman, M.A., Richter, W., Sitter, H.: Epitaxy: Physical Principles and Technical Implementation. Springer, New York (2004) Nakamura, J., Natori, A.: Phys. Rev. B. 71, 113303 (2005) Ohtomi, K., Kato, T., Suzuki, T.: Surf. Sci. 588, 127 (2005) Reuter, K., Stampf, C., Scheffler, M.: Ab initio atomistic thermodynamics and statistical mechanics of surface properties and functions. In: Handbook of Materials Modeling, p. 149. Springer Netherlands, Dordrecht (2005) Alfe, D., Gillan, M.J.: J. Phys. Condens. Matter. 18, 435 (2006) Olivier, S., Tre´glia, G., Sau´l, A., Willaime, F.: Surf. Sci. 600, 5131 (2006) Silva, J.L.F.D., Stampfl, C., Scheffler, M.: Surf. Sci. 600, 703 (2006)

3 Physics mechanisms of the surface structure formation

[06Squ] [07Gei] [07Kag] [07Kas] [07Sfe] [08Haf] [08Oht] [08Pan] [09Cas] [09Gia]

[09Gon]

[09Gro] [09Jan] [10Die] [10Lüt] [10Kla] [10Rei] [11Che] [11Net] [12Gao] [12Mic] [12Nov] [13Zhu] [14Pie]

9

Sque, S.J., Jones, R., Briddon, P.R.: Phys. Rev. B. 73, 085313 (2006) Geim, A.K., Novoselov, K.S.: Nat. Mater. 6, 183 (2007) Kaghazchi, P., Jacob, T.: Phys. Rev. B. 76, 245425 (2007) Kasap, S., Cappe, P.: In: Kasap, S., Capper, P. (eds.) Springer Handbook of Electronic and Photonic Materials. Springer, New York (2007) Sferco, S.J., Blaha, P., Schwarz, K.: Phys. Rev. B. 76, 075428 (2007) Hafner, J.: J. Comput. Chem. 29, 2044 (2008) Ohtake, A.: Surf. Sci. Rep. 63, 295 (2008) Pan, B., He, H.: Phys. Rev. B. 77, 113302 (2008) Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.K.: Rev. Mod. Phys. 81, 109 (2009) Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I., Corso, A.D., Gironcoli, S.D., Fabris, S., Fratesi, G., Gebauer, R., Gerstmann, U., Gougoussis, C., Kokalj, A., Lazzeri, M., Martin-Samos, L., et al.: J. Phys. Condens. Matter. 21, 395502 (2009) Gonze, X., Amadon, B., Anglade, P., Beuken, J., Bottin, F., Boulanger, P., Bruneval, F., Caliste, D., Caracas, R., Coˆte´, M., Deutsch, T., Genovese, L., Ghosez, P., Giantomassi, M., Goedecker, S., Hamann, D.R., Hermet, P., Jollet, F., Jomard, G., Leroux, S., et al.: Comput. Phys. Commun. 180, 2582 (2009) Gross, A.: Theoretical Surface Science. A Microscopic Perspective. Originally published in the series: Advanced Texts in Physics, 2nd ed. 342 p. 132 illus (2009) Janotti, A., Van de Walle, C.G.: Rep. Prog. Phys. 72, 126501 (2009) Diebold, U., Li, S., Schmid, M.: Annu. Rev. Phys. Chem. 61, 129 (2010) Lüth, H.: Solid Surfaces, Interfaces and Thin Films. Springer, New York (2010) Wandelt, K.: Surface and Interface Science. Volume 2, Properties of Elemental Surfaces. Wiley-VCH, Weinheim (2010) Reis, D.D.D., Negreiros, F.R., Carvalho, V.E.D., Soares, E.A.: Surf. Sci. 604, 568 (2010) Chen, W., Schmidt, D., Schneider, W.F., Wolverton, C.: Phys. Rev. B. 83, 075415 (2011) Neto, A.H.C., Novoselov, K.: Reports on Progress in Physics. 74, 082501 (2011) Gao, G., Gao, W., Cannuccia, E., et al.: Nano Lett. 12, 3518 (2012) Michaelides, A., Scheffler, M.: An introduction to the theory of metal surfaces, Chapter 2. In: Wandelt, K. (ed.) Textbook of Surface and Interface Science, vol. I. Wiley-VCH, Weinheim (2012) Novoselov, K.S., Fal0 ko, V.I., Colombo, L., Gellert, P.R., Schwab, M.G., Kim, K.: Nature. 490, 192 (2012) Zhu, T., Sun, S., van Santen, R.A., Hensen, E.J.M.: J. Phys. Chem. C. 117, 11251 (2013) Pierre, D.L., Bruno, M., Manfredotti, C., Nestola, F., Prencipe, M., Manfredotti, C.: Mol. Phys. 112, 1030 (2014)

Chapter 4

Compilation of the theoretical frameworks for surface structure simulations A. Shkrebtii and M. Rohlfing

The key quantity for any approach to solid surface structural optimization is the internal energy of the !
! system as a function of the atomic coordinates, U R . In here, R denotes the 3N coordinates of the N atomic !
!
nuclei. At zero temperature, U R is the total energy of the system Etot R . In case of a periodic surface system with 2D translational symmetry, only the atoms within the periodically repeated unit cell are relevant. The surface terminates the bulk material, which therefore loses its periodicity along the surface normal. Such a situation requires a so-called semi-infinite unit cell, with possible connection between bulk and surface in terms of surface Green functions [78Pol, 86Krü, 90Krü, 95Krü]. Most of the modern surface atomic structure simulation approaches, however, are significantly more efficient or even only tractable if three-dimensional periodicity is imposed on the system, which allows the momentum-space formulation be used (see, e.g., Chap. 3 of [03Bec]). This is usually termed as periodic boundary conditions (PBC) within the so-called repeated slab geometry, which is given by a periodically repeated supercell. In principle, the finite slab thickness and the finite inter-slab distance in such a supercell constitute a misrepresentation of the semi-infinite system. However, at sufficiently large slab thickness, bulk properties are achieved deep inside the slab, and the intra-slab interaction between its two surfaces (at the “top” and at the “bottom” of the slab) vanishes. Furthermore, at very large inter-slab separation, the spurious interaction between the two surfaces across the separating vacuum vanishes, as well. Both quantities (slab thickness and separation between the slabs) must therefore be chosen sufficiently large to suppress artificial interaction effects and falsifications below an acceptable amount. In practice, most surface properties can often be converged to their correct values by choosing a slab thickness of about 10 Å or somewhat more, depending on the material and on the physical property under consideration. As an alternative to configurations with two-dimensional periodicity, a cluster configuration allows the employment of quantum-chemical approaches or software (see, for instance, [91Ver, 01Hea, 03Nau]). Here a finite-size flake of the surface is surrounded by vacuum in all three directions, essentially constituting a large “molecule.” Similar to a slab configuration, convergence of the surface properties to their correct values can in principle be achieved by choosing the cluster sufficiently large in all three directions. Such approach, however, is rarely used in physics of the solid surfaces. In the surface structure simulations, atomic cores are usually treated classically. It should be mentioned that restricting nuclear coordinates as classical quantities constitutes an approximation (similar to the BornOppenheimer approximation for nuclear motion, as discussed below), since the nuclei may behave as quantum-mechanical particles, in principle. Nonclassical behavior of the nuclei is to be expected pronounced for light atoms (such as hydrogen) in situations when, for instance, hydrogen bridge bonds are formed [08Mor]. But even then the changes in structure and in total energy appear small, thus validating the classical approach to treat atomic cores.

A. Shkrebtii (*) Faculty of Science, University of Ontario Institute of Technology (UOIT), Oshawa, ON, Canada e-mail: [email protected] M. Rohlfing Institut für Festk€orpertheorie, Universität Münster, Münster, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_4

1

2

A. Shkrebtii and M. Rohlfing

Concerning the structural optimization of a (surface) system in its electronic ground state, two main !
problems must be considered: (i) the realistic and efficient determination of the total energy Etot R for a ! !
given atomic configuration R , preferably including the forces, ∇! Etot R , and (ii) the search for the R !
global minimum of the landscape (the so-called potential energy surface) Etot R (or, in more general !
terms, the determination of the thermodynamical properties related to Etot R ), which may go beyond simply finding its minimum and instead involve more complicated discussion of, e.g., temperature, pressure, or chemical potentials. Symbols and abbreviations Short form

Full form

PBC 2D

periodic boundary conditions two-dimensional

References [78Pol] [86Krü] [90Krü] [91Ver] [95Krü] [01Hea] [03Bec] [03Nau] [08Mor]

Pollmann, J., Pantelides, S.T.: Phys. Rev. B. 18, 5524 (1978) Krüger, P., Mazur, A., Pollmann, J., Wolfgarten, G.: Phys. Rev. Lett. 57, 1468 (1986) Krüger, P., Pollmann, J.: Phys. Rev. Lett. 64, 1808 (1990) Verwoerd, W.S., Nolting, V., Badziag, P.: Surf. Sci. 241, 135 (1991) Krüger, P., Pollmann, J.: Phys. Rev. Lett. 74, 1155 (1995) Healy, S.B., Filippi, C., Kratzer, P., Penev, E., Scheffler, M.: Phys. Rev. Lett. 87, 016105 (2001) Bechstedt, F.: Principles of Surface Physics. Springer, Berlin (2003) Naumkin, F.Y., Polanyi, J.C., Rogers, D., Hofer, W., Fisher, A.: Surf. Sci. 547, 324 (2003) Morrone, J.A., Car, R.: Phys. Rev. Lett. 101, 017801 (2008)

Chapter 5

Determination of the total energy of a many-particle system A. Shkrebtii and M. Rohlfing

In principle, the total energy of a given structure in its electronic ground state results from the quantummechanical many-body Hamilton operator [04Mar, 06Koh, 09Gro, 15Bec]: b¼ H

Xn b p 2j j¼1

2m

þ

Xn

 !

Xn R !  e2 b b V r þ  j !  þ H kin, nucl þ H pot, nucl j¼1 nucl, e i APDBs with local (2
2) and c(4
2) structure and aligned par
>; allel to < 110 APDB crossings with (√3
√3) structure Studies on 1 and 2 vicinal surfaces APDBs with local (2
2) structure aligned  
parallel to 110 with BV ¼ (1,0,-1); Partly APDBs with (8
8) structure between domains of identical rotational orientation – Hexagonal domains of (2
2) phases separated by APDB network; APDBs with c(4
2) structure Conclusions from diffraction spot splitting UHV cleavage and APDBs mainly annealing disordered but with short range c(2
4) and (2
2) order and additional holes UHV cleavage and Additional elecannealing tronic states in the band gap for APDBs

Ref. [91Fee] [92Fee] [93Fee] [05Fee]

Fig.

[93Mol1]

[93Mol2]

Fig. 39.4

[94Mol]

[98Ein]

[05Fee]

(continued)

6

J. Wollschläger

Table 39.1 (continued) Miller index (113)

Major experimental Superstructure techniques (3
2) STM at RT

SPA-LEED

Supporting experimental techniques DFT-LDA

AES

Results Sample preparation Remarks Ar+ ISA (/850  C) DBs aligned  parallel to 332
or  
110

Ref. [98Lar]

Ar+ ISA (500 V, 800 K/970 K)

[99Igl]

APDBs aligned  
parallel to 3
32 with regular spacing due to repulsive interaction for T with BV ¼ 1/2(1,1,0) or BV ¼ 1/2(1,-1,0) (both arrows in the upper part of the drawing). Inclined aligned paralle to < 110 APDBs exhibit kinks with BV ¼ (1,0,0) or BV ¼ (0,1,0) (both arrows in the lower part of the drawing) antiphase domains with unity width lead locally to the formation of c(2
8) unit cells as demonstrated on the left side

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_41

1

2

J. Wollschläger

Fig. 41.2 Schematical drawing of APDBs for Si doped GaAs-(2
4)-As as concluded form STM (Adopted from [97Ish]): straight and inclined APDBs  > with BV ¼ 1/2 with respect to < 110 (1,1,0) (both vertical arrows in the upper part of the drawing) or BV ¼ 1/2(1,-1,0) (both horizontal arrows in the lower part of the drawing). Inclined APDBs have regularly arranged kinks

Fig. 41.3 Schematical drawing of APDB on GaAs(111)B-(2
2)-As (Adopted from STM micrograph from [90Bie1]). The APDB is aligned parallel to 011 with BV ¼ (2,-1-1) (arrow) and with local (√3
2) structure

41

Structure of domain boundaries: group III–V compounds: GaAs

3

Table 41.1 GaAs Miller index (001)

Superstructure

Major experimental techniques

Supporting experimental techniques

(2
4)-As

RHEED

–

GaAs MBE on GaAs(001) at 800 K

RHEED

–

–

RHEED LEED

AES ARUPS

GaAs MBE on GaAs(001) at 550  C

STM

LEED RHEED

GaAs MBE on GaAs(001) at 600  C

STM

LEED AES ARPES

Results Sample preparation

GaAs MBE on GaAs(001) at 640  C; cooling to

Remarks

Ref.

APDBs aligned parallel to [110]; Proposed models with BV ¼ (1,0,0), BV¼1/2(1,-3,0), or BV¼1/2(3,-1,0) Conclusions from curved RHEED streaks APDBs  aligned to  110 (1D disorder) Concluded from curved RHEED streaks at intermediate azimuth APDBs paral aligned   lel to 110 with BV ¼ 1/2(-1,1,0) and local c(2
8) structure Model of c(2
8) due to periodic arrangement of APDBs APDBs paral  aligned  with lel to 110    leadBV ¼ 1/2 110 ing to local c(2
8) structure; Locally kinked APDBs aligned parallel to [110] with different BVs due to boundary kinks: K1: APDB aligned parallel to [110] and BV ¼ (-1,0,0) leading to local (2
4) structure for    , missing row in 110 K2: inclined APDB and BV ¼ (-1,0,0) leading to local c(2
8) structure  for  , missing row in 110 K3: inclined APDB and BV ¼ (0, -1,0) leading to local c(2
8) structure for miss  ing row in 110

[82Dob]

Deposition of As capping at RT and removing at 370  C APDBs paral aligned   lel to 110 (
4 direction) BV ¼ 1/2(-1,1,0)

Fig.

[84Joy]

[88Lar]

[88Pas]

Fig. 41.1

[90Bie2]

(continued)

4

J. Wollschläger

Table 41.1 (continued) Miller index

Superstructure

Major experimental techniques

Supporting experimental techniques

Results Sample preparation

Remarks

Ref.

APDBs aligned in [110] with BV ¼ 1/2 (1,1,0); Asymmetric mean APDB distances:    10–30 nm in 110 ; 30–100 nm in [110] Straight and inclined APDBs with respect to with BV ¼ 1/2 (1,1,0) or BV ¼ 1/2 (1, -1,0) APDBs paral aligned   lel to 110

[94Zho]

Kinked APDBs due to inclination with respect to [110] with inclination depending on Si-doping Kinks ¼ surface acceptors APDBs due to atomic steps parallel  aligned   (A steps) or to 110 aligned parallel to [110] (B steps) APDBs   inclined to  for n-doped 110 GaAs(001); Straight APDBs for p-doped GaAs(001) APDBs paral aligned   with lel to 110 BV ¼ 1/2(-1,1,0)

[91Pas1] [91Pas2] [92Pas1] [92Pas2]

APDBs with local c (2
8) structure initiated by vacancies APDBs aligned in [110] with BV ¼ 1/2(1,1,0); Asymmetric mean APDB distances:    and 10–30 nm in 110 30–100 nm in [110] Kinked APDBs    ; aligned in 110 APDBs aligned parallel to [110] with

[93Xu]

Fig.



(2
4)/c(2
8)-As

α(2
4)-As

500 C under As flux and quenching to RT GaAs MBE (Si-doped) at 580  C

FI-STM RHEED

–

STM

RHEED XPS

GaAs MBE (Si-doped) on GaAs(001)

RHEED

–

STM/STS LEED

LEED RHEED AES

GaAs MBE on GaAs(001) at 800 K GaAs MBE (Si-doped) on GaAs(001) at 560  C

STM

RHEED

GaAs MBE on vicinal GaAs(001) at 560–600  C

STM

RHEED

GaAs MBE (n- and p-doped) on GaAs(001) at 560–600  C

FI-STM

RHEED

FI-STM

–

FI-STM RHEED

–

GaAs MBE (Si-doped) on GaAs(001); cooling to 500  C under as flux GaAs MBE (Si-doped) at 580  C GaAs MBE (Si-doped) at 580  C

FI-STM RHEED

–

GaAs MBE (Si-doped) on GaAs(001) at 540–630  C

[97Ish]

Fig. 41.2

[83Van]

[92Pas3]

[93Pas]

[93Tan]

[94Zho]

[94Has]

(continued)

41

Structure of domain boundaries: group III–V compounds: GaAs

5

Table 41.1 (continued) Miller index

Superstructure

Major experimental techniques

Supporting experimental techniques

Results Sample preparation with As excess flux

β(2
4)-As

β2(2
4)-As

STM RHEED

–

GaAs MBE at 540–630  C

SXRD SR-XRD

RHEED

GaAs MBE at 550  C, 106 Torr As

FI-STM RHEED

–

GaAs MBE (Si-doped) on GaAs(001) at 540–630  C with As excess flux

STM RHEED

–

GaAs MBE at 540–630  C

GIXRD

RHEED

GaAs MBE; PDA under As4 flux at 550  C

RHEED STM

–

GaAs MBE at 580  C

Remarks BV ¼ 1/2(1,1,0); domain   size 6 nm for  and domain size 110 50 nm for [110] APDBs   aligned to  110 with BV ¼ 1/2 (-1,1,0) with local formation of c(2
8)-As; Kinked APDBs aligned to [110] with BV ¼ 1/2(1,1,0); Average kink distances 50 nm 3 % heavy APDBs with BV ¼ 1/2 (-1,-1,0); 8 % light APDBs with BV ¼ 1/2(1,1,0); 4 % super light APDBs with BV ¼ (1,1,0) Measurement at 605  C under 5
107 Torr As Straight APDBs    ; aligned to 110 APDBs aligned to [110] with BV ¼ 1/2(1,1,0); domain   size 30 nm for  and 300 nm for 110 [110] APDBs   aligned to  110 with BV ¼ 1/2 (-1,1,0) and local formation of c(2
8)-As; Kinked APDBs aligned to [110] with BV ¼ 1/2(1,1,0); Average kink distances 300 nm APDBs aligned parallel to [110], probably with BV ¼ 1/2(1,1,0); Negligible number of APDBs with BV ¼ (1,1,0) Concluded from diffraction peak broadening APDBs paral aligned   with lel to 110 c(2
8) structure;

Ref.

Fig.

[95Has1] [95Has2] [95Ich] [96Xue]

[03Tak]

[94Has]

[95Has1] [95Has2] [95Ich] [96Xue]

[96Gar]

[05Pas]

(continued)

6

J. Wollschläger

Table 41.1 (continued) Miller index

Superstructure

Supporting experimental techniques

Results Sample preparation

RHEED

–

GaAs MBE at 580  C

FI-STM RHEED

–

GaAs MBE (Si-doped) on GaAs(001) at 540–630  C; As excess flux

STM RHEED

–

GaAs MBE at 540–630  C

SXRD SR-XRD

RHEED

GaAs MBE at 550  C, 106 Torr As

(3
2)/ (3
n)

STM

LEED XPS

c(4
4)

RT-STM

RAS

GaAs MOVPE on GaAs(001) at 600  C; PDA in TBAs and H2 for 10 min GaAs MBE; As capping; decapping at 350  C

(2
2)-As

STM/STS

LEED RHEED SR-PES

STM

LEED RHEED

γ(2
4)-As

(111) B

Major experimental techniques

GaAs MBE at 600  C; cooling under As4 flux; As capping; decapping at 315–340  C GaAs MBE at 600  C; capping by As; decapping at 340  C

Remarks Relaxation of atoms close to APDBs APDBs stable for T < 580  C under As2 flux; Kinked APDBs concluded from 2/4 order diffraction peak Kinked APDBs    ; aligned in 110 APDBs aligned to [110] with BV ¼ 1/2(1,1,0); domain   size 6 nm for  direction and 110 domain size 10 nm for [110] direction APDBs   aligned to  110 with BV ¼ 1/2 (-1,1,0) (local formation of c(2
8)-As); Kinked APDBs aligned to [110] with BV ¼ 1/2(1,1,0); Average kink distances 50 nm 14 % heavy APDBs and 1 % light APDBs Measurement at 480  C under 5
107 Torr As APDBs paral  aligned  with lel to 110 BV ¼ (-1,1,0); and local (2
1) structure

APDBs with missing first layer As-dimer (defect A) and missing first and second layer As-dimer (defect B) APDBs paral aligned   (local (√3 lel to 110
2) structure) with BV ¼ (1,1,-2)

Charged defects at intersections of DBs; Fermi-level pinning due to charged defects

Ref.

Fig.

[09Pas]

[94Has]

[95Has1] [95Has2] [95Ich] [96Xue]

[03Tak]

[98Li]

[13Bru]

[90Bie1] [94Kim] [95Tho] [96Mor]

[94Fu]

Fig. 41.3

41

Structure of domain boundaries: group III–V compounds: GaAs

7

Symbols and abbreviations Short form

Full form

APDB STM BV RHEED LEED MBE 1D AES STS ARPES FI-STM SXRD SR-XRD GIXRD PDA TBA RT-STM SR-PES XPS MOVPE RAS

antiphase domain boundary scanning tunneling microscopy Burgers vector reflection high-electron energy diffraction low-energy electron diffraction molecular beam epitaxy one-dimensional Auger electron spectroscopy scanning tunneling spectroscopy angle-resolved photoelectron spectroscopy field ion – scanning tunneling microscopy surface X-ray diffraction synchrotron radiation X-ray diffraction grazing incidence X-ray diffraction post-deposition annealing tertiary butyl arsine room tempetature scanning tunneling micriscopy synchrotron radiation photoelectron emission spectroscopy X-ray photoelectron spectroscopy metal organic vapor phase epitaxy reflection anisotropy spectroscopy

References [82Dob] [83Van] [84Joy] [88Lar] [88Pas] [90Bie1] [90Bie2] [91Pas1] [91Pas2] [92Pas1] [92Pas2] [92Pas3] [93Pas] [93Tan] [93Xu] [94Fu] [94Has] [94Kim] [94Zho] [95Has1] [95Has2] [95Ich] [95Tho] [96Gar] [96Mor] [96Xue]

Dobson, P.J., Neave, J.H., Joyce, B.A.: Surf. Sci. 119, L339 (1982) Van Hove, J.M., Cohen, P.I., Lent, C.S.: J. Vac. Sci. Technol. A1, 546 (1983) Joyce, B.A., Neave, J.H., Dobson, P.J., Larsen, P.K.: Phys. Rev. B29, 814 (1984) Larsen, P.K., Chadi, D.J.: Phys. Rev. B37, 8282 (1988) Pashley, M.D., Haberern, K.W., Friday, W., Woodall, J.M., Kirchner, P.D.: Phys. Rev. Lett. 60, 2176 (1988) Biegelsen, D.K., Bringans, R.D., Northrup, J.E., Swartz, L.-E.: Phys. Rev. Lett. 65, 452 (1990) Biegelsen, D.K., Swartz, L.-E., Bringans, R.D.: J. Vac. Sci. Technol. A8, 280 (1990) Pashley, M.D., Haberern, K.W., Gaines, J.M.: J. Vac. Sci. Technol. B9, 938 (1991) Pashley, M.D., Haberern, K.W.: Phys. Rev. Lett. 67, 2697 (1991) Pashley, M.D., Haberern, K.W.: Ultramicroscopy. 42–44, 1281 (1992) Pashley, M.D., Haberern, K.W., Feenstra, R.M.: J. Vac. Sci. Technol. B10, 1874 (1992) Pashley, M.D., Haberern, K.W., Gaines, J.W.: Surf. Sci. 267, 153 (1992) Pashley, M.D., Haberern, K.W., Feenstra, R.M., Kirchner, P.D.: Phys. Rev. B48, 4612 (1993) Tanaka, I., Ohkouchi, S.: Jpn. J. Appl. Phys. 32, 2152 (1993) Xu, H., Hashizume, T., Sakurai, T.: Jpn. J. Appl. Phys. 32, 1511 (1993) Fu, J., Kim, J., Gallagher, M.C., Willis, R.F., Miller, D.L.: Surf. Sci. 318, 349 (1994) Hahizume, T., Xue, Q.K., Zhou, J., Ichmiya, A., Sakurai, T.: Phys. Rev. Lett. 73, 2208 (1994) Kim, J., Gallagher, M.C., Willis, R.F., Fu, J., Miller, D.L.: J. Vac. Sci. Technol. A12, 2145 (1994) Zhou, J., Xue, Q., Chaya, H., Hashizume, T., Sakurai, T.: Appl. Phys. Lett. 64, 583 (1994) Hashizume, T., Xue, Q.-K., Ichimiya, A., Sakurai, T.: Phys. Rev. B51, 4200 (1995) Hashizume, T., Xue, Q.-K., Ichimiya, A., Sakurai, T.: Appl. Surf. Sci. 87/88, 373 (1995) Ichimiya, A., Xue, Q.-K., Hashizume, T., Sakurai, T.: J. Cryst. Growth. 150, 136 (1995) Thornton, J.M.C., Weightman, P., Woolf, D.A., Dunscombe, C.J.: Phys. Rev. B51, 14459 (1995) Garreau, Y., Sauvage-Simkin, M., Jedrecy, N., Pinchaux, R., Veron, M.B.: Phys. Rev. B54, 17638 (1996) Moriarty, P., Beton, P.H., Henini, M., Woolf, D.A.: J. Vac. Sci. Technol. B14, 1024 (1996) Xue, Q., Hashizume, T., Sakata, T., Hasegawa, Y., Ichimiya, A., Ohno, T., Sakurai, T.: Thin Solid Films. 281–282, 556 (1996)

8

[97Ish] [98Li] [03Tak] [05Pas] [09Pas] [13Bru]

J. Wollschläger

Ishikawa, Y., Fukui, T., Hasegawa, H.: Jpn. J. Appl. Phys. 36, 1749 (1997) Li, L., Han, B., Gan, S., Qi, H., Hicks, R.F.: Surf. Sci. 398, 386 (1998) Takahasi, M., Yoneda, Y., Yamamoto, N., Mizuki, J.: Phys. Rev. B68, 085321 (2003) Pashley, D.W., Neave, J.H., Joyce, B.A.: Surf. Sci. 582, 189 (2005) Pashley, D.W., Neave, J.H., Joyce, B.A.: Surf. Sci. 603, L1 (2009) Bruhn, T., Fimland, B.-O., Esser, N., Vogt, P.: Surf. Sci. 617, 162 (2013)

Chapter 42

Structure of domain boundaries: other III–V compounds: GaP, GaSb, InAs, InP, InSb J. Wollschläger

See Figs. 42.1, 42.2, and Table 42.1.

Fig. 42.1 Schematic of two different arrangements of APDBs on InP(001)-(2
4)-In (Adopted from [97Ish1]).  drawing 
are inclined with BV ¼ 1/2(1,-1,0) (horizontal arrows in both drawings). Straight APDBs in [110] APDBs running in 110 have (a) BV ¼ 1/2(1,1,0) (vertical arrows) or (b) BV ¼ (1,1,0) (vertical arrows)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_42

1

2

J. Wollschläger

Fig. 42.2 STM micrograph from InSb(001)-c(8
2)LT with MDBs aligned parallel to [110] (From [07Gor]). White rectangles indicate c(8
2) unit cells

Table 42.1 other III-V compounds: GaP, GaSb, InAs, InP, InSb Miller index GaP (001)

GaP (111) B GaSb (001)

Major experimental Superstructure techniques

Supporting experimental techniques

(2
2)-P

LEED

RAS DFT-LDA

(4
2)/ c(8
2)
31 25
41

STM

LEED

LEED STM

–

Ar+ ISA (-/500–600  C)

(1
3)

SXRD

RHEED

(1
5)

SXRD

RHEED

α(4
3)

DFT

–

GaSb MBE on GaSb(001) at 370  C GaSb MBE on GaSb(001) at 370  C –

25

Results Sample preparation GaP MOVPE on GaP(001); As/P capping layer; decapping at 690 K Ar+ ISA (500 eV/450  C)

Remarks

Ref.

APDBs aligned parallel to [110] with BV ¼ 1/2(-1,1,0) Concluded from diffraction streaks

[99Ess]

DB aligned  parallel
to 110 Straight DB slightly  inclined to 112


[96Wat]

Fig.

[03Hat]

33 nm distance of APDBs

[08Tin]

42 nm distance of APDBs

[08Tin]

Building energy for APDBs: (1) parallel to   APDB
110 direction of different types: A1 with BV ¼ 1/2 (-1,1,0) and 0.05 meV/nm,

[09Rom]

(continued)

42

Structure of domain boundaries: other III–V compounds: GaP, GaSb, InAs, InP, InSb

3

Table 42.1 (continued) Miller index

Major experimental Superstructure techniques

β(4
3)

DFT

Supporting experimental techniques

Results Sample preparation

–

–

InAs (001)

(4
2)/c(8
STM 2)

LEED AES

Ar+ ISA (0.5–1 keV, 300  C/ 420–480  C)

InP (001)

(4
2)-P

LEED

XPS UPS ISS

Ne+ ISA (500 eV/650 K)

(2
4)-In

STM

RHEED XPS

InP MBE on GaAs(001)

Remarks A2 with BV ¼ (-1,1,0) and 0.2 meV/nm, A3 with BV ¼ 3/2 (-1,1,0) and 0.05 meV/nm; (2) APDB parallel to [110] direction of different types: B1 with BV ¼ 1/2 (1,1,0) and 1.1 meV/nm, B2 with BV ¼ (1,1,0) and 3.2 meV/nm Determination of building energy for APDBs: (1) parallel to   APDB
110 direction of different types: A1 with BV ¼ 1/2 (-1,1,0) and 0.02 meV/nm, A2 with BV ¼ (-1,1,0) and 0.2 meV/nm, A3 with BV ¼ 3/2 (-1,1,0) and 0.02 meV/nm (2) APDB parallel to [110] direction of different types: B1 with BV ¼ 1/2 (1,1,0) and 6.9 meV/nm, B2 with BV ¼ (1,1,0) and 8.4 meV/nm APDB preferentially running in [110] with BV ¼ 1/2(-1,10) or BV ¼ (1,1,0) APDBs aligned  par
allel to 110 with BV ¼ 1/2(-1,1,0) APDBs   inclined to
with BV ¼ 1/2 110 (1,-1,0); ABDBs aligned parallel to [110] with BV ¼ 1/2(1,1,0) or BV ¼ (1,1,0)

Ref.

Fig.

[09Rom]

[96Ken]

[90Wei]

[97Ish1] [97Ish2]

Fig. 42.1

(continued)

4

J. Wollschläger

Table 42.1 (continued) Miller index

InSb (001)

Major experimental Superstructure techniques NC-AFM

Supporting experimental techniques –

c(8
2)-LT

LT-STM

LEED

c(8
2)/ (1
3)

VT-STM

–

Results Sample Remarks preparation ISA (300 eV, APDBs aligned par600 K/700–750 K) allel to [110] with BV ¼ 1/2(1,1,0) Ar+ ISA MDBs aligned paral(700 eV/700 K) lel  toboth [110] and
110 Ar+ ISA (700 eV/425  C)

DBs by atomic steps aligned parallel to [110]

Ref. [06Suc]

Fig.

[07Gor]

Fig. 42.2

[11God]

Symbols and abbreviations Short form

Full form

STM APDB NC-AFM LT-STM VT-STM DFT SXRD LEED BV

scanning tunneling microscopy antiphase domain boundary noncontact atomic force microscopy low-temperature scanning tunneling microscopy variable temperature scanning tunneling microscopy density functional theory surface X-ray diffraction low-energy electron diffraction Burgers vector

References [90Wei] [96Ken] [96Wat] [97Ish1] [97Ish2] [99Ess]

Weiss, W., Hornstein, R., Schmeisser, D., G€ opel, W.: J. Vac. Sci. Technol. B8, 715 (1990) Kendrick, C., LeLay, G., Kahn, A.: Phys. Rev. B54, 17877 (1996) Watanabe, A., Shimaya, H., Naitoh, M., Nishigaki, S.: J. Vac. Sci. Technol. B14, 3599 (1996) Ishikawa, Y., Fukui, T., Hasegawa, H.: Jpn. J. Appl. Phys. 36, 1749 (1997) Ishikawa, Y., Fukui, T., Hasegawa, H.: J. Vac. Sci. Technol. B15, 1163 (1997) Esser, N., Schmidt, W.G., Bernholc, J., Frisch, A.M., Vogt, P., Zorn, M., Pristovsek, M., Richter, W., Bechstedt, F., Hannappel, T., Visbeck, S.: J. Vac. Sci. Technol. B17, 1691 (1999) [03Hat] Hattori, K., Ishihara, K., Miyatake, Y., Matsui, F., Takeda, S., Daimon, H., Komori, F.: Surf. Sci. 525, 57 (2003) [06Suc] Such, B., Kolodziej, J.J., Krok, F., Piatkowski, P., Szymonski, M.: Surf. Sci. 600, 2379 (2006) [07Gor] Goryl, G., Boelling, O., Godlewski, S., Kolodziej, J.J., Such, B., Szymonski, M.: Surf. Sci. 601, 3605 (2007) [08Tin] Tinkham, B.P., Romanyuk, O., Braun, W., Ploog, K.H., Grosse, F., Takahasi, M., Kaizu, T., Mizuki, J.: J. Electron. Mater. 37, 1793 (2008) [09Rom] Romanyuk, O., Grosse, F., Braun, W.: Phys. Rev. B79, 235330 (2009) [11God] Godlewski, S., Szymonski, M.: Appl. Surf. Sci. 258, 1300 (2011)

Chapter 43

Structure of domain boundaries: II–VI compounds: CdTe, HgTe J. Wollschläger

See Figs. 43.1, 43.2, and Table 43.1.

Fig. 43.1 STM micrograph of CdTe(001) with coexisting (2
1) and c(2
2) domains (Reproduced from [Seehofer, L., et al.: Appl. Phys. Lett. 67, 1680 (1995)], with the permission of AIP Publishing.). DBs are aligned in [100] direction. In the upper part, a APDB of the c(2
2) phase with BV ¼ 1/2(0,1,0) is seen while APDBs in the (2
1) phase have BV ¼ 1/2(1,0,0) (cf. part to the signed (2
1) unit cell)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_43

1

2

J. Wollschläger

Fig. 43.2 High resolution SPA-LEED pattern of CdTe (001)-c(2
2) (Reproduced from [Oehling, S., et al.: Appl. Phys. Lett. 73, 3205 (1998)], with the permission of AIP Publishing). (1/2,1/2) diffraction spots  Streaky   are elongated in 110 due to APDBs running in [110] with BV ¼ 1/2(-1,1,0)

Table 43.1 II–VI compounds Major Supporting Miller experimental experimental index Superstructure techniques techniques CdTe (001)

HgTe (001)

(2
1)

STM

LEED

c(2
2)

STM

LEED

c(2
2)

STM SPA-LEED

RHEED XPS

Results Sample preparation MBE on Cd0.96Zn0.04Te (001) at 230  C; Ar+ ISA (500 eV/250  C) MBE on Cd0.96Zn0.04Te (001) at 230  C; Ar+ ISA (500 eV/250  C) MBE on CdTe buffer at 300  C; PDA from 300 to 100  C (Hg flux)

Remarks

Ref.

Fig.

APDBs aligned parallel to [110] with local c(2
2) structure (half unit cell) and BV ¼ 1/2(1,1,0) APDBs aligned parallel to [110] with local (2
1) structure and BV ¼ 1/2(-1,1,0)

[95See]

Fig. 43.1

[95See]

Fig. 43.1

APDBs with local (2
1) structure aligned parallel to [110] with BV ¼ 1/2(-1,1,0)

[98Oeh]

Fig. 43.2

Symbols and abbreviations Short form

Full form

STM BV APDB LEED SPA-LEED MBE ISA

scanning tunneling microscopy Burgers vector antiphase domain boundary low-energy electron diffraction spot profile analysis of low-energy electron diffraction molecular beam epitaxy ion sputtering and annealing (continued)

43

Structure of domain boundaries: II–VI compounds: CdTe, HgTe

Short form RHEED XPS PDA

3

Full form reflection high-electron energy diffraction X-ray photoelectron spectroscopy post-deposition annealing

References [95See] Seehofer, L., Falkenberg, G., Johnson, R.L., Etgens, V.H., Tatarenko, S., Brun, D., Daudin, B.: Appl. Phys. Lett. 67, 1680 (1995) [98Oeh] Oehling, S., Ehinger, M., Gerhard, T., Becker, C.R., Landwehr, G., Schneider, M., Eich, D., Neureiter, H., Fink, R., Sokolowski, M., Umbach, E.: Appl. Phys. Lett. 73, 3205 (1998)

Chapter 44

Structure of domain boundaries: binary oxides: Al2O3 J. Wollschläger

See Figs. 44.1, 44.2, and Table 44.1.

Fig. 44.1 NC-AFM micrograph of Al2O3(0001)-(√31  √31)R9 (From [01Bar]). DWs are periodically arranged and form a rhombical lattice

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_44

1

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J. Wollschläger


 Fig. 44.2 NC-AFM micrograph of Al2O3 1120 (12  4) (From [12Ven]). DWs are reguarly arranged to form the superstructure

Table 44.1 α-Al2O3 Miller index (0001)

(11-20)

Superstructure

Major experimental techniques

Supporting experimental techniques

(√31  √31) R9

NC-AFM

(3√3  3√3) R30

SXRD

RHEED AES

(√31  √31) R9

NC-AFM

DFT

(12  4)

NC-AFM

Results Sample preparation UHV annealing at 1300  C UHV annealing at 1250  C

UHV annealing at 1500 K

Ar+ ISA (1.5 keV/1200  C)

Remarks

Ref.

Fig.

Rhombically arranged regular lattice of DWs

[01Bar]

Fig. 44.1

Hexagonal DW network with fcc(001) stacking of Al adatoms; Triangularly shaped domains with fcc(111) arranged Al adatoms Hexagonal network of DW between two types of domains due to differently coordinated surface adatoms DWs consist of al close to hollow sites DWs aligned    to    1101 and 1100

[02Vil]

[09Lau]

[12Ven]

Fig. 44.2

44

Structure of domain boundaries: binary oxides: Al2O3

3

Symbols and abbreviations Short form

Full form

NC-AFM SXRD RHEED AES UHV DW DFT ISA fcc

noncontact atomic force microscopy surface X-ray diffraction reflection high-electron energy diffraction Auger electron spectroscopy ultrahigh vacuum domain wall density functional theory ion sputtering and annealing face-centered cubic

References [01Bar] Barth, C., Reichling, M.: Nature. 414, 54 (2001) [02Vil] Vilfan, I., Deutsch, T., Lancon, F., Renaud, G.: Surf. Sci. 505, L215 (2002) [09Lau] Lauritsen, J.V., Jensen, M.C.R., Venkataramani, K., Hinnemann, B., Helveg, S., Clausen, B.S., Besenbacher, F.: Phys. Rev. Lett. 103, 076103 (2009) [12Ven] Venkataramani, K., Jensen, T.N., Helveg, S., Reichling, M., Besenbacher, F., Lauritsen, J.V.: Phys. Chem. Chem. Phys. 14, 2092 (2012)

Chapter 45

Structure of domain boundaries: binary oxides: Al2O3 films J. Wollschläger

See Figs. 45.1, 45.2, and Table 45.1.

a

(00)

FWHM ⎪% G⎪110⎪⎪

Al2O3/NiAl(110)

> 3.0 % > 2.8 % > 2.6 % > 2.4 % > 2.2 % > 2.0 %

3.5

[001] [110] Fig. 45.1 Diffraction analysis of Al2O3/ NiAl(110) (From [94Lib]). (a) Scheme of the SPA-LEED diffraction pattern showing diffraction peaks  of different
broadening along 110 . (b) Depen 
of the dence of the FWHM in 110 superstructure diffraction peaks on their lateral position in reciprocal space named by the lateral scattering Kx. Both FWHM and Kx are scaled with respect to the reciprocal lattice vector G
 of the

b

3.0 2.5 2.0

110

1.5 –150

–100

–50

0

50

100

150

Lateral scattering vector Kx [% G[110]]

NiAl(110) substrate from which one concludes the domain size of 12 nm in  
direction and BV ¼ (1,1,0) 110

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_45

1

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J. Wollschläger

Fig. 45.2 Network of DBs observed for alumina films on NiAl(110) (From [11Sim]). (a) Schematic drawing of the orientation of the alumina film with A and B mirrored domains. (b) Schematic drawing of the different types I–IV of APDBs (small grey lines) for A and B domains and the MDBs (thick grey lines) between A and B domains. (c) STM micrograph (100  100 nm2) with various DBs and a monoatomic step running in the center of the micrograph from bottom to top and also acting as DB

Table 45.1 Al2O3 films

Support

Major Supporting experimental experimental Sample Superstructure techniques techniques preparation

Al70Pd20Mn10

CoAl(001)

LEED

(2  1)

Cu91Al9(111) (√3  √3) R30

Ni(111)

(5√3  5√3) R30

144 L O2 exposure at 740 K; POA at 1000 K 100 L O2 exposure at 800 K

STM LEED

AES EELS

LEED

AES SEM XPS

O2 exposure at 995 K

STM

AES LEIS

STM

LEED AES

100 L O2 exposure at 680  C; POA at 1050 K Exposure of Al film to 1200 L O2 at

Results Remarks

Ref.

Regularly arranged honeycomb network of APDBs

[10Bur]

RDBs aligned to [010]; Average RDB distance of 6.8 nm DW network with (7/√3  7/√3)R30 periodicity

[05Ros]

Large domains with irregular DBs (exclusively MDBs)

Irregularly shaped MDBs;

Fig.

[03Son] [03Yam] [03Yos1] [03Yos2] [06Nem] [08Nap]

[10Pre]

(continued)

45

Structure of domain boundaries: binary oxides: Al2O3 films

3

Table 45.1 (continued)

Support

NiAl(001)

NiAl(110)

Major Supporting experimental experimental Sample Superstructure techniques techniques preparation

(2  1)



3:37  1 2:534



RT; POA at 1000 K Oxidation at RT; POA at 1500 K Oxidation at RT; POA at 1000–1400 K

LEED

AES HR-EELS

SPA-LEED STM

NICISS

SPA-LEED STM

AES ISS

1200 L O2 exposure at 550 K; POA at 1150–1200 K

VT-STM

–

5400 L O2 exposure at 300  C; POA at 900  C

SXRD

NC-AFM STM

LEED

LT-STM

LEED

1800 L O2 exposure at 540 K; POA at 1070 K 12000 L O2 exposure at 550 K; POA at 1200 K

1200 L O2 exposure at 280  C; POA at 800  C

Results Remarks

Ref.

Fig.

Straight and uniform APDBs APDBs aligned to [010]; Preferred APDB distance of 3.0 nm Periodically arranged APDBs with BV ¼ (1,0,0) and average domain size 2.6 nm; quasi (9  1) structure due to periodically arranged APDBs Diffraction spot broadening or splitting due to APDBs; Type A: APDB aligned parallel to [001] and BV ¼ (1,1,0); Type B: APDB running under 40 oblique angle; Additional MDBs concluded from twinning of diffraction pattern APDBs and MDBs observed as apparent protrusions and depressions for positive and negative tip voltage, respectively APDB width ¼ 0.33 nm; MDB with periodic arrangement of holes Oxide rows shift laterally by 0.36 nm (perpendicular to row direction) Appearance of DBs (trenches/ridges) depending on status of scanning tip Well-ordered atomically resolved APDBs due to insertion of additional O row between type A domains or between

[94Gas]

[98Blu]

[91Jae] [94Lib]

Fig. 45.1

[01Han]

[01Sti] [04Sti]

[02Pan]

[03Kul]

(continued)

4

J. Wollschläger

Table 45.1 (continued)

Support

Major Supporting experimental experimental Sample Superstructure techniques techniques preparation

LT-STM

–

1000 L O2 exposure at 280  C; POA at 800  C

LT-STM

DFT

Oxidation at 500–550 K; POA at 1000–1100 K

LEEM

–

O2 exposure at low temperature; POA at 950–1000  C

FM-DFM (5K) NC-AFM, STM/STS

LEED

O2 exposure; POA at 1100 K

Results Remarks type B domains: (1) Type-I APDBs: Straight with extra O row aligned to lattice vector b1 of oxide film, (2) Type-II APDBs: Extra O row inclined by 60 with respect to lattice vector b2 of oxide film; No characteristic structure for MDBs between type A and type B (mirrored) domains Additional electronic defect state 2.6 eV above Fermi energy for straight APDB APDB due to oxygen deficiency with downward electronic band bending due to three unoccupied electronic states APDBs aligned to lattice vector b1 of oxide film or inclined by 60 with respect to lattice vector b2 of oxide film Atomically resolved APDBs: (1) BVs of APDBs (length 0.3 nm) follow hexagonal sublattices of Al and O, (2) APDBs have rectangular building blocks with eight oxygen sites or quadratic building blocks with four oxygen sites, (3) Straight APDBs (type I) aligned to lattice vector b1 of oxide film with additional bridging

Ref.

Fig.

[04Nil]

[06Sch]

[06McC]

[09Sim] [11Sim] [12Sim]

Fig. 45.2

(continued)

45

Structure of domain boundaries: binary oxides: Al2O3 films

5

Table 45.1 (continued)

Support

Major Supporting experimental experimental Sample Superstructure techniques techniques preparation

FM-DFM at 5K

STM/STS

1800 L O2 exposure at 550 K; POA at 1050 K

–

1800 L O2 exposure at 600 K; POA at 1100 K

Results Remarks oxygen (length of 0.3 nm for O-O bridge) and additional kinks (jogs), (4) Zigzagged APDBs (type II) inclined to the direction of lattice vector b2 (components of both lattice vectors b1 and b2) and building blocks with 7, 9, and 11 oxygen sites, (5) bridging APDBs (type III, no depression in FM-DFM) between APDBs of type I and type II, (6) APDBs (type IV): Straight line inclined by 39 to the direction of lattice vector b1 of oxide film, BV length ¼ 1.2 nm in direction of lattice vector b2 of oxide film; MDBs inclined by 24 with respect to NiAl[1-10] support form coincidence site lattice with low Σ ¼ 19 Local electronic structure of APDBs (with F2+-like centers) similar to local electronic structure at atomic steps; Local work function of APDBs ΔΦ ¼ (5–10)meV; MDBs induced by atomic steps APDB with electronic state 2.5 eV above Fermi energy

Ref.

Fig.

[10Hei]

[13Ben]

(continued)

6

J. Wollschläger

Table 45.1 (continued)

Support Ni3Al(111)

Major experimental Superstructure techniques (6√3  6√3) LEED R30 (√67  √67) STM R12.2 SPA-LEED

Supporting experimental techniques XPS LEIS AES

(√79  √79) R17

DFT

STM NC-AFM

Results Sample preparation Oxidation at 900 K O2 exposure at 3  106 Pa, 1000 K; POA at 1050 K O2 exposure at 1000 K; POA at 1050 K

Remarks Hexagonal DW network Moire´ pattern of DWs with 4.16 nm periodicity

Coexistence of parallel arranged DWs with honeycomb network DWs

Ref. [92Bar]

Fig.

[99Ros] [00Ros] [05Deg]

[07Gri1] [07Gri2] [07Sch]

Symbols and abbreviations Short form

Full form

SPA-LEED DB MDB APDB LEED POA STM AES EELS SEM XPS DW RDB HR-EELS RT ISS NC-AFM LT-STM DFT LEEM FM-DEM BV LEIS

spot profile analysis of low-energy electron diffraction domain boundary mirrored domains boundary antiphase domain boundary low-energy electron diffraction post-oxidation annealing scanning tunneling microscopy Auger electron spectroscopy electron energy-loss spectroscopy scanning electron microscopy X-ray photoelectron spectroscopy domain wall rotated domain boundary high-resolution electron energy-loss spectroscopy room temperature ion scattering spectroscopy noncontact atomic force microscopy low-temperature scanning tunneling microscopy density functional theory low-energy electron microscopy frequency modulation – dynamic force microscopy Burgers vector low-energy ion spectroscopy

References [91Jae] [92Bar] [94Gas] [94Lib] [98Blu] [99Ros] [00Ros]

Jaeger, R.M., Kuhlenbeck, H., Freund, H.-J., Wuttig, M., Hoffmann, W., Franchy, R., Ibach, H.: Surf. Sci. 259, 235 (1991) Bardi, U., Atrei, A., Rovida, G.: Surf. Sci. 268, 87 (1992) Gassmann, P., Franchy, R., Ibach, H.: Surf. Sci. 319, 95 (1994) Libuda, J., Winkelmann, F., Bäumer, M., Freund, H.-J., Bertrams, T., Neddermeyer, H., Müller, K.: Surf. Sci. 318, 61 (1994) Blum, R.-P., Ahlbehrendt, D., Niehus, H.: Surf. Sci. 396, 176 (1998) Rosenhahn, A., Schneider, J., Kandler, J., Becker, C., Wandelt, K.: Surf. Sci. 433–435, 705 (1999) Rosenhahn, A., Schneider, J., Becker, C., Wandelt, K.: J. Vac. Sci. Technol. A18, 1923 (2000)

45

Structure of domain boundaries: binary oxides: Al2O3 films

[01Han] [01Sti] [02Pan] [03Kul] [03Son] [03Yam] [03Yos1] [03Yos2] [06McC] [04Nil] [04Sti] [05Deg]

7

Hansen, K.H., Worren, T., Laegsgaard, E., Besenbacher, F., Stensgaard, I.: Surf. Sci. 475, 96 (2001) Stierle, A., Renner, F., Streitel, R., Dosch, H.: Phys. Rev. B64, 165413 (2001) Pang, C.L., Raza, H., Haycock, S.A., Thornton, G.: Phys. Rev. B65, 201401 (2002) Kulawik, M., Nilius, N., Rust, H.-P., Freund, H.-J.: Phys. Rev. Lett. 91, 256101 (2003) Song, W., Yoshitake, M., Bera, S., Yamauchi, Y.: Jpn. J. Appl. Phys. 42, 4716 (2003) Yamauchi, Y., Yoshitake, M., Song, W.: Jpn. J. Appl. Phys. 42, 4721 (2003) Yoshitake, M., Bera, S., Yamauchi, Y., Song, W.: J. Vac. Sci. Technol. A21, 1290 (2003) Yoshitake, M., Bera, S., Yamauchi, Y.: Surf. Interface Anal. 35, 824 (2003) McCarthy, K.F., Pierce, J.P., Carter, C.B.: Appl. Phys. Lett. 88, 141902 (2003) Nilius, N., Kulawik, M., Rust, H.-P., Freund, H.-J.: Phys. Rev. B69, 121401 (2004) Stierle, A., Renner, F., Streitel, R., Dosch, H., Drube, W., Cowie, B.C.: Science. 303, 1652 (2004) Degen, S., Krupski, A., Kralj, M., Langner, A., Becker, C., Sokolowski, M., Wandelt, K.: Surf. Sci. 576, L57 (2005) [05Ros] Rose, V., Podgursky, V., Costina, I., Franchy, R., Ibach, H.: Surf. Sci. 577, 139 (2005) [06Nem] Nemsak, S., Yoshitake, M., Masek, K.: Surf. Sci. 600, 4357 (2006) [06Sch] Schmid, M., Shishkin, M., Kresse, G., Napetschnig, E., Varga, P., Kulawik, M., Nilius, N., Rust, H.-P., Freund, H.J.: Phys. Rev. Lett. 97, 046101 (2006) [07Gri1] Gritschneder, S., Degen, S., Becker, C., Wandelt, K., Reichling, M.: Phys. Rev. B76, 014123 (2007) [07Gri2] Gritschneder, S., Becker, C., Wandelt, K., Reichling, M.: J. Am. Chem. Soc. 129, 4925 (2007) [07Sch] Schmid, M., Kresse, G., Buchsbaum, A., Napetschnig, E., Gritschneder, S., Reichling, M., Varga, P.: Phys. Rev. Lett. 99, 196104 (2007) [08Nap] Napetschnig, E., Schmid, M., Varga, P.: Surf. Sci. 602, 1750 (2008) [09Sim] Simon, G.H., K€ onig, T., Rust, H.-P., Heyde, M., Freund, H.-J.: New J. Phys. 11, 093009 (2009) [10Bur] Burkardt, S., Erbudak, M.: Phys. Rev. B81, 085417 (2010) [10Hei] Heinke, L., Lichtenstein, L., Simon, G.H., K€ onig, T., Heyde, M., Freund, H.-J.: Phys. Rev. B82, 075430 (2010) [10Pre] Pre´vot, G., Naitabdi, A., Bernard, R., Borensztein, Y.: Phys. Rev. B81, 085405 (2010) [11Sim] Simon, G.H., K€ onig, T., Heinke, L., Lichtenstein, L., Heyde, M., Freund, H.-J.: New J. Phys. 13, 123028 (2011) [12Sim] Simon, G.H., Heyde, M., Freund, H.-J.: J. Phys. Condens. Matter. 24, 084007 (2012) [13Ben] Beniya, A., Isomura, N., Hirata, H., Watanabe, Y.: Chem. Phys. Lett. 576, 49 (2013)

Chapter 46

Structure of domain boundaries: binary oxides: Fe3O4 J. Wollschläger

See Figs. 46.1, 46.2, and Table 46.1.

Fig. 46.1 STM micrograph (200
200 nm2) of Fe3O4(001)-(1
4) (From [04Mar]). The superstructure is caused by segregated Ca and K and forms periodically arranged vacancy rows. RDBs are aligned parallel to

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_46

1

2

J. Wollschläger

Fig. 46.2 STM micrograph of Fe3O4(001)(√2
√2)R45 (From [12Par]). Here, w and n denote sites where the distance between surface features is wide and narrow, respectively. APDBs are preferentially aligned parallel to with BV ¼ 1/2 (1,1,0). The APDBs show enhanced contrast due to adsorbed hydrogen. Yellow and blue lines mark the phase shift between adjacent antiphase domains. The (√2
√2) R45 unit cell is shown in red

Table 46.1 Fe3O4 Miller index (001)

Superstructure

Major experimental techniques

Supporting experimental techniques

Results

(2
1)

STM

LEED AES

Annealing at 990(10)K in UHV

(1
4)

STM

LEED AES

Annealing at 990(10)K in UHV

(√2
√2) R45

STM

LEED DFT + U

Ar+ ISA (1 keV/700  C, 2
106 mbar O2)

Sample preparation

Remarks

Ref.

Fig.

RDBs aligned parallel to with regular distance of 2.4 nm Reconstruction due to Ca and K segregation after annealing for several hours Straight APDBs (trenches) par aligned   ; allel to 110 Regular APDB distance of 2.2 nm, 3.5 nm, or 5.0 nm depends on annealing Reconstruction due to Ca and K segregation after annealing for several hours APDBs preferentially aligned to with BV ¼ 1/2(1, 1, 0) Enhanced contrast in STM due to adsorbed H

[04Mar]

Fig. 46.1

[04Ceb] [04Mar]

[12Par]

Fig. 46.2

46

Structure of domain boundaries: binary oxides: Fe3O4

3

Symbols and abbreviations Short form

Full form

STM RDB LEED AES BV UHV APDB DFT+U

scanning tunneling microscopy rotated domain boundary low-energy electron diffraction Auger electron spectroscopy Burgers vector ultrahigh vacuum antiphase domain boundary density functional theory with Hubbard U parameter for electron correlation

References [04Ceb] Ceballos, S.F., Mariotto, G., Jordan, K., Murphy, S., Seoighe, C., Shvets, I.V.: Surf. Sci. 548, 106 (2004) [04Mar] Mariotto, G., Murphy, S., Berdunov, N., Ceballos, S.F., Shvets, I.V.: Surf. Sci. 564, 79 (2004) [12Par] Parkinson, G.S., Manz, T.A., Novotny´, Z., Sprunger, P.T., Kurtz, R.L., Schmid, M., Sholl, D.S., Diebold, U.: Phys. Rev. B85, 195450 (2012)

Chapter 47

Structure of domain boundaries: binary oxides: Fe3O4 films on MgO(001) J. Wollschläger

See Figs. 47.1, 47.2, 47.3, 47.4, 47.5, and Table 47.1.

Fig. 47.1 Schematic drawing of   110 for APDBs aligned in Fe3O4(001)-(√2
√2)R45 on MgO (001) (Adopted from [12Ike]). APDBs are parallel to rows of octahedrally coordinated Fe ions. (a) Heavy APDBs have BV ¼ 1/2(1,1,0) (arrow) while (b) light APDBs have BV ¼ 3/2 (1,1,0) (arrow)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_47

1

2

J. Wollschläger

Fig. 47.2 Schematic drawing of APDBs aligned in [110] for Fe3O4(001)-(√2
√2) R45 on MgO(001) (Adopted from [12Ike]). APDBs perpendicular to rows of octahedrally coordinated Fe ions are caused by APDBs in the A sublattice of tetrahedrally coordinate Fe. (a) Light  APDBs have BV ¼ 3/2( 1,1,0) (arrow).  (b) Heavy APDBs have BV ¼ 1/2( 1,1,0) (arrow)

Fig. 47.3 Schematic drawing of APDBs aligned in for Fe3O4(001)-(√2
√2)R45 on MgO(001) (Adopted from [12Ike]). APDBs are 45 inclinded with respect to rows of octahedrally coordinated Fe ions. BV ¼ (1,2,0) (arrow) for APDB aligned parallel to [100]

47

Structure of domain boundaries: binary oxides: Fe3O4 films on MgO(001)

3

Fig. 47.4 Schematic drawing of RDBs for Fe3O4(001)-(√2
√2) R45 on MgO(001) with coexisiting 90 domains due to rotated rows of octahedrally coordinated Fe (Adopted from [12Ike]). (a) straight RDB aligned parallel to [100]. (b) Kinked RDB

Fig. 47.5 STM micrograph (50
50 nm2) of Fe3O4(001)-(1
4) film on MgO(001) due to Mg segregation (From [97And]). RDBs are aligned parallel to both and

4

J. Wollschläger

Table 47.1 Fe3O4 films on MgO(001) Major Supporting experimental experimental techniques techniques

Miller index Superstructure (001)

(√2
√2) R45



STM

LEED LEIS XPS

STM

STM

STM LEED

OPA-MBE; PDA at 510–530 K, 107 – 106 mbar O2 MBE at 250  C, 7
107 – 3
106 mbar O2

MBE at 225–250  C, 107 – 105 mbar O2 MBE at 250  C, 7
107– 3
106 mbar O2

STM

(1
4)

Results Sample preparation

XPS

Oxygen PA-MBE at 570 K, PDA at 890 K, 2
106 mbar O2

Remarks

Ref.

APDBs  aligned parallel to 110 with regular distance of 1.2 nm between DBs

[00Sta]

Four types of APDB aligned parallel to : (1) APDB aligned parallel to surface (octahedral) Fe row with BV¼3/2 (1,1,0) (light APDB) containing octahedrally coordinated Fe, (2) APDB aligned parallel to surface (octahedral) Fe row with BV¼1/2 (1,1,0) (heavy APDB) containing tetrahedrally coordinated Fe, (3) APDB aligned perpendicular to surface (octahedral) Fe row with BV¼1/2(-1,1,0) (heavy APDB) or BV¼3/2 (-1,1,0) (light APDB) containing octahedrally coordinated Fe, (4) APDB aligned perpendicular to surface (octahedral) Fe row and containing surface (tetrahedral) Fe; APDBs aligned parallel to and BV ¼ 1/2(1,0,0) 90 RDBs aligned parallel to [100] and [010]

[12Ike]

Two types of 90 RDBs: (1) Aligned parallel to [100], (2)Aligned parallel  to  130 RDBs aligned parallel to and Reconstruction due to Mg segregation due to annealing

Fig.

Figs. 47.1, 47.2, and 47.3

[97Gai] [07Sub]

[12Ike]

Fig. 47.4

[97And] Fig. 47.5

47

Structure of domain boundaries: binary oxides: Fe3O4 films on MgO(001)

5

Symbols and abbreviations Short form

Full form

APDB BV RDB STM LEED LEIS XPS MBE PDA PA-MBE

antiphase domain boundary Burgers vector rotated domain boundary scanning tunneling microscopy low-energy electron diffraction low-energy ion spectroscopy X-ray photoelectron spectroscopy molecular beam epitaxy post-deposition annealing plasma-assisted molecular beam epitaxy

References [97And] Anderson, J.F., Kuhn, M., Diebold, U., Shaw, K., Stoyanov, P., Lind, D.: Phys. Rev. B56, 9902 (1997) [97Gai] Gaines, J.M., Bloemen, P.J.H., Kohlhepp, J.T., Bulle-Lieuwman, C.W.T., Wolf, R.M., Reinders, A., Jungblut, R.M., van der Heijden, P.A.A., van Eemeren, J.T.W.M., van de Stegge, J., de Jonge, W.J.M.: Surf. Sci. 373, 85 (1997) [00Sta] Stanka, B., Hebenstreit, W., Diebold, U., Chambers, S.A.: Surf. Sci. 448, 49 (2000) [07Sub] Subagyo, A., Sasaki, Y., Oka, H., Sueoka, K.: Phys. Status Solidi B. 244, 4482 (2007) [12Ike] Ikeuchi, A., Hiura, S., Mizuno, T., Kaji, E., Subagyo, A., Sueoka, K.: Jpn. J. Appl Phys. 51, 08KB02 (2012)

Chapter 48

Structure of domain boundaries: binary oxides: TiO2 (anatase) J. Wollschläger

See Table 48.1.

Table 48.1 TiO2 (anatase) Miller index (001)

Superstructure

Major experimental techniques

Supporting experimental techniques

(4
1)

STM

LEED XPS

Results Sample preparation

Remarks

Ref.

OPA-MBE on SrTiO3:Nb at 550  C, 2
105TorrO2

APDB of (4
1) aligned parallel to [010] and BV ¼ (0,n,0)

[01Lia]

Fig.

Symbols and abbreviations Short form

Full form

STM LEED XPS OPA-MBE APDB

scanning tunneling microscopy low-energy electron diffraction X-ray photoelectron spectroscopy oxygen plasma-assisted molecular beam epitaxy antiphase domain boundary

References [01Lia]

Liang, Y., Gan, S., Chambers, S.A., Altman, E.I.: Phys. Rev. B63, 235402 (2001)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_48

1

Chapter 49

Structure of domain boundaries: binary oxides: TiO2 (rutile) J. Wollschläger

See Figs. 49.1, 49.2, and Table 49.1.

Fig. 49.1 STM micrograph (25
22 nm2) of TiO2(110-(1
2) (From [98Tan]) with antiphase domains A and B. Straight, long APDBs (dashed lines) parallel to [001] have local (1
3) structure. Atomic rows in different domains  separated   having by short APDBs aligned to 110 BV (1,-1,2). The dash-dotted line marks a step edge

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_49

1

2

J. Wollschläger

Fig. 49.2 STM micrographs from TiO2(110)-(1
2) (From [03Tak]). (a) Micrograph with bright strands (BS) which are 0.40 nm separated (dark lines). (b) Atomically resolved micrograph of cross-linked DB. (c) Schematic drawing of linked (1
2) structures: (i) hook shaped single link, (ii) linear single link, (iii) cross-link

Table 49.1 TiO2 (rutile) Miller index (011)

(100)

Superstructure

Major experimental techniques

Supporting experimental techniques

Sample preparation

(2
1)

STM

–

–

STM

LEED LEIS XPS

Ar+ ISA (1 keV/750  C) and annealing in O2 (108 – 105 mbar)

STM

LEED AES

Ar+ ISA (/870 K)

STM

–

Ar+ ISA (1.5 keV/800  C)

(1
3)

Results Remarks

Ref.

APDB mainly aligned   parallel to 211 with BV ¼ (1,0,0) Data taken from figure Striped antiphase domains with width of 4–8 unit cells; APDBs mainly aligned   parallel to  with BV ¼ 1/2 011 (1,0,0) Ca segregation Rough APDBs aligned parallel to [010]; Straight APDBs aligned parallel to [001] (including atomic step) Straight APDBs aligned parallel to [010]

[04Bec]

Fig.

[06Dul]

[92Cla] [94Mur1] [94Mur2]

[06Klu]

(continued)

49

Structure of domain boundaries: binary oxides: TiO2 (rutile)

3

Table 49.1 (continued) Miller index (110)

Superstructure (1
2)

Major experimental techniques STM LEED STM

Supporting experimental techniques –

STM/STS

LEED

Ar+ ISA (500 eV/1200 K)

STM

–

Ar+ ISA (500 eV/1070 K)

STM

LEED

Ar+ ISA (600 eV/1200 K)

STM

–

Ar+ ISA (3 keV/900 K)

STM

LEED AES

Ar+ ISA (/1100 K)

LEED AES

Results Sample preparation Ar+ ISA (3 keV/ 600–800 K) UHV annealing at 1000 K, reoxidation at 1030 K in O2 (107 Torr)

Remarks APDBs aligned parallel to [001] APDB aligned  paral ; lel to 110 Cross-linked DBs due to oxygen incorporation Cross-linked DBs with 0.59 nm width (local (2
2) structure) Reduced conductivity for APDB Extended straight APDBs with BV ¼ (1,1,0) (local (1
3) structure) aligned parallel to [001]; Typical APDB distance 1.3 nm; Short APDBs  aligned   parallel to 110 with BV ¼ (1,1,0) Cross-linked APDBs aligned   parallel to  with BV ¼ 110 (0,0,3) and local c (2
2) structure Structure of DB assigned to Ti2O3 units Coexistence of crosslinked APDBs aligned   parallel to  with BV ¼ 110 (0,0,3) and linear single-linked APDBs with BV ¼ (0,0,1) APDBs aligned  par ; allel to 110 Single-link and crosslinked APDBs

Ref. [94Oni]

Fig.

[94San] [95Sza]

[95Mur]

[98Tan]

Fig. 49.1

[99Ben]

[03Tak2]

Fig. 49.2

[13San]

Symbols and abbreviations Short form

Full form

STM DB BS APDB BV

scanning tunneling microscopy domain boundary bright strands antiphase domain boundary Burgers vector (continued)

4 Short form LEED LEIS XPS UHV AES ISA STS

J. Wollschläger Full form low-energy electron diffraction low-energy ion spectroscopy X-ray photoelectron spectroscopy ultrahigh vacuum Auger electron spectroscopy ion sputtering and annealing scanning tunneling spectroscopy

References [92Cla] Clark, G.W., Kesmodel, L.L.: Ultramicroscopy. 41, 77 (1992) [94Mur1] Murray, P.W., Leibsle, F.M., Muryn, C.A., Fisher, H.J., Flipse, C.F.J., Thornton, G.: Phys. Rev. Lett. 72, 689 (1994) [94Mur2] Murray, P.W., Leibsle, F.M., Muryn, C.A., Fisher, H.J., Flipse, C.F.J., Thornton, G.: Surf. Sci. 321, 217 (1994) [94Oni] Onishi, H., Iwasawa, Y.: Surf. Sci. 313, L783 (1994) [94San] Sander, M., Engel, T.: Surf. Sci. 302, L263 (1994) [95Mur] Murray, P.W., Condon, N.G., Thornton, G.: Phys. Rev. B51, 10989 (1995) [95Sza] Szabo, A., Engel, T.: Surf. Sci. 329, 241 (1995) [98Tan] Tanner, R.E., Castell, M.R., Briggs, G.A.D.: Surf. Sci. 412/413, 672 (1998) [99Ben] Bennett, R.A., Stone, P., Price, N.J., Bowker, M.: Phys. Rev. Lett. 82, 3831 (1999) [03Tak] Takakusagi, S., Fukui, K., Nariyuki, F., Iwasawa, Y.: Surf. Sci. 523, L41 (2003) [04Bec] Beck, T.J., Klust, A., Batzill, M., Diebold, U., Di Valentin, C., Selloni, A.: Phys. Rev. Lett. 93, 036104 (2004) [06Dul] Dulub, O., Di Valentin, C., Selloni, A., Diebold, U.: Surf. Sci. 600, 4407 (2006) [06Klu] Klusek, Z., Busiakiewicz, A., Datta, P.K.: Surf. Sci. 600, 1619 (2006) [13San] Sa´nchez-Sa´nchez, C., Martı´n-Gago, J.A., Lo´pez, M.F.: Surf. Sci. 607, 159 (2013)

Chapter 50

Structure of domain boundaries: other binary oxides: SiO2, SnO2, and WO3 J. Wollschläger

See Table 50.1.

Table 50.1 Other binary oxides Major Supporting experimental experimental Sample Miller index Superstructure techniques techniques preparation SiO2

c(2
2)

SPA-LEED

AES XPS

SnO2(110) (rutile)

(4
1)

STM

LEED ISS

STM

LEED XPS

STM

LEED AES

STM

LEED AES

γ-WO3(100) c(2
2)

(n
2)

Si MBE on Mo (112) at 300 K; PDO (800 K); POA at 1000–1050 K in 5
106 mbar O2 Ar+ ISA (1 keV/1100 K, 103 mbar O2)

Cleavage in air and UHV annealing at 650  C in 105 mbar O2 Cleavage in air and annealing in 2
105 Torr O2 RF-magneto sputtering at 875–900 K on LAO; Annealing at 620 K in O2 or NO2

Results Remarks

Ref.

APDBs  aligned parallel  with BV ¼ to 011 (1,-1,0) or with BV ¼ 1/2(-1,1,3)

[01Sch] [02Sch]

APDBs aligned parallel to [001]; BV with component in [001] (direction of fourfold periodicity) APDBs aligned parallel to [100]

[03Bat]

Fig.

[95Jon]

APDBs with local c(4
2) and (6
2) structure

[01Tan]

DBs between (2
2) and (1
1) aligned to [010]; Irregular DBs between (2
2) and (4
2); Straight DBs between (4
2) and (3
2) aligned to [001]; Straight DBs between (3
2) and (2
 4)  ; aligned to 011 Irregular DBs between (3
2) and (1
1)

[03Li] [04Li1] [04Li2]

(continued) J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_50

1

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J. Wollschläger

Table 50.1 (continued) Major experimental Miller index Superstructure techniques (3
2) STM

(4
2)

STM

Supporting experimental techniques LEED AES

LEED AES

Results Sample preparation RF-magnetosputtering at 875–900 K on LAO; PDA at 820 K in O2 and at 970 K in UHV RF-magneto sputtering at 875–900 K; Annealing at 800 K in O2

Remarks RDBs between (3
2) and (2
3) aligned parallel to [011]

Ref. [04Li1]

RDBs between (4
2) and (2
4) aligned parallel to [011]

[04Li2]

Fig.

Symbols and abbreviations Short form

Full form

STM LEED XPS UHV POA AES MBE DB APBD LAO PDA

scanning tunneling microscopy low-energy electron diffraction X-ray photoelectron spectroscopy ultrahigh vacuum post-oxidation annealing Auger electron spectroscopy molecular beam epitaxy domain boundary antiphase domain boundary lanthanum aluminum oxide (LaAlO3) post-deposition annealing

References [95Jon] Jones, F.H., Rawlings, K., Foord, J.S., Cox, P.A., Egdell, R.G., Pethica, J.B., Wanklyn, B.M.R.: Phys. Rev. B52, R14392 (1995) [01Sch] Schroeder, T., Hammoudeh, A., Pykavy, M., Magg, N., Adelt, M., Bäumer, M., Freund, H.-J.: Solid State Electron. 45, 1471 (2001) [01Tan] Tanner, R.E., Altman, E.I.: J. Vac. Sci. Technol. A19, 1502 (2001) [02Sch] Schroeder, T., Giorgi, A., Bäumer, M., Freund, H.-J.: Phys. Rev. B66, 165422 (2002) [03Bat] Batzill, M., Katsiev, K., Diebold, U.: Surf. Sci. 529, 295 (2003) [03Li] Li, M., Altman, E.I., Posadas, A., Ahn, C.H.: Surf. Sci. 542, 22 (2003) [04Li1] Li, M., Altman, E.I., Posadas, A., Ahn, C.H.: Thin Solid Films. 446, 238 (2004) [04Li2] Li, M., Altman, E.I., Posadas, A., Ahn, C.H.: J. Vac. Sci. Technol. A22, 1682 (2004)

Chapter 51

Structure of domain boundaries: ternary oxides: titanates (BaTiO3, SrTiO3) J. Wollschläger

See Figs. 51.1, 51.2, and Table 51.1.

Fig. 51.1 (a) STM micrograph of DBs on SrTiO3(001)-(√5
√5)R26.6 (From [92Mat]). A and C denote antiphase domains while B is a mirrored domain compared to the domains A and C. (b) Schematic drawing of APDB (Adopted from micrograph (a)): The APDB is aligned parallel to [130] with BV ¼ (2,-1,0) (arrow)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_51

1

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J. Wollschläger

Fig. 51.2 STM micrograph of quasi periodically arranged APDBs on SrTiO3(110)-(4
1) (From [13Wan]). APDBs exhibit pairs of Ti2O3 vacancies and Sr adatoms

Table 51.1 Titanates (MTiO3, M ¼ Ba, Sr)

Miller index

Superstructure

BaTiO3(001)

(√5
√5) R26.6 (√5
√5) R26.6

SrTiO3(001)

SrTiO3(110)

(N
1) with N ¼ 4 or 5

Major experimental techniques

Supporting experimental techniques

Results

STM

DFT

STM

RHEED

NC-AFM STM

–

Annealing at 1200  C in UHV

STM

DFT

Nb-doped crystal with Ar+ ISA (-/1000  C)

Sample preparation Annealing at 1373 K Annealing at 1185–1200  C in UHV

Remarks

Ref.

RDBs aligned to [001] Rough APDB aligned to ; BV ¼ (2,1,0) for APDB aligned parallel to [130]; RDBs aligned to

(√5
√5) R26.6 named (2
2) by mistake in [92Mat] Rough APDB aligned to ; RDBs aligned to

APDBs preferentially aligned parallel to [001]; Two types of APDBs: C-type and W-type; APDBs consist of TixOy vacancies Quasi (4
10)superstructure due to almost periodic spacing of APDBs

[08Kol] [92Mat] [97Aki]

Fig.

Fig. 51.1

[01Kub]

[13Wan] [14Wan]

Fig. 51.2

51

Structure of domain boundaries: ternary oxides: titanates (BaTiO3, SrTiO3)

3

Symbols and abbreviations Short form

Full form

APDB DB BV DFT RHEED STM NC-AFM RDB UHV ISA

antiphase domain boundary domain boundary Burgers vector density functional theory reflection high-electron energy diffraction scanning tunneling microscopy noncontact atomic force microscopy rotated domain boundary ultrahigh vacuum ion sputtering and annealing

References [92Mat] [97Aki] [01Kub] [08Kol] [13Wan] [14Wan]

Matsumoto, T., Tanaka, H., Kawai, T., Kawai, S.: Surf. Sci. 278, L153 (1992) Akiyama, R., Matsumoto, T., Tanaka, H., Kawai, T.: Jpn. J. Appl. Phys. 36, 3881 (1997) Kubo, T., Nozoye, H.: Phys. Rev. Lett. 86, 1801 (2001) Kolpak, A.M., Li, D., Shao, R., Rappe, A.M., Bonnell, D.A.: Phys. Rev. Lett. 101, 036102 (2008) Wang, Z., Li, F., Meng, S., Zhang, J., Plummer, E.W., Diebold, U., Guo, J.: Phys. Rev. Lett. 111, 056101 (2013) Wang, Z., Hao, X., Gerhold, S., Schmid, M., Franchini, C., Diebold, U.: Phys. Rev. B90, 035436 (2014)

Chapter 52

Decoration of domain boundaries: metals: Au (decoration by metals) J. Wollschläger

See Figs. 52.1, 52.2, 52.3, 52.4, 52.5, and Table 52.1.

Fig. 52.1 STM micrograph (100
100 nm2) after deposition of 0.3 ML Co on Au(111) at 300 K (From [99Pad2]). Co cluster exclusively decorate the elbows of the DWs

Fig. 52.2 STM micrograph (54
54 nm2) after deposition of Mo on Au(111) via Mo(CO)6 CVD (From [03Son1]). Mo preferentially nucleates at DW elbows and grows on fcc domains

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_52

1

2

J. Wollschläger

Fig. 52.3 STM micrograph after deposition of Ni on Au(111) at RT (From [09Tra]): (a) 0.05 ML Ni (micrograph size 140
140 nm2) and (b) 0.8 ML Ni (micrograph size 53
53 nm2). Ni cluster preferentially nucleate at elbows of the DWs

Fig. 52.4 (a) STM micrograph (99
90 nm2) from Au(111) after deposition of 0.25 ML Ni at 300 K. Ni clusters preferentially nucleate at the elbows of the DWs as shown by the inset. (b) Schematic drawing demonstrating that the preferred nucleation sites are the elbow pinches (From [99Cul])

52

Decoration of domain boundaries: metals: Au (decoration by metals)

3

Fig. 52.5 STM micrograph (320
220 nm2) recorded on Au(111) in 0.5 M H2SO4 at 0V after deposition of 0.3 ML Ru from 0.5 M H2SO4 + 104 M RuCl3 at 0V (From [99Str]). Ru decorates exclusively fcc domains

Table 52.1 Au – decoration by metals Miller Sample index Superstructure Deposit preparation (111)

(√3
N ) N ¼ 22–23

Results Supporting Major Deposition experimental experimental Remarks techniques technique techniques

Ref. [89Dov]

Ag

Au PVD on mica

Ag MBE

STM

–

Ag ECD

STM

–

Au

(111) Facet on a single crystal bead of Au Au deposition on mica at 500  C Au deposited on mica

Au MBE at STM RT Ba MBE STM

–

Single Au(111) crystal; Ne+ ISA (1.5 keV/600  C)

Co MBE at STM 300 K

–

Single Au(111) crystal; Ar+ ISA (700 eV/800 K)

Co MBE

–

Ba

Co

STM HAS

–

Elongated Ag islands aligned parallel to DWs Growth of elongated Ag islands aligned parallel to DWs Au preferentially nucleated at DWs Ba island alignment to DWs after PDA at 450  C No preferred initial Ba nucleation sites Co nucleation at DW elbows; Co islands with apparent height of 2 ML Preferential nucleation at DW elbows with Co(0001) clusters of 2 ML height with coalescence in < 11
2> direction at 0.7 ML and in <
110 > direction at 1.5 ML

Fig.

[08Tak]

[89Lan] [12Wu]

[91Voi2] [92Wol]

[97T€ ol1] [97T€ ol2]

(continued)

4

J. Wollschläger

Table 52.1 (continued) Miller Sample index Superstructure Deposit preparation Single Au(111) crystal; Ar+ ISA (1 keV/ 1000 K)

Cr

Results Supporting Major Deposition experimental experimental Remarks techniques technique techniques Co MBE at VT-STM 305 K and PDA at 440 K

LEED AES LMOKE PMOKE

–

Co MBE at GISAXS RT STM

–

Single Au(111) crystal; Ar+ ISA (1 keV/ 1000 K)

Co MBE

VT-STM

LEED

Single Au(111) crystal; Ar+ ISA (1.5 keV/900 K)

Co MBE

STM

AES

Co MBE at STM RT and PDA at 520 K Co MBE at LT-STM/ STS RT; Partly PDA at 330 K

Single Au(111) Cr MBE crystal; for + Ar ISA (-/1000 K) 10–300 K

STM

LEED AES

–

LEED AES XAS XMCD

Co nucleation at DW elbows at 300 K with pattern 9.2 nm
25.4 nm; Apparent Co island height 2 ML No preferential nucleation at elbows at 30 K Nucleation of Co at DW elbows and coalescence of islands in row at 2 ML different stages of Co nucleation: At 70 K: Co nucleation (2 ML apparent height) at one type of elbow At 120 K: Nucleation at both types of elbows (coexistence of 1 ML and 2 ML high Co islands) Above 150 K: Exclusive nucleation of 2 ML high Co island at elbows At RT preferential nucleation at x-elbows Co nucleation at DW elbows and further growth along DWs

Ref.

Fig.

[98Pad] Fig. 52.1 [99Pad1] [99Pad2]

[00Cha] [00Pad] [03Fru]

[04Cha]

[07Mor]

[02Spi]

Co islands with hex- [08Sch] agonal shape nucleated at DW elbows; Island heights of 1 ML and 2 ML during initial stage (0.02 ML); Only islands of 2 ML height during later stage (0.12 ML) Standing electronic waves in Co islands proved [05Boe] Nucleation of Cr islands at DW elbows (preferential height of 1 ML); Further growth aligned to DWs (coalescence for 0.5–0.75 ML)

(continued)

52

Decoration of domain boundaries: metals: Au (decoration by metals)

5

Table 52.1 (continued) Miller Sample index Superstructure Deposit preparation

Results Supporting Major Deposition experimental experimental Remarks techniques technique techniques

Ref. [11Gri]

Cu

Single Au(111) crystal; Ar+ ISA (-/800–900 K)

Cu MBE

Fe

Single Au(111) crystal; Ne+ ISA (1.5 keV/600  C)

Fe MBE at STM RT

–

Single Au(111) crystal; Ne+ ISA (-/500  C)

Fe MBE at STM RT

–

Single Au(111) crystal; Ar+ ISA (-/1000 K) Single Au(111) crystal; Ar+ ISA (-/1000 K)

Fe MBE

GIXRD

–

Mn MBE

STM

LEED

Single Au(111) crystal; Ar+ ISA (1 keV/900 K)

Mo MBE

STM

LEED AES

Single Au(111) crystal; Ne+ ISA (600 eV/900 K)

Mo(CO)6 CVD at 500 K and PDA at 600 K Ni MBE

STM

LEED AES

STM

AES

Single Au(111) crystal; Ar+ ISA (900 eV/600  C)

Ni MBE

STM

LEED AES MEIS

25 ML Au MBE on Ru(0001); PDA at 600 K

Ni MBE at STM RT

Mn

Mo

Ni

Single Au(111) crystal; Ar+ ISA (1 keV/600  C)

STM

LEED DFT

–

Nucleation close to DW elbows in both hcp and fcc regions; Further growth preferred for hcp situated Cu islands Partially Cu-Au alloying Fe nucleation at DW elbows; Mainly 1 ML high Fe island height, partly 2 ML high Fe islands (0.25 ML) Fe nucleation at DW elbows; Island distance 12.5 nm in < 11
2 > and 7.3 nm in < 1
10 >; 1 ML apparent fcc-Fe island height Au(111) reconstruction not influenced by Fe deposit Mn nucleation at DW elbows; Cluster aligned parallel to < 11
2>; 1 ML apparent Mn island height Preferential Mo nucleation at DW elbows; 1 ML and 2 ML island heights DW distortion for deposition at 525 K due to alloy formation Inhomogeneous distribution of nuclei at DW elbows and fcc domain sites for low coverages Nucleation between DW close to elbows; Regular cluster spacing of 7.3 nm in < 1
21 > and 14 nm in < 1
10 >, cluster height 1 ML (hexagonal shape) Nucleation at DW elbows at 300 K; Coalescence in < 1
21 > for >0.8 ML Initial alloying of Ni at DW elbows

Fig.

[91Voi1]

[92Str]

[04Bul]

[03Fon]

[05Bie]

[03Son]

Fig. 52.2

[91Cha1] [91Cha2]

[09Tra]

Fig. 52.3

[96Mey]

(continued)

6

J. Wollschläger

Table 52.1 (continued) Miller Sample index Superstructure Deposit preparation

Pd

Rh

Ru

Sn

Results Supporting Major Deposition experimental experimental Remarks techniques technique techniques

Au PVD on mica Ni MBE at 775 K; Ne+ ISA (500 eV/725–775 K)

STM

AES

Single Au(111) crystal; Ar+ ISA (600 eV/720 K)

STM

LEED AES

Pd MBE

Au deposited on Pd MBE mica; Ar+ ISA (1 keV at 800 K/800 K)

VT-STM

Au deposited on mica

Rh MBE

STM

LEED AES

Single Au(111) crystal; Ar+ ISA (1 keV/ 1000 K)

Rh MBE

VT-STM

LEED AES

Single Au(111) crystal; ISA (-/-)

Ru3(CO)12 STM CVD and PDA 400–600 K

XPS

Flame annealed Au(111) single crystal Flame annealed Au(111) single crystal

Ru ECD

STM

–

Sn ECD

STM

–

Ni nucleation at DW elbows; Hexagonally and triangularly shaped Ni clusters 180 rotation of triangularly shaped clusters in adjacent DWs aligned to < 1
21 >; Partly Ni-Au alloying Nucleation of polygonally shaped Pd islands at DW elbows; Higher nucleation rate at bilged elbows compared to pinched elbows Preferential nucleation at DW elbows Nucleation attributed to Pd-Au exchange mechanism close to elbows Preferential nucleation of Rh island pairs close to DW elbows at RT; 1 ML Rh island height Alloying and restructuring after PDA at 400  C–525  C Preferential nucleation of Rh island pairs close to DW elbows at 300 K; 1 ML and 2 ML height of Rh islands For deposition at 30 K no preferential nucleation at domain walls Nucleation of irregularly shaped clusters at DW elbows at RT; Reduced nucleation probability at DW elbows for deposition at T > 500 K Strongly preferred Ru nucleation in fcc domains Preferential Sn nucleation in fcc domains; Preferential  island  growth in 11
2 due to repulsive domain walls

Ref.

Fig.

[99Cul]

Fig. 52.4

[98Ste]

[09Cas]

[94Alt]

[01Cha]

[03Cai]

[99Str]

Fig. 52.5

[02Mao]

(continued)

52

Decoration of domain boundaries: metals: Au (decoration by metals)

7

Table 52.1 (continued) Miller Sample index Superstructure Deposit preparation Ti

Single Au(111) crystal; Ar+ ISA (1 keV/ 850 K)

Results Supporting Major Deposition experimental experimental Remarks techniques technique techniques

Ref.

Ti MBE

[14Car]

STM/STS

–

Preferential Ti nucleation at DW elbows at RT Nucleation also on domain sites during early stages of growth

Symbols and abbreviations Short from

Full form

STM CVD DW ML PVD MBE PDA HAS ISA RT LEED AES PMOKE LMOKE GISAX-S LT-STM STS VT-STM XAS XMCD GIXRD DFT MEIS ECD fcc

scanning tunneling microscopy chemical vapor deposition domain wall monolayer physical vapor deposition molecular beam epitaxy post-deposition annealing helium atom scattering ion sputtering and annealing room temperature low-energy electron diffraction Auger electron spectroscopy polar magneto-optical Kerr effect longitudinal magneto-optical Kerr effect grazing incidence small angle X-ray scattering low-temperature scanning tunneling microscopy scanning tunneling spectroscopy variable temperature scanning tunneling microscopy X-ray absorption spectroscopy X-ray magnetic circular dichroism grazing incidence X-ray diffraction density functional theory medium-energy ion scattering electrochemical deposition face centered cubic

References [89Dov] [89Lan] [91Cha1] [91Cha2] [91Voi1] [91Voi2] [92Str] [92Wol] [94Alt] [96Mey] [97T€ol1] [97T€ol2] [98Pad] [98Ste] [99Cul] [99Pad1]

Dovek, M.M., Lang, C.A., Nogami, J., Quate, C.F.: Phys. Rev. B40, 11973 (1989) Lang, C.A., Dovek, M.M., Nogami, J., Quate, C.F.: Surf. Sci. 224, L947 (1989) Chambliss, D.D., Wilson, R.J., Chiang, S.: J. Vac. Sci. Technol. B9, 933 (1991) Chambliss, D.D., Wilson, R.J., Chiang, S.: Phys. Rev. Lett. 66, 1721 (1991) Voigtländer, B., Meyer, G., Amer, N.M.: Surf. Sci. 255, L529 (1991) Voigtländer, B., Meyer, G., Amer, N.M.: Phys. Rev. B44, 10354 (1991) Stroscio, J.A., Pierce, D.T., Dragoset, R.A., First, P.N.: J. Vac. Sci. Technol. A10, 1981 (1992) Wollschläger, J., Amer, N.M.: Surf. Sci. 277, 1 (1992) Altman, E.I., Colton, R.J.: Surf. Sci. 304, L400 (1994) Meyer, J.A., Baikie, I.D., Kopatzki, E., Behm, R.J.: Surf. Sci. 365, L647 (1996) T€olkes, C., Zeppenfeld, P., Krzyzowski, M.A., David, R., Comsa, G.: Phys. Rev. B55, 13932 (1997) T€olkes, C., Zeppenfeld, P., Krzyzowski, M.A., David, R., Comsa, G.: Surf. Sci. 394, 170 (1997) Padovani, S., Molinas-Mata, P., Scheurer, F., Bucher, J.P.: Appl. Phys. A66, S1199 (1998) Stephenson, A.W., Baddeley, C.J., Tikhov, M.S., Lambert, R.M.: Surf. Sci. 398, 172 (1998) Cullen, W.G., First, P.N.: Surf. Sci. 420, 53 (1999) Padovani, S., Scheurer, F., Bucher, J.P.: Europhys. Lett. 45, 327 (1999)

Fig.

8

[99Pad2] [99Str] [00Cha] [00Pad] [01Cha] [02Mao] [02Spi] [03Cai] [03Fon] [03Fru] [03Son] [04Bul] [04Cha] [05Bie] [05Boe] [07Mor] [08Sch] [08Tak] [09Cas] [09Tra] [11Gri] [12Wu] [14Car]

J. Wollschläger

Padovani, S., Chado, I., Scheurer, F., Bucher, J.P.: Phys. Rev. B59, 11887 (1999) Strbac, S., Magnussen, O.M., Behm, R.J.: Phys. Rev. Lett. 83, 3246 (1999) Chado, I., Padovani, S., Scheurer, F., Bucher, J.P.: Appl. Surf. Sci. 164, 42 (2000) Padovani, S., Scheurer, F., Chado, I., Bucher, J.P.: Phys. Rev. B61, 72 (2000) Chado, I., Scheurer, F., Bucher, J.P.: Phys. Rev. B64, 094410 (2001) Mao, B.-W., Tang, J., Randler, R.: Langmuir. 18, 5329 (2002) Spiridis, N., Kisielewski, M., Maziewski, A., Slezak, T., Cyganik, P., Korecki, J.: Surf. Sci. 507–510, 546 (2002) Cai, T., Song, Z., Chang, Z., Liu, G., Rodriguez, J.A., Hrbek, J.: Surf. Sci. 538, 76 (2003) Fonin, M., Dedkov, Y.S., Rüdiger, U., Güntherodt, G.: Surf. Sci. 529, L275 (2003) Fruchart, O., Renaud, G., Barbier, A., Noblet, M., Ulrich, O., Deville, J.-P., Scheurer, F., Mane-Mane, J., Repain, V., Baudot, G., Rousset, S.: Europhys. Lett. 62, 275 (2003) Song, Z., Cai, T., Rodriguez, J.A., Hrbek, J., Chan, A.S.Y., Friend, C.M.: J. Phys. Chem. B107, 1036 (2003) Bulou, H., Scheurer, F., Ohresser, P., Barbier, A., Stanescu, S., Quiros, C.: Phys. Rev. B69, 155413 (2004) Chado, I., Goyhenex, C., Bulou, H., Bucher, J.P.: Phys. Rev. B69, 085413 (2004) Biener, M.M., Biener, J., Schalek, R., Friend, C.M.: Surf. Sci. 594, 221 (2005) Boeglin, C., Ohresser, P., Decker, R., Bulou, H., Scheurer, F., Chado, I., Dhesi, S.S., Gaudry, E., Lazarovits, B.: Phys. Status Solidi B. 242, 1775 (2005) Morgenstern, K., Kibsgaard, J., Lauritsen, J.V., Laegsgaard, E., Besenbacher, F.: Surf. Sci. 601, 1967 (2007) Schouteden, K., Lijnen, E., Janssens, E., Ceulemans, A., Chibotaru, L.F., Lievens, P., Van Haesendonck, C.: New J. Phys. 10, 043016 (2008) Takakusagi, S., Kitamura, K., Uosaki, K.: J. Phys. Chem. C112, 3073 (2008) Casari, C.S., Foglio, S., Siviero, F., Li Bassi, A., Passoni, M., Bottani, C.E.: Phys. Rev. B79, 195402 (2009) Trant, A.G., Jones, T.E., Gustafson, J., Noakes, T.C.Q., Bailey, P., Baddeley, C.J.: Surf. Sci. 603, 571 (2009) Grillo, F., Früchtl, H., Francis, S.M., Richardson, N.V.: New J. Phys. 13, 013044 (2011) Wu, C., Castell, M.R.: Surf. Sci. 606, 181 (2012) Carrozzo, P., Tumino, F., Passoni, M., Bottani, C.E., Casari, C.S., Li Bassi, A.: Surf. Sci. 619, 77 (2014)

Chapter 53

Decoration of domain boundaries: metals: Au (decoration by molecules) J. Wollschläger

See Figs. 53.1, 53.2, 53.3, and Table 53.1.

Fig. 53.1 STM micrograph (80
80 nm2) obtained after deposition of C58 on Au(111) (Reproduced from [Bajales, N., et al.: J. Chem. Phys. 138, 104703 (2013)], with the permission of AIP Publishing). C58 cluster preferentially nucleate at elbows of the DWs

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_53

1

2

J. Wollschläger

Fig. 53.2 STM micrograph obtained after deposition of NN on Au(111) (From [00B€ oh]). NN cluster grow in fcc domains

Fig. 53.3 STM micrograph obtained after deposition of VOPc on Au(111) (From [12Niu]). VOPc molecules nucleate preferentially at elbows of the DWs and grow in fcc domains

53

Decoration of domain boundaries: metals: Au (decoration by molecules)

3

Table 53.1 Au – decoration by molecules Major Supporting Results experimental experimental Remarks techniques techniques

Ref.

4-Mercapto- Au(111) film on ECD pyridine mica

STM

RHEED

Preferential nucleation at DW elbows

[96Har]

C58

Single Au(111) LECBD crystal; Ar+ ISA (-/-)

LT-STM

–

Preferential nucleation at DW elbows

[13Baj]

C60

Au(111) film on OMBE mica; Ar+ ISA (3 keV/1000 K)

LT-STM

–

[96Fuj] Preferential nucleation at DW elbows at 30 K; No preferred nucleation at DW elbows at 80 K and above

C60

Au(111) film on OMBE HOPG; Ar+ ISA (-/-)

LT-STM

–

Two types of molecules nucleation at DW elbows

Miller index Superstructure Deposit (111)

(√3
N ) N ¼ 22–23

Sample preparation

Deposition technique

Fig.

Fig. 53.1

[10Tan]

Weak bonded C60 on top of elbow site NN

Single Au(111) Adsorption from gas crystal; Ar+ ISA (-/1000 phase K)

LT-STM

–

oh] Clusters aligned [00B€ to DWs at 50 K avoiding direct adsorption on DWs

CH3SH

Single Au(111) Adsorption crystal; Ar+ ISA from gas (-/500  C) phase

LT-STM

DFT

Preferential nucleation at DW elbows at 77 K

[05Mak] [08Mak]

DH6T

Single Au(111) OMBE crystal; Ar+ ISA (-/500  C)

STM

–

Preferential nucleation at DW elbows

[07Glo]

H2Pc

Single Au(111) OMBE crystal; Ar+ ISA (-/500  C)

STM

–

Clusters aligned [10Kom] to DWs avoiding direct adsorption on DWs

VOPc

Single Au(111) OMBE crystal; Ar+ ISA (700 eV/800 K)

LT-STM

–

Preferential nucleation at DW elbows

ET

Single Au(111) Adsorption crystal; Ar+ ISA from gas (1 keV/950 K) phase

LT-STM

–

[12Li] At 120 K initially preferential nucleation at DW elbows; Decoration of fcc domains during later stages of adsorption

MnPc, H-MnPc

Single Au(111) OMBE crystal; Ar+ ISA (-/800 K)

LT-STM

DFT

Preferential nucleation at DW elbows

[12Niu]

[13Liu]

Fig. 53.2

Fig. 53.3

4

J. Wollschläger

Symbols and abbreviations Short form

Full form

STM DW VOPc ECD LECBD LT-STM ISA OMBE DFT ET HOPG DH6T H2Pc fcc NN

scanning tunneling microscopy domain wall vanadyl phthalocyanine electrochemical deposition low-energy cluster ion beam deposition low-temperature scanning tunneling microscopy ion sputtering and annealing organic molecular beam epitaxy density functional theory exactly triangular highly ordered (or oriented) pyrolytic graphite α,ω-dihexylsexithiophene H2-phthalocyanine face-centered cubic 1-nitronaphtalene

References [96Fuj] [96Har] [00B€oh] [05Mak] [07Glo] [08Mak] [10Kom] [10Tan] [12Li] [12Niu] [13Baj] [13Liu]

Fujita, D., Yakabe, T., Nejoh, H., Sato, T., Iwatsuki, M.: Surf. Sci. 366, 93 (1996) Hara, M., Sasabe, H., Knoll, W.: Thin Solid Films. 273, 66 (1996) B€ohringer, M., Morgenstern, K., Schneider, W.-D., Berndt, R.: Surf. Sci. 457, 37 (2000) Maksymovych, P., Sorescu, D.C., Dougherty, D., Yates Jr., J.T.: J. Phys. Chem. B109, 22463 (2005) Glowatzki, H., Duhm, S., Braun, K.-F., Rabe, J.P., Koch, N.: Phys. Rev. B76, 125425 (2007) Maksymovych, P., Dougherty, D.B.: Surf. Sci. 602, 2017 (2008) Komeda, T., Isshiki, H., Liu, J.: Sci. Technol. Adv. Mater. 11, 054602 (2010) Tang, L., Zhang, X., Guo, Q., Wu, Y.-N., Wang, L.-L., Cheng, H.-P.: Phys. Rev. B82, 125414 (2010) Li, F., Tang, L., Gao, J., Zhou, W., Guo, Q.: Langmuir. 28, 11115 (2012) Niu, T., Zhou, C., Zhang, J., Zhong, S., Cheng, H., Chen, W.: J. Phys. Chem. C116, 11565 (2012) Bajales, N., Schmaus, S., Miyamashi, T., Wulfhekel, W., Wilhelm, J., Walz, M., Stendel, M., Bagrets, A., Evers, F., Ulas, S., Kern, B., B€ ottcher, A., Kappes, M.M.: J. Chem. Phys. 138, 104703 (2013) Liu, L.W., Yang, K., Xiao, W.D., Jiang, Y.H., Song, B.Q., Du, S.X., Gao, H.-J.: Appl. Phys. Lett. 103, 023110 (2013)

Chapter 54

Decoration of domain boundaries – group IV elements and IV–IV compounds – Si (001) J. Wollschläger

See Figs. 54.1, 54.2, and Table 54.1.

Fig. 54.1 STM micrograph obtained for homoepitaxy of Si (001)-(2  1) (From [90Ham]). APDBs appear in the first ML (labeled 1) due to nucleation on different sublattices of the (2  1) reconstruction. The inset shows the decoration of an APDB of type AP2 due to second layer nucleation (labeled 2a)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_54

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Fig. 54.2 STM micrograph (32  32 nm2) obtained for homoepitaxy of Si(001)-(2  1) via Si2H6 CVD (10 6 Pa Si2H6 at 670 K) (From [97Owe2]). The arrow indicates a B-type APDB of the first ML which is decorated by a second layer island

Table 54.1 Si(001) Primary remark: the freshly prepared Si(001) surface is free of APDBs. APDBs are formed during the initial stage of epitaxy in the first Si layer. Therefore, decoration of APDBs does not occur before the second layer starts to grow (cf. [89Ham, 90Ham1]) Miller Sample index Superstructure Deposit preparation (001)

(2  1)

Si

Major Supporting Results Deposition experimental experimental Remarks technique techniques techniques

Ref.

Fig.

Flash annealing at 1425 K and rapid cooling to 1175 K Flash annealing at 1450 K

Si PVD at STM 580–750 K

–

Decoration of type- [89Ham] Fig. 54.1 AP2 APDBs during [90Ham] second-layer nucleation

Si PVD at STM 750 K

LEED

Flash annealing at 1500 K

Si2H6 CVD STM at 720 K

–

Nucleation of Si [90Hoe1] islands at type-AP2 [90Hoe2] APDB of first ML running perpendicular to step edges followed by island growth perpendicular to APDB Type-AP2 APDB in center of terrace 0.5 misorientation toward [110] Preferential nucle- [93Bro] ation at first layer type-AP2 APDBs

(continued)

54

Decoration of domain boundaries – group IV elements and IV–IV compounds – Si (001)

3

Table 54.1 (continued) Miller Sample index Superstructure Deposit preparation Xe+ ISA (1 keV/ 1150  C) Flash annealing at 1500 K

Deposition technique Xe+ ISA (200 eV/ 370  C) Si2H6 CVD at 300 K and PDA at 700 K Flash CVD of annealing at SiH4 or 1400 K and Si2H6 at fast cooling 690–900 K to 900 K Flash SiH4 CVD annealing at at RT–700 1400 K and K fast cooling to 900 K Flash Si MBE at annealing at 725–775 K 1500 K

Major experimental techniques STM

STM

Supporting Results experimental Remarks techniques LEED Self-decoration of APDB formed by Xe+ bombardment – Preferential nucleation of islands at type-AP2 APDBs

STM

AES

VT-STM

DFT-LDA

MBE-STM

–

Flash Si PVD at STM annealing at RT–800 K 1500–1575 K

–

Flash annealing at 1450 K

Si PVD at STM 500–700 K

–

Flash annealing

SPE with PDA at 500–700  C

STM

–

Si PVD at SPA-LEED Flash STM annealing at 525 K 1100  C

–

Ref. [93Bed] [94Bed]

Fig.

[94Wan]

Nucleation of Si islands at type-AP2 APDBs for deposition at 690 K and PDA at 850 K Nucleation of Si islands at type-B APDBs at 700 K

[96Feh] [98Spi]

Si nucleation at APDBs of first Si layer Vicinal surface surface roughens during growing sample due to inhomogeneous nucleation at APDBs Si nucleation at type-AP1 APDBs Formation of B-type doublelayer steps due to nucleation at typeAP1 APDBs and anisotropic diffusion attachment Arrhenius study of APDB density: APDB density follows density of nuclei Self-decoration of AP2-APDBs after ion bombardment AP2-APDBs stable up to 700  C Surface roughening due to nucleation at APDBs

[97Voi]

[97Owe1] Fig. 54.2 [97Owe2]

[01Zan]

[02Zoe]

[03Kim]

[04Ess]

4

J. Wollschläger

Symbols and abbreviations Short form

Full form

STM CVD APDB DFT-LDA MBE VT-STM LEED AES RT PVD MBE-STM

scanning tunneling microscopy chemical vapor deposition antiphase domain boundary density functional theory with local density approximation molecular beam epitaxy variable temperature scanning tunneling microscopy low-energy electron diffraction Auger electron spectroscopy room temperature physical vapor deposition molecular beam epitaxy scanning tunneling microscopy

References [89Ham] [90Ham] [90Hoe1] [90Hoe2] [93Bed] [93Bro] [94Bed] [94Wan] [96Feh] [97Owe1] [97Owe2] [97Voi2] [98Spi] [01Zan] [02Zoe] [03Kim] [04Ess]

Hamers, R.J., K€ ohler, U.K., Demuth, J.E.: Ultramicroscopy. 31, 10 (1989) Hamers, R.J., K€ ohler, U.K., Demuth, J.E.: J. Vac. Sci. Technol. A8, 195 (1990) Hoeven, A.J., Dijkamp, D., van Loenen, E.J., Lenssinck, J.M., Dieleman, J.: J. Vac. Sci. Technol. A8, 207 (1990) Hoeven, A.J., Dijkamp, D., Lenssinck, J.M., van Loenen, E.J.: J. Vac. Sci. Technol. A8, 3657 (1990) Bedrossian, P., Kaxiaras, E.: Phys. Rev. Lett. 70, 2589 (1993) Bronikowski, M.J., Wang, Y., Hamers, R.J.: Phys. Rev. B48, 12361 (1993) Bedrossian, P.: Surf. Sci. 301, 223 (1994) Wang, Y., Bronikowski, M.J., Hamers, R.J.: Surf. Sci. 311, 64 (1994) Fehrenbacher, M., Rauscher, H., Behm, R.J.: Phys. Rev. B54, R17284 (1996) Owen, J.H.G., Miki, K., Bowler, D.R., Goringe, C.M., Goldfarb, I., Briggs, G.A.D.: Surf. Sci. 394, 79 (1997) Owen, J.H.G., Miki, K., Bowler, D.R., Goringe, C.M., Goldfarb, I., Briggs, G.A.D.: Surf. Sci. 394, 91 (1997) Voigtländer, B., Bonzel, H.P., Ibach, H.: Z. Phys. Chem. 198, 189 (1997) Spitzmüller, J., Fehrenbacher, M., Haug, F., Rauscher, H., Behm, R.J.: Appl. Phys. A66, S1025 (1998) Zandvliet, H.J.W., Zoethout, E., Wulfhekel, W., Poelsema, B.: Surf. Sci. 482–485, 391 (2001) Zoethout, E., van den Hoogenhof, P.W., Zandvliet, H.J.W., Poelsema, B.: J. Appl. Phys. 92, 5785 (2002) Kim, J.C., Ji, J.-Y., Kline, J.S., Tucker, J.R., Shen, T.-C.: Surf. Sci. 538, L471 (2003) Esser, M., Zoethout, E., Zandvliet, H.J.W., Wormeester, H., Poelsema, B.: Surf. Sci. 552, 35 (2004)

Chapter 55

Decoration of domain boundaries: group IV elements and IV–IV compounds: Si (111) (decoration by elemental metals and semiconductors) J. Wollschläger

See Figs. 55.1, 55.2, 55.3, 55.4, 55.5, and Table 55.1.

Fig. 55.1 Bright-field LEEM images (field of view 5000nm) of Si(111) during Ga deposition at 650
C (From [07Sch]). (a) Clean Si(111)-(7  7) surface with APDBs (dark lines). (b) Nucleation of (√3  √3)-Ga domains (0.08 ML) at (7  7) APDBs. (c) Continued (√3  √3)-Ga domain growth (13 ML Ga)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_55

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Fig. 55.2 STM micrograph obtained for decoration of Si(111)-(7  7) APDB by Ge (From [91K€ oh]). The guiding line runs through the corner holes on the left side domain while it does not run through corner holes on the right indicating an APDB between both parts. The APDB is decorated by a Ge(111) island with mostly (5  5) reconstruction

Fig. 55.3 STM micrograph (2000  2000 nm2) obtained for decoration of APDBs on vicinal Si (111)-(7  7) after Ge deposition at 550
C (From [12Roy]). Both atomic steps and APDBs are preferential nucleation sites as seen by bright lines. However, a large number of nuclei are also formed in the antiphase domains (spotted pattern between bright lines). Note that the circles mark areas without nucleation in the inner part of the domain

55

Decoration of domain boundaries: group IV elements and IV–IV compounds: Si (111). . .

3

Fig. 55.4 STM micrograph obtained after decoration of an APDB of Si(111)-(7  7) by Si during Si homoepitaxy at oh]). The guiding white line connects 330
C (From [89K€ corner holes on the lower half of the micrograph but not for the upper part demonstrating the existence of the APDB decorated by Si islands

Fig. 55.5 STM micrograph obtained during homoepitaxy on Si(111)-(7  7) at 670 K (From [96Voi2]). (a) First layer Si island with APDB as demonstrated by the grid (dark lines) connecting corner holes. (b) A second layer Si layer is nucleated at the APDB

4

J. Wollschläger

Table 55.1 Si(111) – decoration by elemental metals and semiconductors Major Supporting Results Miller Sample Deposition experimental experimental Remarks index Superstructure Deposit preparation technique techniques techniques (111)

(7  7)

Cu

Flash Cu MBE at STM annealing 340–600 LEEM at 1250
C
C exposure to atomic H

LEED

Ga

Ga MBE at VT-STM Flash annealing RT at 1200
C

LEED

Ga MBE at LEEM Flash annealing 650
C at 1200
C

LEED SPELEEM XPEEM

Flash Ge MBE annealing at 1250
C

LEED AES

Ge

STM

Ge SPE at SESM Flash annealing RT and at 1220
C PDA at 250 – 400
C Flash Ge MBE at STM annealing 400
C at 1200
C

–

–

Ge MBE at NC-AFM Flash annealing 450
C at 1200
C

–

Ge MBE at VT-STM Flash annealing 550
C at 1200
C

–

Preferential nucleation of crystalline β Cu-Si alloy clusters at APDBs and atomic steps Preferential Ga nucleation at APDB at RT Formation of (6.3  6.3)Ga starts at APDB Nucleation of domains with (√3  √3) superstructure at APDBs Surface miscut   in    , 112 , 110    or 112

Ref.

Fig.

[01Yas1] [01Yas2] [03Kur]

[04Gan]

[05Sch] Fig. 55.1 [07Sch1] [09Sch]

direction Nucleation of [91K€ oh] Fig. 55.2 Ge island at APDB Ge islands partially with (5  5) but also other building blocks Ge nucleation [95Hom] at APDBs for T > 200
C

Nucleation of [01Tom] Ge islands with (5  5) and (7  7) structure at APDBs Preferential [02Ara] nucleation at APDBs and step edges Preferential [12Roy] Fig. 55.3 nucleation at APDBs Some additional Ge nuclei on (continued)

55

Decoration of domain boundaries: group IV elements and IV–IV compounds: Si (111). . .

5

Table 55.1 (continued) Major Supporting Results Miller Sample Deposition experimental experimental Remarks index Superstructure Deposit preparation technique techniques techniques

K

Flash K PVD annealing at 1150
C

STM

Si

Si MBE at STM Flash annealing RT – at 1200
C 550
C

QMS

LEED

Thermal treatment

Si MBE at STM 500
C

–

Flash annealing at 1250
C Flash annealing at 1150
C

Si MBE at STM 350
C

–

Si MBE at SPA-LEED 425–525
C;

AES

Si MBE at STM Flash annealing 420
C at 1250
C and fast cooling to 900
C followed by slow cooling to 250
C

–

Si MBE at Dynamical Flash HT-STM annealing 350
C at 1200
C

–

defect free terraces Nucleation at APDBs after dosing of 0.01 ML K Si nucleation at APDBs of substrate for deposition at 330
C; Si nucleation of second bilayer at APDBs of first-layer Si islands Preferred initial Si nucleation at APDBs Preferred Si nucleation at APDBs Critical nucleus size of i* ¼ 1–2 for nucleation at APDBs Conclusion from variation of Si deposition rate APDBs decorated by Si islands with (2  1), (5  5), or (7  7) structure (7  7) structure exclusively for Si islands nucleated on defect-free Si (111)-(7  7) terraces Preferred Si nucleation on unfaulted halves of (7  7) unit cells adjacent to APDBs

Ref.

Fig.

[98Gor]

[89K€ oh]

Fig. 55.4

[93Voi]

[94Has2]

[94Hor]

[95Yan]

[96Has]

(continued)

6

J. Wollschläger

Table 55.1 (continued) Major Miller Sample Deposition experimental index Superstructure Deposit preparation technique techniques – Si MBE at MBE-STM 670–700 K

Si MBE at STM Flash annealing 280–410 at 1270
C
C

Ar+ ISA IG-STM Flash annealing (1 keV/500 at 1200
C
C)

Supporting Results experimental Remarks techniques – Nucleation of second-layer Si island at APDB of firstlayer Si island – Nucleation of metastable (2  1) and (5  5) islands at APDBs – Nucleation of Si atoms at APDBs

Ref. Fig. [96Voi1] Fig. 55.5 [96Voi2] [97Voi2]

[98Lan]

[05Uch]

Symbols and abbreviations Short form

Full form

STM APDB LEED MBE VT-STM SPELEEM

scanning tunneling microscopy antiphase domain boundary low-energy electron diffraction molecular beam epitaxy variable temperature scanning tunneling microscopy spectroscopic photoemission and low-energy electron microscopy X-ray photoemission electron microscopy room temperature Auger electron spectroscopy noncontact atomic force microscopy quadrupole mass spectrometry physical vapor deposition monolayer post-deposition annealing spot profile analysis of low-energy electron diffraction ion gun (high temperature) scanning tunneling microscopy ion sputtering and annealing high-temperature scanning tunneling microscopy scanning electron surface microscopy solid-phase epitaxy

XPEEM RT AES NC-AFM QMS PVD ML PDA SPA-LEED IG-STM ISA HT-STM SESM SPE

References [89K€oh] [91K€oh] [93Voi] [94Has] [94Hor] [95Hom] [95Yan] [96Has] [96Voi1] [96Voi2] [97Voi]

K€ohler, U., Demuth, J.E., Hamers, R.J.: J. Vac. Sci. Technol. A7, 2860 (1989) K€ohler, U., Jusko, O., Pietsch, G., Müller, B., Henzler, M.: Surf. Sci. 248, 321 (1991) Voigtländer, B., Zinner, A.: Surf. Sci. 292, L775 (1993) Hasegawa, T., Kohno, M., Hosaka, S., Hosoki, S.: J. Vac. Sci. Technol. B12, 2078 (1994) Horn-von Hoegen, M., Pietsch, H.: Surf. Sci. 321, L129 (1994) Homma, Y., Hibino, H., Aizawa, N.: Surf. Sci. 324, L333 (1995) Yang, Y.-N., Williams, E.D.: Phys. Rev. B51, 13238 (1995) Hasegawa, T., Shimada, W., Tochihara, H., Hosoki, S.: J. Cryst. Growth. 166, 314 (1996) Voigtländer, B., Weber, T.: Phys. Rev. B54, 7709 (1996) Voigtländer, B., Weber, T.: Phys. Rev. Lett. 77, 3861 (1996) Voigtländer, B., Bonzel, H.P., Ibach, H.: Z. Phys. Chem. 198, 189 (1997)

55

Decoration of domain boundaries: group IV elements and IV–IV compounds: Si (111). . .

[98Gor] [98Lan] [01Tom] [01Yas1] [01Yas2] [02Ara] [03Kur] [04Gan] [05Sch] [05Uch] [07Sch] [09Sch] [12Roy]

7

Gorelik, D., Aloni, S., Eitle, J., Meyler, D., Haase, G.: J. Chem. Phys. 108, 9877 (1998) Lanczycki, C.J., Kotlyar, R., Fu, E., Yang, Y.-N., Williams, E.D., Das Sarma, S.: Phys. Rev. B57, 13132 (1998) Tomitori, M., Hirade, M., Suganuma, Y., Arai, T.: Surf. Sci. 493, 49 (2001) Yasue, T., Koshikawa, T., Jalochowski, M., Bauer, E.: Surf. Sci. 480, 118 (2001) Yasue, T., Koshikawa, T., Jalochowski, M., Bauer, E.: Surf. Sci. 493, 381 (2001) Arai, T., Tomitori, M.: Appl. Surf. Sci. 188, 292 (2002) Kuroiwa, N., Fukushima, Y., Rajasekar, P., Neddermeyer, H., Jalochowski, M., Bauer, E., Yasue, T., Koshikawa, T.: Surf. Interface Anal. 35, 24 (2003) Gangopadhyay, S., Schmidt, T., Falta, J.: Surf. Sci. 552, 63 (2004) Schmidt, T., Gangopadhyay, S., Flege, J.I., Clausen, T., Locatelli, A., Heun, S., Falta, J.: New J. Phys. 7, 193 (2005) Uchigasaki, M., Tomiki, K., Kamioka, T., Nakayama, E., Watanabe, T., Ohdomari, I.: Jpn. J. Appl. Phys. 44, L313 (2005) Schmidt, T., Flege, J.I., Gangopadhyay, S., Clausen, T., Locatelli, A., Heun, S., Falta, J.: Phys. Rev. Lett. 98, 066104 (2007) Schmidt, T., Flege, J.I., Speckmann, M., Clausen, T., Gangopadhyay, S., Locatelli, A., Mentes, T.O., Heun, S., Guo, F.Z., Sutter, P., Falta, J.: Phys. Status Solidi. A206, 1718 (2009) Roy, A., Bagarti, T., Bhattacharjee, K., Kundu, K., Dev, B.N.: Surf. Sci. 606, 777 (2012)

Chapter 56

Decoration of domain boundaries: group IV elements and IV–IV compounds: Si(111) (decoration by compounds) J. Wollschläger

See Table 56.1.

Table 56.1 Si(111) – decoration by compounds Miller Sample Deposition index Superstructure Deposit preparation technique (111)

(7  7)

Major Supporting Results experimental experimental Remarks techniques techniques

BaF2

BaF2 MBE Flash annealing at 1250  C

HT-STM at 400  C

–

CaF2

CaF2 MBE Flash annealing at 1250  C

HT-STM at 400  C

–

Si MBE at Flash annealing 450–600  C at 1250  C

STM

AFM

O2 exposure at STM 850–1130 K

AES

SiOx

Flash annealing at 1450 K

BaF2 nucleation exclusively at APDBs and monoatomic steps CaF2 nucleation at APDBs, monoatomic steps and on terraces Elongated CaF2 island at APDBs T > 550  C nucleation only at APDBs and atomic steps Additional nucleation on terraces for T < 550  C Preferred nucleation of SiOx at APDBs due to exposure to O2

Ref.

Fig.

[96Sum]

[96Sum]

[02Wol] [03Wol]

[94Fel]

(continued)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_56

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Table 56.1 (continued) Miller Sample index Superstructure Deposit preparation Flash annealing at 1200  C

Major Supporting Deposition experimental experimental technique techniques techniques O2 exposure, STM RHEED PLA at 400  C–600  C

Results Remarks Ref. Preferred [98Shi] nucleation of [99Shi] SiOx at DBs between (7  7) and (1  1) domains due to exposure of O2

Symbols and abbreviations Short form

Full form

HT-STM AFM MBE STM AES APDB RHEED DB PLA

high-temperature scanning tunneling microscopy atomic force microscopy molecular beam epitaxy scanning tunneling microscopy Auger electron spectroscopy antiphase domain boundary reflection high-electron energy diffraction domain boundary pulsed laser annealing

References [94Fel] [96Sum] [98Shi] [99Shi] [02Wol] [03Wol]

Feltz, A., Memmert, U., Behm, R.J.: Surf. Sci. 314, 34 (1994) Sumiya, T., Miura, T., Fujinuma, H., Tanaka, S.: Jpn. J. Appl. Phys. 35, L1077 (1996) Shimada, K., Ishimaru, T., Katsube, S., Kawada, H., Ohdomari, I.: Appl. Surf. Sci. 130–132, 170 (1998) Shimada, K., Katsube, S., Ishimaru, T., Kawada, H., Ohdomari, I.: Surf. Sci. 433–435, 460 (1999) Wollschläger, J.: Appl. Phys. A75, 155 (2002) Wollschläger, J., Bierkandt, M., Larsson, M.I.: Appl. Surf. Sci. 219, 107 (2003)

Fig.

Chapter 57

Decoration of domain boundaries: group IV elements and IV–IV compounds: Si(111) (decoration by molecules) J. Wollschläger

See Fig. 57.1 and Table 57.1.

Fig. 57.1 STM micrograph (100  70 nm2) obtained after exposure of Si(111)-(7  7) to 4800L SiH4 at 690 K (From [97Feh]). The dashed line marks an APDB which are decorated by Si islands Table 57.1 Si(111) – decoration by molecules Miller Sample Deposition index Superstructure Deposit preparation technique (111)

(7  7)

Results Supporting Major experimental experimental Remarks techniques techniques

Ref.

STM

[97Itc]

Br2

Flash annealing at 1400 K

Br2 adsorption from electrochemical cell

Cl2

Flash annealing

Exposure to Cl2 STM at 1030 K

AES

SiH4

Flash annealing at 1400 K Flash annealing at 1200  C

SiH4 CVD STM (2% SiH4 in Ar) at 800 K Si2H6 CVD at STM 485  C

AES

Si2H6

–

–

Preferred formation of (1  1)-Br domains at APDBs of (7  7) superstructure Nucleation of (1  1)Cl domains at APDB of (7  7) superstructure Formation of network of (7  7) APDBs after Cl desorption due to independent nucleation of (7  7) domains Increased decoration of APDBs (and steps) due to higher reactivity Initial Si nucleation at APDBs

Fig.

[94Fel]

[95Mem] Fig. 57.1 [96Feh] [97Feh] [93K€ oh]

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_57

1

2

J. Wollschläger

Symbols and abbreviations Short form

Full form

STM APDB AES CVD

scanning tunneling microscopy antiphase domain boundary Auger electron spectroscopy chemical vapor deposition

References [93K€oh] [94Fel] [95Mem] [96Feh] [97Feh] [97Itc]

K€ohler, U., Andersohn, L., Dahlheimer, B.: Appl. Phys. A57, 491 (1993) Feltz, A., Memmert, U., Behm, R.J.: Surf. Sci. 307–309, 216 (1994) Memmert, U., Berko´, A., Behm, R.J.: Surf. Sci. 325, L441 (1995) Fehrenbacher, M., Spitzmüller, J., Memmert, U., Rauscher, H., Behm, R.J.: J. Vac. Sci. Technol. A14, 1499 (1996) Fehrenbacher, M., Rauscher, H., Memmert, U., Behm, R.J.: Surf. Sci. 385, 123 (1997) Itchkawitz, B.S., McEllistrem, M., Grube, H., Boland, J.J.: Surf. Sci. 385, 281 (1997)

Chapter 58

Decoration of domain boundaries: group IV elements and IV–IV compounds: other Si surfaces J. Wollschläger

See Table 58.1.

Table 58.1 Other Si surfaces Miller index Superstructure

Deposit

Sample Deposition preparation technique

(110)

(16  2)

Ge

Flash annealing at 1500 K

(113)

(3  2)

Sb4

Sb4PVD at Flash annealing RT at 1250  C

Ge MBE

Major experimental techniques

Supporting experimental techniques

Results Remarks

Ref.

STM

LEED

[13Yok]

STM

LEED AES

Decoration of RDBs by Ge after annealing at 700  C Preferential Sb4 nucleation at APDBs

Fig.

[96Müs]

Symbols and abbreviations Short form

Full form

STM LEED RDB APDB MBE PVD RT

scanning tunneling microscopy low-energy electron diffraction rotated domain boundary antiphase domain boundary molecular beam epitaxy physical vapor deposition room temperature

References [96Müs] Müssig, H.-J., Dabrowski, J., Arabczyk, W., Hinrich, S., Wolff, G.: J. Vac. Sci. Technol. B14, 982 (1996) [13Yok] Yokoyama, Y., Yamazaki, T., Asaoka, H.: J. Cryst. Growth.378, 230 (2013)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_58

1

Chapter 59

Decoration of domain boundaries: group IV elements and IV–IV compounds: Ge J. Wollschläger

See Fig. 59.1 and Table 59.1.

Fig. 59.1 STM micrograph (44  44 nm2) obtained after deposition of 0.4 ML Si on Ge(001)-(2  1) (Reproduced from [Zoethout, E., et al.: J. Appl. Phys. 92, 5785 (2002], with the permission of AIP Publishing). Dashed lines mark APDBs which are partly decorated by Si islands (bright islands)

Table 59.1 Ge Miller Sample index Superstructure Deposit preparation

Deposition technique

Results Supporting Major experimental experimental Remarks techniques techniques

Ref.

Fig.

[02Zoe]

Fig. 59.1

(001)

(2  1)/c(4  Si 2)

Ar+ ISA (800 eV/1100 K)

Ge PVD at 500–700 K

STM

–

(111)

c(2  8)

Cleavage of Ge (111)

Co MBE at 77 K

LT-STM

–

Co

Equivalent Arrhenius-like behavior of APDB density and density of nuclei Subsurface Co agglomeration at RDBs and APDBs Subsurface Co diffusion

[12Muz1] [12Muz2]

(continued)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_59

1

2

J. Wollschläger

Table 59.1 (continued) Miller Sample index Superstructure Deposit preparation

Deposition technique

Results Supporting Major experimental experimental Remarks techniques techniques

Ref. [14Tom]

Ni

Ar+ ISA (1 keV/ 1100 K)

Ni MBE at RT

VT-STM

–

O

Ne+ ISA (1 keV/ 800  C)

Exposure to O2 at RT

STM

LEED QMS

Ni decoration of APDBs Additional nucleation at point defects Preferential oxidation at RDBs

Fig.

[91Kli]

Symbols and abbreviations Short form

Full form

ISA PVD STM APDB RDB MBE RT VT-STM LEED LT-STM QMS

ion sputtering and annealing physical vapor deposition scanning tunneling microscopy antiphase domain boundary rotated domain boundary molecular beam epitaxy room temperature variable temperature scanning tunneling microscopy low-energy electron diffraction low-temperature scanning tunneling microscopy quadrupole mass spectrometry

References [91Kli] Klitsner, T., Becker, R.S., Vickers, J.S.: Phys. Rev. B44, 1817 (1991) [02Zoe] Zoethout, E., van den Hoogenhof, P.W., Zandvliet, H.J.W., Poelsema, B.: J. Appl. Phys. 92, 5785 (2002) [12Muz1] Muzychenko, D.A., Schouteden, K., Houssa, M., Savinov, S.V.,, van Haesendonck, C.: Phys. Rev. B85 (2012) 125412. [12Muz2] Muzychenko, D.A., Schouteden, K., Panov, V.I., van Haesendonck, C.: Nanotechology. 23, 435605 (2012) [14Tom] Tomaszewska, A., Li, J.-H., Huang, X.-L., Fu, T.-Y.: Mater. Sci. Pol. 32, 641 (2014)

Chapter 60

Decoration of domain boundaries: group IV elements and IV–IV compounds: SiC J. Wollschläger

See Table 60.1.

Table 60.1 SiC Miller index Superstructure Deposit

Sample preparation

Major Deposition experimental technique techniques

Supporting Results experimental Remarks techniques

β-(001) (2  1)

SiCMBE on 4 vicinal Si(001)

CVD of SiH4 or Si3H8

–

SiH4, Si3H8

STM

Si decoration of DBs between (3  2) and c(4  2) domains

Ref.

Fig.

[97Sou1] [97Sou2]

Symbols and abbreviations Short form

Full form

CVD DB MBE STM

chemical vapor deposition domain boundary molecular beam epitaxy scanning tunneling microscopy

References [97Sou1] Soukiassian, P., Semond, F., Douillard, L., Mayne, A., Dujardin, G., Pizzagalli, L., Joachim, C.: Phys. Rev. Lett. 78, 907 (1997) [97Sou2] Soukiassian, P., Semond, F., Mayne, A., Dujardin, G.: Phys. Rev. Lett. 79, 2498 (1997)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_60

1

Chapter 61

Decoration of domain boundaries: group III–V compounds: InSb J. Wollschläger

See Table 61.1. Table 61.1 InSb Miller Sample index Superstructure Deposit preparation InSb (001)

(8  4)

FePc

Major Supporting Results Deposition experimental experimental Remarks technique techniques techniques

Ar+-ISA PVD of LT-STM (700 eV/670 K) FePc at RT

LEED AES

Ref.

Fig.

Decoration [08Ahl] of DBs aligned parallel to [-110] by FePc at 70 K

Symbols and abbreviations Short form

Full form

ISA PVD RT LT-STM AES LEED DB

ion sputtering and annealing physical vapor deposition room temperature low-temperature scanning tunneling microscopy Auger electron spectroscopy low-energy electron diffraction domain boundary

References [08Ahl] Ahlund, J., Nilson, K., Palmgren, P., G€ othelid, E., Schiessling, J., G€ othelid, M., Martensson, N., Puglia, C.: J. Phys. Chem. C112, 6887 (2008)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_61

1

Chapter 62

Decoration of domain boundaries: binary oxides: Al2O3 J. Wollschläger

See Fig. 62.1 and Table 62.1.


 Fig. 62.1 NC-AFM micrograph of Al2O3 1120 recorded after deposition of 0.3 ML Co and PDA at 200  C (From [12Ven]). Co cluster decorate the periodically arranged crossings of DWs

Table 62.1 α-Al2O3 Miller Sample index Superstructure Deposit preparation (0001) (√31  √31) R9

Ni

Major Supporting Results Deposition experimental experimental Remarks technique techniques techniques

Ar+ ISA (1.5 MBE at RT NC-AFM keV/1200  C)

DFT

Ref.

Fig.

Preferred [10Ven] Ni nucleation in one domain of the underlying DW system (continued)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_62

1

2

J. Wollschläger

Table 62.1 (continued) Miller Sample index Superstructure Deposit preparation
 (12  4) Co Ar+ ISA (1.5 1120 keV/1200  C)

Ni

Deposition technique MBE at RT; PDA at 100–300  C Ar+ ISA (1.5 MBE at RT keV/1200  C)

Major experimental techniques NC-AFM

Supporting Results experimental Remarks techniques Ref. XPS Preferred [12Ven] Co nucleation at DW crossings

NC-AFM

XPS

Fig. Fig. 62.1

Preferred [12Ven] Ni nucleation at DW crossings

Symbols and abbreviations Short form

Full form

DW PDA ML RT MBE NC-AFM XPS DFT ISA

domain wall post-deposition annealing monolayer room temperature molecular beam epitaxy noncontact atomic force microscopy X-ray photoelectron spectroscopy density functional theory ion sputtering and annealing

References [10Ven] Venkataramani, K., Helveg, S., Hinnemann, B., Reichling, M., Besenbacher, F., Lauritsen, J.V.: Nanotechnology. 21, 265602 (2010) [12Ven] Venkataramani, K., Jensen, T.N., Helveg, S., Reichling, M., Besenbacher, F., Lauritsen, J.V.: Phys. Chem. Chem. Phys. 14, 2092 (2012)

Chapter 63

Decoration of domain boundaries: binary oxides: Al2O3 films J. Wollschläger

See Figs. 63.1, 63.2, and Table 63.1.

Fig. 63.1 STM mircographs (100  100 nm2 both) of Al2O3/NiAl(110) recorded after deposition of 0.023 ML Pd (left) and 0.23 ML Rh (right) at 300 K (From [00Bäu]). Pd and Rh cluster decorated APDBs and MDBs of the alumina film

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_63

1

2

J. Wollschläger

Fig. 63.2 STM micrograph (72  72 nm2) of Al2O3/Ni3Al(111) recorded after deposition of 0.36 ML Pd at 300K (From [04Deg]). Pd cluster preferentially nucleate at the crossing of the (√67  √67) R12.2 DW network

Table 63.1 Al2O3 films Sample preparation

Deposition technique

Major experimental techniques

Supporting Results experimental Remarks techniques

Support

Superstructure

Deposit

Cu91Al9 (111)

(√3  √3) R30

Pd

100 L O2 exposure at 680  C and POA at 1050 K

Pd MBE at RT

STM

AES LEIS

Pd

3600 L O2 exposure at 550 K and POA at 1120 K

Pd MBE at 90–300 K

VT-STM

LEED XPS

Oxidation at 290  C and POA at 750  C

MBE at RT – 300  C

STM

AES LEIS

Pt

1800 L O2 exposure at 600 K and POA at 1100 K

Deposition of sizeselected Pt7 clusters at 300 K

STM/STS

–

Rh

3600 L O2 exposure at 550 K and

MBE at 90–300 K

SPA-LEED STM

TPD LEED XPS

NiAl (110)



3:37 1 2:534



Enhanced nucleation probability of crystalline Pd clusters at MDBs Decoration of DBs (mainly MDBs) at 300 K by Pd particles; no preferential decoration of DBs at 90 K decoration of MDBs and APDBs with Pd clusters for RT deposition; Equilibrium shape of truncated sphere for Pd clusters nucleated at MDB (111) orientation for Pd cluster nucleated at APDBs Preferential Pt7 nucleation at APDBs; no preferential nucleation at MDBs Decoration of DBs at 300 K by (mostly

Ref.

Fig.

[07Sch]

[00Bäu] [00Fra] [08Des]

Fig. 63.1

[07Nap]

[13Ben]

[97Bäu] [00Bäu] [00Bäu]

(continued)

63

Decoration of domain boundaries: binary oxides: Al2O3 films

3

Table 63.1 (continued)

Support

Superstructure

Deposit

Sample preparation

Deposition technique

Major experimental techniques

Results Supporting experimental Remarks techniques

POA at 1120 K

Ni3Al (111)

(√67  67) R12.2

Ag

Au

Cu

Fe

Mn

Pd

V

50 L O2 exposure at 1000 K and POA at 1050 K 50 L O2 exposure at 1000 K and POA at 1050 K 50 L O2 exposure at 1000 K and POA at 1050 K O2 exposure at 1000 K and POA at 1050 K

Ag PVD at RT

STM

AES

Au PVD at RT

STM

AES

Cu PVD at RT

STM

AES

Fe MBE

STM

AES

50 L O2 exposure at 1000 K and POA at 1050 K 40 L O2 exposure at 1000 K and POA at 1050 K

Mn PVD at RT

STM

AES

Pd MBE

STM

AES

50 L O2 exposure at 1000 K and POA at 1050 K

V PVD

STM

AES

disordered) Rh particles; no preferential decoration of DBs at 90 K Initial nucleation on dot structure of hexagonal DW network Initial nucleation on dot structure of hexagonal DW network Initial nucleation on dot structure of hexagonal DW network Preferential nucleation at network structure 2D clusters at 130–150 K and 3D clusters at 300 K Initial nucleation on dot structure of hexagonal DW network Preferential nucleation at crossings of hexagonal DW; decoration for deposition at RT – 500 K Decoration of 2.6 nm network structure for deposition at 550 K No decoration effect at RT

Ref.

Fig.

[02Bec]

[02Bec]

[02Bec]

[06Leh]

[02Bec]

[04Deg] [06Ham]

Fig. 63.2

[02Bec]

Symbols and abbreviations Short form

Full form

ML APDB MDB STM RT AES LEIS LEED XPS MBE

monolayer antiphase domain boundary mirrored domains boundary scanning tunneling microscopy room temperature Auger electron spectroscopy low-energy ion spectroscopy low-energy electron diffraction X-ray photoelectron spectroscopy molecular beam epitaxy

(continued)

4 Short form POA VT-STM DB PVD DW STS TPD SPA-LEED 2D 3D

J. Wollschläger Full form post-oxidation annealing variable temperature scanning tunneling microscopy domain boundary physical vapor deposition domain wall scanning tunneling spectroscopy temperature-programmed desorption spot profile analysis of low-energy electron diffraction two-dimensional three-dimensional

References [97Bäu] [00Bäu] [00Fra] [02Bec]

Bäumer, M., Frank, M., Libuda, J., Stempel, S., Freund, H.-J.: Surf. Sci. 391, 204 (1997) Bäumer, M., Frank, M., Heemeier, M., Kühnemuth, R., Stempel, S., Freund, H.-J.: Surf. Sci. 454–456, 957 (2000) Frank, M., Bäumer, M.: Phys. Chem. Chem. Phys. 2, 3723 (2000) Becker, C., Rosenhahn, A., Wiltner, A., von Bergmann, K., Schneider, J., Pervan, P., Milun, M., Kralj, M., Wandelt, K.: New J. Phys. 4, 75 (2002) [04Deg] Degen, S., Becker, C., Wandelt, K.: Faraday Discuss. 125, 343 (2004) [06Ham] Hamm, G., Becker, C., Henry, C.R.: Nanotechnology. 17, 1943 (2006) [06Leh] Lehnert, A., Krupski, A., Degen, S., Franke, K., Decker, R., Rusponi, S., Kralj, M., Becker, C., Brune, H., Wandelt, K.: Surf. Sci. 600, 1804 (2006) [07Nap] Napetschnig, E., Schmid, M., Varga, P.: Surf. Sci. 601, 3233 (2007) [07Sch] Schmid, M., Kresse, G., Buchsbaum, A., Napetschnig, E., Gritschneder, S., Reichling, M., Varga, P.: Phys. Rev. Lett. 99, 196104 (2007) [08Des] Desikusumastuti, A., Qin, Z., Staudt, T., Happel, M., Lykhach, Y., Laurin, M., Shaikhutdinov, S., Libuda, J.: Surf. Sci. 603, L9 (2008) [13Ben] Beniya, A., Isomura, N., Hirata, H., Watanabe, Y.: Chem. Phys. Lett. 576, 49 (2013)

Chapter 64

Decoration of domain boundaries: binary oxides: Fe3O4 J. Wollschläger

See Table 64.1. Table 64.1 Fe3O4 Miller index (001)

Superstructure

Deposit

(√2  √2) R45

H

Sample preparation Ar+ ISA (1 keV/ 700  C, 2  10 6 mbar O2)

Deposition technique

Major experimental techniques

Supporting experimental techniques

Results Remarks

Ref.

STM

LEED DFT+U

Decoration of APDBs by OH groups due to H adsorbed from residual gas

[12Par]

Fig.

Symbols and abbreviations Short form

Full form

ISA STM LEED DFT+U

ion sputtering and annealing scanning tunneling microscopy low-energy electron diffraction density functional theory with Hubbard U parameter for electron correlation antiphase domain boundary

APDB

References [12Par] Parkinson, G.S., Manz, T.A., Novotny´, Z., Sprunger, P.T., Kurtz, R.L., Schmid, M., Sholl, D.S., Diebold, U.: Phys. Rev. B85, 195450 (2012)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_64

1

Chapter 65

Decoration of domain boundaries: binary oxides: TiO2 J. Wollschläger

See Fig. 65.1 and Table 65.1.

Fig. 65.1 STM micrograph (20  14 nm2) of TiO2(110)-(1  2) where cross-linked APDB are decorated by Pt cluster after deposition at RT and PDA at 825K (From [13San])

Table 65.1 TiO2 (rutile) Miller index

Major Supporting Results Sample Deposition experimental experimental Remarks Superstructure Deposit preparation technique techniques techniques

Ref.

(011)

(2  1)

H

Ar+ ISA (1 keV/ 750  C)

–

STM

LEED LEIS XPS

[06Dul]

(110)

(1  2)

Cu

Ar+ ISA (1 keV/ 1050 K)

Cu PVD at STM RT

LEED XPS

Decoration of DBs by hydrogen atoms from residual gas Preferential Cu cluster nucleation at the end of “bright” rows due to DBs between (1  1) and (1  2) domains

Fig.

[01Red]

(continued)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_65

1

2

J. Wollschläger

Table 65.1 (continued) Miller index

Sample Superstructure Deposit preparation Pt ISA (-/500  C, 2  10 5 Torr O2)

Major Supporting Deposition experimental experimental technique techniques techniques Pt PVD at STM LEED RT XPS

Ar+ ISA (-/ Pt PVD at 1100 K) RT

STM

LEED AES

Results Remarks Preferential Pt decoration of cross-link DBs and of DBs between (1  1) and (1  2) domains Preferential Pt cluster nucleation at crosslink DBs after annealing at 825 K

Symbols and abbreviations Short form

Full form

ISA STM LEED LEIS APDB RT XPS PVD AES DB

ion sputtering and annealing scanning tunneling microscopy low-energy electron diffraction low-energy ion spectroscopy antiphase domain boundary room temperature X-ray photoelectron spectroscopy physical vapor deposition Auger electron spectroscopy domain boundary

References [01Gan] Gan, S., Liang, Y., Baer, D.R., Grant, A.W.: Surf. Sci. 475, 159 (2001) [01Red] Reddic, J.E., Zhou, J., Chen, D.A.: Surf. Sci. 494, L767 (2001) [06Dul] Dulub, O., Di Valentin, C., Selloni, A., Diebold, U.: Surf. Sci. 600, 4407 (2006) [13San] Sa´nchez-Sa´nchez, C., Martı´n-Gago, J.A., Lo´pez, M.F.: Surf. Sci. 607, 159 (2013)

Ref. Fig. [01Gan]

[13San] Fig. 65.1

Chapter 66

Decoration of domain boundaries: ternary oxides: SrTiO3 J. Wollschläger

See Table 66.1.

Table 66.1 SrTiO3 Miller index Superstructure Deposit (001)

(√5  √5) R26.6

–

–

–

Sample preparation Annealing at 1200  C in UHV Annealing at 1185  C in UHV Annealing at 1200  C in UHV

Supporting Major Deposition experimental experimental techniques technique techniques

Results Remarks

Ref.

–

STM

–

–

STM

RHEED

[92Mat] [93Tan] [94Mat] [97Aki]

–

NC-AFM STM

–

Self-decoration of DB by unknown species Decoration of APDBs and MDBs by Sr and SrO Decoration of APDBs and MDBs by Sr and SrO

Fig.

[01Kub]

Symbols and abbreviations Short form

Full form

APDB RHEED STM UHV MDB NC-AFM

antiphase domain boundary reflection high-electron energy diffraction scanning tunneling microscopy ultrahigh vacuum mirrored domains boundary noncontact atomic force microscopy

References [92Mat] [93Tan] [94Mat] [97Aki] [01Kub]

Matsumoto, T., Tanaka, H., Kawai, T., Kawai, S.: Surf. Sci. 278, L153 (1992) Tanaka, H., Matsumoto, T., Kawai, T., Kawai, S.: Jpn. J. Appl. Phys. 32, 1405 (1993) Matsumoto, T., Tanaka, H., Kouguchi, K., Kawai, T., Kawai, S.: Surf. Sci. 312, 21 (1994) Akiyama, R., Matsumoto, T., Tanaka, H., Kawai, T.: Jpn. J. Appl. Phys. 36, 3881 (1997) Kubo, T., Nozoye, H.: Phys. Rev. Lett. 86, 1801 (2001)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_66

1

Chapter 67

Coexistence of domains: metals: Au J. Wollschläger

See Fig. 67.1, 67.2, and Table 67.1. [110] b c d

a − [110]

10−1 T = 650K

INTENSITY (counts per moniter)

10−2

(a)

10−3 10−4 10−4

(b)

10−5 (c) 10−3 10−4

10−5 (d) 10−4 10−5 −1.5 −1.0 −0.5 0 0.5 1.0 1.5 In-plane sample rotation angle w [deg]

Fig. 67.1 Angular SXRD in-plane ω-scans (rocking curves where ω denotes the sample rotation for fixed scattering angle) for Au(001)-hex with respect to the [001] surface normal (From [90Gib]). In the upper part, the scan directions of the individual scans (a–d) are denoted for reciprocal space. The satellites for the scans (a–c) are attributed to hexagonal domains rotated by
0.81

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_67

1

2

J. Wollschläger

Fig. 67.2 STM micrograph from Au(001)aqueous electrochemcial interface with coexisting (5  27) and (1  1) domains (From [92Gao])

Table 67.1 Au Major experimental techniques

Supporting experimental techniques

Sample preparation Remarks

Ref.

(5  1)/(1  5) rotated domains

LEEM

LEED AES

[90Tel]


0.81 rotated hexagonal phases

SXRD

LEED AES

Annealing at 900–1100 K in 107 Torr O2 Coexistence below TC ¼ 1050 K; dark field microscopy Ar+ ISA (1 keV/-)

Various phases of (5  N ) (N ¼ 15–21) Various matrix phases (5  1)/c(26  28)

UHV-HRTEM

LEED AES

Xe+ ISA (2 keV/340  C)

[90Moc] [90Gib] [91Ock] [92Dun]

REM

–

Xe+ ISA (1 keV/700  C)

[93Wan]

EC-STM

–

[91Gao]

(5  27)/(1  1)

EC-STM

–

(5  27)/(27  5) rotated domains (5  n)/(n  5) rotated domains

EC-STM

–

Electrochemical preparation in 0.1 M HClO4 Electrochemical preparation in 0.1 M HClO4 at 0.3 V potential Sample in 0.1 M HClO4

EC-STM

–

Miller index

Coexisting domains

(001)

(110)

(1  3)/(1  2)

STM

–

Sample in 0.01 M Na2SO4 + 1 mM HCl at 0.2 V potential Ar+ ISA (-/250  C)

(111)

Fcc and hcp domains

HAS

–

Ne+ ISA (- at 600 K/900 K)

[92Gao]

Fig.

Fig. 67.1

Fig. 67.2

[92Gao] [93Gao] [04Lab]

[83Bin]

[85Har]

Fig. 31.1[https://doi. org/10.1007/978-3662-53908-8_31] Fig. 31.5[https://doi. org/10.1007/978-3662-53908-8_31]

(continued)

67

Coexistence of domains: metals: Au

3

Table 67.1 (continued) Miller index

Coexisting domains

Major experimental techniques STM

Supporting experimental techniques LEED AES

SXRD

LEED AES –

DFT MD

Sample preparation Remarks Ar+ ISA (500 eV/900–1000 K) Herring bone pattern of DWs due to coexisting RDs Ar+ ISA (1 keV/-) Born-Oppenheimer MD; Energetic degeneracy of hcp and fcc sites

Ref. [89W€ol] [90Bar] [94Has]

Fig. Fig. 31.6[https://doi. org/10.1007/978-3662-53908-8_31]

[91San] [93San] [91Tak] [07Wan]

Symbols and abbreviations Short form

Full form

UHV-HR-TEM

ultrahigh vacuum high-resolution transmission electron microscopy low-energy electron diffraction Auger electron spectroscopy reflection electron microscopy electrochemical scanning tunneling microscopy ion sputtering and annealing helium atom scattering scanning tunneling microscopy domain wall surface X-ray diffraction molecular dynamics density functional theory low-energy electron microscopy critical temperature face-centered cubic hexagonal close packed

LEED AES REM EC-STM ISA HAS STM DW SXRD MD DFT LEEM TC fcc hcp

References [83Bin] [85Har] [89W€ol] [90Bar] [90Gib] [90Moc] [90Tel] [91Gao] [91Ock] [91San] [91Tak] [92Dun] [92Gao] [93Gao] [93San] [93Wan] [94Has] [04Lab] [07Wan]

Binnig, G., Rohrer, H., Gerber, C., Weibel, E.: Surf. Sci. 131, L379 (1983) Harten, U., Lahee, A.M., Toennies, J.P., W€ oll, C.: Phys. Rev. Lett. 54, 2619 (1985) W€oll, C., Chiang, S., Wilson, R.J., Lippel, P.H.: Phys. Rev. B39, 7988 (1989) Barth, J.V., Brune, H., Ertl, G., Behm, R.J.: Phys. Rev. B42, 9307 (1990) Gibbs, D., Ocko, B.M., Zehner, D.M., Mochrie, S.G.J.: Phys. Rev. B42, 7330 (1990) Mochrie, S.G.J., Zehner, D.M., Ocko, B.M., Gibbs, D.: Phys. Rev. Lett. 64, 2925 (1990) Telieps, W., Mundschau, M., Bauer, E.: Surf. Sci. 225, 87 (1990) Gao, X., Hamelin, A., Weaver, M.J.: Phys. Rev. Lett. 67, 618 (1991) Ocko, B.M., Gibbs, D., Huang, K.G., Zehner, D.M., Mochrie, S.G.J.: Phys. Rev. B44, 6429 (1991) Sandy, A.R., Mochrie, S.G.J., Zehner, D.M., Huang, K.G., Gibbs, D.: Phys. Rev. B43, 4667 (1991) Takeuchi, N., Chan, C.T., Ho, K.M.: Phys. Rev. B43, 13899 (1991) Dunn, D.N., Zhang, J.P., Marks, L.D.: Surf. Sci. 260, 220 (1992) Gao, X., Hamelin, A., Weaver, M.J.: Phys. Rev. B46, 7096 (1992) Gao, X., Edens, G.J., Hamelin, A., Weaver, M.J.: Surf. Sci. 296, 333 (1993) Sandy, A.R., Mochrie, S.G.J., Zehner, D.M., Grübel, G., Huang, K.G., Gibbs, D.: Surf. Sci. 287/288, 321 (1993) Wang, N., Uchida, Y., Lehmpfuhl, G.: Surf. Sci. 284, L419 (1993) Hasegawa, Y., Avouris, P.: J. Vac. Sci. Technol. B12, 1797 (1994) Labayen, M., Magnussen, O.M.: Surf. Sci. 573, 128 (2004) Wang, Y., Hush, N.S., Reimers, J.R.: Phys. Rev. B75, 233416 (2007)

Chapter 68

Coexistence of domains: metals: other metals (Ir, Pt, W) J. Wollschläger

See Fig. 68.1 and Table 68.1.

Fig. 68.1 (a) STM micrograph (25  15 nm2) from Ir(001) with coexisting (1  4) and (1  3) domains (From [97Kun]). (b) Model for DB between coexiting (1  4) and (1  3) domains (Adopted from [97Kun])

Table 68.1 Other metals: Ir, Pt, W Major experimental techniques

Supporting Sample preparation experimental Remarks techniques

(5  1)/ (1  5) rotated domains

LEED

–

(1  1)/ (1  3) (1  2)/ (1  3) (1  3)/ (1  4)

TOF-SARS NICISS LEED

LEED FIM

Ar+ ISA (500 eV/1300 K, 5  10 7 mbar O2) Coexistence after annealing above 930 K Ar+ ISA (-/1400  C, O2 atmosphere) Ne+ ISA (2 keV/600–900 K)

STM LEED

RHEED AES

Annealing at 950–1050 K for 30 min; slow cooling to RT (1–5 K/min)

Miller index

Coexisting domains

Ir (001)

Ir (110)

Ref.

Fig.

[85Hei]

[90Bu] [92H€ of] [89Het] [97Kun] Fig. 68.1 (continued)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_68

1

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J. Wollschläger

Table 68.1 (continued) Miller index Pt (001)

W (001)

Coexisting domains (2  1)/ (5  1)   14 1 1 5 with 4.1 mirrored domains c(2  2) rotated domains

Major experimental techniques LEED

Supporting Sample preparation experimental Remarks techniques – Ar+ or Xe+ ISA (340 eV/>900  C)

STM

LEED

Ar+ ISA (500 eV/830–910  C)

[94Bor] Fig. 35.1[https:// doi.org/10.1007/ 978-3-66253908-8_35]

LEED

–

Annealing at 2000 K in 10 5 Torr O2; flash annealing at 2200 K Average domain size 13  2 nm singular surface, 6  3 nm for vicinal surface

[85Wen]

Ref. Fig. [67Lyo]

Symbols and abbreviations Short form

Full form

TOF-SARS LEED AES FIM ISA NICISS STM RHEED DB RT

time-of-flight scattering and recoiling spectrometry low-energy electron diffraction Auger electron spectroscopy field ion microscopy ion sputtering and annealing noble gas impact collision ion scattering spectroscopy scanning tunneling microscopy reflection high-electron energy diffraction domain boundary room temperature

References [67Lyo] Lyon, H.B., Somorjai, G.A.: J. Chem. Phys. 46, 2539 (1967) [85Hei] Heinz, K., Schmidt, G., Hammer, L., Müller, K.: Phys. Rev. B32, 6214 (1985) [85Wen] Wendelken, J.F., Wang, G.-C.: Phys. Rev. B32, 7542 (1985) [89Het] Hetterich, W., Heiland, W.: Surf. Sci. 210, 129 (1989) [90Bu] Bu, H., Shi, M., Masson, F., Rabalais, J.W.: Surf. Sci. 230, L140 (1990) [92H€of] H€ofner, C., Hetterich, W., Niehus, H., Heiland, W.: Nucl. Inst. Meth. Phys. Res. B67, 328 (1992) [94Bor] Borg, A., Hilmen, A.-M., Bergene, E.: Surf. Sci. 306, 10 (1994) [97Kun] Kuntze, J., B€ omermann, J., Rauch, T., Speller, S., Heiland, W.: Surf. Sci. 394, 150 (1997)

Chapter 69

Coexistence of domains: group IV elements and IV–IV compounds: diamond J. Wollschläger

See Table 69.1.

Table 69.1 Diamond Miller index

Coexisting domains

(001)

(1  2)/(2  1) rotated domains

Major experimental techniques

Supporting experimental techniques

Sample preparation Remarks

Ref.

LEED

AES EELS –

UHV annealing at 1300  C MPA-CVD (CH4, H2) at 830  C MPA-CVD (CO, CH4, H2) at 800–900  C; B doping via B2H6 MPA-CVD on type-Ia natural diamond at 875  C; PDA in H-plasma at 875  C for 10 min CVD growth (CH4, H2) of diamond film at 800  C

[77Lur] [90Ham] [91Tsu]

RHEED STM STM

REM

STM

–

STM

–

Fig.

[95Kaw]

[95Kua] [96Kua]

Fig. 37.1[https://doi. org/10.1007/978-3662-53908-8_37]

[96Sta]

Symbols and abbreviations Short form

Full form

RHEED LEED AES EELS MPA-CVD PDA STM CVD REM

reflection high-electron energy diffraction low-energy electron diffraction Auger electron spectroscopy electron energy-loss spectroscopy microwave plasma-assisted chemical vapor deposition post-deposition annealing scanning tunneling microscopy chemical vapor deposition reflection electron microscopy

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_69

1

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References [77Lur] [90Ham] [91Tsu] [95Kaw] [95Kua] [96Kua] [96Sta]

Lurie, P.G., Wilson, J.M.: Surf. Sci. 65, 453 (1977) Hamza, A.V., Kubiak, G.D., Stulen, R.H.: Surf. Sci. 237, 35 (1990) Tsuno, T., Imai, T., Nishibayashi, Y., Hamada, K., Fujimori, N.: Jpn. J. Appl. Phys. 30, 1063 (1991) Kawarada, H., Sasaki, H., Sato, A.: Phys. Rev. B52, 11351 (1995) Kuang, Y., Wang, Y., Lee, N., Badzian, A., Badzian, T., Tsong, T.T.: Appl. Phys. Lett. 67, 3721 (1995) Kuang, Y., Badzian, A., Tsong, T.T., Lee, N., Badzian, T., Chen, C.: Thin Solid Films. 272, 49 (1996) Stallcup II, R.E., Villarreal, L.M., Lim, S.C., Akwani, I., Aviles, A.F., Perez, J.M.: J. Vac. Sci. Technol. B14, 929 (1996)

Chapter 70

Coexistence of domains: group IV elements and IV–IV compounds: Si J. Wollschläger

See Figs. 70.1, 70.2, 70.3, 70.4, 70.5, 70.6, 70.7, and Table 70.1.

Fig. 70.1 STM micrograph (15
25 nm2) from Si(001)-(2
1) with coexisting (2
1) and (1
2) rotated domains on adjacent terraces due to dimerization at the surface combinded with the diamond structure of Si (From [88Nie])

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_70

1

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J. Wollschläger

Fig. 70.2 STM micrograph (11
11 nm2) from Si (001) with coexisting (2
2) (lower right corner) and c(2
4) (zigzag pattern in the upper part) domains recorded at 120 K (From [92Wol]). A marks a point defect in the c(2
4) domain

Fig. 70.3 STM micrograph (80
60 nm2) from Si(001)-(2
8) with coexisting (2
8) and (8
2) rotated domains on adjacent terraces (From [95Zan])

70

Coexistence of domains: group IV elements and IV–IV compounds: Si

3

Fig. 70.4 LEED pattern recorded for Si(110) (From [87Ish]). (a) Coexisting of (16
2) mirrored domains for low off-angles surfaces. (b) Single (16
2) domains for high off-angles surfaces

Fig. 70.5 STM micrograph recorded at 765 K from Si(111) with coexisting (7
7) domain (left hand) and disordered quasi-(1
1) region (right side) (From [98Shi])

Fig. 70.6 STM micrograph recorded from Si(111) with coexisting domains of (7
7), (9
9), (11
11), (2
2), c(2
4), or (√3
√3)R30 structure (From [94Yan]). The large variety of phases is obtained by flash annealing and rapid quenching from the high-temperature phase to lower temperatures

4

J. Wollschläger

Fig. 70.7 STM micrograph recorded from Si bilayer on Si(111) epitaxially grown at ohler, U., 520  C (Reproduced from [K€ et al.: J. Vac. Sci. Technol. A7, 2860 (1989)], with the permission of AIP Publishing). The Si island exhibits coexisting domains of (5
5), (7
7), and (9
9)

Table 70.1 Si Major experimental techniques

Supporting experimental techniques

Sample preparation Remarks

Ref.

Fig.

LEED STM LEED STM at RT

AES –

Flash annealing at 1170 K Flash annealing at 1300 K

[87Tab] [88Nie]

Fig. 70.1

–

[91Swa]

STM LEED STM

– KMC

(2
1)/c(4
2)

LT-STM

–

(2
2)/c(4
2)

VT-STM

–

LT-STM

–

Flash annealing to 1250  C Miscut 0.04 –0.5 toward [110] Mechanical stress applied to surface to change (1
2):(2
1) ratio Flash annealing; Si MBE at 575–775 K Coexistence during growth; strong decrease of (1
2) coverage for increasing growth temperature Flash annealing at 1450 K; cooling with 3 K/s Flash annealing at 1000  C; coexistence at 120 K Flash annealing at 1200  C; slow cooling to 6 K or 80 K

Miller index

Coexisting domains

(001)

(1
2)/(2
1) rotated domains

(110)

(2
7)/(7
2) rotated domains (2
8)/(8
2) rotated domains

LEED STM LEED

–

(2
1), (4
5), and (5
1)

LEED

AES

RHEED (16
2) mirrored domains

LEED

AES XPS –

(16
2)/ stepped (17,15,1)(2
1)

STM HT-STM

– RHEED

Flash annealing (950–1200  C); rapid quenching (200 K/s) Flash annealing at 1300–1500 K Superstructure caused by small amount of Ni contamination Annealing at 1000  C Ar+ ISA(1 keV/1200  C) Flash annealing at 1200  C    Domain size of several mm in 112 Flash annealing at 1300 K Flash annealing at 1473 K

[91Web] [97Voi]

[94Bad] [97Yok] [92Wol]

Fig. 70.2

[96Shi] [97Shi1] [97Shi2] [86Mar] [88Nie] [95Zan]

Fig. 70.3

[76Sak] [77Ols] [85Ich] [86Yam] [87Ish]

Fig. 70.4

[89Hoe] [00Yam]

(continued)

70

Coexistence of domains: group IV elements and IV–IV compounds: Si

5

Table 70.1 (continued) Miller index (111)

Major experimental techniques HT-STM

Supporting experimental techniques AES

HT-STM

–

(2
1)/(5
5)/ (7
7)

STM

–

(2
1)/(7
7)

STM

–

STM

–

(2
2)/c(4
2)

STM

LEED

(√3
√3)R30 / (7
7)

HT-STM

–

Several (N
N ) phases with N ¼ 5,7,9,11,13

STM

LEED

STM

LEED

SPA-LEED

AES

STM

–

STM

–

STM HT-STM

–

Coexisting domains (1
1)/(7
7)

HT-STM

Sample preparation Remarks Flash annealing; Cl2 exposure at 1030 K Flash annealing and quenching to 765 K Disordered “(1
1)” not atomically resolved   In-situ cleaving in 211 direction and PCA at 100–650  C; PCA 330  C: Fingerlike meandering domains Flash annealing of substrate and 6.5ML Si via MBE at 500  C Flash annealing by heating or laser pulses; quenching with 450 K/s Additional coexistence of c(2
8) Flash annealing; fast cooling due to annealing with Q-switch laser pulse irradiation Apparent (1
1) LEED pattern Flash annealing to obtain large terraces; quenching to RT; very short flash annealing and quenching to 180–260  C Flash annealing; fast cooling due to annealing with Q-switch laser pulse irradiation Coexistence after annealing at 600  C; additional (√3
√3)R30 Flash annealing and fast cooling (1 K/s) MBE growth of Si on Si(111); coexistence at 700–880 K Flash annealing at 1300  C; fast cooling with 10 K/s Coexistence after annealing at 600  C; additional (√3
√3)R30 and c(4
2) Flash annealing and quenching to RT Disorder due to small domains with additional (2
2), c(2
4), c(2
8), and (√3
√3) structures Flash annealing and quenching to 500–600  C Additional (2
2), c(2
4), c(2
8), and (√3
√3) R30 domains Flash annealing at 1100  C; coexistence at 450–490  C Continuous transitions of stacking faults due to mobile adatoms

Ref. [94Fel1]

Fig.

[98Shi]

Fig. 70.5

[90Fee] [91Fee]

[94Yok] [06Ros]

[86Bec]

[01Min]

[86Bec]

[89Bec] [89Hor] [90Tom]

[94Yan] [97Koi] [98Lan]

Fig. 70.6

[95Hos] [96Hos]

[95Kum] [96Kum]

(continued)

6

J. Wollschläger

Table 70.1 (continued) Miller index

(111) vicinal

(113)

(320)

Major experimental techniques STM STM

Supporting experimental techniques – –

STM

LEED

STM

–

STM

–

STM

–

STM STM

AES QMS –

HT-STM

UHV-SEM

AFM

RHEED STM

(7
7)/(5
5)

HT-STM

–

(7
7)/(21
1)

RHEED

AES TPD

(3
1)/(3
2)

LEED

ARUPS

STM

–

STM LEED

AES DFT-LDA

LEED

AES

Coexisting domains

(7
7)/(1
1)

(2
1)/(1
2) rotated domains

Sample preparation Remarks Flash annealing and quenching to RT Flash annealing at 1200  C and quenching to RT Disordered “(1
1)” domains consist of small (√3
√3)R30 , (2
2), c(2
4), c(2
8), and (9
9) structures Flash annealing at 1200  C; Si MBE at 520  C Coexistence in first epitaxial Si layer; additional (2
2) CVD growth of Si film on Si(111) at 530  C using Si3H6 Flash annealing at 1250  C; Si MBE at 420  C Coexistence in first epitaxial Si layer; additional (2
1) Flash annealing; SiH4 exposure at 1100–1200 K; quenching to low temperatures Coexisting with disordered “(1
1)” consisting of (2
2) and (√3
√3)R30 structures Flash annealing at 1400 K; SiH4 CVD (2%SiH4 in Ar) at 690 K Flash annealing at 1270  C and Si MBE at 280–410  C Additional metastable (2
1) and (5
5) islands Flash annealing at 1250  C Miscut toward [11 2 ]; (7
7) on large terraces, small terraces in step bunch regions Flash annealing at 1150  C and quenching to RT (140 K/s) Disordered triangular shaped (1
1) structures in the center of terraces Flash annealing at 1250  C (7
7) on wide terraces, (5
5) on narrow terraces for T 200 K TC deduced from presented graph PT c(2
2) – (1
1) at TC ¼ 250 K TC deduced from presented graph PT c(2
2) – (1
1) at TC ¼ 211 K with critical exponent β ¼ 0.144  0.04 finite size effect for stepped surface: TC ¼ 217 K and β ¼ 0.05  0.01 PT c(2
2) to incommensurate phase at TC ¼ 270 K

[71Yon]

PT c(2
2) – (1
1) at TC ¼ 250 K

Fig.

[77Deb] [77Fel] [79Deb]

[79Hei]

[84Wen] [85Wen]

[87Ern] [89Ern]

[89Jup]

(continued)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_84

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J. Wollschläger

Table 84.1 (continued) Miller index Superstructure

Major experimental techniques SXRD

Supporting experimental techniques –

HAS

–

Results Sample preparation Annealing at 1400 K in 107 Torr O2 and flash annealing 2300 K –

Remarks PT c(2
2) – (1
1) at TC ¼ 230 K with critical exponents: γ ¼ 1.75 and ν ¼ 1 Displacive PT elastic and inelastic scattering analyzed

Ref. [89Rob]

Fig. Fig. 84.1

[92Ern]

Fig. 84.1 SXRD analysis of the PT of W(001)-c(2
2). (a) Model of the displacive arrangement of the W(001)-c(2
2) superstructure. (b) Asymmetric temperature induced broadening of the (3/2,3/2,0) superstructure diffraction peak indicating the formation of asymmetric domains above TC ¼ 230K (From [89Rob])

Symbols and abbreviations Short form

Full form

LEED PT TC AES TPD SR-PES HAS UHV SXRD

low-energy electron diffraction phase transition critical temperature Auger electron spectroscopy temperature-programmed desorption synchrotron radiation photoelectron emission spectroscopy helium atom scattering ultrahigh vacuum surface X-ray diffraction

84

Phase transition: metals: W

3

References [71Yon] [77Deb] [77Fel] [79Deb] [79Hei] [84Wen] [85Wen] [87Ern] [89Ern] [89Jup] [89Rob] [92Ern]

Yonehara, K., Schmidt, L.D.: Surf. Sci. 25, 238 (1971) Debe, M.K., King, D.A.: J. Phys. C Solid State Phys. 10, L303 (1977) Felter, T.E., Barker, R.A., Estrup, P.J.: Phys. Rev. Lett. 38, 1138 (1977) Debe, M.K., King, D.A.: Surf. Sci. 81, 193 (1979) Heilmann, P., Heinz, K., Müller, K.: Surf. Sci. 89, 84 (1979) Wendelken, J.F., Wang, G.-C.: J. Vac. Sci. Technol. A2, 888 (1984) Wendelken, J.F., Wang, G.-C.: Phys. Rev. B32, 7542 (1985) Ernst, H.-J., Hulpke, E., Toennies, J.P.: Phys. Rev. Lett. 58, 1941 (1987) Ernst, H.-J., Hulpke, E., Toennies, J.P.: Europhys. Lett. 10, 747 (1989) Jupille, J., Purcell, K.G., King, D.A.: Phys. Rev. B39, 6871 (1989) Robinson, I.K., MacDowell, A.A., Altman, M.S., Estrup, P.J., Evans-Lutterordt, K., Brock, J.D., Birgenau, R.J.: Phys. Rev. Lett. 62, 1294 (1989) Ernst, H.-J., Hulpke, E., Toennies, J.P.: Phys. Rev. B46, 16081 (1992)

Chapter 85

Phase transition: group IV elements and IV–IV compounds: diamond J. Wollschläger

See Table 85.1.

Table 85.1 Diamond Major Supporting Miller experimental experimental index Superstructure techniques techniques Sample preparation (001)

(111)

(1
1)

(1
1)

LEED

AES EELS

UHV annealing at 1300  C

LEED

–

UHV annealing at 1300  C

LEED LEED

AES EELS ARUPS

UHV annealing at 1300  C Cleaving of natural type-IIb single crystal

LEED

MEIS

UHV annealing of natural type-IIb single crystal at 800  C

Results Remarks

Ref.

Irreversible PT (1
1) ! (2
1)/(1
2) at TC ¼ 1270  C Irreversible PT (1
1) ! (2
1)/(1
2) at TC ¼ 1300  C Irreversible PT (1
1) ! (2
2) at TC ¼ 1270  C Irreversible PT (1
1) ! (2
1)/(2
2) at TC ¼ 900  C Irreversible PT (1
1) ! (2
1)/(2
2) at TC ¼ 950  C

[77Lur]

Fig.

[90Ham]

[77Lur] [81Him]

[86Der] [98Hui]

Symbols and abbreviations Short form

Full form

LEED PT TC AES UHV EELS ARUPS MEIS

low-energy electron diffraction phase transition critical temperature Auger electron spectroscopy ultrahigh vacuum electron energy-loss spectroscopy angle-resolved ultraviolet photoelectron spectroscopy medium-energy ion scattering

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_85

1

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J. Wollschläger

References [77Lur] [81Him] [86Der] [90Ham] [98Hui]

Lurie, P.G., Wilson, J.M.: Surf. Sci. 65, 453 (1977) Himpsel, F.J., Eastman, D.E., Heimann, P., van der Veen, J.F.: Phys. Rev. B24, 7270 (1981) Derry, T.E., Smit, L., van der Veen, J.F.: Surf. Sci. 167, 502 (1986) Hamza, A.V., Kubiak, G.D., Stulen, R.H.: Surf. Sci. 237, 35 (1990) Huisman, W.J., Peters, J.F., van der Veen, J.F.: Surf. Sci. 396, 253 (1998)

Chapter 86

Phase transition: group IV elements and IV–IV compounds: Si J. Wollschläger

See Figs. 86.1, 86.2, 86.3, 86.4, and Table 86.1. 20 15 (1 ½)

10

INTENSITY (a.u.)

(1 1)

8 (

3 3 ) 2 4

4

2

100

200 Temperature T [K]

300

Fig. 86.1 Temperature dependence of different LEED peaks obtained from Si(001) (From [87Tab]). The intensity of the (3/2,3/4) superstructure diffraction peak drastically decreases close to TC ¼ 200 K while the intensities of both the (1,1) and (1,1/2) diffraction peaks show only gradual intensity decrease due to the Debye-Waller factor (solid lines). This indicates the PT c(4  2) to (2  1) at TC

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_86

1

2

J. Wollschläger

~ I (T) (Arb.units)

1.0 0.8 0.6 0.4

0.2 0 1000

1050

1100

1150

INTENSITY (counts per 50 seconds)

Temperature T [K]

400

a

(6/7,0)

6000

b

(1,0)

T=1100 K

T=1100 K

Fig. 86.2 Temperature-dependent LEED experiment on Si(111)-(7  7) (From [81Ben]). Intensity of (3/7,3/7) superstructure diffraction peak versus temperature. The solid line shows a fit for second order PT with β ¼ 0.11

300

5000 4000 3000

200

2000 100

1000

0 0 1.57 1.58 1.59 1.60 1.61 1.62 1.85 1.86 1.87 1.88 1.89 Lateral scattering vector qx [Å−1] Lateral scattering vector qx [Å−1]

INTEGRATED INTENSITY (arb.units)

600 500

c

(6/7,0)

6000

d

(1,0)

5000

400

4000

300

3000

200

2000

100

1000

0 1050

1100

1150

Temperature T [K]

1200

1100

1150

Temperature T [K]

0 1200

Fig. 86.3 Temperature-dependent SXRD experiment on Si(111)-(7  7) (From [91Noh]). (a, b) Show in-plane scans of the (6/7,0) and (1,0) diffraction peaks, respectively, where  qx denotes the lateral scattering vector in 2
1
1 direction while (c, d) present temperature-dependent intensities of the (6/7,0) and (1,0) diffraction peaks, respectively, indicating a first order PT

86

Phase transition: group IV elements and IV–IV compounds: Si 8000

954 K

3

y

5000 2000 120 80

x

963 K

40

Si(113)

INTENSITY (arb.)

30

(5/3 –qx,1)

970 K 15 10 978 K 5 3.5 2.5

995 K

1.5

ε

kx

2.0 1.5

1025 K

1.0 0 0.05 0.10 Relative lateral scattering vector Δqx [Å–1]

Fig. 86.4 Temperature-dependent SXRD experiment on Si(113)(3  1) (From [93Abe]). In-plane diffraction scans Δqx in [ 1
10 ] direction showing the lateral shift of the (5/3,1) diffraction peak. The scans are presented with in-plane scattering vector Δqx relative to the low temperature commensurate position of the (5/3,1) Bragg peak. The diffraction peak shift above TC ¼ 959 K is attributed to chiral melting of (3  1) phase

Table 86.1 Si Major Supporting Miller experimental experimental Sample index Superstructure techniques techniques preparation (001)

c(4  2)

LEED

AES

Flash annealing 1170 K –

LEED

KMC simulation

LEED

–

Flash annealing 1000 K

LT-STM

–

Flash annealing 1450 K

Results Remarks

Ref.

Fig.

PT c(4  2) – (2  1) at TC ¼ 200 K PT c(4  2) – (2  1) at TC ¼ 200 K wide transition range attributed to defects PT c(4  2) – (2  2) at TC ¼ 200 K attributed to strong anisotropic Ising system PT c(4  2) – (2  2) at TC ¼ 200 K PT complete on A terraces, incomplete on B terraces

[87Tab]

Fig. 86.1

[94Ino]

[94Kub]

[98Yok]

(continued)

4

J. Wollschläger

Table 86.1 (continued) Major Miller experimental index Superstructure techniques (110) (2  1) LEED

LEED

Work function –

Ar+ ISA (500 eV/1500 K) ISA (-/1100 C)

LEED

AES

LEED

Work function AES AES XPS

Ar+ ISA (-/-) and flash annealing Ar+ ISA (500 eV/1500 K) Annealing at 1000  C Ar+ ISA (1 keV/ 1200  C) –

LEED (4  5)

(16  2)

(111)

(2  1)

Supporting experimental Sample techniques preparation AES Ar+ ISA (-/-) and flash annealing

LEED RHEED

STM

–

HT-STM

RHEED

Flash annealing at 1473 K

LEED

–

Cleavage

LEED

Surface con- Cleavage for ductivity, {111} plane
> SEM, optical along < 211 microscopy

LEED

LEED

Work function, surface conductivity UPS

Cleavage

LEED

–

Cleavage

LEED

Theory

Cleavage

STM

–

Si(111)  cleaved in 2
1
1 and PCA at 100–650  C

Cleavage

Results Remarks PT (2  1) – (5  1) at TC ¼ 750  C with intermediate phases (9  1) and (7  1) PT (2  1) – (5  1) at TC ¼ 1020 K PT (4  5) – (5  1) at TC ¼ 600  C PT (4  5) – (2  1) at TC ¼ 600  C PT (4  5) – (2  1) at TC ¼ 570 K PT (16  2) – (1  1) at TC ¼ 740  C PT (16  2) – (1  1) at TC ¼ 760  C PT (16  2) – (1  1) at TC ¼ 700  C PT (16  2) – (17,15,1)-(2  1) at TC ¼ 968 K Irreversible PT (2  1) ! (7  7) at TC ¼ 700  C Irreversible PT (2  1) ! (7  7) at TC ¼ 370  C drop of surface conductivity at TC Irreversible PT (2  1) ! (7  7) at TC ¼ 330–390  C Irreversible PT (2  1) ! (7  7) at TC ¼ 400  C Irreversible PT (2  1) ! (7  7) at TC ¼ 280  C Irreversible PT (2  1) ! (1  1) at TC ¼ 350–400  C Two reaction paths for irreversible PT: (1) (2  1) ! (5  5) ! (7  7) for TC ¼ 350  C and TC ¼ 600  C, respectively, (2) (2  1) ! “1  1” for TC ¼ 300  C followed by “1x1” ! (7  7) for TC ¼ 400  C “1  1” ¼ disordered structure with small patches of (5  5) and (7  7) due to disordered adatom arrangement

Ref. [81Ols]

Fig.

[86Nes] [73Hag] [81Ols1] [86Nes] [85Ich] [86Yam] [93Yam] [00Yam]

[63Lan] [64Lan] [72Bäu] [73Hen] [74Hen] [74Aue]

[74Row] [79Aue] [89Han1] [89Han2] [90Fee] [91Fee]

(continued)

86

Phase transition: group IV elements and IV–IV compounds: Si

5

Table 86.1 (continued) Major Supporting Miller experimental experimental Sample index Superstructure techniques techniques preparation (7  7) LEED – Cleavage and annealing LEED AES Thermal treatment

Theory

–

LEED

–

RHEED

–

REM

–

LEED

AES

LEED

AES

REM

–

LEEM

LEED

Results

Remarks PT (7  7) – (1  1) at Tc ¼ 900  C Second-order PT (7  7) – (1  1) close to Tc ¼ 900  C conclusion from fluctuating LEED intensities – First-order PT (7  7) – (1  1) due to consideration of symmetry PT (7  7) – (1  1) at ISA (-/830–1110  C) TC ¼ 830  C – PT (7  7) – (1  1) at TC ¼ 830  C additional (√3  √3)R30o above TC Flash annealing First-order PT at Tc ¼ 830  C (1) (7  7) domains nucleate on upper terraces during cooling, (2) (1  1) domains nucleate at APDBs of (7  7) during temperature increase Flash annealing Second-order PT (7  7) – (1  1) at Tc ¼ 1126(3) K with critical exponent β ¼ 0.11 for LRO diffuse scattering due to SRO Ar+ ISA (-/-) and PT (7  7) – (1  1) at flash annealing TC ¼ 880  C Flash annealing Second-order PT (7  7) – (1  1) at TC ¼ 830  C TC depends on terrace size, slight increase on smaller terraces Flash annealing First order PT (7  7) – at 1450 K (1  1) at Tc ¼ 1100(15) K concluded from inhomogeneous coverage of large terraces for quenched surfaces (1) preferred nucleation of (7  7) domain at monoatomic step edges, (2) three preferred crystallographic directions for growth of (7  7) domains

Ref. [64Lan]

Fig.

[70Flo]

[73Bla]

[73Hag] [77Ino]

[80Osa] [81Osa]

[81Ben]

Fig. 86.2

[81Ols] [83Tan]

[85Tel]

(continued)

6

J. Wollschläger

Table 86.1 (continued) Major Supporting Miller experimental experimental Sample index Superstructure techniques techniques preparation SR-PES LEED Ar+ ISA (600 eV, 600  C/ 800  C)

REM

–

HT-STM

–

SXRD

HT-STM

(111) (7  7) vicinal

(113)

(3  1)

HT-STM

–

HT-STM

UHV-SEM

LEED

–

LEED

AES

HR-LEED LEED

–

Results

Remarks PT (7  7) – (1  1) at TC ¼ 870  C Local (2  1) configuration for high temperature (1  1) phase – PT (7  7) – (1  1) at TC ¼ 830  C PT accompanied by moving atomic steps due to emission/incorporation of vacancies from the removed (7  7) domains Flash annealing PT (7  7) – (1  1) at TC ¼ 860  C at 900  C Flash annealing First-order PT (7  7) – at 1525 K (1  1) at TC ¼ 1129–1135 K Transition region widened for vicinal surface RCA cleaning Nucleation of (7  7) triand flash angular shaped domains at annealing to steps for T < Tc; fluctuating (7  7) domain size 1500 K close to Tc Critical domain size of six (7  7) units Flash annealing PT (7  7) – (1  1) at TC ¼ 777–787  C at 1250  C  (1)  10 miscut toward 11
2 , (2) TC decreased by 80–90 K compared to singular surface Flash annealing Gradual PT (1  1) – (7  7) at TC ¼ at 1250  C 820–830  C; TC varies for different Si terraces   1.8 miscut toward 11
2 Cleaving Reversible PT (7  7) – (5  5) at TC ¼ 625  C PT due to prolonged annealing Ar+ ISA (1 keV/ PT (3  1) – (1  1) at TC ¼ 600  C 750–800  C) Flash annealing Second-order PT (3  1) – at 1520 K (1  1) at TC ¼ 844 K with critical exponents (Potts universality class): α ¼ 0.32(0.06), β ¼ 0.11 (0.04), γ ¼ 1.03(0.19), ν ¼ 0.99(0.18)

Ref. [90Hri]

Fig.

[90Lat]

[91Kit] [91Noh]

Fig. 86.3

[92Mik]

[93Hib] [93Suz]

[94Hib]

[63Lan] [64Lan]

[90Xin] [90Yan]

(continued)

86

Phase transition: group IV elements and IV–IV compounds: Si

7

Table 86.1 (continued) Major Supporting Miller experimental experimental Sample index Superstructure techniques techniques preparation SXRD AES Flash annealing at 1520 K

LEED

–

LEEM

–

TBMD

–

HT-STM (3  2)

LEED

AES

LEED

STM

DFT-LDA

SR-PES

LEED

(115)

(3  1)

LEED

AES

(210)

(2  2)

LEED

AES

Results

Remarks Second-order PT (3  1) – (1  1) at TC ¼ 959 K with critical exponents: β ¼ 0.11(0.02), γ ¼ 1.56 (0.13), νx ¼ 0.65(0.07), νy ¼ 1.06(0.07) anisotropic critical behavior attributed to chiral melting Flash annealing Second-order PT (3  1) – at 1200 K and (1  1) due to chiral meltAr+ ISA ing at TC ¼ 929(20)K (500–1000 with critical exponents: eV/1200 K) α ¼ 0.71(0.10), β ¼ 0.093(0.02), γ ¼ 1.20 (0.20), νx ¼ 0.75(0.10) formation of light DW concluded from shift of diffraction spot for HTP Flash annealing PT (3  1) – (1  1) at TC ¼ 693(1) C with at 1250 C critical exponent α ¼ 0.6 TC deduced from critical fluctuations in LEEM micrographs – PT (3  1) – (1  1) at TC ¼ 950 K with anisotropic disorder quasi-liquid at surface for T ¼ 1000–1400 K Flash annealing PT (3  1) – (1  1) due to formation of heavy APDBs at 1250  C Ar+ ISA (1 keV, PT (3  2) – (3  1) at 450  C/750–800 TC ¼ 400–450  C  C) Flash annealing PT (3  2) – (3  1) a TC ¼ 780 K at 1200 K and Ar+ ISA (0.5–1 keV/1200 K) Flash annealing PT (3  2) – (3  1) attributed to addition/ at 1250  C extraction of interstitial atoms Flash annealing PT (3  2) – (3  1) for at 1500 K TC ¼ 800 K (1) No change of local structure between LTP and HTP, (2) PT attributed to two different types of tetramers apparent in the LTP Ar+ ISA (-/-) and PT (3  1) – (1  1) at flash annealing TC ¼ 620  C Ar+ ISA (-/-) and PT (2  2) – (1  1) at flash annealing TC ¼ 850  C

Ref. [93Abe] [94Abe]

Fig. Fig. 86.4

[94Sch]

[96Tro]

[96Wee]

[97Hib] [90Xin]

[94Sch]

[94Dab] [96Sak]

[01Hwa]

[81Ols] [81Ols] (continued)

8

J. Wollschläger

Table 86.1 (continued) Major Miller experimental index Superstructure techniques (320) (1  2) LEED

(331)

(510)

Supporting experimental Sample techniques preparation AES Ar+ ISA (-/-) and flash annealing

(12  1)

LEED

–

(13  1)

LEED

AES

(1  2)

LEED

AES

Results

Remarks Gradual PT from (1  2) to (11) for temperature range 680–850  C PT accompanied by formation of facets in critical temperature range Flash annealing PT (12  1) – (1  1) at 810  C at 1250  C + Ar ISA (-/-) and PT (13  1) – (1  1) at flash annealing TC ¼ 800  C Ar+ ISA (-/-) and PT (1  2) – (1  1) at flash annealing TC ¼ 700  C

Ref. [81Ols]

Fig.

[91Wei] [81Ols] [81Ols]

Symbols and abbreviations Short form

Full form

LEED PT TC AES UHV LTP HTP SR-PES STM DFT-LDA HT-STM TBMD LEEM SXRD UHV-SEM HR-LEED LT-STM ISA KMC RHEED XPS UPS REM SEM

low-energy electron diffraction phase transition critical temperature Auger electron spectroscopy ultrahigh vacuum low-temperature phase high-temperature phase synchrotron radiation photoelectron emission spectroscopy scanning tunneling microscopy density functional theory with local density approximation high-temperature scanning tunneling microscopy tight-binding molecular dynamics low-energy electron microscopy surface X-ray diffraction ultrahigh vacuum scanning electron microscopy high-resolution low-energy electron diffraction low-temperature scanning tunneling microscopy ion sputtering and annealing kinetic Monte Carlo simulation reflection high-electron energy diffraction X-ray photoelectron spectroscopy ultraviolet photoelectron spectroscopy reflection electron microscopy scanning electron microscopy

References [63Lan] [64Lan] [70Flo] [72Bäu] [73Bla]

Lander, J.J., Gobeli, G.W., Morrison, J.: J. Appl. Phys. 34, 2298 (1963) Lander, J.J.: Surf. Sci. 1, 125 (1964) Florio, J.V., Robertson, W.D.: Surf. Sci. 22, 459 (1970) Bäuerle, F., M€ onch, W., Henzler, M.: J. Appl. Phys. 43, 3917 (1972) Blandin, A.: Phys. Lett. 45A, 275 (1973)

86

Phase transition: group IV elements and IV–IV compounds: Si

[73Hag] [73Hen] [74Aue] [74Hen] [74Row] [77Ino] [79Aue] [80Osa] [81Ben] [81Ols] [81Osa] [83Tan] [85Ich] [85Tel] [86Nes] [86Yam] [87Tab] [89Han1] [89Han2] [90Fee] [90Hri] [90Lat] [90Xin] [90Yan] [91Fee] [91Kit] [91Noh] [91Wei] [92Mik] [93Abe] [93Hib] [93Suz] [93Yam] [94Abe] [94Dab] [94Hib] [94Ino] [94Kub] [94Sch] [96Sak] [96Tro] [96Wee] [97Hib] [98Yok] [00Yam] [01Hwa]

9

Hagstrum, H.D., Becker, G.E.: Phys. Rev. B8, 1580 (1973) Henzler, M.: Surf. Sci. 36, 109 (1973) Auer, P.P., M€ onch, W.: Jpn. J. Appl. Phys. Suppl. 2, 397 (1974) Henzler, M., Clabes, J.: Jpn. J. Appl. Phys. Suppl. 2, 389 (1974) Rowe, J.E., Phillips, J.C.: Phys. Rev. Lett. 32, 1315 (1974) Ino, S.: Jpn. J. Appl. Phys. 16, 891 (1977) Auer, P.P., M€ onch, W.: Surf. Sci. 80, 45 (1979) Osakabe, N., Yagi, K., Honjo, G.: Jpn. J. Appl. Phys. 19, L309 (1980) Bennett, P.A., Webb, M.B.: Surf. Sci. 104, 74 (1981) Olshanetsky, B.Z., Mashanov, V.I.: Surf. Sci. 111, 414 (1981) Osakabe, N., Tanishiro, Y., Yagi, K., Honjo, G.: Surf. Sci. 109, 353 (1981) Tanishiro, Y., Takaynagi, K., Yagi, K.: Ultramicroscopy. 11, 95 (1983) Ichinokawa, T., Ampo, H., Miura, S., Tamura, A.: Phys. Rev. B31, 5183 (1985) Telieps, W., Bauer, E.: Surf. Sci. 162, 163 (1985) Nesterenko, B.A., Brovii, A.V., Sorokovykh, A.I.: Surf. Sci. 171, 495 (1986) Yamamoto, Y., Ino, S., Ichikawa, T.: Jpn. J. Appl. Phys. 25, L331 (1986) Tabata, T., Aruga, T., Murata, Y.: Surf. Sci. 179, L63 (1987) Haneman, D., Chernov, A.A.: Surf. Sci. 215, 135 (1989) Haneman, D., Rownd, J.J., Lagally, M.G.: Surf. Sci. 224, L965 (1989) Feenstra, R.M., Lutz, M.A.: Phys. Rev. B42, 5391 (1990) Hricovini, K., Le Lay, G., Abraham, M., Bonnet, J.E.: Phys. Rev. B41, 1258 (1990) Latychev, A.V., Aseev, A.L., Krasilnikov, A.B., Stenin, S.I.: Surf. Sci. 227, 24 (1990) Xing, Y.R., Zhang, J.P., Wu, J.A., Liu, C.Z., Wang, C.H.: Surf. Sci. 232, L215 (1990) Yang, Y.-N., Williams, E.D., Park, R.L., Bartelt, N.C., Einstein, T.L.: Phys. Rev. Lett. 64, 2410 (1990) Feenstra, R.M., Lutz, M.A.: Surf. Sci. 243, 151 (1991) Kitamura, S., Sato, T., Iwatsuki, M.: Nature. 351, 215 (1991) Noh, D.Y., Blum, K.I., Ramstad, M.J., Birgeneau, R.J.: Phys. Rev. B44, 10969 (1991) Wei, J., Williams, E.D., Park, R.L.: Surf. Sci. 250, L368 (1991) Miki, K., Morita, Y., Tokumoto, H., Sato, T., Iwatsuki, M., Suzuki, M., Fukuda, T.: Ultramicroscopy. 42–44, 851 (1992) Abernathy, D.L., Birgeneau, R.J., Blum, K.I., Mochrie, S.G.J.: Phys. Rev. Lett. 71, 750 (1993) Hibino, H., Fukuda, T., Suzuki, M., Homma, Y., Sato, T., Iwatsuki, M., Miki, K., Tokumoto, H.: Phys. Rev. B47, 13027 (1993) Suzuki, M., Homma, Y., Hibino, H., Fukuda, T., Sato, T., Iwatsuki, M., Miki, K., Tokumoto, H.: J. Vac. Sci. Technol. A11, 1640 (1993) Yamamoto, Y., Sueyoshi, T., Sato, T., Iwatsuki, M.: Jpn. J. Appl. Phys. 32, L532 (1993) Abernathy, D.L., Song, S., Blum, K.I., Birgeneau, R.J., Mochrie, S.G.J.: Phys. Rev. B49, 2691 (1994) Dabrowski, J., Müssig, H.-J., Wolff, G.: Phys. Rev. Lett. 73, 1660 (1994) Hibino, H., Ogino, T.: Phys. Rev. Lett. 72, 657 (1994) Inoue, K., Morikawa, Y., Terakura, K., Nakayama, M.: Phys. Rev. B49, 14774 (1994) Kubota, M., Murata, Y.: Phys. Rev. B49, 4810 (1994) Schreiner, J., Jacobi, K., Selke, W.: Phys. Rev. B49, 2706 (1994) Sakama, H., Kunimatsu, D., Kageshima, M., Kawazu, A.: Phys. Rev. B53, 6927 (1996) Tromp, R.M., Theis, W., Bartelt, N.C.: Phys. Rev. Lett. 77, 2522 (1996) Wee, T.H., Feng, Y.P., Ong, C.K., Poon, H.C.: J. Phys. Condens. Matter. 8, 6511 (1996) Hibino, H., Ogino, T.: Phys. Rev. B56, 4092 (1997) Yokoyama, T., Takayanagi, K.: Phys. Rev. B57, R4226 (1998) Yamamoto, Y., Sueyoshi, T., Sato, T., Iwatsuki, M.: Surf. Sci. 466, 183 (2000) Hwang, C.C., Kim, H.S., Kim, Y.K., Ihm, K.W., Park, C.Y., An, K.S., Kim, K.J., Kang, T.-H., Kim, B.: Phys. Rev. B64, 045305 (2001)

Chapter 87

Phase transition: group IV elements and IV–IV compounds: Ge J. Wollschläger

See Figs. 87.1, 87.2, and Table 87.1. (1.5 0) x 50 Inverse peak intensity 1/Ip

0.10 (1.75 0.5)

0.05

0.00 150

200 250 300 Temperature T [K]

350

Fig. 87.1 Temperature-dependent SXRD experiment on Ge(001)c(4
2) (From [93Luc]). The c(4
2) – (2
1) PT is confirmed by the constant intensity of (3/2,0) diffraction peak (open circles) and the decreasing intensity of (7/4,0) diffraction peak (open triangles) above TC

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_87

1

2

J. Wollschläger

Fig. 87.2 STM micrograph recorded at 280  C from Ge(001)-c(2
8) (From [92Fee]). A disordered band with apparent (1
1) structure is formed between two rotated domains. The width and total area of disordered bands increases with increasing temperature until the c (2
8) completely vanishes above TC ¼ 315  C

Table 87.1 Ge Major Miller experimental index Superstructure techniques (001)

(110)

Supporting experimental techniques

(2
1)

SXRD

RHEED

c(4
2)

LEED

SR-PES AES

HAS

LEED AES

SXRD

LEED

SXRD

–

LEED

–

c(8
10)

Results Sample preparation

Remarks

Ar+ ISA PT (2
1) – (1
1) at TC ¼ 955(7)K (800 eV/980 K) Ar+ ISA (-/800 K) PT c(4
2) – (2
1) at TC ¼ 220 K existence of (2
2) or c (2
2) above TC cannot be excluded from weak (1/2, 1/2) diffraction intensity Ar+ ISA (-/900 K) Gradual transition c(4
2) ! (2
1) for increasing temperature from 150 to 300 K PT c(4
2) – (2
1) at Ar+ ISA TC ¼ 250–280 K (800 eV/700  C) temperatures concluded from graphics – PT c(4
2) – (2
1) at TC ¼ 184(10) K with critical exponents: β ¼ 0.88  0.03, γ ¼ 0.74  0.10 Thermal removal PT from c(8
10) to of sulfur capping facetted surface with {17 15 1} facets and (2
1) superstructure after annealing at 380–430  C; Reversible PT for annealing at TA > 430  C

Ref.

Fig.

[91Joh] [84Kev] [85Kev]

[87Lam]

[93Luc] Fig. 87.1

[96Alv]

[77Ols] [81Ols2]

(continued)

87

Phase transition: group IV elements and IV–IV compounds: Ge

3

Table 87.1 (continued) Major Miller experimental index Superstructure techniques RHEED

(111)

(2
1)

c(8
2)

Supporting experimental techniques LEED AES

HT-STM

–

LEED

–

LEED

AES

LEED

PSV

STM

–

LEED

AES

RHEED

–

LEED

AES

LEED

AES

RHEED

SR-PES

LEED

AES

Spectroscopic LEED ellipsometry AES

Results Sample preparation Ar+ ISA (1 keV/ 720  C)

Remarks PT 10) to  c(8
 11 5 after 2 2 annealing at TA > 380  C +  Ar ISA (-/720 C) Irreversible PT c(8
10) ! (16
2) at TC ¼ 380  C PT (16
2) – (1
1) at TC ¼ 450  C UHV cleaving Irreversible PT (2
1) ! (12
12) at TC ¼ 300  C UHV cleaving Irreversible PT (2
1) ! c(8
2) at TC ¼ 300–350  C UHV cleaving Irreversible PT (2
1) ! c(8
2) at TC ¼ 670  C UHV cleaving Irreversible PT (2
1) ! c(2
8) via disordered intermediate phase with c (2
4) and (2
2) patches (1) (2
1)-RDB nucleation centers for PT, (2) (2
1)-APDB stable Cleavaging and PT c(8
2) – (1
1) at PCA TC ¼ 200–400  C – PT c(8
2) – (1
1) via intermediate (2
2) phase Ar+ ISA (-/-) PT c(8
2) – (1
1) in two stages: (1) Deterioration of LRO at TC ¼ 300  C, (2) Complete disorder at 550  C +  Ar ISA (-/850 C) First-order PT c(8
2) – (2
1) via incommensurate phase at TC ¼ 675  C Ge MBE on Ge PT c(2
8) – (1
1) at (111) at 550  C TC ¼ 300  C Ne+ ISA (800 eV, Continuous PT c(2
8) – (1
1) at TC ¼ 1058 550  C/700  C) (10) K with critical exponent β ¼ 0.15 due to domain-disorder mechanism of laterally strained domains only fundamental spots measured Ar+ ISA (600 eV, PT c(2
8) – (1
1) at TC ¼ 250  C 600  C/800  C)

Ref. Fig. [85Nor]

[95Ich] [03Ich]

[63Lan] [68Pal] [69Hen] [74Hen] [98Ein]

[68Pal] [80Ich]

[81Ols]

[85Pha]

[88Aar] [87McR] [88McR]

[90Abr] (continued)

4

J. Wollschläger

Table 87.1 (continued) Major Miller experimental index Superstructure techniques SR-PES

(113)

Supporting experimental techniques LEED

Results Sample preparation Ar+ ISA (600 eV, 600  C/800  C)

Remarks PT c(2
8) – (1
1) at TC ¼ 260–300  C local (2
1) configuration for hightemperature (1
1) phase PT c(2
8) – (1
1) at TC ¼ 1060 K disordering of first 1.0–1.5 ML Ge PT c(2
8) – (1
1) at TC ¼ 315  C

MEIS

AES

Ar+ ISA (700 eV/1050 K)

HT-STM

STM at RT

(12
12)

LEED

–

(3
1)

LEED

–

(3
2)

LEED

–

STM

DFT-LDA

SPA-LEED

AES

Sample cleaved and annealed at 400  C Cleaving and PCA PT (12
12) – c(8
2) at TC ¼ 200  C Flash annealing at Second-order 1150 K commensurateincommensurate PT (3
1) – (1
1) due to chiral melting at TC ¼ 1063 (10) K with critical exponents: α ¼ 0.71(0.10), β ¼ 0.10(0.01), γ ¼ 1.27(0.10), ν|| ¼ 0.72(0.05), ν⊥ ¼ 0.71(0.10) formation of light DW concluded from shift of diffraction spot for HTP Flash annealing at PT (3
2) – (3
1) at TC ¼ 750 K 1150 K Ar+ ISA (-/850  C) PT (3
2) – (3
1) attributed to short hops by interstitial atoms across the surface Ar+ ISA (500 eV, Loss of regular APDB 900 K/1180 K) spacing for T > 370 K Ar+ ISA (-/-) PT (3
1) – (1
1) at TC ¼ 600  C Ar+ ISA (-/-) PT (2
2) – (1
1) at TC ¼ 500  C + Ar ISA (-/-) PT (5
1) – (1
1) at TC ¼ 630  C Ar+ ISA (-/-) PT (5
2) – (1
1) at TC ¼ 630  C + Ar ISA (-/-) PT (1
2) – (1
1) at TC ¼ 520  C

(115)

(3
1)

LEED

AES

(210)

(2
2)

LEED

AES

(331)

(5
1)

LEED

AES

(551)

(5
2)

LEED

AES

(510)

(1
2)

LEED

AES

Ref. [90Hri]

Fig.

[91Den]

[91Fee] Fig. 87.2 [92Fee] [93Fee] [63Lan] [94Sch]

[94Sch] [98Lar]

[99Igl] [81Ols] [81Ols] [81Ols] [81Ols] [81Ols]

87

Phase transition: group IV elements and IV–IV compounds: Ge

5

Symbols and abbreviations Short form

Full form

LEED PT TC AES SXRD RHEED SR-PES ISA STM HAS UHV PSV LRO RT MBE PCA HT-STM DW APDB DFT-LDA SPA-LEED MEIS ML

low-energy electron diffraction phase transition critical temperature Auger electron spectroscopy surface X-ray diffraction reflection high-electron energy diffraction synchrotron radiation photoelectron emission spectroscopy ion sputtering and annealing scanning tunneling microscopy helium atom scattering ultrahigh vacuum photo-surface voltage long range order room temperature molecular beam epitaxy post-cleavage annealing high-temperature scanning tunneling microscopy domain wall antiphase domain boundary density functional theory with local density approximation spot profile analysis of low-energy electron diffraction medium-energy ion scattering monolayer

References [63Lan] [68Pal] [69Hen] [74Hen] [77Ols1] [77Ols2] [80Ich] [81Ols] [84Kev] [85Kev] [85Nor] [85Pha] [87Lam] [87McR] [88Aar] [88McR] [90Abr] [90Hri] [91Den] [91Fee] [91Joh] [92Fee] [93Fee] [93Luc]

Lander, J.J., Gobeli, G.W., Morrison, J.: J. Appl. Phys. 34, 2298 (1963) Palmberg, P.W.: Surf. Sci. 11, 153 (1968) Henzler, M.: J. Appl. Phys. 40, 3758 (1969) Henzler, M., Clabes, J.: Jpn. J. Appl. Phys. Suppl. 2, 389 (1974) Olshanetsky, B.Z., Repinsky, S.M., Shklyaev, A.A.: Surf. Sci. 64, 224 (1977) Olshanetsky, B.Z., Repinsky, S.M., Shklyaev, A.A.: Surf. Sci. 69, 205 (1977) Ichikawa, T., Ino, S.: Solid State Commun. 34, 349 (1980) Olshanetsky, B.Z., Mashanov, V.I., Nikiforov, A.I.: Surf. Sci. 111, 429 (1981) Kevan, S.D., Stoffel, N.G.: Phys. Rev. Lett. 53, 702 (1984) Kevan, S.D.: Phys. Rev. B32, 2344 (1985) Noro, H., Ichikawa, T.: Jpn. J. Appl. Phys. 24, 1288 (1985) Phaneuf, R.J., Webb, M.B.: Surf. Sci. 164, 167 (1985) Lambert, W.R., Trevor, P.L., Cardillo, M.J., Sakai, A., Hamann, D.R.: Phys. Rev. B35, 8055 (1987) McRae, E.G., Malic, R.A.: Phys. Rev. Lett. 58, 1437 (1987) Aarts, J., Hoeven, A.-J., Larsen, P.K.: Phys. Rev. B38, 3925 (1988) McRae, E.G., Malic, R.A.: Phys. Rev. B38, 13163 (1988) Abraham, M., Le Lay, G., Hila, J.: Phys. Rev. B41, 9828 (1990) Hricovini, K., Le Lay, G., Abraham, M., Bonnet, J.E.: Phys. Rev. B41, 1258 (1990) Denier van der Gon, A.W., Gay, J.M., Frenken, J.W.M., van der Veen, J.F.: Surf. Sci. 241, 335 (1991) Feenstra, R.M., Slavin, A.J., Held, G.A., Lutz, M.A.: Phys. Rev. Lett. 66, 3257 (1991) Johnson, A.D., Norris, C., Frenken, J.W.M., Derbyshire, H.S., MacDonald, J.E., Van Silfhout, R.G., Van Der Veen, J.F.: Phys. Rev. B44, 1134 (1991) Feenstra, R.M., Slavin, A.J., Held, G.A., Lutz, M.A.: Ultramicroscopy 42–44, 33 (1992) Feenstra, R.M., Held, G.A.: Physica. D66, 43 (1993) Lucas, C.A., Dower, C.S., McMorrow, D.F., Wong, G.C.L., Lamelas, F.J., Fuoss, P.H.: Phys. Rev. B47, 10375 (1993)

6

[94Sch] [95Ich] [96Alv] [98Ein] [98Lar] [99Igl] [03Ich]

J. Wollschläger

Schreiner, J., Jacobi, K., Selke, W.: Phys. Rev. B49, 2706 (1994) Ichikawa, T., Sueyosi, T., Sato, T., Iwatsuki, M., Udagawa, F., Sumita, I.: Solid State Commun. 93, 541 (1995) Alvarez, J., Etgens, V.H., Torrelles, X., van der Vegt, H.A., Fajardo, P., Ferrer, S.: Phys. Rev. B. 54, 5581 (1996) Einaga, Y., Hirayama, H., Takayanagi, K.: Phys. Rev. B57, 15567 (1998) Laracuente, A., Erwin, S.C., Whitman, L.J.: Phys. Rev. Lett. 81, 5177 (1998) Iglesias, A., Gierer, M., Wolf, D., Moritz, W.: Surf. Sci. 442, 357 (1999) Ichikawa, T.: Surf. Sci. 544, 58 (2003)

Chapter 88

Phase transition: group IV elements and IV–IV compounds: SiC J. Wollschläger

See Table 88.1.

Table 88.1 SiC Miller index (001)-β

Superstructure

Major experimental techniques

Supporting experimental techniques

(3  2)

STM

–

Results Sample preparation

Remarks

Ref.

CVD (C3H8, SiH4) on 4 vicinal Si(001)

PT (3  2) – c(4  2) at 1150  C

[97Sou1] [97Sou2]

Fig.

Symbols and abbreviations Short form

Full form

STM PT CVD

scanning tunneling microscopy phase transition chemical vapor deposition

References [97Sou1] Soukiassian, P., Semond, F., Douillard, L., Mayne, A., Dujardin, G., Pizzagalli, L., Joachim, C.: Phys. Rev. Lett. 78, 907 (1997) [97Sou2] Soukiassian, P., Semond, F., Mayne, A., Dujardin, G.: Phys. Rev. Lett. 79, 2498 (1997)

J. Wollschläger (*) Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_88

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Part V

Photoelectron Spectroscopies Applied to Condensed Matter Systems

Chapter 89

Historical remarks and introduction to photoemission P. D. Johnson

Photoemission has seen a long and distinguished history since the photoelectric effect was first discovered by Heinrich Hertz in 1865. Those very first observations ultimately lead to the identification of the electron as the first elementary particle independently by Lenard and Thomson. Subsequently, Millikan refined the experimental measurement and made the first accurate determination of Planck’s constant using Einstein’s equation and thereby confirming the underlying quantum nature of the physical world. The technique continued to evolve, and major advances took place in the middle of the twentieth century largely motivated by the need to identify better cathodes for use in television technologies. Photoemission was seen as the perfect tool to investigate the electronic structure of different materials. Technical developments driving this period represented improved photon sources, better vacuum technology, and evolving electron spectrometers. The period is characterized by an experimental verification of theoretical calculations of the electronic structure of atoms, molecules, and condensed matter systems. In particular, in the latter case, photoemission studies clearly demonstrated the gradual movement to higher binding of different orbitals or bands as the periodic table was crossed. There was also an improved understanding of the photoemission process itself. For instance, the direct momentum or k-conserving transitions reflecting the electronic excitation was shown to be mediated by the crystal lattice momentum. The introduction of new light sources in the form of resonance lamps and synchrotron radiation sources extended the capabilities considerably. In the field of condensed matter, these developments enabled studies of not only the bulk electronic structure but also allowed refined studies of the unique electronic states existing at the surface of materials. The development of capabilities allowing the determination of the spin of electrons also enabled detailed studies of the electronic properties of magnetic systems, not only in the bulk and surface but also in thin films. Many of these developments have been discussed and documented in excellent reviews published elsewhere [92K1, 03H1]. In the present part, we will extend some of these earlier reports but also focus on developments that have taken place since the early 1990s. A major advance that came about in the mid-1990s was the introduction of new electron spectrometers that enabled the acquisition of information on the photoelectron for a range of energies and momenta simultaneously. With high resolution in both energy and momentum, this development has enabled detailed photoemission studies of the role of collective excitations in condensed matter systems. More recently still, new capabilities have been introduced into the field through the use of lasers for the generation of incident photon beams. Interestingly, this latter development takes the field right back into the photon energy ranges widely used in the 1960s. However, now with considerably better energy and momentum resolution. It is important to note that the latter improvements in resolution over the early days again essentially reflect the improvements in electron spectrometry. However, the use of lasers does lead to new possibilities in studies of the time structure of the photoemission process and also possibilities in studies using pump-probe technologies which we will explore later. Finally, we note that there has been a continued interest in the use of inverse photoemission as a probe of the unoccupied states. Because the cross section for this technique is much lower than the related photoelectron process, approximately 10 5 in the UV range [85J1] the capabilities are still not at the

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_89

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level required to examine collective phenomena. However, important insights are obtained on the unoccupied electron states that often complement studies of the occupied states. These studies will also be explored in the present part. We will not provide detailed descriptions of experimental instruments. These have often been reviewed in detail elsewhere. We will however discuss the results of experimental studies dealing in general with the period from about 1990 onward. There are many reviews of studies dating before that period, including an excellent review by Bradshaw and colleagues in this series. As noted earlier, since the mid-1990s, the field has been characterized by the introduction of new instrumentation [94M1] allowing for the possibility of detailed studies of a variety of self-energy effects reflecting many-body interactions. We firstly review our current understanding of the photoemission process and the methodology of its current application to the study of condensed matter systems, including studies of both the occupied and unoccupied states and including those in magnetic systems. The new results, with respect to the earlier data collection in this series (the early 1990s), include both higher-resolution studies of the occupied states and high-resolution studies of the unoccupied states, including image states with measurements of both their binding energies and their lifetimes. These new high-resolution studies often include observations relating to the coupling to collective excitations. The data sets are arranged as closely as possible to position in the periodic table. We provide a detailed overview of the application to surface electronic structure not only of electronic systems but also the more complex “quantum materials,” the latter being the subject of much current study. Here we are including the high Tc superconducting materials and the many different topological systems. However, note that the collection of data presented here is not exhaustive and often serves to point the reader to the original source for further information and direction.

References [85J1] [92K1] [94M1] [03H1]

Johnson, P.D., Davenport, J.W.: Phys. Rev. B. 31, 7521 (1985) Kevan, S.D. (ed.): Angle-Resolved Photoemission, Theory and Current Applications. Elsevier, Amsterdam (1992) Martensson, N., et al.: J. Electron. Spectrosc.Relat.Phenom.70, 117 (1994) Hufner, S.: Photoelectron Spectroscopy, 3rd edn. Springer, Berlin (2003)

Chapter 90

The photoemission process P. D. Johnson

At the simplest level, the photoexcitation process is described by the well-known energy conserving Einstein equation, namely Ef ¼ Ei þ ħω:

ð90:1Þ

That is, the energy of the photoelectron in the final state energy, Ef, is given by the energy Ei of the electron in the initial state plus the energy of the absorbed photon, ħω. This description captures the basic process as illustrated in Fig. 90.1.

Fig. 90.1 A schematic of the photoemission process. The incident photon with energy ħω excites an electron from an initial state below the Fermi level EF to some final state above the vacuum level Evac. The left panel shows the electron originating either from the valence band or the more localized core level. The right panel displays the excited electron energy distribution in the final state

On a more formal level, in the absence of spin-orbit coupling, it can be shown for linearly polarized incident light that the Schrodinger equation provides an adequate description of the spin-conserving transitions of the photoexcitation process. Thus from Fermi’s golden rule, the photocurrent per unit solid angle and per unit energy, J(k) reflecting excitation from some initial state |ψ i> to some final state |ψ f>, is given by [92I1]  pffiffiffiffiffi X    < ψ f A:p þ p:Ajjψ i >j2 δ Ef  Ei  ħω ð90:2Þ J ðkÞ / Ef where again the δ function describes the energy conservation implicit in Eq. 90.1, and the sum is overall possible excitations. In a many electron system with N electrons, the initial ground state |ψ i> is represented

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_90

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by |N, 0>. The final state |ψ f> is represented by |k; N  1, s> where now the excitation of a number of different final states |N  1, s> along with the photoexcited electron k are possible. Neglecting a diamagnetic term |A|2 which is always small at the photon energies typically used in photoemission studies and noting that ∇.A is nonzero only in the surface region, Eq. 90.2 is usually reduced to the simpler form X    < ψ f A:pjjψ i >j2 δ Ef  Ei  ħω : ð90:3Þ J ðkÞ / Not discussed further here, the matrix element in Eq. 90.3 introduces selection rules, which can be exploited to determine the symmetry of the initial state. To proceed further, one now makes the assumption of the sudden approximation. That is, one assumes that the photoexcitation process occurs on sufficiently fast timescales that one can neglect the relaxation processes associated with the formation of the photohole. It is then possible to show that the intensity I(k,ω) measured in the photoemission process is given by I ðk, ωÞ ¼ jMj2 Aðω, kÞf ðωÞRðω, kÞ

ð90:4Þ

where M now represents the matrix element contained in Eq. 90.3, f(ω) is the Fermi function because the photoemission process is restricted to excitation from occupied initial states, R(ω,k) is the experimental resolution function, and A(ω,k) is the single-particle spectral function [92I1]. The latter, which is different from the operator associated with the photon field, A, in Eq. 90.3, is related to the electron propagator or Green’s function, G(ω,k), by the expression Aðω; kÞ ¼

1 : πImGðω; kÞ

ð90:5Þ

In the independent electron case, G(ω,k) is given simply by 1/(ω  ε0). Collective excitations or many body interactions are accounted for through introduction of a self-energy term Σ such that the Green’s function evolves into Gðω; kÞ ¼

1 P : ω 2o ðkÞ  ðk; ωÞ

The single-particle spectral function then takes the form P 2 ðk; ωÞ Aðω; kÞ ¼  2 P 2 P ω  ε0  1 ðk; ωÞ þ 2 ðk; ωÞ

ð90:6Þ

ð90:7Þ

where the real part, ∑1(k, ω), gives a shift in energy and associated mass enhancement and the imaginary part, ∑2(k, ω), reflects the lifetime broadening h/τk associated with the excitation. We will return to a discussion of the interaction with collective excitations later. As described above, photoemission spectra have traditionally been recorded in the form of so-called energy distribution curves (EDC) whereby the intensity of photoelectrons is measured as a function of kinetic energy at constant momentum. With the introduction of more modern electron spectrometers that multiplex in energy and momentum, it became possible to also analyze the photoemitted intensity in momentum space. Thus, as shown in Fig. 90.2, instead of measuring the intensity of photoemitted electrons as a function of binding energy, it became possible to measure the intensity as a function of momentum at constant binding energy. The latter form of analysis is referred to as the momentum distribution curve (MDC) [99V2].

90

The photoemission process

3

200

Binding energy ω [meV]

100

0

–100

–200

–300 0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

Parallel wavevector k// [Å–1]

Fig. 90.2 Two-dimensional spectral plot showing the intensity of emission in the (π,π) direction of the Brillouin zone as a function of ω, the binding energy, and k||, the parallel momentum. The photon energy is 21.2 eV and the sample temperature is 48 K. Clockwise from the upper left, the insets show the region of the Brillouin zone sampled in the experiment, a cross section through the intensity at constant energy (ω ¼ 0) as a function of momentum (an MDC), and a cross section through the intensity at constant angle or momentum (k ¼ kF) as a function of ω (an EDC) (From 99 V2)

Consider Eq. 90.7. In momentum space the spectral response peaks with an intensity 1/Σ 2 at some momentum km such that ω ¼ ε0(km) + ∑1(km, ω). Assuming that in the vicinity of the Fermi level ε0(k) ¼ v0k, where v0 is the bare velocity and that Σ is momentum independent, it is a simple matter to show that at some small Δk away from km corresponding to the half width at half-max, Δk is given by Δk ¼ Σ 2/v0. Thus the FWHM, Δk, is given by Δk ¼

2Σ2 : v0

ð90:8Þ

Just as the EDC width is related to the inverse lifetime, the MDC width is related to the inverse mean free path, l. Noting that the measured or renormalized velocity v¼

vo ð1 þ λÞ

ð90:9Þ

where λ represents the coupling constant, the equivalent EDC has a width ΔE such that ΔE ¼ vΔk ¼

2Σ2 2Σ2 ¼ : 1 ð1 þ λÞ 1  dΣ dω

ð90:10Þ

If the real part of the self-energy displays no frequency dependence, the width ΔE is directly related to the scattering rate. Both EDCs and MDCs will have a Lorentzian line shape. However, this is no longer true if the real part of the self-energy is frequency dependent, and particularly in the vicinity of a mode, the width of the EDC, ΔE, will be strongly dependent on the renormalization of the velocity. This can result in the EDC having a complex two-peaked structure that is more difficult to interpret.

4

P. D. Johnson

We briefly return to a discussion of the experimental resolution function, R(ω,k) introduced in Eq. 90.4. This is a limitation that exists in every experiment, reflecting the physical properties of the electron spectrometer among other things. Although not discussed in detail here, we note that methods of analysis have been developed that allow for the minimization of the broadening effects associated with experimental resolution. In particular, we highlight the so-called Lucy-Richardson method which aside from approximating the resolution function in energy and momentum makes no further assumptions that might relate to the physics of the excitation process. Forgetting for now the matrix element which is just a constant with value depending on the symmetries, we look for an “inverse resolution” kernel Q(ω,k) such that Aðω; kÞ ¼ Aðω; kÞf ðωÞ ¼ I ðω; kÞQðω; kÞ:

ð90:11Þ

As discussed in reference [10R1], Q can be defined such that Qðω; kÞ ¼

Aðω; kÞ:Rðω; kÞ I 0 ðω; kÞ

ð90:12Þ

where I0 denotes the original spectrum as measured. An iteration procedure is used to find the most appropriate representation of the initial spectral function such that ZZ A: rþ1 ðω, kÞ I 0 ðω, kÞQr ðω, kÞdωdk: ð90:13Þ

References [92I1]

Inglesfield, J.E., Plummer, E.W.: Chapter 2. In: Kevan, S.D. (ed.) Angle-Resolved Photoemission, Theory and Current Applications. Elsevier, Amsterdam (1992) [99V2] Valla, T., Fedorov, A.V., Johnson, P.D., Wells, B.O., Hulbert, S.L., Li, Q., Gu, G.D., Koshizuka, N.: Science. 285, 2110 (1999) [10R1] Rameau, J.D., Yang, H.-B., Johnson, P.D.: J. Electron. Spectrosc. Relat. Phenom. 181, 35–43 (2010)

Chapter 91

Inverse photoemission P. D. Johnson

Inverse photoemission is a related technique that developed to allow studies of the unoccupied states in a system. It is usually considered as the time reversal of the photoemission process. Thus rather than an incident photon exciting an electron from a bound state, an incident electron is “captured” by a bound state resulting in the emission of a photon. Johnson and Davenport considered the differential cross section dσ/ dΩ for such an event. The density of final states for the emitted photons results in a differential cross section given by [85J1] dσ α ω 1 ¼ jhbjA:pjkij2 dΩ 2π mc2 k

ð91:1Þ

where the incident electron has momentum ħk and the outgoing photon energy ħω. Within the same framework with consideration of the density of final states for the outgoing electrons, Eq. 91.3 describing the photoemission process would be given by dσ α k 1 ¼ jhkjA:pjbij2 dΩ 2π m ω

ð91:2Þ

Thus for the same time-reversed transition, the ratio of the two cross sections will be given by R¼

ω2 q2 λelec 2 jdσ=dΩjinv ¼ 2 2 ¼ 2 ¼ λphot jdσ=dΩjpes c k k

ð91:3Þ

with q the wave vector of the photon. Thus in the UV range, with R proportional to the square of the wavelength of the incident “particle,” the cross section for inverse photoemission is lower than that of photoemission by a factor of approximately 105. This fact makes the experiment considerably more difficult, and as yet the ultrahigh resolutions available in photoemission have not been achieved in inverse photoemission.

References [85J1]

Johnson, P.D., Davenport, J.W.: Phys. Rev. B. 31, 7521 (1985)

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_91

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Chapter 92

Spin-polarized photoemission P. D. Johnson

We will make reference in this chapter to experiments using the technique of spin-polarized photoemission where the spin of the electron is measured as well as the energy and momentum. Again we will not provide any detailed description of experimental apparatus as these have been reviewed extensively elsewhere [97J1]. Suffice it to say that spin detection involves either measuring the spin asymmetry in the scattering of the photoemitted electrons from a ferromagnetic surface or the scattering of the electrons from heavy atoms using the spin-orbit interaction to distinguish the two spin states. Either way spin polarimeters are compared through their figure of merit (FOM) which is given by FOM ¼ S2

I I0

ð92:1Þ

where S, the Sherman function, is a measure of the ability of the device to distinguish different spins, I is the total scattered current collected by the device, and I0 is the incident current. The spin polarization of the incident beam P is given by P¼

1 IA  IB S IA þ IB

ð92:2Þ

where IA and IB are the currents measured in two opposite scattering channels. Having measured the polarization P, the individual spin-resolved spectra are obtained via the expressions I " ¼ I ð1 þ PÞ=2 and I # ¼ I ð1 þ PÞ=2

ð92:3Þ

As in the case of regular photoemission, the time reversal of this process allows for the investigation of the spin of unoccupied states. However, in such experiments the key requirement becomes the need for a spinpolarized electron source. Symbols and abbreviations Short form

Full form

FOM

figure of merit

References [97J1]

Johnson, P.D.: Rep. Prog. Phys. 60, 1217 (1997)

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_92

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Chapter 93

Two-photon photoemission P. D. Johnson

With the introduction of lasers into the field of photoemission, it has become possible to explore not only the occupied states but also the unoccupied states with high resolution. A number of variants have evolved with time, including the possibility of direct excitation from the valence bands with the UV light or pumpprobe experiments where the pump and probe can be at the same energy or different energies. Pump-probe experiments involve the introduction of some finite delay between the incident pump photons and the probe photons allowing the direct measurement of the lifetime of intermediate states above the chemical potential. Excitation is possible with UV light generated though higher harmonic generation in crystals or in gases. In the former case, third or fourth harmonic generation is used to provide the probe photon, which in the case of Ti-sapphire lasers would have an energy of 4.5 or 6 eV. With different lasers and crystals, 7 eV is also possible. Such sources can run at much higher rep rates into the Mhz range. In the case of generation in gases, it is possible to get to higher photon energies but normally at lower rep rates. The pump pulse is typically in the IR range. However as noted it is possible that the two photons have the same energy. In the latter case, a variety of excitation channels exist as indicated in Fig. 93.1. These include resonant and non-resonant photoemission and virtual state transitions.

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_93

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a b A

B

C

n=2 n=1

EV

c

4

3

4000 Electron Counts

Energy E –EF [eV]

5000

2 1

k||=0 Å–1 k||=–0.18

A Å–1

Cu(111) hν=4.29 eV

3000 2000

B

C

1000

EF

0 n=0

–1 –0.4 –0.2 0.0 0.2 0.4 Parallel wavevector k// [Å–1]

0 3.0

3.2

3.8 3.4 3.6 Kinetic Energy (eV)

4.0

4.2

Fig. 93.1 (a) Schemes of resonant and nonresonant photoemission channels of intermediate-state excitation observed in 2PPE for Cu(111): (A) resonant transition, (B) virtual-state transition, and (C) nonresonant indirect excitation. The shaded areas denote the bulk band projection along the – direction for Cu(111). The solid curves inside the dashed box above the vacuum level EV reflect the measured 2PPE final-state kinetic energies. (b) A zoom-in of the dashed box. (c) EDCs from Cu(111) with hν ¼ 4.29 eV, which provides representative near-resonant and off-resonant conditions. Spectra are shown for k|| ¼ 0.018 Å1 (squares), which corresponds to resonant-photoemission channel A yielding a single peak, and k|| ¼ 0 Å1 (circles), which corresponds to nonresonant photoemission channels B and C yielding two peaks; note that the corresponding C channel shown in (b) is slightly displaced from k|| ¼ 0.0 to distinguish between processes B and C (From 12Y1)

Symbols and abbreviations Short form

Full form

EDC PPE

energy distribution curve two-photon photoemission spectroscopy

References [12Y1] Yilmaz M. B. et al., J. Vac. Sci. Tech A 30, 041403 (2012)

Chapter 94

Core-level excitation and related resonant phenomena P. D. Johnson

At higher photon energies, it becomes possible to excite electrons from the more localized core levels into the continuum. Such studies are capable of providing more “localized” on-site information. The spectrum associated with core-level excitation may well contain several satellite peaks accompanying the mainline. The satellites represent different valence band configurations in the final state. R An important observation is that the summed intensities over the main line and satellites are such that A(w)dw ¼ 1. In the event that the incident photon or excitation energy is close to or at the core-level binding energy, an absorption edge, a number of resonant phenomena become possible. These include both resonant photoemission and resonant inelastic X-ray emission or scattering (RIXS). In the former case, the excited intermediate state decays via an Auger-like or autoionization transition such that an electron is excited from the valence band to a final state coincident with the direct photoemission process. In the case of RIXS, the excited intermediate state decays via a radiative photon-emitting process. We can write down the transition operator from initial state | i > to final state | f > for the two different deexcitation mechanisms and see how they compare. The initial state | i > represents the same N electron valence state plus core level in both cases. In the case of resonant photoemission, the final state is represented by the (N-1) valence state and a free photoelectron. In the case of RIXS, the final state represents the N electron valence state plus an emitted photon. e From our earlier discussion, we know that the dipole operator Hint takes the form H int ¼ mc A:p: Thus in the case of resonant photoemission, the transition operator Tif within the matrix element is given by T if ¼ H int þ H A

X mE

jmihmj Hint m  Ei  hv  Γm =2

ð94:1Þ

where Em and Γm represent the energy and lifetime of the intermediate state |m>. HA represents the operator associated with the Auger process and is given by e2/r12. The interference between the direct and resonant channels evident in the transition operator for resonant photoemission results in a characteristic Fano line shape in the cross section for the process. For RIXS the transition operator, Tif, is given by [94J1] T if ¼ H int

X mE

jmihmj Hint  E m i  hv  Γm =2

ð94:2Þ

where the notation carries the same meaning although note that the emitted photon does not necessarily have the same energy as the incident photon (hence the “inelastic”) and the intermediate state |m > does not have the same form, reflecting the different participation of the valence electrons.

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_94

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Symbols and abbreviations Short form

Full form

RIXS

resonant inelastic X-ray emission or scattering

References [94J1]

Johnson, P.D., Ma, Y.: Phys. Rev. B. 49, 5024 (1994)

Chapter 95

Escape depth of the photoelectrons P. D. Johnson

Here we briefly comment on the surface sensitivity of photoemission in general. The surface sensitivity derives from the low escape depth of elastically scattered electrons with kinetic energies in the range 10–1000 eV. The mean free path for inelastic scattering shows in fact a kinetic energy dependence (Fig. 95.1) with a minimum of about 5–10 Å at approximately 50 eV [79Sl]. This surface sensitivity can be enhanced by changing the emission angle or by varying the photon energy. Similar considerations apply to inverse photoemission where the high surface sensitivity is determined by the low penetration depth of the incoming electrons. 6.102 nm

102

Mean free path λ [nm]

10

1

10–1 1

10 102 Energy E (eV)

103

eV 104

Fig. 95.1 The inelastic mean free path for electrons in a material. The data points are taken from measurements on different solids. The curve is the result of a leastsquares fit to the empirical function λ ¼ A/E2 +BE1/2, where the electron energy E is Ekin, measured relative to the Fermi level [79Sl]

This limitation on the escape depth associated with UV excitation has promoted two new avenues of research in photoemission, notably the use of lasers where the excitation energy is lower, taking the

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_95

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experimental range to the left-hand side of Fig. 95.1 and photoemission at very high energies where it is hoped that the escape depth will increase as indicated on the right-hand side. Symbols and abbreviations Short form

Full form

UV

ultraviolet

References [79Sl]

Seah, M.P., Dench, W.: J. Surf. Interf. Anal. 1, l (1979)

Chapter 96

Electronic structure in the surface region: bulk and surface states P. D. Johnson

This chapter is primarily a review of photoemission studies of the two-dimensional electronic structure found in the surface region of condensed matter systems. However before discussing surface electron states, it is appropriate to review the photoemission process associated with the bulk electronic structure. It is now well established that photoexcitation from a bulk state represents a direct transition with momentum conservation mediated through the intervention of the crystal momentum such that kf ¼ ki þ G

ð96:1Þ

where ki and kf are the wave vectors associated with the initial and final states and G represents a suitable lattice vector. The nearly free electron model of the electronic structure provides an excellent basis for our discussion. Consider initial and final states defined by the wave functions exp[ik.r] and exp[i(k+G).r], respectively. The allowed energies available to these states are given by the solution of the equation:



ℏ2 k 2

E VG


¼0
2m ð96:2Þ 2 2

ℏ ðk þ G Þ
V  E


G 2m where again G is the bulk reciprocal lattice vector and VG is the associated Fourier component of the pseudopotential. At the zone boundary, G/2, a bandgap is opened up with width 2VG as shown in Fig. 96.1. The solutions to Eq. 96.2 are given by Energy E

Q’ Δ Bandgap Δ = 2VG P’

−P /a

F.E.

Periodic Q V(x )

V=const P

Wavevector k || [Å–1]

kx kx =P /a

Fig. 96.1 Schematic of the electronic band structure associated with a periodic potential showing the opening of a bandgap of magnitude 2Vg at the zone boundaries given by k ¼  π/a

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_96

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 1 E ¼ ε0k þ ε0kþG  2

" #1=2 2 ε0k  ε0kþG 2 þ jV G j 2

ð96:3Þ

Figure 96.1 shows the two-band nearly free electron dispersion defined by Eq. 96.2. However the direct k-conserving transitions are better demonstrated in the reduced zone scheme shown in Fig. 96.2. Here the direct transitions between the initial state ji> and final state jf> are also shown as spin-conserving transitions. By measuring the photoemitted current as a function of photon energy, it becomes possible to map the dispersion of different initial states or the “band structure” of a solid. Energy E

min. maj.

⎮f >

Ef ↓ Ef ↑

ћω EV

EF ⎮i > Wavevector k

Ei↓ Ei ↑

Fig. 96.2 A schematic of the direct k-conserving transition in the photoemission process. The incident photon excites an electron from an initial state Ei below the Fermi level EF to some final state Ef above the vacuum level EV. Spin conservation is maintained in the transition

Within the band gaps associated with the bulk bands, there is the possibility of electronic states that are localized within the surface region and indeed in any photoemission experiment the incoming photons will excite electrons from both the bulk states and the surface states. The surface states are usually distinguished in two ways, either through their lack of a kz dependence, that is, their dependence on the incident photon energy, or through adsorption studies. In the latter case, if a given state is affected through adsorption of impurity atoms, it is usually taken as an indication that the state is localized in the surface region. Shockley was one of the first to consider the possibility of surface states [39S1]. If the VG shown in Fig. 96.1 is negative, corresponding to the electrons experiencing an attractive potential in the vicinity of each atom, the wave functions at the gap edges are found to be p-like at point P and s-like at point Q. In an analysis of wave function matching at the solid-vacuum interface, defined to be one half lattice spacing beyond the center of the last row of atoms, Shockley found that such an inverted gap was a necessary condition for the existence of surface states within the gap. Goodwin was the first to derive the wave function of the surface state existing in such a gap [39G1]. Such states carry momentum in the complex plane such that k ¼ p + iq. The corresponding wave function is then given by Ψ ¼ eqz cos ðpz þ δÞ

ð96:4Þ

and the state is localized in the surface region with q describing the decay away from the surface. The phase shift δ in Eq. 96.4 is given by

96

Electronic structure in the surface region: bulk and surface states

3



ℏ2

2pq

sin ð2δÞ ¼ 
: 2m V g


ð96:5Þ

Varying the incident photon energy is a relatively straightforward way of identifying the dimensionality of a state. A state that is delocalized in real space, such as a bulk band, is localized in momentum space, and thus as noted above, a transition from an initial state is observed at some well-defined momentum reflecting a direct transition at that photon energy. However a two-dimensional state, such as a surface state, that is localized in real space is effectively delocalized in momentum space and is observed at all photon energies as shown in Fig. 96.3. In fact in the case of a surface state, there will be an intensity variation as a function of photon energy that reflects the degree of localization in the surface region as indicated in Fig. 96.3 (right panel) [80L1].

normal emission 70° e– S3

ћw S1(eV) =

ћw =30

50

70

90

110 eV

32 s,p S1

:theory :experiment

Photoemission intensity I

s,p

c1= 1.8

49

a G

ћw =30

G 50

70

90

110 eV

70 S3 c3= 1.6

b

82 G

L

G

Wavevector K  [2P/a] 100 10

8

6

4

2 Ef 0

binding energy [eV]

Fig. 96.3 Left panel Photoemission spectra recorded from a Cu(111) surface as a function of photon energy as indicated. The spectra include emission from two surface states S1 and S2. Right panel Intensity of emission from the two surface states as a function of k⊥or photon energy (From [80L1])

The parallel momentum k|| of the outgoing photoelectron

4

P. D. Johnson

kjj ¼

 1=2 2m E1=2 sinθ ℏ2

ð96:6Þ

is conserved on crossing the solid-vacuum interface. A measurement of the parallel momentum in the vacuum therefore provides a good measure of the parallel momentum of the initial electron state within the solid, ideal for mapping the dispersion of two-dimensional states. An example is shown in Fig. 96.4 where we show the results of a high-resolution study by Reinert et al. of the dispersion of the surface state at the center of the zone on the Cu(111) surface [01R1]. Using a least-squares fit analysis, the authors were able to extract three parameters, the maximum binding energy E0 ¼ 435 meV, the c, m* ¼ 0.412, and the Fermi vector kf ¼ 0.215 Å. high 0

200 intensity

300 400 500

binding energy [meV]

binding energy [meV]

100

600

–6

–4

4 –2 0 2 angle off normal [°]

6

low

700 –0.2

–0.1

–0.0

–0.1

0.2

momentum [Å–1]

Fig. 96.4 Measured dispersion of the Cu(111) surface state existing in the band gap at the center of the zone in the ΓL direction. The left panel shows the dispersion measured in a modern analyzer and presented on a logarithmic intensity scale; the right panel shows a more traditional presentation showing the positions of maximum intensity in the left panel and indicating the bulk band edges. The crossing of the Fermi level at θ ¼ 5.85 is equivalent to Fermi vectors at kF ¼ 0.215 Å (From [01R1])

The Cu (111) surface state, shown in Fig. 96.4, [01R1] is probably one of the most well-characterized two-dimensional surface states. Aside from numerous photoemission studies, its dispersion above the Fermi level has also been studied using the technique, inverse photoemission [85H1]. Results of such studies are presented in Fig. 96.5 where we show spectra recorded as a function of the angle of incidence of the electron beam. In the figure transitions are indicated not only into both bulk bands (BB) and surface states (SS) but also into another class of surface state, the image state (IS). The latter states, first predicted by Echenique and Pendry [78E1] and first observed by Johnson and Smith [83J1], are discussed in more detail in the next part.

96

Electronic structure in the surface region: bulk and surface states

5

q =+59°

+54° BB +49°

INTENSITY (arb. units)

+44

+29 +24

+19 IS SS

+14 +9 +4

–1

–1 EV EF 1 2 3 4 5 ENERGY ABOVE EF (eV)

Fig. 96.5 Inverse photoemission spectra recorded from a Cu(111) surface as a function of angle of incidence of the electron beam. BB represents an unoccupied bulk band. SS a Shockley surface state and IS an image state (From [85H1])

Before discussing surface and image states in more detail, we make one further observation with respect to photoemission from two-dimensional systems. The photoexcitation process results in a spectrum showing peaks with finite widths. The latter can reflect both the lifetime of the photohole and the lifetimes associated with scattering events experienced by the outgoing photoelectron. Thus the total width Γ is given by [93S1]
  

vh vh

1
Γ ¼ Γh þ Γe
1  v
ve e

ð96:7Þ

where Γh is the width of the hole state, Γe the width of the excited electron state, and vh and ve are the respective perpendicular velocities. In a two-dimensional system with vh ¼ 0, the width of the photoemission peak is determined entirely by the inverse lifetime of photohole Γh as can be seen from Eq. 96.7. Symbols and abbreviations Short form

Full form

SS BB IS

surface state bulk band image-potential states

6

P. D. Johnson

References [39G1] [39S1] [78E1] [80L1] [83J1] [85H1] [93S1] [01R1]

Goodwin, E.T.: Proc. Camb. Philol. Soc. 35, 205 (1939) Schockley, W.: Phys. Rev. 56, 317 (1939) Echenique, P.M., Pendry, J.B.: J. Phys. C. 11, 2065 (1978) Louie, S.G., Thiry, P., Pinchaux, R., Petroff, Y., Chandesris, D., Lecante, J.: Phys. Rev. Lett. 44, 549 (1980) Johnson, P.D., Smith, N.V.: Phys. Rev. B. 27, 2527 (1983) Hulbert, S.L., Johnson, P.D., Stoffel, N.G., Royer, W.A., Smith, N.V.: Phys. Rev. B. 31, 6815 (1985) Smith, N.V., Thiry, P., Petroff, Y.: Phys. Rev. B. 47, 15476 (1993) Reinert, F., Nicolay, G., Schmidt, S., Ehm, D., Hufner, S.: Phys. Rev. B. 63, 115415 (2001)

Chapter 97

Electronic structure in the surface region: Shockley surface states and image states P. D. Johnson

Here we provide a more detailed discussion of the electronic states localized in the surface region. We outline the development of a notation labeling the different states because it informs our presentation of the experimental results, particularly when discussing studies of the unoccupied states probed either by two-photon photoemission or inverse photoemission. A significant contribution to our understanding of surface states came with inverse photoemission studies (IPES) of unoccupied states in the early 1980s. In particular, Johnson and Smith [83J1], followed by others [84Dl, 84S2], demonstrated that IPES is capable of observing a particular class of surface state derived from the long-range image potential. These states are generally referred to as image states. The experimental observation confirmed the earlier theoretical prediction of such states by Echenique and Pendry [78El]. Following these early studies, a further development came with the observation that the Rydberg series of image states display binding energies dependent on the particular crystallographic plane [85Hl]. Based on this observation, it was shown that a simple one-dimensional potential model, the multiple reflection or phase model, could be used to predict the binding energies of these states and further that the same Bohr-Sommerfeld-type model provided the link between the image states and the Shockley or crystal-derived surface states. An electron located outside of a substrate of dielectric constant ε experiences a potential: V ðzÞ ¼

e2 ððε  1ÞÞ=ðε þ 1Þ 4z

ð97:1Þ

where z is the distance from the surface. This one-dimensional potential is hydrogenic in form, and the solution of Schr€ odinger’s equation yields an infinite series of states converging on the vacuum level. For an infinitely repulsive metal surface (ε ¼ 0), the binding energies Eb of this series have the form Eb ¼

0:85 eV n ¼ 1, 2, 3 n2

ð97:2Þ

However, if the condition of infinite repulsion is relaxed, wave function penetration of the substrate may be accounted for through the introduction of a “quantum defect” parameter a. Thus,

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_97

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P. D. Johnson

Eb ¼

0:85 eV ð n þ aÞ 2

ð97:3Þ

If the reflectivity of the electron wave at the substrate is described by a phase change øc then for the limited energy range of the Rydberg series (Eq. 97.2), the quantum defect parameter may be written [79M2]:
 1 ϕc 1 a¼ 2 π

ð97:4Þ

Given that ϕc changes from 0 to π on crossing the “Shockley inverted” bandgap, it may be anticipated from Eqs. 97.3 and 97.4 that the binding energy of the image states will reflect the position of the vacuum level within the gap. It was the observation of this phenomena in a comparison of the n ¼ 1 image states on the Cu (001) and Cu (111) surfaces [85Hl] that lead to a more detailed examination of the multiple reflection model of surface states [78El, 79M2]. As noted, in this model the electrons are considered to be trapped in the surface region through multiple reflections between the crystal barrier on the one hand and the surface barrier due to the image potential on the other. Using a scattering formulation, Echenique and Pendry [78El] demonstrated that the bound states or surface states would be given by singularities in the function: Ψþ ¼

1 1  r c r b eiðϕc þϕb Þ

ð97:5Þ

where r c eiϕc and r b eiϕcb are the reflectivities from the crystal and image barrier, respectively. If one assumes that rc ¼ rb ¼ 1, then the requirement of a singularity in ψ + leads to the quantization condition for the existence of surface states: ϕc þ ϕb ¼ 2πn

ð97:6Þ

A quantitative description of the different phases in Eq. 97.6 is presented elsewhere. Here we simply show in Fig. 97.1 the result of applying the quantization condition, Eq. 97.6, to the copper (001) and (111) [85Hl]. Not only is good agreement found for the binding energies of the image states, but the figure shows that the condition n ¼ 0 gives an excellent prediction for the binding energy of the Shockley-type surface state at the bottom of the (111) bandgap [83K1, 01R1] and also a surface resonance on the (001) surface [85W2]. This was an important observation and immediately pointed to the practicality of the BohrSommerfeld description of surface states.

97

Electronic structure in the surface region: Shockley surface states and image states

a

P

0

2P

3

3P

6 VACUUM LEVEL 4

L1

IS (n=1)

fB f

2 fC

FERMI LEVEL

ELECTRON ENERGY (eV)

0 L2⬘

SS

Cu (111)

–2

b 8

Cu (001)

X1 fC

6

VACUUM LEVEL 4

2

fB

X4⬘

f

IS (n=1)

SR FERMI LEVEL

0 0

P PHASE

2P

3P

Fig. 97.1 Energy variation of the phases ϕc, ϕb, and ϕ ¼ ϕ + ϕb showing the n ¼ 1 image-potential states (IS) and (a) the “n ¼ 0” crystal-induced state (SS) for Cu(111), (b) the proposed “n ¼ 0” surface resonance (SR) for Cu(001) (From [85Hl])

Simple one-dimensional models of the crystal-derived or Shockley states have traditionally employed a step potential at the termination of the crystal. Using wave function matching with appropriate Whittaker functions describing the electron states in the image region, Weinert et al. [85W1] rederived the results of the multiple reflection model and from the form of the wave functions concluded that the quantum number n of the particular state is simply related to the number of extrema in the wave function beyond the crystal boundary, Fig. 97.1. Thus the one-dimensional potential running perpendicular to the surface supports an infinite series of states in an identical fashion to the coulombic potential of the hydrogen atom. However for the latter coulombic potential, n ¼ 0 represents a nonphysical solution, the wave function having a singularity at the origin. The image potential on the other hand saturates in the surface region (see unit 12) allowing a n ¼ 0 lowest-order solution which in the limit has an identical form to the wave function appropriate to the step potential. The step potential may therefore be viewed as a screened image potential, and as with any short-range potential, the number of allowed states is finite (Fig. 97.2).

4

P. D. Johnson Cu (111) .15 n=1

density [a.u.]

.10 .05 0. .15

n=0

.10 .05 0. –60

–40

0

–20

20

Distance from the surface z [a.u.]

Fig. 97.2 Calculated charge densities of the n ¼ 0 surface state and the n ¼ 1 image state for Cu(111) (From Ref. [85W1])

Rhie and coworkers have provided an excellent analysis of the lifetimes of the lowest n ¼ 1 image states as studied by two-photon photoemission [03R1]. In the latter study it was shown that the inverse lifetime of an image state is given by 1=τ ¼ ð2π=ℏÞM2 S

ð97:7Þ

where M represents a transition matrix element and S given by ZE S¼

Z0 dε

EF ¼0

  0  0 0 dE ρðE  εÞρ E ρ E þ ε

ð97:8Þ

ε

describes the phase space available for the inelastic scattering processes. Smith and coworkers produced a table showing the measured and calculated lifetimes of image states on face-centered cubic metal surfaces, the penetration length z0, and the phase space parameter S. We reproduce the table below. The penetration length, z0, is given by h 1=2   i12 z0 ¼ d 4Eg E=V 2 þ 1  Eg þ E =V

ð97:9Þ

where d ¼ [2mV/ℏ2]1/2, E the energy of the image state, 2 V width of the bandgap, and Eg the energy at the middle of the bandgap (Table 97.1). Table 97.1 Lifetime τ, penetration length z0, and phase space parameter S, for the lowest energy image states on facecentered cubic metal surfaces (From [03R1]) Surface

τ (fs)

z0 (Å)

S (102 eV1)

Cu(100) Theory Cu(111) Theory Ag(100)

40  6 30 18  5 17.5 55  5

5.08

13.9

23.9

14.0

6.72

8.6 (continued)

97

Electronic structure in the surface region: Shockley surface states and image states

5

Table 97.1 (continued) Surface Theory Ag(111) Theory Pd(111) Theory Pt(111) Theory Ni(100) Ni(111)

τ (fs) 26.5 30  6 6 25  4 22 26  7 29 16  5 13  5

z0 (Å)

S (102 eV1)

21.2

7.6

4.68

76.4

8.55

70.5

4.50 5.17

155.9 155.3

In a series of papers, N.V. Smith and coworkers [85S1, 86G1, 87C1, 88S2] applied the phase model to a number of zone boundary surface states. Within the NFE model, the wave function inside the crystal for zone boundary states must now be described by four plane waves rather than two. The electron waves again make multiple reflections between the crystal potential and the one-dimensional image potential. In each complete cycle, the surface barrier is approached twice and the quantization condition gives 2ϕC þ ϕb1 þ ϕb2 ¼ 2πn

ð97:10Þ

If h ϕbi is written as the average phase change on reflection from the surface barrier, then ϕC þ ϕb ¼ πn

ð97:11Þ

showing that now the number of surface state solutions has doubled. The wave functions within the crystal may be expressed as even and odd combinations of the plane waves; thus,   Ψ þ ¼ eqz cos gk r k cos ðpz þ δÞ and   Ψ  ¼ eqz sin gk r k sin ðpz þ δÞ

ð97:12Þ

where at the boundary of the surface Brillouin zone k|| ¼ g||/2 and p, q, and δ carry the same meaning as in Eq. 96.4. A complete analysis including detailed derivations of these different parameters has been presented by Chen and Smith [87C1]. Symbols and abbreviations Short form

Full form

IPES SR SS IS NFE

inverse photoemission studies surface resonance surface state image-potential states nearly free electron

References [78El] Echenique, P.M., Pendry, J.B.: J. Phys. C. 11, 2065 (1978) [79M2] Mcrae, E.G.: Rev. Mod. Phys. 51, 351 (1979) [83J1] Johnson, P.D., Smith, N.V.: Phys. Rev. B. 27, 2527 (1983)

6

[83K1] [84Dl] [84S2] [85Hl] [85S1] [85W1] [85W2] [86G1] [87C1] [88S2] [01R1] [03R1]

P. D. Johnson

Kevan, S.D.: Phys. Rev. Lett. 50, 526 (1983) Dose, V., Altmann, W., Goldmann, A., Kolac, U., Rogozik, J.: Phys. Rev. Lett. 52, 1919 (1984) Straub, D., Himpsel, F.J.: Phys. Rev. Lett. 52, 1922 (1984) Hulbert, S.L., Johnson, P.D., Stoffel, N.G., Royer, W.A., Smith, N.V.: Phys. Rev. B. 31, 6815 (1985) Smith, N.V.: Phys. Rev. B. 32, 3549 (1985) Weinert, M., Hulbert, S.L., Johnson, P.D.: Phys. Rev. Lett. 55, 2055 (1985) Woodruff, D.P., Hulbert, S.L., Johnson, P.D., Smith, N.V.: Phys. Rev. B. 31, 4046 (1985) Garrett, R.F., Smith, N.V.: Phys. Rev. B. 33, 3549 (1986) Chen, C.T., Smith, N.V.: Phys. Rev. B. 35, 5407 (1987) Smith, N.V., Chen, C.T., Tranquada, J.M., Johnson, P.D.: Phys. Rev. B. 38, 12259 (1988) Reinert, F., Nicolay, G., Schmidt, S., Ehm, D., Hufner, S.: Phys. Rev. B. 63, 115415 (2001) Rhie, H.S., Link, S., Durr, H.A., Eberhardt, W., Smith, N.V.: Phys. Rev. B. 68, 33410 (2003)

Chapter 98

Electronic structure in the surface region: the Rashba effect and surface states P. D. Johnson

The spin-orbit interaction has recently been the source of considerable interest in ARPES studies of surface states. Indeed, this relativistic effect describing the coupling between the spin of the electron and its orbital component manifests itself in two distinct areas; the Rashba effect observed primarily via a lifting of the spin degeneracy in, for instance, the Shockley states observed on the noble metal surfaces and the metallic states observed on the surface of the Topological Insulators to be discussed later. Here we will show examples of the Rashba effect first observed in studies of the Au(111) surface. The Hamiltonian of an electron with spin-orbit coupling in a potential V(r) is given by H¼

p2 ℏ þ V þ 2 2 ð∇VxpÞ:σ 4m c 2m

ð98:1Þ

where σ is the spin operator and p the momentum operator. At the surface of a crystal, the gradient in the surface potential, ∇V, results in eigenvalues associated with the Hamiltonian H taking the values E ¼

ℏ2 k2k 2m

 γ so k2k

ð98:2Þ

where the parameter γ so is related to the derivative of V and determines the strength of the Rashba spin-orbit interaction. In effect the interaction results in two distinct parabolas with different spin polarizations displaced in momentum space. The observation of this phenomenon was first made by Jensen and coworkers in a study of Au(111) [96L1]. The results of that early study are shown in Fig. 98.1. As suggested in Eq. 98.1, the spin-orbit interaction has a strong dependence on the magnitude of the atomic scattering potential and hence ∇V. As such we may anticipate that any effect due to this interaction will be stronger in Au than the other noble metals. The atomic spin-orbit splitting in Ag is only smaller than that in Au by a factor of four. However, the spin-orbit splitting in the L-gap surface state of Ag(111) has proven difficult to observe, presumably because the latter state is so close to the Fermi level, even at the center of the zone. The Rashba effect in Cu (111) has only recently been observed in laser-based photoemission studies [13T1].

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_98

1

2

P. D. Johnson

EF

0

Binding Energy (eV)

110meV –0.1

–0.2

–0.3

–0.4 –0.2

–0.1

0

0.1

Parallel wavevector k // [Å-1]

0.2

Fig. 98.1 The two parabolas associated with the Rashba splitting of the surface state at the center of the zone on the Au(111) surface. The measured data points indicated by open circles and triangles are determined from the data shown in Fig. 2 of reference [96L1]

Symbols and abbreviations Short form

Full form

ARPES

angle-resolved photoelectron spectroscopy

References [96L1] LaShell, S., McDougall, B.A., Jensen, E.A.: Phys. Rev. Lett. 77, 3419 (1996) [13T1] Tamai, A., Meevasana, W., King, P.D.C., Nicholson, C.W., de la Torre, A., Rozbicki, E., Baumberger, F.: Phys. Rev. B. 87, 075113 (2013)

Chapter 99

Electronic structure in the surface region: quantum well states P. D. Johnson

The phase analysis approach applied to surface states has also been applied to the description of the quantum well states found in thin film overlayers and multilayers. As in any one-dimensional quantum well, the binding energies of the confined electron states reflect the width of the well. Quantization effects have long been studied in semiconductor heterostructures [91W1]. They have also been extensively studied in thin metallic films [88M1, 87L1, 88L1]. Interestingly the same model that has been shown to be so very effective in describing the properties of surface states can also be applied to the properties of the quantum well states that are observed in thin films or multilayers. In fact quantum well states in thin films might well be considered as a form of nanoengineered surface state. To quantify the electronic structure associated with the quantum well state in a thin film, we simply recognize that the wavefunction has to be cognizant of the underlying atomic structure. Thus, the quantization condition of Eq. 97.6 [https://doi.org/10.1007/978-3-662-53908-8_97] now becomes ϕc þ 2kma þ ϕb ¼ 2πn

ð99:1Þ

where m represents the number of layers in the thin film, a the interlayer spacing, and k the wavevector associated with the nearly free electron moving through the film [94S1]. Here 2kma represents the phase change accumulated on the round trip across the well. This description has been applied in studies of noble metal films deposited on noble metal substrates where the potential well is defined by the bandstructure offset of the two metals involved. As an example, Miller and co-workers [88M1] have studied the quantization of the Ag sp-band in Ag films deposited on an Au(111) substrate. Here the potential barrier was provided by an offset of 1 eV between the L4 critical points for the Au and Ag. Lindgren and Wallden [87L1, 88L1] have applied a similar model to the study of alkali metal films deposited on a Cu(111) substrate. Quantum well states in a noble metal thin film deposited on a ferromagnetic substrate were first observed in silver films deposited on an Fe(001) substrate [91B1]. In the limit of a single monolayer, the quantum well state can clearly be considered as an interface state. Shown later, as the films become thicker than one monolayer, the photoemission studies show that the interface state evolves into a series of states that move up to and through the Fermi level. The movement to lower binding energy simply reflects the fact that with each new layer the wavefunction describing the quantum well state has to gain an extra half-wavelength to accommodate the new atomic potential [94S1]. Thus, the quantization condition of Eq. 97.9[https://doi.org/ 10.1007/978-3-662-53908-8_97] becomes ϕc þ 2ðk þ ΔkÞðm þ 1Þa þ ϕb ¼ 2ðn þ 1Þπ

ð99:2Þ

Smith et al. [94S1] applied Eq. 99.2 to the study of Ag thin films deposited a Fe(001) substrate. From the graphical solutions for the electron energies, Fig. 99.1, the authors concluded that the appropriate quantum P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_99

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P. D. Johnson

numbers for classifying the quantum well states are not n, the number of nodes, or m, the number of layers, but rather v ¼ m – n. Examination of the figure shows the states moving up to and through the Fermi level as the films thickness increases. It is a relatively simple matter to show that the Fermi surface is sampled every Δm layers such that Δm ¼ ð1  kF =kBZ Þ1

ð42Þ

where kF represents the Fermi wavevector. Experimental measurements of the same system as the overlayer becomes thicker are shown in Fig. 99.2.

2

n=

0

3

4

5

6

7

8

9

10 11

12 X4’ EU

ν= 0

1 E-EF (eV)

2

1

0

EF

1 2

–1

3

4

–2 –3 m=0 1 2

EL

3 4 5 6 7 8 9 10 1112 13 14 15

Ag Layers on Fe (001) (minority spin)

–4 –5

Γ1 0

2

4

6 Phase/2π

8

10

12

Fig. 99.1 Graphical solutions ( full circles) for the energies of quantum well states of Ag overlayers on Fe(001) using the phase accumulation model. Full bold curves represent the phase 2πn –ϕC ϕB and dashed curves represent the quantum well phase accumulation m2ka. States characterized by the quantum number v ¼ (m – n) are connected by the full thin curves (From [94S1])

99

Electronic structure in the surface region: quantum well states

Ag/Fe(100) hν = 16 eV

3

Thickness (ML) 119

Photoemission Intensity (arb. units)

95 71 57 42.5 42 48 27.5

14

12 2

0 1 Binding Energy (eV)

Fig. 99.2 Normal emission spectra (dots) for Ag on Fe(100) at various coverages. Also shown are the fits and background functions (curves) (From Paggel [99P1])

References [87L1] [88L1] [88M1] [91B1] [91W1] [94S1] [99P1]

Lindgren, S.A., Wallden, L.: Phys. Rev. Lett. 59, 3003 (1987) Lindgren, S.A., Wallden, L.: Phys. Rev. B. 38, 3060 (1988) Miller, T., Samsavar, A., Franklin, G.E., Chiang, T.C.: Phys. Rev. Lett. 61, 1404 (1988) Brookes, N.B., Chang, Y., Johnson, P.D.: Phys. Rev. Lett. 67, 354 (1991) Weisbuch, C.: Onde Electronique. 71, 42 (1991) Smith, N.V., Brookes, N.B., Chang, Y., Johnson, P.D.: Phys. Rev. B. 49, 332 (1994) Paggel, J.J., Miller, T., Chiang, T.C.: Science. 283, 1709 (1999)

Chapter 100

Electronic structure in the surface region: electron-boson coupling in metallic systems P. D. Johnson

Finally before presenting detailed data sets we focus in this chapter on the physics behind photoemission studies that reveal the interaction of the electrons with collective excitations in condensed matter systems. The process of coupling is illustrated in Fig. 100.1 where we consider coupling to a mode described in this case by an Eliashberg function, α2F. Here α2F represents the product of the density of states of the relevant excitation and a matrix element reflecting the coupling strength [81G1]. For the present purposes, α2F in Fig. 100.1a is simply represented by a single Gaussian peak at energy ωo. Coupling to such a mode (at T ¼ 0) will result in a broadened step function in the scattering rate or imaginary part of the self-energy, Σ 2. The step function reflects the observation that when the photo-hole has enough energy to create the mode (ω  ωo), scattering from the mode opens up a new decay channel, thereby shortening the lifetime. The real and imaginary parts of the self-energy are related via causality through a Kramers-Kronig transform. Thus the step function in Σ 2 results in a cusp function for Σ1 (panel (c)). Such an energy dependence of the self-energy affects the measured spectra in two ways. Above and below the mode energy there will be a noticeable change in the spectral function as illustrated in panel (d). Secondly, as noted above, the measured dispersion will again be given by ε0(k) + Σ 1(k, ω). Thus with Σ1 taking the form shown in panel (c), the dispersion will display the mass enhancement observed immediately below the Fermi level as presented in Fig. 100.1e. w0

a α2F

e ω w0

Im∑∼Γ

Energy w

b

c Re∑

d

A(K,ω)

K ω

Distance from the surface

Fig. 100.1 An electron scattering from a mode with α2F as in (a) will experience a step function at the mode energy in the imaginary component of its self-energy, ImΣ or Σ2 as in panel (b). A Kramers-Kronig transform of Σ 2 will produce a cusp in the real part of the self-energy. ReΣ or Σ1 as shown in panel (c). The Σ 2 in panel (b) results in a spectral function having the form shown in panel (d) above and below the mode energy. Panel (e) shows the mass renormalization in the immediate vicinity of EF

P. D. Johnson (*) Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY, USA e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_100

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More formally in the case of electron-phonon coupling, the contribution, Γe-ph, to the total scattering rate may be calculated via the Eliashberg equation such that [90M1] Z1 Γeph ðω; T Þ ¼ 2πℏ

 0   0 i h  0  2  0α 0 dω F ω 2n ω þ f ω þ ω þ ω  ω

ð100:1Þ

0

where again α2F is the Eliashberg coupling constant and f(ω) and n(ω) are the Fermi and Bose-Einstein functions, respectively. Γe  ph increases monotonically with energy up to some cut-off defined by the Debye energy. At T ¼ 0 the electron-phonon coupling, constant is given by [81G1] Z1 λ¼2 0

 0 α2 F ω 0 dω 0 ω

ð100:2Þ

Early photoemission studies focused on the observation that at higher temperatures, above approximately one third the Debye energy, Eq. 100.1 reduces to Γe-ph ¼ πλkBT. Thus a measurement of the width of a photoemission peak as a function of temperature provides direct access to the coupling constant, λ. This approach has been used in several investigations including studies of the electron-phonon contribution to quasi-particle lifetimes of surface states on the Cu(111) [95M1] and Be(0001) [98B1] surfaces. In the former case the electron-phonon coupling constant for the surface, λ ¼ 0.14 was close to that measured for bulk copper, λ ¼ 0.15. In the case of Be, the surface was found to have a dramatically enhanced value of λ ¼ 1.15, which is to be compared with the bulk value of λ ¼ 0.24. Hengsberger, et al., found a similar value, λ ¼ 1.18, for the electron-phonon coupling parameter in the surface region of Be by measuring the velocity renormalization in the surface band [99H1]. However, a subsequent study of the same surface reduced the value λ to 0.65, a value obtained from a determination of the rate of change of the real part of the selfenergy,  (dΣ1/dω), in the vicinity of EF [00L2]. More recently a high resolution photoemission of the same surface has attributed the enhanced electron-phonon coupling to the broken translational symmetry in the surface region [15C2]. Enhanced values of λ have led to speculation on the possibility of enhanced superconducting transition temperatures in the surface region [98B1]. This approach has been applied to studies of the Mg(0001) surface as shown in Fig. 100.2 [05K1].

150 0.40

Reduced χ2 (χν2)

1.35

100

50

1.30 0.35 1.25 0.30

1.20 1.15

Coupling costant λ

Surface State Linewidth FWHM (meV)

200

0.25 1.10 300

0 0

100

150

400 500 600 700 800 Debye Temperature, ΘD (K)

300

Temperature T [K]

400

900

500

Fig. 100.2 Temperature dependence of the Mg(0001) surface state linewidth at. The open circles give the experimental results. The solid line is the result of the three-dimensional (3D) Debye model fit (see reference for details). The inset shows the reduced value, and the coupling constant λ as a function of the Debye temperature used in the fit (From [05K1])

The introduction of the new instrumentation in the 1990s allowed the first direct imaging of the mass renormalization due to electron-phonon coupling. Studies quickly demonstrated the phenomena in Mo [99V1] and Be [99H1]. Figure 100.3 shows the study of the Be(0001) surface. In the vicinity of the Fermi level there is a notable change in the rate of dispersion, or mass enhancement and a rapid change in the

100

Electronic structure in the surface region: electron-boson coupling in metallic systems

3

width of the band The self-energy corrections resulting in these changes reflect three principal contributions, electron-electron scattering, electron-phonon scattering and electron impurity scattering. These different contributions all add linearly to give the total scattering rate Г such that [99V1] Γ ¼ Γee þ Γeph þ Γimp

ð100:3Þ

K–KF (Å–1) .094 .063

Normalized intensities (arb. units)

.031

.016

0

–.017 –.033 –.049 –.065 –.098

–1000

–800

–600 –400 –200 Binding energy (meV)

EF

Fig. 100.3 High-resolution photoemission spectra of the Be (0001) surface state near kF at T ¼ 12 K (From [99H1])

In a Fermi liquid the electron-electron scattering term is given by Γe-e(ω,T) ¼ 2β [(πkBT )2 + ω2] where, within the Born approximation, 2β ¼ (πU2)/2 W3), with U the on-site Coulomb repulsion and W the bandwidth of the state. As noted earlier the electron-phonon contribution may be calculated via the Eliashberg equation, Eq. 100.1. The final contribution in Eq. 100.3, impurity scattering, is elastic in that the impurity atoms are considered to have no internal excitations. Thus the scattering-rate, Γimp, is proportional to the impurity concentration, but independent of energy and temperature. At sufficiently low temperature, impurity scattering represents the dominant decay mechanism for a hole close to EF. Figure 100.4 shows the measured Σ2 or ImΣ of the Mo surface state as a function of binding energy [99V1]. The data points are extracted from the measured spectra in two ways, either from EDC’s or from MDC’s. The calculated electron-phonon contribution to the self-energy is indicated in the figure. In the vicinity of the Fermi level, the agreement between the calculation using the theoretical α2F of bulk molybdenum [96S1] and the experimentally measured widths is excellent. There is a rapid change in the scattering rate up to the Debye energy at ~30 meV. At binding energies greater than this, the electronphonon contribution saturates. However, also shown in the figure is a quadratic fit to the measured widths at the higher binding energies. The quadratic dependence is an indication that electron-electron scattering, as in a Fermi liquid, plays an important role. In a purely two dimensional system there should be a logarithmic correction to the quadratic term [71H1]. Thus Γe-e will be proportional to ω21nω. However, the simple quadratic fit works well as indicated in the figure because the surface state in question represents a surface resonance with good coupling to bulk states [89J1]. The quadratic fit is consistent with the prefactor in the expression for Γe-e having U ~0.6 eV, as predicted for molybdenum [80H1], and W ~1.3 eV the

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P. D. Johnson

160

120

100

15

Re ∑

0

10

–50

5

–100

0

0.23 0.24 Parallel wavevector k // [Å–1]

80

Re ∑ (meV)

2 ⎢Im ∑ ⎢ (meV)

140

Energy E – EF [meV]

approximate bandwidth of the surface state. The measured widths also have an energy-independent contribution due to scattering from hydrogen impurity centers [99V1].

–5 2 ⎢Im ∑ ⎢

60

–10

40

–400

–15 –100 200 –300 Energy E-EF [meV]

0

Fig. 100.4 The photohole self-energy as a function of binding energy at 70 K. The real part is obtained from the dispersion shown in the inset. The imaginary part is obtained from the width of the quasiparticle peak. The solid line is a quadratic fit to the high-binding energy data (ω b reflects the optical anisotropy of the surface.

138

Sb-terminated Si(001) and Ge(001)

3

Fig. 138.2 Raman spectra at room temperature for clean (thin line) and a Sb-terminated (thick lines) vicinal Si (001) surface for different polarization configurations at incident photon energy of 2.41 eV. The substrate temperature during Sb deposition was held at 360  C. The phonons of the Sb-terminated surface are marked by vertical lines. The intensities in the different polarization configurations are normalized for equal accumulation times [00H]

With the help of the symmetry selection rule, the domain imbalance of the Sb-terminated Si(001) surface can be determined (Fig. 138.2). On vicinal Si(001), an imbalance of the Raman intensities for the two polarization configurations occurs up to 400  C annealing temperatures, indicating that the step structure of the surface (double steps and single steps) is preserved. After annealing to 600  C, the step structure is partly disrupted leading to a more balanced domain distribution. The anisotropy of the parallel Raman polarization configuration has fully vanished in samples grown at 600  C. The Sb dimer-related surface modes have also been found on Sb dimer-terminated Ge(001) surface, here appearing at 141 cm1 (Fig. 138.3). As on Si(001), the same Raman polarization selection rules hold with high Raman scattering efficiency for parallel polarization configuration along the Sb dimer direction [00P]. Furthermore, the Raman signal of the Sb dimer was used as indicator for the surfactant-mediated Ge epitaxy on Si(001). A two-dimensional pseudomorphic growth of a thin Ge layer on Sb dimerterminated Si(001) is induced by the surfactant. Sb exchanges from the Si surface to the Ge surface during Ge growth, as indicated by the replacement of the Sb dimer-related vibrational mode at 130.5 cm1 against the one at 141 cm1, being indicative of Sb surface dimers on Si(001) and Ge(001), respectively (Fig. 138.4). The Sb surfactant during Ge heteroepitaxy induces the two-dimensional fully strained growth, whereas on clean Si-relaxed Ge, islands coalesce. This is indicated in the Raman spectra by the observation of the Sb dimer mode together with the TO-LO signature of a strained 20 ML Ge layer, as opposed by the unstrained LO mode of an Ge island on Si(001) layer without Sb [00P], accordingly.

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N. Esser and E. Speiser

Fig. 138.3 Raman spectra, using a 514.5 nm excitation wavelength, of the Ge(001) surface after growth of a 10 ML Ge buffer layer and after the growth of 1 ML of Sb on this surface. The parallel polarization combination ei||es||[110] was used. The sample was cooled down to room temperature before data acquisition. The spectra were normalized to the LO phonon of bulk Ge [00P]

514.5nm, ei||es||[110]

LO (314.5cm–1)

ωSb-Si

(130.5cm–1)

ωSb-Ge

(141cm–1)

20ML Ge (oxidized)

TO (296cm–1)

Raman intensity (arb. units)

Ge-epilayer phonon 20ML Ge

5.0ML

3.5ML 2.55ML 1.65ML 0.75ML

0.25ML

Si(001)-(2x1).Sb

100

200

300

Raman Shift

400

(cm–1)

Fig. 138.4 Raman difference of Ge/Sb-covered surfaces minus clean Si(001) surface using 514.5 nm excitation wavelength, taken at different stages during the growth of up to 20 MLs of Ge on the vicinal Si(001)-(2
1)-Sb surface. The Ge growth was interrupted at the coverages indicated and the sample was cooled down to room temperature before data acquisition. The coverages shown are cumulative and the parallel polarization combination ei||es||[110] was used where the polarization vectors are parallel to the Sb-Sb dimer bond of the initial (2
1)-Sb surface [00P]

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Sb-terminated Si(001) and Ge(001)

5

Symbols and abbreviations Short form

Full form

ML LO TO

monolayer longitudinal optical transverse optical

References [98T] [00H] [00P]

Tütüncü, H.M., Jenkins, S.J., Srivastava, G.P.: Surf. Sci. 402–404, 42 (1998) Hinrichs, K., Power, J.R., Esser, N., Richter, W.: Appl. Surf. Sci. 166, 185 (2000) Power, J.R., Hinrichs, K., Peters, S., Haberland, K., Esser, N., Richter, W.: Phys. Rev. B. 62, 7378 (2000)

Chapter 139

As-terminated Si(111) N. Esser and E. Speiser

Unsaturated dangling bonds at the surface are the driving force for surface reconstruction. Thus, by means of a passivating layer, the surface structural properties may be greatly affected. One example of such passivating monolayer systems is As on Si(111) [92B]. By adsorption of an As monolayer, it has been shown that the (7  7) reconstruction of clean Si(111) is replaced by a simple (1  1) surface structure. Similar as the Sb on III–V(110), the As on Si(111) continues the Si structure, leading to a (1  1) structure with a doubly occupied dangling bond orbital per surface As atom. The surface vibrational properties of the As/Si(111) system have also attracted considerable interest. The optical surface modes were investigated by HREELS [94S] showing a weak mode at 200 cm 1 and two stronger surface modes at 356 cm 1 and 520 cm 1. The mode at 356 cm 1 was interpreted as a surface mode with z-polarized character localized in the underlying Si layer. The 520 cm 1 mode, coincident with the Si bulk TO phonon, was associated with a shear-horizontal optical surface mode. Optical surface phonon modes of the As-monolayer-terminated Si(111) surface have also been observed by Raman spectroscopy [91W, 93E2]. A strong surface phonon mode was identified by Raman scattering at 356 cm l, in agreement with the HREELS results; moreover, a weak indication of a lower-energy mode around 230 cm 1 was reported (Fig. 139.1). The surface mode at The 520 cm 1 mode is not visible by Raman spectroscopy due to the overlap with the strong Si bulk TO phonon.

N. Esser (*) • E. Speiser Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V., Interface Analytics Department, Berlin, Germany e-mail: [email protected]; [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_139

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Fig. 139.1 Raman spectra of an As-capped Si wafer taken after several annealing steps as indicated. The monolayer vibrational modes are marked by the arrows. The incident laser photon energy was 2.54 eV [93E2]

The polarization selection rules and the resonance dependence of the Raman scattering cross section have been investigated for the surface mode at 356 cm 1 (Fig. 139.2) [91W, 93E2]. The surface mode at 356 cm 1 is observed for parallel as well as for crossed polarization configurations. The As-terminated Si (111) surface has C3v symmetry with a threefold rotation axis along the [111]-direction. Modes with displacements along the C3 axis (surface normal, z-direction) refer to A-modes (diagonal polarization configuration); the modes with in-plane displacements in the x- and y-directions refer to E-modes (crossed and diagonal polarization configuration). Thus the observed mode at 356 cm 1 has E-character. The E-symmetry of the 356 cm 1 mode was also obtained by a calculation based on an ab initio DFT approach [96H]. They reveal an xy-polarized displacement pattern at Γ, in agreement with the Raman selection rules.

139

As-terminated Si(111)

RAMAN INTENSITY

0.2

3

counts

(||,⊥)

s . mW

(||,||)

280

320

360

Raman shift [cm–1]

400

Fig. 139.2 Raman spectra of 1 ML-As/Si(111) for parallel and crossed polarizations of incident and scattered light as indicated in the figure. The incident laser photon energy was 2.41 eV. The monolayer mode at 356 cm l is of E symmetry type [93E2]

Also the Raman resonance behavior has been analyzed and a surface Raman resonance was suggested [93E2]. However, further experimental verification of the surface resonance with Raman excitation in the UV spectral range is required. Symbols and abbreviations Short form

Full form

ML HREELS TO DFT

monolayer high-resolution electron energy-loss spectroscopy transverse optical density functional theory

References [91W] Wilhelm, H., Richter, W., Rossow, U., Zahn, D.R.T., Woolf, D.A., Westwood, D.I., Williams, R.H.: Surf. Sci. 251/ 252, 556 (1991) [92B] Bringans, R.D.: Crit. Rev. Solid State Mater. Sci. 17, 353 (1992) [93E2] Esser, N., K€ opp, M., Haier, P., Richter, W.: J. Electron. Spectrosc. Relat. Phenom. 64/65, 85 (1993) [94S] Schmidt, S.J., Ibach, H.: Phys. Rev. B. 50, 14354 (1994) [96H] Honke, R., Pavone, P., Schr€ oder, U.: Surf. Sci. 367, 75 (1996)

Chapter 140

In-terminated Si(111) N. Esser and E. Speiser

140.1

Surface Phonons

Surface phonon modes in the range from 20 cm
1 up to 500 cm
1 have been identified by surface Raman spectroscopy for the (4  1) and (8  2) surface structures (Fig. 140.1) [03F, 07F, 10S, 16S]. By corresponding frozen phonon calculations, a detailed microscopic picture of the surface phonon modes of both the (4  1) and (8  2) surface phonon modes has been developed [16S]. Surface vibrational modes at high frequencies involve mainly displacements of the Si atoms in the subsurface layers underneath the In-adsorbate layer, while in the low-frequency range < 80 cm
1, the surface vibrational modes involve mainly displacements of the In atoms of the upper atomic layer. The separation in the two frequency domains is simply due to the large atomic mass difference of In (115 amu) and Si (28 amu) [07F].

N. Esser (*) • E. Speiser Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V., Interface Analytics Department, Berlin, Germany e-mail: [email protected]; [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_140

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Fig. 140.1 Raman spectra of the (4  1) and (8  2) phases taken in A0 and A00 symmetries, using an incident laser energy of 1.91 eV. The positions of the Raman modes are marked by dotted lines (see also Table 140.1). New (8  2) modes, assigned to backfolding of the phonon branches, are indicated by gray lines, while blue-shifting of modes upon cooling is marked by black arrows. The spectral range from 240 to 370 cm
1 is omitted as it is dominated by the bulk Si 2TA structure [07F]

DFT-based frozen phonon calculations [10W, 07S] for the In(Si(111) (4  1) and (8  2) structures reveal a rich surface mode structure with high-energy phonons between about 90 and 480 cm
1. Tables 140.1 and 140.2 give an overview on experimentally determined frequencies of Raman modes (including Si-Si vibrations in the near-surface region) and associated mode frequencies from frozen phonon calculations localized in the top In-layer, including the symmetry properties for the respective modes [16S,  10W]. Due to the doubling of the surface unit cell along the two main surface directions, i.e., 112;    perpendicular and 110 parallel to the chain direction, the surface unit mesh contains four times more atoms in the low-temperature structure than in the room temperature structure. Correspondingly, the number of surface optical modes at Γ should scale with n
2 (with n-atom number in the surface unit cell in a two-dimensional lattice). Neglecting the structural rearrangement within the In chains, the additional phonon modes of the low-temperature (8  2) structure would arise from backfolding of the respective (4  1) surface modes at the X, Y, and M points of the surface Brillouin zone of the (4  1) structure [16S]. However, the (8  2) eigenmodes do not refer simply to the (4  1) backfolded modes but

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In-terminated Si(111)

3

depend also on the structural modification within the unit mesh, i.e., the transition from the In chain structure to the In hexagon structure. Thus the surface phonon modes depend both on translational symmetry change, i.e., backfolding according to the change of the surface unit mesh size, and local bonding configuration according to the change from chain-like to hexagon-like surface structure [16S]. Table 140.1 Measured (4  1) RT phonon mode frequencies (cm
1) in the range from 10 to 500 cm
1 (excitation energy of 1.91 eV). For comparison frozen phonon DFT-based calculated frequencies of In-layer related surface localized modes are shown. The experimental values are extracted from measurements by fitting the spectra with Voigt lineshapes. The Gaussian component corresponds to the spectral resolution of 1.2 cm
1 No

Energy (cm
1)

Linewidth (cm
1)

Symmetry

Calculation (cm
1)

1a 2 3 4 5 6 7 8 9 10 11 12 13

17.9  1.8 27.5  0.1 31.2  2.5 38.1  0.5 51.7  0.1 61.4  0.1 71.6  1.1 105  1 118  1 148  7 428  1 467  1.5 487  2.6

12.6  5.0 6.6  0.1 9.2  7.8 12.8  3.4 1.8  0.2 2.3  0.2 4.4  4.2 83 92 16  12 14  4 77 10  2

A00 A00 A0 A0 A0 , A00 A0 , A00 A0 A0 A0 A0 A0 A0 A0

20.2 32.3 44.4 50.8 64.6 64.6 67.8

Table 140.2 Measured (8  2) low-temperature (LT) phonon mode frequencies (cm
1) in comparison to frozen phonon DFT-based calculations (only In-layer related calculated surface localized modes are shown) No I II III IV V4  1 VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX XXI XXII XXIII XXIV XXV

Energy (cm
1) 19.6  0.1 23.4  0.1 27.1  0.5 28.3  0.1 35.0  0.4 37.7  0.1 41.4  0.1 48.1  0.2 55.5  0.0 57.8  0.1 60.0  0.1 63.5  0.5 69.0  0.0 80.6  0.3 85.4  0.3 139  1.2 154  2 185  2 255  4 264  3 412  2.5 435.1  0.7 458  1.2 473  2 495  5

Linewidth (cm
1) 4.0  0.6 2.4  0.2 3.1  1.3 2.9  0.4 9.5  3.6 1.0  0.5 2.5  0.1 2.8  0.8 4.0  0.2 1.4  1.0 4.1  1.1 10.4  5.0 1.4  0.2 11.4  6.0 6.7  0.7 11  6 76 12  8 76 74 10  8 22  10 3  1.5 44 18  14

Symmetry 0

A A00 A0 A0 A00 A0 A0 , A00 A0 , A00 A0 A0 A0 A0 , A00 A0 A0 A0 , A00 A0 A0 A0 , A00 A0 , A00 A0 A0 A0 A00 A0 A0

Calculation (cm
1) 20.0 22.2 26.8 27.4 32.3(4  1)Γ 53.8 59.0 69.6

87.2

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N. Esser and E. Speiser

From the surface Raman spectra, the phase transition from (4  1) to (8  2) structures is immediately evident from the number and frequencies of the surface vibrational modes (Fig. 140.2) [07F]. Accordingly, the phase transition can be monitored by recording Raman spectra for different temperatures around the phase transition temperature. The phase transition was also studied by ab initio based calculations yielding soft phonon modes as a mechanism for the displacive transition [10W]. Recently the phase transititon was explained within a grand canomical ensemble involving the electronic srtucture as well [16S].

Fig. 140.2 Polarized Raman scattering from low-temperature phase Si(111)-In:(8  2) ( full blue lines) and room temperature (4  1) (dotted red lines). Spectra taken at zðxxÞ z, zðxyÞ z, zðyyÞ z, zðyxÞ z scattering geometries are shown. The polarization vector of the exciting laser radiation is perpendicular (x) and parallel to the direction of the Indium chains (y) [16S]

140.2

Raman Selection Rules and Surface Resonance

Symmetry elements of the (4  1) In zigzag chain structure are a twofold rotation, a mirror and a glide plane according to “pmg” 2D space group. The (8  2) hexagon structure has only a glide reflection plane according to a “pg” 2D space group (Fig. 140.3). The associated 3D space groups for the (4  1) and (8  2) reconstructions are the orthorhombic C2v and the monoclinic CS. The normal modes separate into A0 and 00 With x and y referring to the A surface  modes,  conserving and breaking the symmetry plane, respectively. 0   112 and 110 directions, under the (x, x) and (y, y) configurations (A ), the Raman tensor components “a” and “b” are selected, under the (y, x)- and (x, y)-configurations (A00 ), the tensor component “c.” The difference between tensor elements “a” and “b,” from the fact that the surface unit cell is  results   direction. This has a strong impact on the surface anisotropic, with the In chains extending along the 110 electronic band structure and related surface optical transitions which are important for the Raman scattering process, as discussed above. The analysis of the surface optical anisotropy [09C] yields that In-Si bonds lead to surface electronic states the first atomic layers which show a pronounced optical  within   absorption for light polarized along the 112 direction in the visible range (around 1.5 eV). This optical anisotropy of the surface structure is reflected in the a and b tensor components of the Raman tensor: in parallel configuration a strong Raman signal of the A0 modes shows up in xx polarization, while in yy polarization, a weak A0 Raman signal [07F, 15S]. Since the Raman experiments were recorded with

140

In-terminated Si(111)

5

1.91 eV laser excitation, the surface electronic transition with x polarization is resonantly excited. The A00 scattering depends on crossed xy and yx polarization configuration involving both x and y polarizations and thus is equivalent for xy and yx.

Fig. 140.3 Surface unit cells and symmetry elements in the low-temperature In:Si(111)(8  2) (a) and room temperature (4  1) phase (b),  respectively.    The surface
coordinate system  , zk½111 in the Si bulk high is indicated xk 112 , yk 110 symmetry directions). In (c), the corresponding surface Brillouin zones with characteristic points are shown [15S]

Experimentally it has been demonstrated the In-Si surface modes indeed show pronounced surface resonances, by choosing various different laser excitation lines in the visible spectral range [07F]. The resonance enhancement and spectral dependence of the resonance enhancement differ for the individual surface modes, showing that the deformation potential of the individual modes is distinct and in particular will affect different electronic states of the surface electronic band structure, depending on the displacement pattern of the surface mode. Resonant Raman scattering at the Si bulk phonon modes occurs at the E0 and E1 gaps of Si around 3.4 eV. This is spectrally well separated from the surface resonances, and thus by surface resonant excitation, the surface modes are selectively enhanced. Symbols and abbreviations Short form

Full form

1D 2D 3D DFT LT TA

one-dimensional two-dimensional three-dimensional density functional theory low-temperature transverse acoustic

References [01H1] Himpsel, F.J., Altmann, K.N., Bennewitz, R., Crain, J.N., Kirakosian, A., Lin, J.-L., McChesney, J.L.: J. Phys. Condens. Matter. 13, 11097 (2001) [03F] Fleischer, K., Chandola, S., Esser, N., Richter, W., McGilp, J.F.: Phys. Rev. B. 67, 235318 (2003) [07F] Fleischer, K., Chandola, S., Esser, N., Richter, W., McGilp, J.: Phys. Rev. B. 76, 205406 (2007) [07S] Stekolnikov, A.A., Bechstedt, F., Schmidt, W.G.: Phys. Rev. Lett. 98, 026105 (2007)

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[09C]

N. Esser and E. Speiser

Chandola, S., Hinrichs, K., Gensch, M., Esser, N., Wippermann, S., Schmidt, W.G., Bechstedt, F., Fleischer, K., McGilp, J.F.: Phys. Rev. Lett. 102, 226805 (2009) [10S] Speiser, E., Chandola, S., Hinrichs, K., Gensch, M., Cobet, C., Wippermann, S., Schmidt, W.G., Bechstedt, F., Richter, W., Fleischer, K., McGilp, J.F., Esser, N.: Phys. Status Solidi B. 247(8), 2033 (2010) [10W] Wippermann, S., Schmidt, W.G.: Phys. Rev. Lett. 105, 126102 (2010) [15S] Speiser, E., Hinrichs, K., Prete, P., Lovergine, N., Esser, N.: Phys. Status Solidi B. 252(1), 11 (2015) [16J] Jeckelmann, E., Sanna, S., Schmidt, W.G., Speiser, E., Esser, E.: Grand canomical Peierls transition in In/Si(111). Phys. Rev. B. 93, 241407 (R) (2016) [16L] Liebhaber, M., Halbig, B., Bass, U., Geurts, J., Neufeld S., Sanna, S. Schmidt, W.G., Spieser, E., Rathel, J., Chandola, S., Esser, N.: vibration eigenmodes of the Au-(5x2)/Si(111) surface by Raman spectroscopy and first-principle calculations. Phys. Rev. B. 94, 235304 (2016) [16S] Speiser, E., Esser, N., Wippermann, S., Schmidt, W.G.: Surface vibrational Raman modes of In:Si(111)(4x1) and (8x2) Nanowires. Phys. Rev. B. 94, 075417 (2016)

Chapter 141

Au-terminated Si(111) N. Esser and E. Speiser

Gold-induced reconstructions on Si(111) are known for their large variety of possible atomic arrangements depending on surface vicinality, Au coverage, and preparation conditions. A remarkable sensitivity to structural properties in atomically ordered surfaces was demonstrated in the investigation of Au-induced reconstructions on Si(111) by Raman spectroscopy (Figs. 141.1 and 141.2) [15R]. Not only the difference between (√3
√3) and (5
2) reconstructions is clearly elaborated by the comparison of the measured and calculated vibrational modes, but also the slight variations in atomic geometry induced by faint Au coverage altering of 0.05 monolayers can deliver different spectral shapes as confirmed by calculations.

N. Esser (*) • E. Speiser Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V., Interface Analytics Department, Berlin, Germany e-mail: [email protected]; [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_141

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Fig. 141.1 Raman spectra of the Au/Si (111)-(5
2)-reconstructed surface at room temperature. In the polarization configurations zðyyÞ z (upper panel) and zðyxÞ z (lower panel), the reconstructed Au/Si (111) – (5
2) (red) and the disordered Si(111) shown surface (black) are shown for comparison. The differences in the intensities of reconstructed and disordered surfaces are displayed below. Five identified Raman lines in both polarization configurations zðyyÞ z and zðyxÞ z can be assigned to the phonons of the Au/Si (111) – (5
2) reconstruction [15R, 16L]

141

Au-terminated Si(111)

3

Fig. 141.2 Room temperature Raman spectrum of the Au/Si(111) – (√3
√3) R30 reconstructed surface (red line upper panel) in the polarization configuration z ðy; x þ yÞ z . The Raman spectrum of the disordered Si(111) is shown for comparison (black line upper panel). The difference of the intensities is shown in lower panel. The seven identified Raman lines (marked by vertical lines) can be assigned to the phonon modes of the Au/Si(111) – (√3
√3) R30 [15R, 15S4]

References [15R] Räthel, J.: PhD thesis, TU Berlin (2015) [16L] Liebhaber, M., Halbig, B., Bass, U., Geurts, J., Neufeld S., Sanna, S. Schmidt, W.G., Spieser, E., Rathel, J., Chandola, S., Esser, N.: vibration eigenmodes of the Au-(5x2)/Si(111) surface by Raman spectroscopy and first-principle calculations. Phys. Rev. B. 94, 235304 (2016)

Chapter 142

Au-terminated Si(553) N. Esser and E. Speiser

In the case of Au-terminated Si(111)-(5  2) surface, five surface vibrations have been identified experimentally by Raman scattering and assigned by DFT-based calculations to distinct vibrational eigenmodes with unambiguous vibrational patterns [15R]. In spite of similar local atomic arrangement (same surface and adsorbate are involved), clear differences in measured eigenfrequencies are observed in (√3  √3) related spectra. This confirms a strong dependence of surface vibrations not only on local atomic configuration but also on the collective behavior of surface atoms. The vicinal Au-terminated Si(553)-(5  2) surface exhibits Au chains on the terraces and a so called “Si honeycomb” structure near the step edge. Although no ferromagnetic species are involved in the surface reconstruction, spin polarization of Si step edge atoms was found in calculations, and correspondingly every third Si atom on the step edge should be spin polarized in an antiferromagnetic order. This assumption is supported by an additional threefold periodicity on the surface along the step edge, while other experimental evidence is still lacking. The “spin-polarized structure” (at low temperatures) is accompanied by a structural change at the step edge in comparison to the nonpolarized one (at room temperature). Due to thermally activated spin flipping (on the timescale of ps), the additional threefold periodicity is blurred out. The spin-polarized atoms are located by 0, 03 nm lower than in the nonpolarized structure, a remarkable structural change which possibly alters the vibrational properties. In Raman spectra in Fig. 142.1, a comparison between spectra at low and room temperatures is shown. Several modes related to the surface are identified at 88, 398, and 406 cm 1. In these spectral regions, the spectra undergo a clear change: While the 88 cm 1 line is appearing only at low temperature, the high-energy vibration at 406 cm 1 is hindered, possibly by the presumed static spin polarization.

N. Esser (*) • E. Speiser Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V., Interface Analytics Department, Berlin, Germany e-mail: [email protected]; [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_142

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Fig. 142.1 Comparison between room temperature (upper panel) and low temperature (lower panel) Raman spectra of a vicinal Si(553) (5  2) surface with Au chains on the terraces. Beside the Au diatomic chain on the terraces this surface exhibits a so-called “honeycomb” structure on the step edge having a ferromagnetic spin ordering at the every third edge Si atom. Slight structural changes and the thermal disorder of the step edge structure could be the reason for the distinctive difference in the shown spectra, especially in the range around 88 and 390–425 cm 1, where vibrational modes are located with edge atoms involved [15R]

Symbols and abbreviations Short form

Full form

DFT

density functional theory

References [15R]

Räthel, J.: PhD thesis, TU Berlin (2015)

Chapter 143

Metal surfaces: Si nanoribbons on Ag(110) N. Esser and E. Speiser

Surface phonons of Si nanoribbons on Ag(110) have been detected by Raman spectroscopy [14S]. In the formation   of silicon nanoribbons on Ag(110), one-dimensional atomic-size nanostructures extending along  direction on the surface were reported for the first time in 2005 [07L]. Such nanostructures may be the 110 grown at partial coverage, obtaining isolated nanoribbons, or at full silicon coverage, achieving an ordered grid of adjacent nanoribbons on the whole substrate area. In 2009 it was suggested from DFT-based ab initio calculations that the Si/Ag(110) surface would show a silicene-like structure consisting of a single Si-buckled layer in a honeycomb structure. Despite the recent efforts, however, the atomic structure of the Si nanoribbons grown on the Ag(110) surface is still not clear [13B]. Raman spectroscopy was applied to the Si nanoribbons to investigate the structure and in particular to compare surface vibrational modes with calculated silicene modes [14S]. The surface vibrational response related to the Si nanoribbons is clearly visible in Raman spectra taken in UHV on the nanoribbon terminated Ag(110) surface (Fig. 143.1). Raman spectra taken on the clean Ag(110) surface show no detectable Raman signal; thus, difference spectra are not necessary to resolve the surface Raman response. Four strong vibrational modes are identified at 459, 441, 266, and 203 cm 1; no further phonon modes show up at higher energies (up to 1000 cm 1). The Raman spectra show a strong dependence on the polarization of the exciting and detected light: The surface phonon modes at 459 and 202 cm 1 appear only upon excitation with polarization oriented along the ribbons, while the two modes at 440 and 266 cm 1 are present also at perpendicular polarization, related to the strong asymmetry of the ribbons. A full set of Raman selection rules has not been determined yet.

N. Esser (*) • E. Speiser Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V., Interface Analytics Department, Berlin, Germany e-mail: [email protected]; [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_143

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Fig. 143.1 Raman spectra from 1.6 nm wide Si nanoribbons (NRs) on Ag(110) substrate. Upper panel: exciting laser and scattered polarization are oriented parallel to the NRs as indicated in the inset. Lower panel: polarizations perpendicular to NRs. Measurement: open circles; best fit by four phonon lines: full line; single Lorentzian line shape components of the fit are indicated with blue and red lines. For clarity, background is subtracted in both spectra [14S]

The surface Raman spectra were taken as an indication that the Si nanoribbons are not forming a silicene-like structure but rely much stronger on the interaction with the Ag(110) substrate than initially assumed. Calculations of the phonon dispersion in silicene sheets [09C2] show a phonon at the Brillouin zone center with an energy significantly higher than that of sp3 bulk silicon, i.e., around 580 cm 1 as compared to 521 cm 1 of the bulk phonon. Neither this predicted silicene-like phonon nor an indication of a Si bulk-like vibration is present in the Raman spectra of the Si nanoribbons. Symbols and abbreviations Short form

Full form

NR DFT UHV

nanoribbon density functional theory ultrahigh vacuum

References Le´andri, C., LeLay, G., Aufray, B., Girardeaux, C., Aviola, J., Davila, M.E., Asensio, M.C., Ottaviani, C., Cricenti, A.: Appl. Phys. Lett. 90, 263110 (2007) [09C2] Cahangirov, S., Topsakal, M., Aktürk, E., Sahin, H., Ciraci, S.: Phys. Rev. Lett. 102, 236804 (2009) [13B] Bernard, R., Leoni, T., Wilson, A., Lelaidier, T., Shahaf, H., Moyen, E., Assaud, L., Santinacci, L., Lerqoy, F., Cheynis, F., Ranguis, A., Jamgotchian, H., Becker, C., Borenzstein, Y., Hanbrücken, M., Prevot, G., Masson, L.: Phys. Rev. B. 88, 121411R (2013) [14S] Speiser, E., Buick, B., Esser, N., Richter, W., Colonna, S., Cricenti, A., Ronci, F.: Appl. Phys. Lett. 104(16), 161612 (2014) [07L]

Part VII

Field Electron and Ion Emission: Basic Formulae and Constants

Chapter 144

Introduction to field electron and ion emission and customary units R. G. Forbes

The application of a sufficiently high electrostatic field to a material surface results in the emission of electrons if the emitter is negatively charged and the emission of ions if the emitter is positively charged. These processes are called field electron emission and field ion emission, respectively, and – depending on the precise materials and processes involved – typically occur in the field ranges (
3) to (
10) V/nm and +15 to +60 V/nm, respectively. The processes are of interest in their own right. More importantly, small, bright, electron and ion sources can be based on these processes, and are used in various technological applications, from electron microscopes to space vehicle thrusters. The processes also form the basis of the projection microscopies and related techniques, including field electron and field ion microscopy and atomprobe tomography. Field electron emission is one of the initiation mechanisms of electrical breakdown and needs to be avoided. Physical explanations of how these processes and techniques work involve various branches of science, but these sometimes need customizing in order to account for the effect of high electric fields on atomic and nanoscale processes. The ensuing theory constitutes a specialized scientific focus that is becoming known as high electric field nanoscience (HEFNS). The various topics within HEFNS include relevant electrostatics, the basic theory of charged surfaces, thermal-field shaping effects and the underlying thermodynamics, electron and ion potential energies at charged surfaces, field electron emission, field ionization and post-field ionization, the charged-particle optics of field emitters, field evaporation and other aspects of field desorption, and the interaction of laser beams with field emitters. The theory of HEFNS contains many universal constants and parameter values. Overall it is more common for the parameter values to be estimated theoretically, rather than measured experimentally. This contribution aims to collect together the most theoretically significant HEFNS formulae, constants, and parameter values. The contribution is mostly arranged by HEFNS topic, each containing an introduction, relevant basic formulae, and relevant tables. This entry differs from the typical LB table entry, because the current state of the literature makes it necessary to place considerable emphasis on describing how parameters are defined, and the contexts of the definitions, rather than simply on tables of parameter values. We also emphasize that only basic theory is addressed: thus, for field electron emission, this basic theory relates to emission from a metal into vacuum, for an emitter that is “not too sharp” (apex radius greater than 10 nm, say), with a free-electron model used for the emitter and the tunneling barrier modeled as a Schottky-Nordheim barrier (see below). The specific problems associated with sharp emitters, or emission from nonmetals, or emission from metals into dielectrics, or photon-assisted emission processes, are not addressed here. As can be seen from the contents of this contribution, the listing of values of parameters and constants related to the basic processes of field electron and field ion emission involves special problems. Values of relevant universal constants are known to the usual high accuracy, and relevant thermodynamic parameters extracted from the literature are (in most cases) known to an accuracy that is more than sufficient for

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_144

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purpose. The problem lies with those parameters that are intrinsically related to situations and processes induced by the presence of very high electrostatic fields. The problem has two main sources. First, in many cases the fundamental physical theory of these situations and processes is not yet sufficiently well established, and existing theory is known to contain errors and approximations (of sizes that are difficult to estimate). Second, field values applying to nanoscale situations and processes of the types under discussion are currently impossible to calibrate accurately. This is because the only satisfactory way to carry out such a calibration is to rely on the theory of some nanoscale process, and it is known that – for all of the processes that might be used – the theory is not fully reliable (to an extent that is unknown). This, in turn, means that, in many of these high-field situations, the normal scientific procedure of comparing theory with experiment is currently impossible to carry out accurately and reliably, at least in respect of absolute values (one can do somewhat better with ratios of values). The values given in this contribution are presented as “the best currently available, in the author’s view.” In many cases, it has been impossible to assess the true likely error in these values. To improve the overall situation, there is an urgent need for improvements to relevant underlying theory, in particular the theories of field ionization, post-field ionization, “best imaging,” and field evaporation. We now turn to basic matters. Modern field emission literature uses the International System of Quantities (ISQ) [06B, 09I] (formerly called the “metre-kilogram-second-ampere” system), but a customary system of ISQ-compatible units. This customary system greatly simplifies commonly occurring calculations where work functions are expressed in eV and fields in V/nm, but current densities are needed in A/m2. Table 144.1 shows values of relevant fundamental constants, expressed both in SI units and in these customary units. Table 144.2 shows values of universal constants commonly used in field emission, in customary units.

Table 144.1 The electronvolt (eV) and fundamental constants used in field emission, given in SI units [10N], and in the dimensionally equivalent atomic-level units (based on the eV) used to make equation evaluation easier. Values in customary units are taken from [11F] (see data supplement) and are given to seven significant figures Name

SI units Symbol Numerical value

Electronvolt Elementary (positive) charge Avogadro constant Elementary constant of amount of substance a) Unified atomic mass constant Electron mass in free space Electric constant Electric constant  4π Planck’s constant Planck’s constant  2π Boltzmann’s constant

eV e L n1 mu me ε0 4πε0 hP ℏ kB

1.602 176 5  10
19 1.602 176 5  10
19 6.022 141 29  10
23 1.660 538 7  10
24 1.660 538 7  10
27 9.109 381 9  10
31 8.854 187 8  10
12 1.112 650 1  10
10 6.626 069 8  10
34 1.054 571 8  10
34 1.380 650 3  10
23

Units

Atomic-level units based on eV Numerical value Units

J C mol
1 mol kg kg F m
1 F m
1 Js Js J K
1

1 1 1 1 1.036 430  10
26 5.685 630  10
30 5.526 350  10
2 0.694 461 6 4.135 667  10
15 6.582 118  10
16 8.617 342  10
5

eV eV V
1 entity
1 a) entity a) eV nm
2 s2 eV nm
2 s2 eV V
2 nm
1 eV V
2 nm
1 eV s eV s eV K
1

a

Name used here, not “official”

Table 144.2 Basic universal emission constants, and combinations, used in field emission theory. Values are given in field emission customary units. For relevance of these constants, see following contributions. Values are mostly taken from [11F], but some have been evaluated for this table Name (where given)

Symbol Derivation

Expression

Numerical value

Units

Coulomb law constant Image-potential-energy constant Sommerfeld supply density a) Universal theoretical Richardson constant Schr€odinger equation constant for electron

– Bim zS AR0 κ

e2/4πε0 e2/16πε0 4πeme/hP3 4πemekB2/hP3 (2me)1/2/ℏ

1.439 964 0.359 991 1 1.618 311  1014 1.201 735  106 5.123 168

eV nm eV nm A m
2 eV
2 A m
2 K
2 eV–1/2 nm
1 (continued)

– – – zSkB2 –

144

Introduction to field electron and ion emission and customary units

3

Table 144.2 (continued) Name (where given) JWKB constant for electron – –

Symbol Derivation 2κ ge cκ (κ/e)1/3 (κ/e)2/3 c2κ

First Fowler-Nordheim constant Second Fowler-Nordheim constant

a b

zS(e/2κ)2 4κ/3e

– Schottky constant – – – – Value of SN barrier function u( f ) at f ¼ 1 b) –

– cS – – – – u1

–

Cq

ab2 – c S2 cS
2 bcS2 acS
4 –dvdf at f¼1 1/(2u1bcS1/ 2 ) Cδ/kB

Cδ

Expression 2(2me)1/2/ℏ (2me)1/6/(eℏ)1/3 (2me)1/3/(eℏ)2/3

Numerical value 10.246 24 1.723 903 2.971 842

Units eV–1/2 nm
1 eV–1/2 (V/nm)–1/3 eV
1 (V/nm)–2/3

e3/8πhP (4/3)(2me)1/2/ eℏ (4/9)zS (e3/4πε0)1/2 e3/4πε0 4πε0/e3 – – 3π/(8 √ 2)

1.541 434 6.830 890

μA eV V
2 eV–3/2 (V/nm)

7.192 493  1013 1.199 985 1.439 964 0.694 461 6 9.836 238 7.433 980  1011 0.833 040 6

A m
2 eV
2 eV (V/nm)–1/2 eV2 (V/nm) (V/nm) eV
2 eV1/2 A m
2 eV
3 –

–

802.118 7

eV (V/nm)–3/4

–

930.819 1

K (V/nm)–3/4

a

The supply density is the electron current crossing a mathematical plane inside the emitter, per unit area of the plane, per unit area of energy space, when the relevant electron states are fully occupied. In a free-electron model for a bulk conductor, the supply density is isotropic, is the same at all points in energy space, and is given by zS. This is an alternative statement of the statistical mechanical principle that the density of states in phase space is constant (see [10F2]) b For definitions of SN barrier functions v( f ) and u( f ), see Chap. 149[https://doi.org/10.1007/978-3-662-53908-8_149].

It needs to be emphasized that, unlike the “atomic units” used in atomic physics, which are set in the context of a Gaussian (unrationalized) system of equations, these field emission customary units are set in the context of what has become the modern (rationalized) international system of equations. Further, since the electronvolt is approved for continued use alongside SI units, use of these FE customary units is fully compatible with the formal rules of the ISQ. Symbols and abbreviations Short form

Full form

SI FE ISQ SN HEFNS

international system (of units) (French: syste‘me international d’unite´s) field electron emission international system of quantities Schottky–Nordheim high electric field nanoscience

References BIPM (Bureau International des Poids et Mesures): The International System of Units (SI). BIPM, Se`vres (2006) International Standard ISO 80000-1:2009: Quantities and Units – Part I: General. International Standards Organization, Geneva (2009) [10F2] Forbes, R.G.: J. Vac. Sci. Technol. B. 28, 1326 (2010) [10N] NIST: 2010 values of the fundamental constants. http://physics.nist.gov/constants [11F] Forbes, R.G., Deane, J.H.B.: Proc. R. Soc. Lond. A. 467, 2927 (2011) [06B] [09I]

Chapter 145

Basic terminology of Fowler-Nordheim electron transmission theory R. G. Forbes

Field electron emission (FE) theory requires models and terminology relating to the potential structure in which emitter electrons move, their behavior in this structure, and the process of escape across the surface barrier. The data presented here relate to a Sommerfeld-type, bulk free-electron model for the emitter and to one-dimensional treatments of transmission across the barrier. This approach is adequate for metal emitters where the apex radius is “not too small” (greater than 10 nm, say), but would need modification for small emitters and nonmetals. Treatment of barrier transmission can be much the same in all cases, but correct treatment of electron supply to the barrier needs to take the emitter nature and material into account. Bulk free-electron theory provides an exemplar and a basis for developing suitable theory for small emitters and nonmetals and is often used as a first approximation (not always validly). The standard electron emission convention is used that fields (F), currents (i), and current densities (J ) are treated as positive, even though they would be negative in classical electromagnetism. Except in the symbol “Ep” defined below, the symbol E denotes the electron total energy measured relative to some chosen reference zero, often the local laboratory earth/ground. Relative to this zero, the total energy of the conduction band base is EC, and the total energy at the local vacuum level (or “outside level”) is EO. Note that Ε O can be different outside different crystallographic faces. In the Sommerfeld model, electrons in the conduction band are taken to move in a potential energy (PE) well of depth equal to the local inner PE χ given by χ ¼ EO  E C ,

ð145:1Þ

to be in plane-wave states defined by elementary quantum mechanics, and to obey Fermi-Dirac (FD) statistics. The Fermi level EF is the total energy of the electron state that has 50% occupancy when thermodynamic equilibrium exists. The Fermi energy KF is defined as EF–EC. KF is positive for a metal, negative for a semiconductor. For a free-electron metal, KF is the kinetic energy (KE) attributed to an electron at the Fermi level, and the local work function ϕ is given by ϕ ¼ EO  EF ¼ χ  K F :

ð145:2Þ

The outward direction normal to the emitter surface is called the forward (or “normal”) direction. Any direction at right angles to this (i.e., parallel to the emitter surface) is called a parallel direction. The parallel energy Ep is the electron energy associated with parallel motion; in a free-electron model, this energy is purely kinetic and is sometimes denoted by εp, Kp, or κ. The (total) forward energy level En is the total electron energy associated with forward motion, measured relative to the same reference zero as E. Total forward electron energy measured relative to the conduction band base is denoted by W. Thus,

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_145

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En ¼ E  Ep ¼ EC þ W:

ð145:3Þ

In a free-electron model, this energy W is purely kinetic in nature and is called the forward KE. The transmission energy w is the total forward electron energy measured relative to the top of the tunneling barrier (which, in barrier models that include exchange and correlation effects, is lowered by the field to a forward energy level Enb). The transmission energy w can be positive, zero, or negative. The zero-field barrier height H (which is a property of the emitter and of the specific forward energy En* of an electron approaching the barrier, rather than a property of the barrier alone) is given by H ¼ χ  W ¼ EO  E ∗ n:

ð145:4Þ

An electron that is moving in the forward direction, with total energy E equal to EF, is said to be in state F. For an emitter that is not so small that quantum confinement effects (e.g., [11Q]) operate, an electron in state F sees a surface barrier of zero-field height H equal to the local work function ϕ. The above definitions are illustrated in Fig. 145.1. Fig. 145.1 The Sommerfeld model: diagram illustrating parameter definitions, made in the text, that relate to energies associated with electron emission. Parameter values assumed in drawing the diagram are local inner potential energy χ ¼ 10 eV; local work function ϕ ¼ 4.5 eV; local barrier field F ¼ 5 V/nm. This choice results in tunneling barriers about 1 nm wide. The heavy dashed line shows the corresponding exactly triangular (ET) barrier; the heavy continuous line shows the corresponding Schottky-Nordheim (SN) barrier. Lefthand-side annotations relate to properties of the emitter and barrier; right-hand-side annotations relate to an electron that is being transmitted across the barrier at a forward (i.e., normal) energy level En ¼ En* that is above the Fermi level but below the top of the barrier. These definitions are illustrated here for a SN barrier but apply to any rounded barrier. Note that (unlike some similar-looking diagrams found in the literature) the vertical axis here specifically represents forward energy level, not total energy level

Fowler-Nordheim (FN) transmission is wave-mechanical electron transmission across an exact or rounded triangular barrier. Transmission above the barrier top (w> 0) is termed flyover; transmission below (w< 0) tunneling. Tunneling well below the barrier top, at a level where the Landau and Lifschitz (LL) expression for transmission probability ([58L], p. 175; [08F3]) is a valid approximation (see below), is deep tunneling. Transmission well above the barrier top is high flyover. The transmission probability (or coefficient) D is the probability that an emitter electron approaching the surface will escape in a single attempt. The one-dimensional, one-particle, time-independent Schrodinger equation for the electron wavefunction Ψ (z), for motion along the coordinate z, can be written
 d2 Ψ =dz2 ¼  2me =ℏ2 ½U ðzÞ  Ez Þ  κ2 MðzÞ,

ð145:5Þ

where U(z) is the total electron potential energy (PE) and Ez is the total energy component related to motion in the z-direction, and other parameters are as in Table 2.2. The quantity [U(z)–Ez] defines the electron motive energy M(z). The barrier form is specified by M(z) and the related barrier strength G by the barrier strength integral:

145

Basic terminology of Fowler-Nordheim electron transmission theory

Z

Z G ¼ 2κ

3

M1=2 ðzÞdz  ge

M1=2 ðzÞdz,

ð145:6Þ

where the integral is taken “across the barrier,” i.e., over the range in z where M(z) > 0. For a conducting emitter that is “not too small,” z can be identified with the direction normal to the emitter surface. The barrier strength G has also been called the “Gamow exponent” and the “JWKB (Jeffreys-WentzelKramers-Brillouin) exponent,” but a physically oriented name is preferred here. The exactly triangular (ET) barrier is specified by MET¼H–eFz, where F is the local barrier field. The ET barrier strength is GET¼bH3/2/F. For other barriers, G is found from Eq. 145.6, by numerical integration if needed, and a barrier form correction factor ν (“nu”) is defined by ν¼

G : GET

Symbols and abbreviations Short form

Full form

FE ET LL FN SN JWKB PE KE

field electron emission exactly triangular Landau and Lifschitz Fowler–Nordheim Schottky–Nordheim Jeffreys–Wentzel–Kramers–Brillouin potential energy kinetic energy

References [58L] [08F3] [11Q]

Landau, L.D., Lifshitz, E.K.: Quantum Mechanics. Pergamon, Oxford (1958) Forbes, R.G.: J. Appl. Phys. 103, 114911 (2008) Qin, X.Z., Wang, W.L., Xu, N.S., Li, Z.B., Forbes, R.G.: Proc. R. Soc. Lond. A. 467, 1029 (2011)

ð145:7Þ

Chapter 146

Transmission probability for an exactly triangular barrier R. G. Forbes

Fowler and Nordheim’s (FN’s) original theoretical discussion [28F2] used an ET barrier. For this barrier the Schr€ odinger equation can be solved exactly, although it is unclear whether FN’s Hankel-function-based derivation is strictly valid mathematically. Modern Airy-function-based treatments (e.g., [11F]) yield DET ¼ h

1 2

þ

1 4πω




A þB 2

2



1

 i ; 02 02 þ 14πω1 A þ B

ð146:1aÞ

where A and B are the values of the Airy functions Ai and Bi, and A0 and B0 the values of their derivatives (see [11F] for exact definitions), at the potential-energy step where the electron enters the barrier at the edge of the Sommerfeld well, and ω is ωcκ F3 W 1=2 ; 1

ð146:1bÞ

where cκ is a universal constant given in Table 146.2. Jensen [07J] reached an equivalent result. Benchmark values derived from Eqns. 146.1a and 146.1b, reevaluated for this article [14D], are given in Table 146.1. Table 146.1 Benchmark values of DET, for χ ¼ 15 eV w [eV]

DET for the field values 1 V/nm

8 V/nm

20 V/nm

5 3 1 0 1 15

– 6.12760  1016 1.03201  103 0.314926 0.642001 0.970563

1.33736  104 1.78658  102 0.307716 0.530515 0.680995 0.970572

3.94784  102 0.216300 0.518419 0.641206 0.730748 0.970629

Table 146.2 Constants related to values of the Airy functions and their derivatives. The parameter x is the mathematically real parameter x as used in [10O] and [11F]. The parameters here denoted by Ai0 and Ai0 0 are termed “initial values” in [10O] Parameter definition Value of Ai(x) at x ¼ 0 Value of ∂Ai/∂(x) at x ¼ 0 Defined by Eq. 146.3b Defined by Eq. 146.3b Defined by Eq. 146.4b

Symbol A0 A0 0 c0 c1 c1

Expression –2/3

3 /Γ(2/3) 3–1/3/Γ(1/3) – – –

Numerical value 0.355 028 1 0.258 819 4 0.682 634 2 0.122 076 1 1.478 931

Units

From

eV–1/2 (V/nm)1/3 eV1/2 (V/nm)–1/3 eV–3/2 (V/nm)

[10O] [10O] [11F] [11F] [11F]

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_146

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Expression (146.1) has different mathematical approximations for w> 0. These approximations are very different in their mathematical forms. This situation gives rise to three main transmission regimes [11F], in each of which one of these three different types of mathematical approximation is a useful working formula. These transmission regimes are: deep tunneling; barrier-top emission; and high flyover. For the w > 0 limits, the Airy functions and Eq. 146.1 have asymptotic expansions that each generates a sequence of approximate formulae of successively decreasing accuracy. The formulae used to define the transmission regimes are not the limiting formulae; rather, they are the “most useful working formulae.” In the deep tunneling regime, the working formula used is the well-known FN form: 

FN DET DT  P exp G

 ET

( ¼

)  4ðHW Þ1=2 bH3=2 exp  ; χ F

ð146:2Þ

where the FN tunneling pre-factor PFN is given by {4(HW)1/2/χ}. For w ¼ 0 (“transmission at the barrier peak”), there is a simple exact solution: h DET w¼0 ¼

1 2

1 13

þ c0 F χ 1=2 þ c1 Fþ3 χ 2 1

1

i

ð146:3aÞ

with:
0 2 c0 ¼ πA20 cκ ; c1 ¼ π A0 c1 κ :

ð146:3bÞ

The barrier-top regime corresponds to |w| small. For this regime (which includes both shallow tunneling and low flyover), a good working formula is [11F] h DET BT 

1

1 2

13

þ c0 F W

i 1 1 1 þ c1 Fþ3 W 2  c1 F1 χW 2 w

1=2

ð146:4aÞ

with: 0

0

c1 ¼ πA0 A0 c3κ ¼ πA0 A0 ðκ=eÞ:

ð146:4bÞ

Values of A0 and A00 , and of the constants c0, c1, and c1, are given in Table 146.2. In the high flyover regime, a suitable working formula is

1=2 2 4w1=2 W 1=2 W  w1=2 DET  ¼ 1  :
1=2 2 HF W 1=2 þ w1=2 W þ w1=2

ð146:5Þ

This is also the standard result for transmission across a rectangular step of height (W–w) ([58L], p.74). Figure 146.1 shows the regimes where these working formulae differ from the exact result by less than 10%.

146

Transmission probability for an exactly triangular barrier

3

Fig. 146.1 Transmission-regime diagram, based on the coordinates F2/3 and w, for field values of practical interest. With these coordinates, the different regimes correspond roughly to circular sectors (“pie slices”). Calculations for this diagram use χ ¼ 15 eV. Regime boundaries show where the relevant “good working formula” is in error by 10%, as compared with the exact result. The chosen regimes are “deep tunneling” (DT) (Eq. 146.2); the “barrier-top (BT) regime” (Eq. 146.4a), which includes “shallow tunneling” (ST) and “low flyover” (LF); and “high flyover” (HF) (Eq. 146.5). For shaded regions, no good working formula has been found. The normal working conditions for cold field electron emission lie in the DT regime, near or below the bottom of this diagram

Symbols and abbreviations Short form

Full form

DT ET BT FN LF HF ST

deep tunneling exactly triangular barrier top Fowler–Nordheim high flyover low flyover shallow tunneling

References [28F2] [58L] [07J] [10O]

[11F] [14D]

Fowler, R.H., Nordheim, L.: Proc. R. Soc. Lond. A. 119, 173 (1928) Landau, L.D., Lifshitz, E.K.: Quantum Mechanics. Pergamon, Oxford (1958) Jensen, K.L.: Electron emission physics. Adv. Imaging Electron Phys. 149, 1 (2007) Olver, F.W.J.: Airy and related functions, Chapter 9. In: Olver, F.W. J., Lozer, D.W., Boisvert, R.F., Clark, C.W. (eds.) NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge, UK (2010). See equations (9.2.3) to (9.2.6) Forbes, R.G., Deane, J.H.B.: Proc. R. Soc. Lond. A. 467, 2927 (2011) Deane, J.H.B.: unpublished calculations

Chapter 147

Transmission probability for a general rounded barrier R. G. Forbes

Except for a few special forms, for rounded barriers the Schr€odinger equation cannot be solved exactly in terms of standard defined mathematical functions; thus approximate methods have to be used. For a rounded barrier, the treatment of Fr€ oman and Fr€ oman (FF) [65F] results in the general expression (thought to be nearly exact): D


PeG 1 : ¼
ð1 þ PeG Þ 1 þ P1 eþG

ð147:1Þ

This yields [08F3] the four different approximations in Table 147.1. In the deep tunneling regime (G> ~5), both exact and rounded triangular barriers lead to formulae with the Landau and Lifschitz (LL) form: "

D
PeG

# νbH3=2 ¼ Pexp  : F

ð147:2Þ

Table 147.1 To show the relationships between the four high-level approximate expressions for transmission probability D Weak barrier G+larger Strong barrier

Fr€ oman and Fr€ oman (FF) formula D ¼ Pe–G/[1 + Pe–G] Landau and Lifschitz (LL) formula D
Pe–G

Kemble formula D
1/[1 + eG] Simple-JWKB formula D
e–G

Sharp barrier+Smooth barrier P+1

It is difficult to calculate the tunneling pre-factor P accurately. For single-hump barriers, it is thought to be of order unity, perhaps typically between 0.5 and 2. Hence, particularly in the deep tunneling regime, P is often approximated as unity. The transmission-decay width d (which is given in eV) relates to the rate of change of transmission probability with barrier height. In the context of the LL approximation, used for deep tunneling, the definition becomes

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_147

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1 ∂D ∂ lnP ∂G 
 þ : d ∂H ∂H ∂H

ð147:3Þ

The elementary approximation takes P ¼ 1 and assumes an ET barrier. The corresponding elementary transmission-decay width is given by 1 ∂GET ð3=2ÞbH 1=2 ¼ : ¼ el ∂H F d

ð147:4Þ

For historical reasons, a transmission-decay-rate correction factor τ is then defined by 1 τ ¼ el : d d

ð147:5Þ

For well-behaved barriers, it is assumed that τ is usually close to unity. Symbols and abbreviations Short form

Full form

ET FF LL JWKB

exactly triangular Fr€ oman and Fr€ oman Landau and Lifschitz Jeffreys–Wentzel–Kramers–Brillouin

References [65F] Fr€oman, N., Fr€ oman, P.O.: JWKB Approximation: Contributions to the Theory. North-Holland, Amsterdam (1965) [08F3] Forbes, R.G.: J. Appl. Phys. 103, 114911 (2008)

Chapter 148

The Schottky effect and related parameters R. G. Forbes

The Schottky-Nordheim (SN) barrier, introduced by Schottky [23S] and first used in FE by Nordheim [28N], adds a planar image-PE term [14S] to the ET barrier and thus has the form M(z) ¼ H – eFz – e2/ 16πε0z. The SN barrier is the simplest realistic barrier and is used in Murphy-Good emission theory [56Mur, 07F] and (more recently) in so-called orthodox emission theory [13F]. As compared with an ET barrier, the top of the SN barrier is lowered by an amount ΔS given by  ΔS ¼ cS F1=2 

e3 4πε0

1=2 F1=2 ,

ð148:1Þ

where cS is the Schottky constant, given in Table 144.2 [https://doi.org/10.1007/978-3-662-53908-8_ 144]. This lowering is called the Schottky effect. The reference field FR needed to lower the barrier height by an amount equal to the local work function ϕ is: FR ¼ cS2ϕ2. A parameter f called the scaled barrier field (for a SN barrier of zero-field height ϕ) is defined by f ¼


F ¼ c2S ϕ2 F  FR



 4πε0 F: e3 ϕ 2

ð148:2Þ

For any ϕ-value, a corresponding value of a dimensionless parameter η can be defined by ηðϕÞ ¼

bϕ3=2 1 ¼ bc2S ϕ2  9:836 238ðeV=ϕÞ1=2 : FR

ð148:3Þ

Hence, the barrier strength GFET for an ET barrier of zero-field height ϕ can be written in the scaled form η GFET ¼ : f

ð148:4Þ

The subscript “F,” here and elsewhere, is used to label parameter values for barriers with H equal to ϕ. Illustrative values for η(ϕ) are given as part of Table 151.1 [https://doi.org/10.1007/978-3-662-53908-8_ 151] below.

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_148

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Symbols and abbreviations Short form

Full form

ET SN FE

exactly triangular Schottky–Nordheim field electron emission

References [14S] [23S] [28N] [56Mur] [07F] [13F]

Schottky, W.: Phys. Z. 15, 872 (1914) Schottky, W.: Z. Phys. 14, 632 (1923) Nordheim, L.W.: Proc. R. Soc. Lond. A121, 626 (1928) Murphy, E.L., Good Jr., E.H.: Phys. Rev. 102, 1464 (1956) Forbes, R.G., Deane, J.H.B.: Proc. R. Soc. Lond. A463, 290 (2007) Forbes, R.G.: Proc. R. Soc. Lond. A. 469, 20130271 (2013)

Chapter 149

Transmission probability for a Schottky-Nordheim barrier R. G. Forbes

For the SN barrier, the physical barrier-form correction factor νSN is given by the mathematical factor v( f ). This factor is obtained by substituting l0 ¼ f into an expression for the principal SN-barrier function v(l0 ) [07F, 08D], where l0 is a complementary elliptic variable [07F]1. Exact and approximate expressions for v ( f ) are known [07F, 08D]. A good, simple approximate expression [06F], better than others of equivalent complexity [10F1], and accurate to within an absolute error of 0.0026 (and to within a percentage error of 0.33%) over the range 0  f  1 [07F], is: vðf Þ  1  f þ ð1=6Þf ln f :

ð149:1Þ

This approximation is more than adequate for most technological purposes. However, for the range 0  f  1, more accurate numerical expressions for v( f ) and dv/df can be derived by fitting the following expressions to the exact results, where j is the order of the approximation v j ðf Þ ¼ ð1  f Þ 

dv df

j X

pi f i þ f ln f

i¼0



¼ u1 þ ð1  f Þ j

j X

ð149:2Þ

qi f i1 ,

i¼1 jþ1 X

si f i þ ln f

i¼0

j X

ð149:3Þ

ti f i ,

i¼0

where u1 ¼ 3π/(8 √ 2). Derived coefficients for the order 4 approximation ( j ¼ 4) are as shown in Table 149.1; these order 4 approximations are accurate to an absolute error of better than 8  1010, over 0  f  1 [07F]. Table 149.1 Coefficients for use in connection with Eqs. 149.2 and 149.3, for an order 4 ( j ¼ 4) numerical approximation i

pi

qi

si

ti

0 1 2 3 4 5

1 0.032 705 304 46 0.009 157 798 739 0.002 644 272 807 0.000 089 871 738 11 –

– 0.187 499 344 1 0.017 506 369 47 0.005 527 069 444 0.001 023 904 180 –

0.053 249 972 7 0.024 222 259 59 0.015 122 059 58 0.007 550 739 834 0.000 639 172 865 9 0.000 048 819 745 89

0.187 5 0.035 155 558 74 0.019 127 526 80 0.011 522 840 09 0.003 624 569 427 –

u1  0.833040 5509. Values are taken from [07F]

1

In recent work, the symbol l0 has been replaced by the symbol x, called the Gauss variable.

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_149

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In orthodox emission theory [56Mur, 07F, 13For2], and in the orthodox method of analyzing FN plots [13For2], several related SN-barrier functions are used. These are defined and can be approximated as uð f Þ ¼  tðf Þ ¼ v 

dv  ð5=6Þ  ð1=6Þf ln f , df

ð149:4Þ

ð4=3Þf dv  1 þ ðf =9Þ½1  ð1=2Þ ln f , df

ð149:5Þ

dðv=f Þ f dv f ¼v ¼ v þ uf  1  , dð1=f Þ df 6   ds f 2 ds ðf ln f Þ ¼  ð1=32Þf 2 6 þ wðf Þ  , dð1=f Þ df ð1  f Þ   ηdv r2012 ðf ; ηÞ ¼ exp  ¼ exp½ηu: df sðf Þ 

ð149:6Þ ð149:7Þ ð149:8Þ

Prior to 2006, the SN-barrier functions were expressed as functions of the Nordheim parameter y [¼f1/2], and this usage still occurs in some current literature. After 2006, it was discovered [06F, 07F, 08D] that using the mathematical variable l0 [¼y2] (or, more recently, the Gauss variable x) and the corresponding physical variable f is better practice. Reasons include (a) the exact series expansion for v( y) only has terms in even powers of y and (b) the parameter f is both easier to understand and more useful than y, especially in connection with the orthodoxy test discussed below, because f is proportional to the barrier field F. The functions u( f ), t( f ), s( f ), and w( f ) that use this new variable were introduced and discussed in [07F] and r2012( f ) in [13For1]. The function r2012( f ) replaces an older function r( f ), introduced in [07F], that was defined differently and is less useful. For all the above functions, numerical values over the range 0  f  1 are shown in Table 149.2. For v( f ), u( f ), t( f ), s( f ) and w( f ), the functions themselves and the sizes of the errors involved in the above approximate forms are shown graphically in [07F].

Table 149.2 Values of the Schottky-Nordheim (SN) barrier functions, tabulated as functions of scaled barrier field f. Columns marked with an asterisk are evaluated for work-function value ϕ ¼ 4.50 eV. The final column gives the related kernel current density for the SN barrier f

v

s

t

t2

u

w

r2012*

JkSN* [A/m2]

0.00 0.05 0.10 0.15 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.45 0.50

1.00000 0.92336 0.85944 0.80021 0.76618 0.74399 0.72215 0.70062 0.67938 0.65841 0.63769 0.61719 0.59690 0.57681 0.55692 0.53720 0.51764 0.48861 0.44095

1.00000 0.99078 0.98175 0.97286 0.96759 0.96409 0.96061 0.95715 0.95370 0.95026 0.94684 0.94343 0.94003 0.93664 0.93327 0.92991 0.92656 0.92155 0.91325

1.00000 0.97402 0.95644 0.94185 1.03472 1.03746 1.04010 1.04265 1.04513 1.04754 1.04989 1.05217 1.05441 1.05659 1.05872 1.06081 1.06286 1.06586 1.07068

1.00000 0.97402 0.95644 0.94185 0.93401 0.92909 0.92438 0.91986 0.91550 0.91129 0.90722 0.90328 0.89946 0.89575 0.89215 0.88864 0.88521 0.88024 0.87233

1 1.34838 1.22309 1.15099 1.11892 1.10051 1.08392 1.06885 1.05504 1.04231 1.03051 1.01950 1.00920 0.99953 0.99041 0.98178 0.97360 0.96208 0.94460

0.00000 0.00046 0.00179 0.00397 0.00568 0.00697 0.00840 0.00996 0.01164 0.01344 0.01537 0.01743 0.01960 0.02190 0.02432 0.02686 0.02952 0.03373 0.04134

nd 519.2 290.4 207.9 179.2 164.5 152.3 142.0 133.2 125.6 118.9 113.0 107.7 103.0 98.7 94.9 91.3 86.6 79.8

0 1.10  1026 3.34  106 2.76  101 5.88  103 8.75  104 8.05  105 5.16  106 2.51  107 9.77  107 3.20  108 9.06  108 2.28  109 5.21  109 1.09  1010 2.14  1010 3.94  1010 8.93  1010 2.84  1011 (continued)

149

Transmission probability for a Schottky-Nordheim barrier

3

Table 149.2 (continued) f 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

v 0.39412 0.34804 0.30263 0.25786 0.21365 0.16999 0.12682 0.08412 0.04185 0.00000

s 0.90501 0.89683 0.88869 0.88061 0.87258 0.86459 0.85664 0.84874 0.84087 0.83304

t 1.07531 1.07976 1.08405 1.08820 1.09222 1.09612 1.09992 1.10361 1.10721 1.11072

t2 0.86484 0.85773 0.85095 0.84447 0.83826 0.83230 0.82657 0.82105 0.81572 0.81057

u 0.92889 0.91465 0.90163 0.88965 0.87857 0.86825 0.85862 0.84958 0.84107 0.83304

w 0.04968 0.05873 0.06850 0.07897 0.09014 0.10199 0.11453 0.12775 0.14164 0.15620

r2012* 74.2 59.6 55.7 52.3 49.3 46.6 44.3 42.2 40.3 38.6

JkSN* [A/m2] 7.39  1011 1.66  1012 3.30  1012 6.02  1012 1.02  1013 1.62  1013 2.45  1013 3.56  1013 4.98  1013 6.77  1013

nd not usefully defined for f ¼ 0 (Adapted from [10F1])

For the SN barrier, Mayer [10M1, 10M3] has calculated values (PSN-values) of the tunneling pre-factor P that appears in Eq. 149.2. Illustrative values are shown in Table 149.3 for selected values of ϕ and F. Table 149.3 Values of the (dimensionless) tunneling pre-factor PSN for the Schottky-Nordheim barrier, shown for selected values of local work function ϕ and barrier field F. Calculated as described by Mayer [10M1] and taken from [10M3]. For value combinations marked “x,” the top of the barrier is below the Fermi level F

For ϕ ¼

[V/nm] 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0

2.0 eV 0.527 x x x x x x x

3.5 eV 0.759 0.713 0.634 0.470 x x x x

4.5 eV 0.912 0.880 0.843 0.789 0.693 0.565 0.443 x

5.5 eV 1.051 1.028 1.003 0.974 0.936 0.878 0.795 0.697

Symbols and abbreviations Short form

Full form

SN FN

Schottky–Nordheim Fowler–Nordheim

References [56Mur] [06F] [07F] [08D] [10F1] [10M1] [10M3]

Murphy, E.L., Good Jr., E.H.: Phys. Rev. 102, 1464 (1956) Forbes, R.G.: Appl. Phys. Lett. 89, 113122 (2006) Forbes, R.G., Deane, J.H.B.: Proc. R. Soc. Lond. A463, 290 (2007) Deane, J.H.B., Forbes, R.G.: J. Phys. A: Math. Theor. 41, 395301 (2008) Forbes, R.G., Deane, J.H.B.: J. Vac. Sci. Technol. B. 28, C2A33 (2010) Mayer, A.: J. Phys. Condens. Matter. 22, 175007 (2010) Mayer, A., Deane, J.H.B., Forbes, R.G.: 23rd International Vacuum Nanoelectronics Conference, Palo Alto (July 2010) [13For1] Forbes, R.G., Fischer, A., Mousa, M.S.: J. Vac. Sci. Technol. B. 31, 02B103 (2013) [13For2] Forbes, R.G.: Proc. R. Soc. Lond. A. 469, 20130271 (2013)

Chapter 150

Local emission current density regimes R. G. Forbes

A need, when discussing the local emission current density (LECD) J, is to have a mathematical formula for LECD in terms of an appropriate set of parameters, for example (but not necessarily), ϕ, F, and temperature T. For most emitters, the LECD can be obtained by summing contributions from all emitterelectron traveling states that are incident on the inside of the emitter surface, taking into account their individual occupation and transmission probabilities. The general form of the result is J ¼ Z s Ds ,

ð150:1Þ

where Zs is an effective incident (or “supply”) current density and Ds is a transmission probability. Depending on circumstances, one of these parameters is specified to be the value at a specific forward energy, and the other is then derived either as J/Ds (particularly in high-F, low-T situations) or as J/Zs (particularly in low-F, high-T situations). One or other of these approaches yields the formulae below. The existence of transmission regimes (Chap. 146[https://doi.org/10.1007/978-3-662-53908-8_146]) (in which a specific approximate mathematical formula holds for D) implies the existence of LECD regimes, in which a specific approximate mathematical expression holds for J. However, the definition of LECD regimes is more complicated, because additionally both the Schottky effect and occupationprobability theory need to be taken into account. Currently, there is no general consensus as to the best method of defining, classifying, and naming LECD regimes. However, it is generally recognized that three main LECD regimes exist. Cold field electron emission (CFE), also known as Fowler-Nordheim field electron emission (FNFE), is a LECD regime in which most electrons escape by deep tunneling from states close to the emitter Fermi level, and the Landau and Lifschitz approximation can be applied. In this case, Eq. 150.1 can be written in the form J ¼ ZF PF exp½GF ,

ð150:2Þ

where “F” labels parameters related to a barrier of zero-field height ϕ, as before. It is convenient, here, to write ZFPF in the equivalent form λCFEaϕ1F2 [08F2, 12F], where a is the first FN constant (see Table 144.2 [https://doi.org/10.1007/978-3-662-53908-8_144],) and λCFE is the local pre-exponential correction factor (for CFE). For CFE from metal emitters that are “not too small,” the LECD J(ϕ,F) is given formally by the linked equations J ¼ λCFE J k , " J k ¼ aϕ1 F2 exp 

νbϕ F

3=2

ð150:3aÞ

# ,

ð150:3bÞ

where Jk is the so-called kernel current density and other parameters have their previous meanings. In this formulation, the pre-factor P is part of λCFE. The reason for splitting the equation in this way is that, for any R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_150

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chosen barrier form and choice of ϕ and F, the kernel current density Jk can be evaluated exactly; other uncertainty in LECD prediction is accumulated into the single parameter λCFE. (However, there will of course be further uncertainty in knowing how well the chosen values of ϕ, F, and ν apply a particular experimental situation under discussion.) Several physical effects contribute to λCFE; some are material specific, and some can be treated with many different models and approximations. For the foreseeable future, there is no possibility of having exact (or even good) general prediction of λCFE values. The best that might currently be done is estimation of the range of values within which λCFE might lie, but even this has only been done for the SN barrier (see below). Nevertheless, Eq. 150 has the property of technical completeness, in the sense that all factors that contribute to CFE are formally included within the equation. Equation 150 is one kind of Fowler-Nordheim-type equation. Despite its name, CFE and Eq. 150 apply up to quite high temperatures, maybe as much as 2000 K or more (depending on the value of F) for a material with work function ϕ ¼ 4.50 eV, for example, tungsten. Barrier-top electron emission (BTE) (also called extended Schottky emission) is an LECD regime where significant numbers of electrons escape both by tunneling and by flyover, and the peak of the normal (i.e., forward) energy distribution is close to the top of the barrier. Thermal electron emission (TE) (also called thermionic emission) is an LECD regime where almost all electrons cross the barrier by means of flyover, although wave-mechanical effects can cause an incident electron with w> 0 be reflected back into the emitter (e.g., [28F1, 28N, 84Mod]). The barrier may be slightly or significantly lowered and modified by the Schottky effect, but not so far that significant tunneling occurs. In the 1920s, the name “thermionic emission” was used to describe the emission of a hypothetical special type of electron, called a “thermion,” which was considered to be in an “agitated” energy state that was different in kind from that of the “conduction electrons” (e.g., [28M]). The work of Fowler and Nordheim [28F2] and later Sommerfeld and Bethe [33S] disproved the existence of thermions, by showing that both field-emitted and thermally emitted electrons came from the same basic electron population (now called the “conduction band”), under different conditions of field and temperature. Nevertheless, the name “thermionic emission” is still widely used. Given that Fowler and Nordheim showed in 1928 that thermions do not exist, the name “thermal electron emission” is preferred here. As far as the author knows, no technically complete general equation has yet been formulated for barrier-top or thermal electron emission, but approximate equations exist for the SN barrier (see below). Symbols and abbreviations Short form

Full form

SN LECD TE CFE BTE FN FE

Schottky–Nordheim local emission current density thermal electron emission cold field electron emission barrier top electron emission Fowler–Nordheim field electron emission

References [28F1] [28F2] [28M] [28N] [33S]

Fowler, R.H.: Proc. R. Soc. Lond. A. 117, 549 (1928) Fowler, R.H., Nordheim, L.: Proc. R. Soc. Lond. A. 119, 173 (1928) Millikan, R.A., Lauritsen, C.C.: Proc. Natl. Acad. Sci. U. S. A. 14, 15 (1928) Nordheim, L.W.: Proc. R. Soc. Lond. A121, 626 (1928) Sommerfeld, A., Bethe, H.: Zur Elektronentheorie der Metalle. In: Flügge, S. (ed.) Handbuch der Physik, vol. 24. Springer, Berlin (1933) [84Mod] Modinos, A.: Field, Thermionic and Secondary Electron Emission Spectroscopy. Plenum, New York (1984). Republished as paperback edition by Springer, New York (2013) [08F2] Forbes, R.G.: J. Vac. Sci. Technol. B. 26, 788 (2008) [12F] Forbes, R.G.: Nanotechnology. 23, 095706 (2012)

Chapter 151

Local emission current densities for a Schottky-Nordheim barrier R. G. Forbes

For CFE through an SN barrier, the local emission current density is given by Eq. 154.3[https://doi.org/ 10.1007/978-3-662-53908-8_154], with ν replaced in Eq. 154.3b[https://doi.org/10.1007/978-3-66253908-8_154] by v( f ), as described above. A work-function-dependent “scaling parameter” θ(ϕ) can be defined by 3 θðϕÞ ¼ aϕ1 F2R ¼ ac4 S ϕ :

ð151:1Þ

Making use of θ(ϕ), and of the parameter η(ϕ) defined earlier, the kernel current density JkSN for the SN barrier can then be written exactly in scaled form as 

J kSN

 η ¼ θf  exp vðf Þ  : f

ð151:2Þ

2

Illustrative values of θ(ϕ) are given in Table 151.1 below. The primary merit of this scaled form is that it is a simple form, with only one independent field-like variable on the right-hand side. But it also allows some results relating to materials with different work functions to be presented in a more uniform way. Table 151.1 This table gives the reference field FR(ϕ), and the scaling parameters η(ϕ) and θ(ϕ), for a SN barrier of zero-field height ϕ. It shows the related f-values that set the “apparently reasonable” range flow  f extr  fup and the “clearly unreasonable” ranges f extr < flb and f extr > fub, as discussed in Chap. 156[https://doi.org/10.1007/978-3-662-53908-8_156], Values listed are taken from Table 2 in [13F] ϕ [eV] 5.50 5.00 4.50 4.00 3.50 3.00 2.50

FR [V/nm] 21.01 17.36 14.06 11.11 8.51 6.25 4.34

η

θ [A/m2]

4.1942 4.3989 4.6368 4.9181 5.2577 5.6790 6.2210

1.24  10 9.29  1013 6.77  1013 4.76  1013 3.19  1013 2.01  1013 1.16  1013 14

flb

flow

fup

fub

0.09 0.095 0.10 0.105 0.11 0.12 0.13

0.14 0.14 0.15 0.16 0.17 0.18 0.20

0.41 0.43 0.45 0.48 0.51 0.54 0.59

0.69 0.71 0.75 0.79 0.85 0.91 0.98

For the SN barrier, it has been possible to identify (e.g., [08F2]) the main factors that contribute to the pre-exponential correction factor λCFE and to estimate the range of values that they might reasonably take. These contributory estimates are shown in Table 151.2. Overall, the best current (2018) guess is that λCFE probably lies in the range 0.005 < λCFE < 11 (this is an improved guess, as compared with earlier

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_151

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publications). Although derived specifically for the SN barrier, this range may be used a first guess for other barrier forms. Table 151.2 Estimated values for λCFE and its component effects (for “orthodox” FN-type equation based on SN barrier) (estimates made in September 2014) Physical origin of correction factor

Symbol for effect

Value of multiplier

Tunneling pre-factor Correct summation over states Combination of above effectsa Temperature effects at 300 K Electronic effects (atomic wave functions and band-structure effects) All effects together

PF λD λDPF λT (300 K) λE λCFE

~ (0.4–1.1) ~ (0.9–1.3) ~ (0.5–1.0) ~ 1.1 ~ (0.01–10) ~ (0.005–11)

Note that high values of λD tend to be associated with low values of PF

a

In treatments of the CFE regime that set P ¼ 1, as in the Murphy and Good work [56Mur], the contributory factor λT that relates to temperature effects is thought to be nearly independent of barrier form [04F] and may be written as pπ , sin ðpπÞ

ð151:3aÞ

kB T kB T kB T ¼ 1 el  el , dF τF d F dF

ð151:3bÞ

λT ¼ p

where p is a parameter given by Eq. 151.3b, T denotes thermodynamic temperature, dF and dFel are values that apply to a barrier of zero-field height ϕ, and 1/dFel ¼ (3/2)bϕ1/2/F. For the barrier-top and thermal electron emission LECD regimes, for the SN barrier, there is a common high-level form for the equation for local emission current density, namely

Z RS

J ¼ Dapp Z RS ,     cS F1=2 ϕ 2  AR0 T exp exp  : kB T kB T

ð151:4aÞ ð151:4bÞ

ZRS is the “classical” Richardson-Schottky expression, in the modified form introduced by Fowler [28F1] (but rarely attributed to him), which takes into account electron spin but not wave-mechanical reflection effects, and AR0 is the universal theoretical Richardson constant given in Table 144.2 [https://doi.org/10. 1007/978-3-662-53908-8_144]. Dapp is the apparent transmission probability, which takes into account electron transmission at the surface barrier and also other factors (including band-structure effects). The related apparent reflection coefficient rapp (for an electron approaching the emitter surface from the inside) is given by rapp ¼ 1 – Dapp. As far as the author knows, no general theory has been developed for Dapp: the low-field case (thermal electron emission) and barrier-top electron emission need to be considered separately. Detailed theory for the low-field limit does exist (e.g., [84Mod]) but involves complicated quantum mechanics. A simple assumption is to take Dapp ~ 0.5 (see [28F1] for related discussion). Experimentally derived values of the product DappAR0[¼(1 – rapp)AR0] can be found in old literature (e.g., 49Her, 56 N), but it is sometimes unclear how reliable such values are. For barrier-top electron emission across a SN barrier, theory based on the Kemble approximation [35K] (see Table 147.1[https://doi.org/10.1007/978-3-662-53908-8_147]) leads to the formula, investigated originally by [56Mur] but given here in an amended form similar to that used by [73S]:

151

Local emission current densities for a Schottky-Nordheim barrier

3

qπ , sin ðqπÞ

ð151:5aÞ

Dapp  q

Cδ F3=4  Cq F3=4 T 1 , kB T

ð151:5bÞ

where Cδ and Cq are universal constants given in Table 144.2[https://doi.org/10.1007/978-3-662-539088_144]. There is some cause [09S1] to think that the validity of Eqns 151.5a and 151.5b (taken together) may be limited, but the exact reason is not yet determined. It might be because its mathematical derivation is valid only for a smaller range of q-values than hitherto thought, or because the approximation of setting P ¼ 1 is poorer than thought, or both. Symbols and abbreviations Short form

Full form

SN LECD CFE FN

Schottky–Nordheim local emission current density cold field electron emission Fowler–Nordheim

References [28F1] [35K] [56Mur] [73S] [84Mod] [04F] [08F2] [09S1] [13F]

Fowler, R.H.: Proc. R. Soc. Lond. A. 117, 549 (1928) Kemble, E.C.: Phys. Rev. 28, 549 (1935) Murphy, E.L., Good Jr., E.H.: Phys. Rev. 102, 1464 (1956) Swanson, L.W., Bell, A.E.: Adv. Electr. Electron. Phys. 32, 193 (1973) Modinos, A.: Field, Thermionic and Secondary Electron Emission Spectroscopy. Plenum, New York (1984). Republished as paperback edition by Springer, New York (2013) Forbes, R.G.: Surf. Interface Anal. 36, 395 (2004) Forbes, R.G.: J. Vac. Sci. Technol. B. 26, 788 (2008) Swanson, L.W., Schwind, G.A.: Chapter 1. In: Orloff, J. (ed) Handbook of Charged Particle Optics (2nd Edition). Boca Raton, CRC Press (2009) Forbes, R.G.: Proc. R. Soc. Lond. A 469, 20130271 (2013)

Chapter 152

Energy distributions for the Schottky-Nordheim barrier R. G. Forbes

Particularly in connection with the theory of field electron emission sources and their electron-optical properties, it is useful to have information about the normal energy distribution (NED), parallel energy distribution (PED), and total energy distribution (TED) of emitted electrons, for each of the LECD regimes. In each case what one ideally needs to know is the mathematical form of the distribution, information about its peak value and average value, and information about the width of the distribution, as assessed by one or more appropriate criteria (such as full width at half maximum). For the cold field electron emission and barrier-top regimes, these values (and analytical formulae for them, where derivable) would depend somewhat on the form assumed for the tunneling barrier and on precisely what other theoretical assumptions are made. In practice, it is only for the Murphy-Good-type theory [56Mur] of emission across the SN barrier that substantial amounts of detailed theory have been developed, and this theory is neither fully complete in its scope nor presently assembled in any one place. It is beyond the scope of this contribution to complete and assemble detailed information concerning energy distribution theory. Useful introductory material may be found in [73S], more details concerning cold field electron emission in [09S2] and more about barrier-top electron emission in [09S1]. Other relevant material may be found in [73G, 84Mod, 96H, 07J]. Symbols and abbreviations Short form

Full form

PED LECD TED NED

parallel energy distribution local emission current density transmission electron diffraction normal energy distribution

References [56Mur] [73G] [73S] [84Mod] [96H] [07J] [09S1] [09S2]

Murphy, E.L., Good Jr., E.H.: Phys. Rev. 102, 1464 (1956) Gadzuk, J.W., Plummer, E.W.: Rev. Mod. Phys. 45, 487 (1973) Swanson, L.W., Bell, A.E.: Adv. Electr. Electron. Phys. 32, 193 (1973) Modinos, A.: Field, Thermionic and Secondary Electron Emission Spectroscopy. Plenum, New York (1984). Republished as paperback edition by Springer, New York (2013) Hawkes, P.W., Kasper, E.: Principles of Electron Optics. Applied Geometrical Optics, vol. 2. Academic, London (1996) Jensen, K.L.: Electron emission physics. Adv. Imaging Electron Phys. 149, 1 (2007) Swanson, L.W., Schwind, G.A.: Chapter 1. In: Orloff, J. (ed) Handbook of Charged Particle Optics (2nd Edition). Boca Raton, CRC Press (2009) Swanson, L.W., Schwind, G.A.: Chapter 2. In: Hawkes, P. (ed.) Cold Field Emission and the Scanning Transmission Electron Microscope. Advances in Imaging and Electron Physics, vol. 139, p. 63. Elsevier, Amsterdam (2009)

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_152

1

Chapter 153

Basic auxiliary relationships R. G. Forbes

Auxiliary relationships are needed to relate (i) local emission current density (LECD) to the total emission current ie and (ii) barrier field to the emission voltage Ve between the emitting region and a counterelectrode. To set these relationships up, it is necessary to consider characteristic parameters relating to a characteristic point “C” on the emitter surface. In the simple models usually considered for a traditional, isolated, single-tip field emitter (STFE), this point is taken at the model apex. With multi-tip large-area field emitters (LAFEs), the characteristic point is considered to be at the apex of a model representing the tip with the highest apex field. A notional emission area An is formally defined by integrating the LECD over the whole emitting area (over all tips, in the multi-tip case) and writing the result in the form AnJC where JC is the characteristic LECD. Thus, Z ie ¼ JdA  An J C : ð153:1Þ Using Eq. 150.3[https://doi.org/10.1007/978-3-662-53908-8_150], this can also be written in terms of a characteristic kernel current density JkC: ie ¼ An λCFE J kC  Af J kC ,

ð153:2Þ

where the formal emission area Af [λCFEAn] is defined by this equation. An is closer to the actual emitting area, but the parameter initially extracted from experiments performed in “orthodox” emission situations (see below) will usually be Af. For LAFEs, both these areas will be much less than the macroscopic area (or “footprint”) of the device, AM. The relationship between a characteristic local barrier field FC at the chosen emitter apex and the emission voltage Ve can be written in any of the equivalent forms FC ¼

βC V e Ve ¼ , ζC kC r a

ð153:3Þ

where βC is the characteristic voltage-to-local-field conversion factor, ζ C is the characteristic local conversion length, ra is the emitter apex radius, and kC is a characteristic shape factor (sometimes called a field factor and denoted by kf). The form involving ζ C is now preferred by the author, because β has other meanings in present-day FE literature and confusion has occurred. ζ C is a mathematical parameter related to the electrostatics of the situation; it is a measure of emitter sharpness, with sharp emitters having small ζ C-values. Except in special cases, ζ C is not given by a physical length. The values of βC, ζ C, and kC depend in principle on the whole system geometry, and may sometimes be current-dependent [16F]. With LAFEs, an alternative measure of emitter sharpness is the characteristic macroscopic field enhancement factor (FEF) γ C. This parameter is a measure of the field-enhancing effect of a single R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_153

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R. G. Forbes

protrusion on a defined substrate (commonly, but not always, the substrate is one of a pair of parallel plates of large extent) and is normally (but not always) defined as follows. The field at the position of the protrusion apex, in the absence of the protrusion, is termed the macroscopic field FM and is related to the emission voltage by FM ¼

Ve , ζM

ð153:4Þ

where ζ M is the macroscopic conversion length. Again, ζ M is a mathematical parameter related to the electrostatics of the situation and is not necessarily a physical length; however, in the common case of an isolated protrusion on one of a pair of smooth parallel plates of large extent and significant separation, it is adequate to identify ζ M with the plate separation. The FEF γ C is then defined and given by γC 

FC ζ M ¼ : FM ζ C

ð153:5Þ

For STFEs not mounted on an extended substrate, the best simple model is the sphere-on-orthogonal-cone (SOC) model [49Hal, 53D]. This predicts that kC is given approximately by kC  n

ðlc =r a Þn n þ ðn þ 1Þðr c =r a Þ2nþ1

o,

ð153:6Þ

where lc is the distance from the center of the core sphere to the counter-electrode, rc is the chosen radius of the core sphere, ra (as before) is the apex radius of curvature, and n is a chosen parameter that relates to the half-angle αcone of the underlying cone. The relationship between n and αcone is indicated in Table 153.1. Experience suggests that, for STFEs in practical situations, the value of kC often lies in the range 3 < kC < 8. Table 153.1 The relationship between the SOC model exponent n and the internal half-angle αcone of the orthogonal cone αcone [deg]

n

αcone [deg]

1 2 3 4 5 6 7 8

0.1052 0.1230 0.1364 0.1479 0.1581 0.1676 0.1766 0.1851

9 10 11 12 13 14 15 16

0.1933 0.2012 0.2090 0.2166 0.2240 0.2314 0.2387 0.2459

αcone [deg]

n

αcone [deg]

n

17 18 19 20 25 30 35 40

0.2531 0.2603 0.2674 0.2745 0.3101 0.3462 0.3834 0.4223

45 50 55 60 65 70 75 80

0.4631 0.5063 0.5523 0.6015 0.6545 0.7118 0.7741 0.8423

Another simple emitter model, the hemisphere-on-a-cylindrical-post (HCP) model, is often used to model a protrusion (such as a carbon nanotube) situated on an extended substrate. For a highly conducting feature of radius ra and height (post + hemisphere) h, when the distance la of the counter-electrode from the tip of the post is such that la>> > h, an approximate formula for the FEF is [03F] γC 

0:7h : ra

ð153:7Þ

In the case where the protrusion is on one of a pair of parallel plates of large extent, separated by a moderate to large distance lp, it follows from Eq. 153.5 that

153

Basic auxiliary relationships

3

ζC 

1:4 lp r a 1:4 lp ; kC  : h h

ð153:8Þ

Some other relevant formulae are given in Tables 153.2 and 153.3.

Table 153.2 Approximate formulae for conversion lengths (ζC) applying to model apex, for selected axially symmetric models of a traditionally mounted, conducting, single-tip field emitter (i.e., no extended substrate behind the emitter) No.

Model

ζC

References

1

Hyperboloid of apex radius ra, facing distant planar electrode, where lf is distance from focus to distant plane Paraboloid of apex radius ra, facing distant confocal paraboloidal electrode, where la is distance between apices of paraboloids Rounded mathematical Taylor cone (with half-angle equal to Taylor angle 49.3 ) of apex radius ra, facing correctly shaped electrode a distance lc from the underlying cone apex Mathematical Taylor cone, with apex protrusion with shape of hemisphere of radius ra on cylindrical post of length h (including hemisphere) measured from cone apex, facing distant electrode a distance lc from the cone apex

(ra/2) ln(4lf/ra)

[28E, 71C]

(ra/2) ln(1 + 2la/ra)

[51B, 68B]

(ralc)1/2

[69S]

ra(lc/h)1/2

[91M]

2 3

4

Table 153.3 Approximate formulae for macroscopic field enhancement factors (γ C) applying to model apex, for selected axially symmetric models of a conducting protrusion on an extended substrate. All models here assume that the counterelectrode is sufficiently far away γC

No.

Model (with alternative approximations, where relevant)

5 6

Hemisphere of any radius. 3 [20J] Floating sphere (of radius ra) at emitter potential, with sphere apex at distance 2.5 + (h/ra) [03F] h above planar emitter Hemisphere of radius ra on cylindrical post of length h (including hemisphere), using μ defined by μ ¼ h/ra. All formulae are fits to numerical results Vibrans 2+μ [64V] Edgecombe and Valdre` (within 25%, for 30  μ  2,000) 0.7μ [01E] Edgecombe and Valdre` (within 3%, for 4  μ  3,000) 1.2  (2.15 + μ)0.9 [01E] Kokkaris et al. (20 < μ < 600) 5.93 + 0.73μ – 104μ2 [01K] Hemi-ellipsoid of height h and base radius ρb, and with apex radius ra, using definitions ν ¼ h/ρb ¼ (h/ra)1/2; θ ¼ (ν2  1)1/2 Full formulaa) θ3/[{νln(ν + θ)} – θ] [81L, 09P1] ν2/[ln(2ν) – 1] Approximate formula (high aspect-ratio)b) Alternative approximate form (high aspect ratio) (2 h/ra)/[ln(4 h/ra) – 2] [91K]

7 7a 7b 7c 7d 8 8a 8b 8c

References

A convenient proof of this formula is obtained from Eq. 6 in [09P1], by recognizing that their parameter ξ (the ellipse eccentricity) is equal to θ/ν and that (1 – ξ2 ¼ 1/ν2) b Derived by approximating θ  ν a

Formulae (153.6, 153.7, and 153.8) above relate to the situation where the counter-electrode is sufficiently far away from the emitter that it has no significant influence on the mathematical form of the equation. This is the case in many applications. When the emitter is sufficiently close to the counterelectrode, modifications to the above formulae are needed (e.g., [67M, 84Mil, 09P2]), but their discussion is considered beyond the scope of this contribution. Using Eq. 150.3[https://doi.org/10.1007/978-3-662-53908-8_150] and these auxiliary relationships, a technically complete FN-type equation for ie(Ve,ϕ), for the CFE regime, may be written formally as

4

R. G. Forbes

" ie ¼

2 A f aϕ1 ζ 2 C V e exp

# νbϕ3=2 ζ C :  Ve

ð153:9Þ

The auxiliary relationships between field and voltage also apply to field ion emitters, but with FC interpreted as a characteristic model field. Symbols and abbreviations Short form

Full form

STFE LECD FN HCP CFE SOC LAFE FEF FE

single-tip field emitter local emission current density Fowler–Nordheim hemisphere-on-cylindrical-post cold field electron emission sphere-on-orthogonal-cone large-area field (electron) emitter field enhancement factor field electron emission

References [20J] [28E] [49Hal] [51B] [53D] [64V] [67M] [68B] [69S] [71C] [81L] [84Mil] [91K] [91M] [01E] [01K] [03F] [09P1] [09P2]

Jeans, J.H.: The Mathematical Theory of Electricity and Magnetism, 4th edn, p. 194. CUP, Cambridge (1920) Eyring, C.F., MacKeown, S.S., Millikan, R.A.: Phys. Rev. 31, 900 (1928) Hall, R.N.: J. Appl. Phys. 20, 925 (1949) Becker, J.A.: Bell Syst. Tech. J. 20, 907 (1951). Formula attributed to S.P. Morgan, private communication Dyke, W.P., Trolan, J.K., Dolan, W.W., Barnes, G.: J. Appl. Phys. 24, 570 (1953) Vibrans, G.E.: J. Appl. Phys. 35, 2855 (1964) Miller, H.C.: J. Appl. Phys. 38, 4501 (1967) Beckey, H.D., Krone, H., R€ ollgen, F.W.: J. Phys. E: Sci. Instr. 1, 118 (1968) Swatik, D.S.: PhD thesis, University of Illinois (1969). See p. 23 Coelho, R., Debeau, J.: J. Phys. D Appl. Phys. 4, 1266 (1971) Latham, R.V.: High Voltage Vacuum Insulation. Academic, London (1981) Miller, H.C.: J. Appl. Phys. 55, 158 (1984) Kosmahl, H.G.: IEEE Trans. Electron Devices. 38, 1534 (1991) Mair, G.L.R., Forbes, R.G.: J. Phys. D Appl. Phys. 24, 2217 (1991) Edgcombe, C.J., Valdre`, U.: J. Microsc. 203, 188 (2001) Kokkaris, G.C., Kyritsakis, A., Xanthakis, J.P.: J. Appl. Phys. 91, 4580 (2001) Forbes, R.G., Edgcombe, C.J., Valdre`, U.: Ultramicroscopy. 95, 57 (2003) Poglerov, E.G., Zhbanov, A.I., Chang, Y.-C.: EPL. 85, 17001 (2009) Poglerov, E.G., Zhbanov, A.I., Chang, Y.-C.: Ultramicroscopy. 109, 373 (2009)

Chapter 154

Field electron emission measurement circuit theory R. G. Forbes

This chapter relates primarily to current-voltage measurements in the CFE regime, which is a topic of particular present interest for experimentalists. The interpretation of measurements in the barrier-top (i.e., “extended Schottky”) regime is technologically important but is a specialized interest well discussed elsewhere [09S1]. Methods of interpreting measurements in the thermal electron emission regime are adequately covered in older literature, e.g., [49Her, 56N]. A schematic diagram representing the circuits used to measure field electron emission current-voltage characteristics is shown in Fig. 154.1. A field electron emitter is a nonlinear circuit device, broadly analogous to a pn-junction diode. When emitting in the CFE regime, it has an effective resistance Re given by Ve ¼ Re ¼ ie




ϕζ 2C A f aV e



"

νF bϕ3=2 ζ C  exp Ve

# ð154:1Þ

Fig. 154.1 Schematic diagram of electrical circuit for the measurement of field electron emitter current-voltage characteristics, showing the distinction between emission parameters {ie, Ve} and measured parameters {im, Vm}. In accordance with the convention often used in electron emission, the arrows show the direction of electron flow, not the direction of conventional current flow

This equation shows that at low emission voltages, Re is very large but that Re becomes much smaller as Ve increases. It is usually possible, by careful system design, to make the parallel resistance Rp shown in Fig. 154.1 very large (effectively infinite), but it is often impossible to eliminate both of the series resistances (which, when Rp ¼ 1, combine to give a total series resistance Rs). As a result, conceptual distinction is needed between the emission quantities {ie, Ve} and the measured quantities {im, Vm}. It is usually legitimate to take ie ¼ im, but Ve and Vm are related by V e ¼ V m  im RS :

ð154:2Þ

Defining a parameter Θ (the voltage ratio) by Ve ¼ ΘVm yields

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_154

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R. G. Forbes

Θ

Ve Re : ¼ V m ð Re þ Rs Þ

ð154:3Þ

Inserting this into Eq. 153.9[https://doi.org/10.1007/978-3-662-53908-8_153], and putting im ¼ ie, yields a technically complete FN-type equation for im(Vm,ϕ), in the CFE regime, namely " im ¼

2 2 A f aϕ1 ζ 2 C Θ V m exp

# νF bϕ3=2 ζ C  : ΘV m

ð154:4Þ

Since Re starts large at low voltage, but then decreases, it follows that if/when Re becomes comparable with Rs, then Θ becomes significantly voltage dependent and begins to decrease from unity. If Rs is very small, as it is for an old-style metal emitter well connected to the high voltage supply, then one can take Θ ¼ 1 throughout the operating range. When there is a poorly conducting element in the conducting path to the high-voltage supply, putting Θ ¼ 1 is likely not to be a valid assumption. If Rs is itself current dependent in the current range of interest, or if there are several different kinds of resistive element in the circuit, then the behavior of Θ may become very complicated. This additional voltage dependence (in Θ) in the exponent of Eq. 154.4, which seems to be relatively common in experiments involving some forms of nontraditional emitter [13F], creates considerable complications for the analysis of current-voltage characteristics. What one needs are a method for analyzing im-Vm characteristics under the assumption that effectively Θ ¼ 1 throughout the range of interest, a method for determining when this assumption is untrue (or is likely to be untrue); and strategies for dealing with situations when Θ is voltage dependent. The first two of these issues are addressed in the following chapters; the third is still a topic of active research [15F, 17F]. Symbols and abbreviations Short form

Full form

CFE

cold field electron emission

References [49Her] Herring, M., Nichols, M.H.: Rev. Mod. Phys. 21, 185 (1949) [56N] Nottingham, W.: Thermionic emission. In: Flügge, S. (ed.) Handbuch der Physik, vol. 21. Springer, Berlin (1956) [09S1] Swanson, L.W., Schwind, G.A.: Chapter 1. In: Orloff, J. (ed) Handbook of Charged Particle Optics (2nd Edition). Boca Raton, CRC Press (2009) [13F] Forbes, R.G.: Proc. R. Soc. Lond. A. 469, 20130271 (2013) [15F] Forbes, R.G., Deane, J.H.B., Fischer A., Mousa, M.S.: Jordan J. Phys. 8, 125 (2015) 125; [arXiv 1504.06134v7] [17F] Forbes, R.G.: Appl. Phys. Lett. 110, 133109 (2016)

Chapter 155

Basic theory of Fowler-Nordheim plots R. G. Forbes

Equation 154.4 [https://doi.org/10.1007/978-3-662-53908-8_154] can be rewritten in the form
     νF bϕ3=2 ζ C νF bϕ3=2 ζ C 2
1
2 2  ln i ¼ ln A

L V
1 =V aϕ ζ Θ  ln C f g m f iV m m C ΘV m ΘV m

ð155:1aÞ

where L and CiV are defined by Eq. 155.1a and are introduced to simplify algebraic presentation. A FowlerNordheim plot is a plot of the form L(Vm
1) vs Vm
1 (or a similar plot using related variables, such as JC and FC). To simplify presentation further, let x denote the variable Vm
1 being plotted on the FN-plot horizontal axis, and let y denote the variable ln{im/Vm2} being plotted on the vertical axis. Equation 155.1a then becomes y ¼ ln fCiV g
vF bϕ3=2 ζ C Θ
1 x:

ð155:1bÞ

The theoretical plot defined by Eq. 155.1a is normally curved. The tangent to Eq. 155.1b, at any value xt of x(i.e., Vm
1) can be written in the form h i y ¼ ln fρðxt Þ:CiV g
σ ðxt Þ:bϕ3=2 ζ C :x,

ð155:2Þ

where σ(x) and ρ(x) are, respectively, slope and intercept correction functions that can (in principle) be determined by mathematical analysis based on Eq. (155.1) (see below). Although other plot forms have been proposed or used (e.g., the Millikan-Lauritsen (ML) plot ln{im} vs Vm
1 [28M]), FN plots are now the commonest tool for characterizing CFE current-voltage data. The aim is to extract values of ζ C and/or Af and, where needed, related parameters such as γ C. Historically, FN plots of experimental data have normally been analyzed by fitting to the plot a straight line with equation y ¼ lnfRfit g þ Sfit x

ð155:3Þ

In the tangent method of FN plot analysis, one assumes that point xt can be identified with the point at which the theoretical tangent is parallel to the fitted line, then identifies Eq. 155.3 with Eq. 155.2 and (in principle) extracts values for ζ C and CiV using the equations S fit ðζ C Þextr ¼
, σ t bϕ3=2

ð155:4aÞ

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_155

1

2

R. G. Forbes

ðCiV Þextr ¼

R fit , ρt

ð155:4bÞ

where σ tσ(xt) and ρtρ(xt). The correction factors σ t and ρt cannot be measured but have to be estimated theoretically using specific, physically plausible, mathematical assumptions about the forms of νF, CiV, and Θ. Herein lie some of the main difficulties of FN plot analysis for nontraditional emitters. In principle, σ and ρ are given by Eq. 155.5. (see [13For1], but note the correction including Θ in Eq. 155.5b here): dL σ ðxÞ ¼ 

dx , bϕ3=2 ζ C  νF ðxÞ ln fρðxÞg ¼ σ ðxÞ
 bϕ3=2 ζ C x: Θ

ð155:5aÞ ð155:5bÞ

These equations look simple enough, but in Eq. 155.1 all of Af, ϕ, ζ C, Θ, and νF can in principle (in some situations) be functions of Vm
1 (i.e., of x). Consequently, the derivative dL/dx contains many terms, some of which have never been investigated systematically. Existing treatments involve the making of a series of simplifications, some of which are now known to be invalid in some or many situations. The basic approximation sets Θ ¼ 1 and assumes that Af, ϕ, and ζ C can be treated as constants. In this case, the only dependences on Vm are the direct dependence and the dependence in the barrier-form correction factor νF. This level of simplification allows the effect of barrier form to be explored and is particularly relevant for exploring effects associated with highly conducting emitters of small apex radius. The orthodox approach assumes, in addition, that the barrier is a SN barrier. In this case σ and ρ are given by the SN-barrier functions s( f ) and r2012( f ), listed in Table 151.2. Since s( f ) is slowly varying, the value σ t ¼ st ¼ 0.95 is usually adequate in Eq. 155.4a. Relatively reliable values can also be extracted [08F1] for ft. and hence rt [r2012( ft)], and an estimate of Af can be derived from extr "
2 extr # ζ 2C CiV ζC ¼ ¼  R fit
1 aϕ rt aϕ
1


Aextr f

ð155:6Þ

Alternatively, this equation can be combined with the orthodox simplification of Eq. 155.4a (i.e., putting σ t ¼ st) to yield a direct formula for Af: Aextr f

h
2 i R fit  S fit ¼ 

2  1=2  rt s2t ab ϕ

ð155:7Þ

The value of ab2 is given in Table 146.2. Further physical interpretation of the extracted formal area (to deduce An from Af) requires knowledge of λCFE in Eq. 155.2, which is usually not reliably available. The elementary approach assumes, in addition to the basic approximation, that the barrier is an ET barrier. In this case σ t ¼ 1 and ρt ¼ 1. The elementary approach is widely used in present-day experimental literature but is never physically valid. In cases where the orthodox approach is adequately valid, the elementary approach will give good estimates of ζ C and γ C but unreliably large estimates of Af. When the orthodox approach is not valid, the elementary approach will not yield good estimates for any parameter. Most FN-plot analysis in the last 50 years or so has used either the orthodox approach (or simpler versions of it) or the elementary approach. But it is becoming increasingly clear that orthodox data-analysis theory may not work well for very sharp emitters and does not work well for poorly conducting emitters. Thus, topics of current research interest are the development, within the context of the basic approximation, of better methods of analyzing FN plots taken from sharply curved emitters [13Fis, 14Kyr] and the development of methods of analyzing FN plots taken from poorly conducting emitter arrangements. Sharply curved emitters can generate FN plots that are noticeably curved, and improved methodology

155

Basic theory of Fowler-Nordheim plots

3

may involve fitting model-generated curves to curved FN or ML plots or to directly plotted current-voltage characteristics. For emitters that may be poorly conducting, the first need is to establish whether an interpretation problem exists, as discussed in the next chapter. Symbols and abbreviations Short form

Full form

ML SN FN ET CFE

Millikan-Lauritsen Schottky–Nordheim Fowler–Nordheim exactly triangular cold field electron emission

References [28M] [08F1] [13Fis] [13For1] [14Kyr]

Millikan, R.A., Lauritsen, C.C.: Proc. Natl. Acad. Sci. U. S. A. 14, 15 (1928) Forbes, R.G.: J. Vac. Sci. Technol. B. 26, 209 (2008) Fischer, A., Mousa, M.S., Forbes, R.G.: J. Vac. Sci. Techol. B. 31, 032201 (2013) Forbes, R.G., Fischer, A., Mousa, M.S.: J. Vac. Sci. Technol. B. 31, 02B103 (2013) Kyritsakis, A., Xanthakis, J.P.: Technical Digest, 2014 27th International Vacuum Nanoelectronics Conference (IVNC) (ISBN: 978-1-4799-5306-6), p. 118. IEEE, Piscatory (2014)

Chapter 156

Testing for lack of field emission orthodoxy R. G. Forbes

One consequence of applying the orthodox approach to emission situations where it is not valid has been the generation and publication of spuriously high (misleadingly high) field-enhancement-factor estimates [13F]. This situation has stimulated the development of a test for whether particular sets of data are not compatible with the so-called orthodox emission hypothesis. Details of the hypothesis and of test development can be found in [13F]. This appears to be the first time, in the 90 or so years of practical field electron emission, that a simple quantitative test for lack of compatibility with theory has been available. The test for lack of orthodoxy applies to any form of FN plot, involving any of the usual pairs of independent and dependent variables, and can be applied to most forms of emitter, including STFEs, LAFEs, and cylindrical wire emitters. The test involves extracting, from an experimental FN plot against the independent variable X
1, apparent values of scaled barrier field f, by using the formula f extr ¼
h

SXfit

st η

1 expt i :  X

ð156:1Þ

Here, SXfit is the fitted slope, and (X
1)expt is the experimental horizontal-axis value of interest. As before, one can take st 0.95. By using Eq. 156.1, f-values can be extracted that correspond to the range of Xvalues measured. This yields an apparent experimental range of f-values. The test consists of assessing whether this extracted f-value range is unreasonable. For any given ϕ-value, a set of four indicative boundary f-values {flb40 33 32.6 34.7 45.6 70.9 75 90.7 108 11 17.2 132 – 23 – 13 24 40 18 28.4 42 20 29.3 51 19 27.7 60 19 31.4 49 31.6 30.7 22 32.7 58

PFI F12

992 758 105 160 148 358 224 50.5 49.8 50.8 49.4 60.7 59.6 59.2 61.5 58.8 90.7 148 99.2 36.2 40.7 47.8 51.7 57.8 52 52.3 51.3 59

F3M

–

– – – – – – – – – –

–

– – – – – – – –

PFI F34

n/a 2860 1960 375 354 888 764 495 493 496 491 153 151 150 154 170 203 349 309 223 120 141 154 172 174 175 173 171

F4M

1 2 1 2 2 1 1 1 1 1 1 2 2 2 2 2 1 1 2 2 2 2 1 2 2 2 2 2

nd

2.9

0.5 0.5 0.7 1.3 2.1 2.7 3 2.8 2.2 2.9

2

[V/nm] 1.3 2.5 2.2 na na 0.9 1.6 2

Fb!s 100nm

Table 158.2 Parameters relevant to field evaporation theory: the work function used in [96M] (listed for comparison); work function values, ϕ, as used here; the first four “thermodynamic terms,” K10 to K40; the calculated dominant escape field FdM(96M)as listed in [96M], which in the Müller-Brandon approach is the predicted zero-barrier evaporation field (ZBEF) (listed for comparison); the first four Müller escape fields, F1M to F4M (the lowest value is the ZBEF predicted here, and is printed in bold); the corresponding predicted dominant escape charge state nd; the field values Fj,j+1PFI at which, if post-field ionization is responsible for the generation of ( j+1)+ ions, equal abundances of j+ and ( j+1)+ ions would be generated, for PFI up to 4+ ions; and the changeover field at which TF shaping changes from blunting to sharpening for a tip of apex radius 100 nm ( Fb!s 100nm )

4 R. G. Forbes

28 10 Ni Ni Ni Ni 29 11 Cu Cu Cu Cu Cu 30 12 Zn Zn Zn 31 13 Ga 32 14 Ge 33 15 As 34 16 Se 37 1 Rb 38 2 Sr 39 3 Y 40 4 Zr 41 5 Nb Nb Nb Nb Nb Nb Nb Nb 42 6 Mo Mo Mo Mo Mo Mo Mo

–

–

5 Rep 100 110 111 4.6 Rep 100 110 111 112 3.8 Rep Poly Poly 4.1 Poly 4.8 Poly 4.7 Poly Poly 2.1 Poly Poly 3.1 Poly 4.2 Poly 4 Rep 1 110 111 112 113 116 310 4.2 Rep 100 110 111 112 113 332

5.2 5.22 5.04 5.35 4.8 5.1 4.48 4.94 4.53 4.3 3.63 4.9* 4.32 5 3.75* 5.9 2.261 2.59* 3.1 4.05 4.3 4.02 4.87 4.36 4.63 4.29 3.95 4.18 4.5 4.53 4.95 4.55 4.36 4.5 4.55

6.9 6.88 7.06 6.75 6.45 6.15 6.77 6.31 6.72 6.44 7.11 5.84 4.5 6.78 7.3 5.99 2.77 4.8 7.36 8.91 10.05 10.33 9.48 9.99 9.72 10.06 10.4 10.17 9.42 9.39 8.97 9.37 9.56 9.42 9.37

19.9 19.8 20.2 19.6 21.9 21.3 22.6 21.7 22.5 20.1 21.4 18.9 20.7 17.7 22.1 21.3 27.8 13.2 16.5 18 19.7 20.3 18.6 19.6 19.1 19.8 20.4 20 21.1 21 20.2 21 21.4 21.1 21

49.9 49.8 50.3 49.4 54 53.1 54.9 53.6 54.8 55.5 57.5 53.7 47.1 46.9 46.7 46.2 65.5 53.5 33.9 36.9 40.5 41.3 38.8 40.3 39.5 40.5 41.5 40.8 43.7 43.6 42.4 43.6 44.1 43.7 43.6

99.6 99.5 100.2 99 106.6 105.4 107.8 106 107.6 110.6 113.3 108.2 106 87.7 93.1 83.2 115.9 108 91.4 67.2 74.5 75.6 72.2 74.2 73.2 74.5 75.9 75 85.6 85.5 83.8 85.4 86.2 85.6 85.4 –

–

41

23.5 28 37

6

15 29 42

33

30

35 33.1 32.9 34.6 31.6 28.9 26.2 31.8 27.6 31.3 28.8 35.1 23.7 14.1 31.9 37 24.9 5.3 16 37.6 55.2 70.1 74.1 62.4 69.3 65.6 70.3 75.1 71.8 61.7 61.3 55.9 61 63.5 61.7 61 – –

–

–

20

17 17

59

26

31

22

30

24

34.3 34.1 35.4 33.2 41.8 39.5 44.3 40.7 43.9 35.1 39.9 31 37.2 27.2 42.5 39.3 67.1 15.2 23.6 28 33.9 35.8 30.1 33.4 31.6 33.9 36.3 34.7 38.6 38.4 35.4 38.2 39.6 38.6 38.2 – –

–

–

40

29 34

87

42

49

81

71

64

63.9 63.8 65.2 62.8 74.9 72.5 77.6 73.8 77.2 79.3 85.2 74.3 57.1 56.7 56.2 54.9 110 73.7 29.6 35 42.2 43.9 38.7 41.8 40.1 42.2 44.4 42.9 49.1 48.9 46.2 48.8 50.1 49.1 48.8 –

– – – – –

– – –

–

–

–

191 191 194 189 219 214 224 217 224 236 248 226 217 148 167 134 259 225 161 87 107 110 101 106 103 107 111 108 141 141 136 141 143 141 141

1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3.2

0.7 0.6 1.2 2 2.6 2.9

The prediction of zero-barrier evaporation field (continued)

na

1.8 1.7

1.9

2.4

2.8

158 5

At Gp El 43 7 Tc 44 8 Ru 45 9 Rh 46 10 Pd Pd Pd 47 11 Ag Ag Ag Ag 48 12 Cd 49 13 In 50 14 Sn-wh 51 15 Sb Sb Sb 52 16 Te 55 1 Cs 56 2 Ba 57 3 La 58 Lan Ce 59 Lan Pr 60 Lan Nd 61 Lan Pm 62 Lan Sm 63 Lan Eu 64 Lan Gd 65 Lan Tb 66 Lan Dy 67 Lan Ho 68 Lan Er 69 Lan Tm

– – – – – – – – – – – –

–

2.1 2.5 3.3

4.1 4.1 4.4 4.6

4.6

ϕ in 96M – 4.5 4.8 5

Table 158.2 (continued)

ϕ as used here type Aprx 4.82c Poly 4.71 Poly 4.98 Rep 5.4 Poly 5.22 111 5.6 Rep 4.6 100 4.64 110 4.52 111 4.74 Poly 4.08 Poly 4.09 Poly 4.42 Rep 4.6 1 4.44 100 4.7 Poly 4.95 Poly 1.95 Poly 2.52 Poly 3.5 Poly 2.9 Repd 2.62c c Rep 2.83c Aprx 2.89d Poly 2.7 Poly 2.5 Poly 2.9 Poly 3 Repc 2.78c Repc 3.03c c Rep 3.09c c Rep 2.94c K 01 9.31 9.34 8.26 6.85 7.03 6.65 5.95 5.91 6.03 5.81 6.07 4.19 6.04 6.73 6.89 6.63 6.08 2.75 4.53 6.5 6.87 6.56 5.98 6.32 5.1 5.02 7.37 6.67 3.84 6.04 6.07 5.76

K 02 19.8 21.4 21.4 20.9 21.2 20.5 22.8 22.7 23 22.5 18.9 19 16.3 18.8 19.1 18.6 19.7 26 12 14.1 14.8 14.5 13.9 14.3 13.5 13.8 16.6 15.2 12.7 14.8 14.9 14.9

K 03 44.5 45.2 47.4 48.4 48.9 47.8 53.1 52.9 53.3 52.6 52.3 42.9 42.3 39.5 39.9 39.2 42.7 59 45.3 29.7 32.1 33.5 33.1 33.7 34.2 36.2 34.3 34.1 32.8 34.6 34.6 35.6

K 04 85.7 90.4 90.5 96 96.7 95.2 104.5 104.3 104.8 103.9 107.2 92.8 78.7 79.1 79.7 78.7 75.2 103.1 91.8 76.2 66 69.9 70.7 72 72.9 76.4 75.4 70.9 71.4 74.1 74.2 75.4 – – – – – – – – – – – –

– 5 13 18

25 12 23 30

24

FdM [96M] – 41 41 37 F1M 60.2 60.6 47.4 32.6 34.3 30.7 24.6 24.2 25.2 23.4 25.6 12.2 25.4 31.4 33 30.5 25.7 5.3 14.3 29.3 32.8 29.9 24.8 27.8 18.1 17.5 37.7 30.9 10.2 25.3 25.6 23.1 – – – – – – – – – – – –

– 55 8 10

22 28 17 21

25

PFI F12 – 22 25 28

F2M 33.9 39.7 39.6 37.8 39.2 36.4 45.2 44.9 45.9 44.1 31 31.2 22.9 30.5 31.6 29.9 33.8 58.5 12.5 17.2 19.1 18.2 16.7 17.8 15.8 16.5 23.8 20 14.1 19 19.3 19.2 – – – – – – – – – – – –

– 71 72 21

75 42 50 35

65

PFI F34 – 43 44 58

F3M 50.9 52.4 57.9 60.3 61.6 58.8 72.4 72.1 73.1 71.3 70.4 47.4 46.1 40 41 39.4 47 89.6 52.9 22.7 26.5 28.9 28.2 29.3 30 33.7 30.2 29.9 27.6 30.8 30.7 32.6 – – – – – – – – – – – – – – –

– – – –

–

PFI F34 – – – –

F4M 142 158 158 178 180 175 210 210 212 208 222 166 119 121 123 119 109 205 163 112 84 94 96 100 102 113 110 97 98 106 106 110 nd 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2

na

0.9 0.6 1.1 1.8 1.8 1.8 1.8 1.8 1.4 1.1 1.7 1.7 1.7 1.7 1.7

1.6 1.6 1.6

2.1

Fb!s 100nm na 3.2 3 2.6

6 R. G. Forbes

70 Lan Yb 71 Lan Lu 72 4 Hf 73 5 Ta Ta Ta Ta Ta 74 6 W W W W W W W 75 7 Re 76 8 Os 77 9 Ir Ir Ir Ir Ir 78 10 Pt Pt Pt Pt Pt Pt 79 11 Au Au Au Au 80 12 Hg 81 13 Tl 82 14 Pb

– –

4.5 3.7 4.1

4.3

5.3

5.1 4.6 5.3

4.5

3.5 4.2

Repc Poly Poly Typ Poly 100 110 111 Rep Poly 100 110 111 113 116 Poly Poly Rep 100 110 111 210 Rep Poly 110 111 320 331 111 100 110 111 1 Poly Poly

2.70c 3.3* 3.9 4.3 4.25 4.15 4.8 4 4.6 4.55 4.63 5.22 4.45 4.46 4.32 4.72 5.93 5.5 5.67 5.42 5.76 5 5.55 5.64 5.84 5.93 5.22 5.12 5.4 5.47 5.37 5.31 4.475 3.84* 4.25 5.29 6.42 9.24 11.35 11.4 11.5 10.85 11.65 12.27 12.22 12.14 11.55 12.32 12.31 12.45 11.2 10.64 10.32 10.2 10.45 10.11 10.87 9.27 9.18 8.98 8.89 9.6 9.7 7.63 7.56 7.66 7.72 6.6 4.15 5.2

14.8 17 20.3 23 23.1 23.3 22 23.6 23.9 23.8 23.6 22.4 24 24 24.2 23.5 21.7 21.8 21.5 22 21.3 22.9 22.3 22.1 21.7 21.5 22.9 23.1 22.4 22.3 22.5 22.6 20.9 20.7 16

37.1 34.7 39.7 40.7 40.9 41.2 39.2 41.6 43.4 43.2 43 41.2 43.5 43.5 43.9 44.8 40.8 43.2 42.9 43.6 42.6 44.9 44.7 44.5 43.9 43.6 45.7 46 47 46.8 47.1 47.3 50.6 46.7 43.7

78 76.6 69.2 69.4 69.6 70 67.4 70.6 73.9 73.7 73.4 71 74.1 74 74.6 78 74.8 76.7 76.2 77.2 75.8 78.9 80.2 79.8 79 78.7 81.5 81.9 85.6 85.3 85.7 86 92.1 93.6 81.7

– –

31 13 20

53

45

45 48 44

52

39 44

19.5 28.6 59.2 89.5 90.2 91.8 81.7 94.2 104.6 103.8 102.4 92.7 105.5 105.3 107.7 87.2 78.6 73.9 72.2 75.8 70.9 82 59.7 58.5 56 54.9 64 65.3 40.4 39.6 40.7 41.3 30.3 11.9 18.8

– –

28 34 18

34

27

22 23 22

28

19 21

18.9 25.1 35.9 46.1 46.5 47.3 42.2 48.6 49.5 49.1 48.4 43.7 49.9 49.8 51 47.9 40.9 41.1 40.2 42.1 39.6 45.4 43.1 42.4 40.9 40.2 45.7 46.5 43.7 43.1 43.9 44.4 37.9 37.3 22.2

– –

66 50 57

51

44

38 35 41

32

31 27

35.4 30.9 40.6 42.7 43 43.7 39.6 44.6 48.4 48.1 47.5 43.7 48.7 48.7 49.6 51.5 42.8 48 47.2 48.9 46.6 51.8 51.5 50.8 49.5 48.9 53.8 54.5 56.9 56.4 57.1 57.5 65.9 56.2 49 – – –

–

–

– –

62 75 64

53

48 47

117 113 92 93 94 95 88 96 105 105 104 97 106 106 107 117 108 113 112 115 111 120 124 123 120 119 128 129 141 141 142 143 164 169 129

2 2 2 3 3 3 3 3 3 3 3 2 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1

1.5 1.4 1.4 (continued)

2.3

2.9

3.5 3.4 3.2

3.4

1.2 2.1 2.7 3.1

158 The prediction of zero-barrier evaporation field 7

Gp 15 3 Act Act

El Bi Ac Th U U U U U

ϕ in 96M 4.3 – – 3.3

ϕ as used here type Poly 4.34 est 4a Poly 3.4 Rep 3.7 K 01 5.12 5.38 9.1 7.91 7.98 7.88 7.71 7.94

K 02 17.5 13.1 17.6 14.8 15 14.8 14.4 14.9

K 03 38.7 29.1 34.2 31.1 31.3 31 30.5 31.2

K 04 79.7 74.1 59.6 – – – – –

FdM [96M] 12 – – – F1M 18.2 20.1 57.6 43.5 44.3 43.2 41.3 43.8

PFI F12 23 – – –

F2M 26.5 15 26.9 19.1 19.4 18.9 18 19.2

PFI F34 37 – – –

F3M 38.5 21.8 30.1 24.9 25.2 24.8 23.9 25

PFI F34 – – – –

F4M 122 106 69 – – – – –

nd 1 2 2 2 2 2 2 2

Fb!s 100nm 1.3 na 2.1 2.6

In the “elements” column, “C-di” means diamond, “C-gr” means graphite, “P-bl” means black phosphorus, and “Sn-wh” means white tin. Work function values used here are experimental values taken from [15H2], unless indicated otherwise as follows: Asterisks indicate values considered approximate by [15H2]. When several experimental values are available for a given material, the present author has (somewhat arbitrarily) also stated a “representative” value, marked “rep” in the column headed “type.” The other abbreviations in this column have meanings as follows: numbers are the Miller indices of the crystal face used in the experiments; “poly” indicates use of a polycrystalline material; “theor” is a theoretically determined value; “est” is an estimated value; “aprx” shows a value is thought approximate by [99D]; and with the silicon entries, “n” indicates “n-doped” and “p” indicates “p-doped.” The fields Fj,j+1PFI were derived by the present author from the ion abundance diagrams published by Kingham in [82K]. The abbreviation “n/a” means “not applicable,” and “na” means “not available”; a dash indicates that calculations for this element+parameter combination combination were not carried out in the data source. Where several work function values are used for a given element, parameters that apply to all cases are given only on the first line of the data for the element. Other field values were derived using the data in Table 158.2 and formulae in the text a Estimated by the present author b Theoretical value from [85T] c Taken from [99D] but considered approximate by [99D] d Taken from [99D] and believed by [99D] to be representative of polycrystalline material

At 83 89 90 92

Table 158.2 (continued)

8 R. G. Forbes

158

The prediction of zero-barrier evaporation field

9

The extraction of data for inclusion in Tables 158.1 and 158.2 is nontrivial and needs comment. Most of this data is needed primarily for calculating basic estimates of escape fields and hence of the zero-barrier evaporation field (ZBEF), using Müller’s formula, Eq. 158.1. Müller’s formula is not a complete theory of the ZBEF and – although adequate as a basic approximation – is not an accurate predictor of escape fields or ZBEF values. Because of past uncertainty [14Mil] over how to deduce “true” ZBEF values from experimental data, the size of the discrepancy between the result of the Müller-Brandon approach and the true ZBEF value is not clearly known for most elements. In some cases, the discrepancy could be as much as 30% or more. Consequently, for most elements, the primary cause of uncertainty in theoretical estimation of the ZBEF lies in incompleteness of theory, rather than with error in the material characterization data used in Eq. 158.1. Thus, although this contribution has attempted to identify the most reliable data values, it has not been thought useful to discuss or record here the uncertainties in these data. If needed and available, this information can be found in the references cited. Data are included here for a wider range of elements than in older tabulations. With some of these materials, it is unlikely (or, in some cases, impossible) that they will be used to fabricate operating elemental field emitters, but the data and the elemental ZBEF predictions are included because they may be of use in the context of field evaporation of alloys containing the element. Specific notes on data origins now follow. Local work functions. The local work function ϕ is defined as the work needed (in a hypothetical slow thermodynamic process) to remove an electron from the emitter Fermi level and place it stationary at a position “somewhat” outside the emitter surface. This position needs to be outside the range of the exchange and correlation forces (i.e., “image forces”) but sufficiently close to the surface that the effects of patch fields can be neglected. These patch fields arise because different crystallographic faces of a specific crystalline material have different local work functions. In practice, this means that the local work function applicable to a small crystal facet is often not well defined. However, local work functions for facets of sufficiently large lateral extent can be measured by several techniques [15H2]. This has been done for specific faces of some elements of particular technological interest. For others, measurements have been recorded for polycrystalline emitters. In a few cases, the state of the surface is either not known or not reported. It is also possible to make theoretical estimates of local work function, but older methods constitute approximations that do not take into account the atomic structure-related effects that lead to the differences as between different crystal faces. Table 158.2 shows work function data extracted mainly from the 2015 online version of the 95th edition of the CRC Handbook of Physics and Chemistry [15H2]. This does not cover all elements. Most of the other values are taken from an unpublished report by Drummond [99D]; a few come from other sources as shown in the table. Where different values for different crystallographic faces are recorded in [15H2], all values are recorded in Table 158.2. In addition, for each relevant element, a single “representative” ϕ-value (near the middle of the range of experimental values) has been chosen by the present author and is tabulated as the first value for each relevant element. For comparison, the values used in the widely respected 1996 book by Miller et al. [96M] are also recorded. Zero-field bonding energies. In FEV theory, the zero-field bonding energy Λ0 is defined as the work needed to be done by a hypothetical external agent, in order remove an atom from the emitter surface to be stationary at a position in remote field-free space, in the absence of any applied electrostatic field. This bonding energy is a difference in system potential energy, as between two states of the emitter+atom system. It is usual to assume that Λ0 can be identified with the work Λ0f needed to remove an atom from a kink site on a large macroscopically flat surface of an elemental solid. This may not be exactly true for very small emitters, where removal of an atom in effect changes the emitter radius, or for the removal of the last few atoms on an atomically flat crystal facet, but (as far as is known) the assumption is adequate in most circumstances. In recent field ion emission literature, Λ0f is often called the sublimation energy. In principle, an unrecognized problem lies in how to deduce Λ0f-values from standard reference-book tabulations of chemical and materials thermodynamic data. This is because some relevant tabulated parameters relate to processes that involve overcoming the bonding energy by heating the emitter and are not necessarily exactly relevant to field evaporation, where the bonding energy is overcome, at cryogenic temperatures, by applying an electrostatic field.

10

R. G. Forbes

In practice, this is less of a problem than it might seem, because – as noted above – Müller’s formula provides only a basic estimate of escape field and high accuracy in the input data is not essential. Most textbook tabulations of values of escape field as defined above are largely based on the thermodynamic parameters used by Tsong [78T], in his original tabulation of Müller’s formula values. In turn, these parameter values were mostly taken from an older tabulation [69M] that estimated escape fields by means of a different formula. In older field ion emission literature, the bonding energy parameter here denoted by Λ0f is variously identified as the “heat of evaporation” [ 56Mul], p. 621 , “heat of vaporization” [60M , p. 101], “heat of adsorption” [60G, p. 87 ], and “Sublimation Energy” [69M , p. 57 ; 73M , p. 82]. It is not specifically named in [78T]. Thus, it is not clear where the Λ0f-values used in the original tables in [69M] and [78T] were actually taken from, and it is still not fully clear what tabulated parameter is best to use. The present author considered the values provided by five sources: the “enthalpies of atomization” given in the well-known MacMillan reference handbook [92J]; the “enthalpies of atomization” given at the “WebElements” website [14Web]; the “latent heats of sublimation” given in the Smithells metals reference handbook [04G1]; the “cohesive energies” given at the “KnowledgeDoor” website [14Kno]; and the “bonding energies” used in the internal data table in the 2013 release of the well-known commercial “sputtering” program “TRIM” [10Zie1, 10Zie2], used in the Surrey Ion Beam Centre. If obvious apparent discrepancies (which are to be expected [10Zha] and may be due either to improved experimental data or to transcription errors) are disregarded, then values from all these sources are much the same, in most cases to within a few tenths of an eV, in some cases better than this. The WebElements list covers the whole periodic table, appears to contain few if any significant discrepancies, and documents the data source(s) for each element; consequently, the values from this list are used here. As compared with older tabulations, most estimates of Λ0f here are within 20 meV or less of the older value as used in [96M]; there are nontrivial differences – around 0.2 eV or more – for B (0.19 eV), W (0.25 eV), and Os (1.13) eV, with the new value being higher in each case. Ionization energies. Data on the first four ionization energies, I1 to I4, are mostly taken from the CRC Handbook [15H3]. Missing values are taken from a comprehensive list [02C] prepared for an IAU Symposium in Uppsala, Sweden, in June 2002, except for the following. The value of I3 for uranium is estimated by the present author as 20 eV, based on the theoretical result of 25.13 eV in [67K] and the tabulated value of 1843 kJ/mol (19.10 eV) given by [14E]. This value is considered to be of limited reliability. No estimates of the value of I4 for uranium could be found. Atomic volumes. Atomic volumes Ω (in nm3) are derived from values of molar volume Vm (evaluated in cm3/mol) by using the conversion formula 
Ω ¼ 1:660539  103  V m = cm3 mol1 : 3 nm

ð158:2Þ

Molar volume values are derived from values of molar mass M and density ρ, via the usual formula Vm ¼ M/ρ. Molar mass values are derived from the 2013 IUPAC-approved list [14C, 14Mej] of “Standard Atomic Weights.” For densities, the values (“near-room temperature”) recommended by the relevant Wikipedia data page [14Wik] have been used. These have checked been against some other sources: for a few materials there are discrepancies in the literature, but the Wikipedia-recommended values (which are given in g/cm3) look a reasonable choice. At cryogenic temperatures, the densities will be slightly higher and the atomic volumes slightly lower, but (in the present state of field evaporation theory) the room temperature values are sufficient for purpose. Static atomic polarizabilities. In the International System of Quantities (the ISQ), two different quantities may in principle be used to describe the property of atomic polarizability, namely, the ISQ atomic polarizability αISQ (defined as p/E, where p is the electric dipole moment induced by an impressed electrostatic field E) and the polarizability volume αv defined in terms of αISQ by αv ¼

αISQ : 4πε0

ð158:3Þ

158

The prediction of zero-barrier evaporation field

11

The SI unit for αISQ is usually stated as “C m2 V1”; an alternative SI unit is “J V2 m2.” In the context of field emission, sometimes a more convenient (ISQ-compatible) atomic level unit is the “meV V2 nm2.” In the older Gaussian and atomic unit systems of equations, which are still in wide theoretical use in discussion of the property of atomic polarizability, the polarizability volume (also called “Gaussian polarizability”) is used. This is commonly measured (and tabulated) either in “atomic units of polarizability volume,” with 1 au being equal to (a0)3 where a0 is the Bohr radius [a0  0.052 9177 nm] or in cubic Angstroms (Å3). In the present tables, it is more convenient (and more SI-friendly) to consider numerical values of αv expressed in Å3 to be numerical values of (1000 αv) expressed in nm3. For each atomic species, Table 158.1 gives three equivalent numerical values: αv in au, 1000αv in nm3, and αISQ in meV V2 nm2. Numerical values of αv in au have been taken from the table made electronically available by Schwerdtfeger [14S], which is an updated version of that published in [06S]. When [14S] lists several results for a given element, an experimental result has been taken, if available; if not, the listed theoretical values have been used by the present author to provide a representative value for use in Table 158.2. Equivalent numerical values in other systems can be found with the conversion formulae ð1000αv Þ ¼ ð0:1481 84 71Þ  fαv =aug nm3
αISQ
¼ 1:648 7773  1041  fαv =aug, J V2 m2

αISQ
¼ 6:241 5093  1039  αISQ = J V2 m2 , meV V2 nm2 αISQ
¼ ð0:102 908 59Þ  fαv =aug: meV V2 nm2

ð158:4aÞ ð158:4bÞ ð158:4cÞ ð158:4dÞ

Surface free energies per unit area. In the context of thermal-field (TF) shaping (Chap. 160 [https://doi.org/ 10.1007/978-3-662-53908-8_160]), the quantity needed is the surface free energy per unit area of a solid (in the absence of any applied electrostatic field), denoted here by γ 0. In principle, what is needed is usually the γ 0 value for a hot solid. The surface free energies of solids are difficult to measure, and it is sufficient (in the context of present theories of TF shaping) to use the value for the liquid element near its melting point. For a liquid, the surface free energy per unit area can be identified with the surface tension. The SI unit of surface tension is usually stated as “N/m” (or “mN/m”), but the equivalent alternative form “J/m2” (or “mJ/m2”) is better when the parameter is regarded as a surface free energy. In the context of the TF shaping of field emitters, the equivalent (ISQ-compatible) atomic level unit “eV/nm2” is often convenient. The conversion formula from “mN/m” to “eV/nm2” is”
 γ0 ¼ 6:241 5083  103  γ 0 =ðmN=mÞ : 2 ðeV=nm Þ

ð158:5Þ

Surface tension values for the rare-earth metals have been taken from [04G2], for other elements (where available) from [15H4], and have been converted using formula (158.5). Symbols and abbreviations Short form

Full form

ZBEF PFI ISQ FEV IUPAC SI

zero-barrier evaporation field post-field ionization international system of quantities field evaporation international union of pure and applied chemistry international system (of units) (French: Syste‘me International d’unite´s) (continued)

12 Short form TF IAU CRC

R. G. Forbes Full form thermal-field international astronomical union chemical rubber company (scientific reference publisher)

References [14S] Schottky, W.: Phys. Z. 15, 872 (1914) [56Mul] Müller, E.W.: Phys. Rev. 102, 618 (1956) [60G] Gomer, R.: Field Emission and Field Ionization. Harvard Univ. Press, Cambridge, Mass (1960). Republished by AIP Press, 1993. [60M] Müller, E.W.: Adv. Electr. Electron. Phys. 13, 83 (1960) [64B] Brandon, D.G.: Surf. Sci. 3, 1 (1964) [67K] Kudria, L.P., Mazeev, M. Y.: At. E´nerg. 22, 83 (1967). (in Russian). [69M] Müller, E.W., Tsong, T.T.: Field Ion Microscopy: Principles and Applications. American Elsevier, New York (1969) [73M] Müller, E.W., Tsong, T.T.: Prog. Surf. Sci. 4, 1 (1973) [78T] Tsong, T.T.: Surf. Sci. 70, 211 (1978) [82K] Kingham, D.R.: Surf. Sci. 116, 273 (1982) [85T] Takahashi, T., Tokailin, H., Suzuki, S., Sagawat, T., Shirotani, I.: J. Phys. C: Solid State Phys. 14, 825 (1985) [92J] James, A.M., Lord, M.P. (eds.): Macmillan’s Chemical and Physical Data, p. 449. Macmillan, London (1992), Sect. XIII, Table XIII [96M] Miller, M.K., Cerezo, A., Hetherington, M.G., Smith, G.D.W.: Atom Probe Field Ion Microscopy. Clarendon, Oxford (1996) [99D] Drummond T.J.: Work Functions of the Transition Metals and Metal Silicides. OSTI Rept 3597 (SAND99-0391J) (1999) [02C] Cowley, C.R.: List of Ionization Energies (eV) of Atoms and Ions, prepared for IAU Symposium 210 (Uppsala, June 2002). Available at: https://dept.astro.lsa.umich.edu/~cowley/iionen.htm (15 Aug 2014) [04G1] See [04G], Sect. 8.2, pp. 8–2, Table 8.1 [04G2] See [04G], Sect. 14.22, pp. 14–10, Table 14.3a [04S] Sa´nchez, C.G., Lozovoi, A.Y., Alavi, A.A.: Mol. Phys. 102, 1045 (2004) [06S] Schwerdtfeger, P.: Atomic static dipole polarizabilities. In: Maroulis, G. (ed.) Computational Aspects of Electric Polarizability Calculatons: Atoms, Molecules and Clusters, p. 1. IOS Press, Amsterdam (2006) [10Zha] Zhang, Y.M., Evans, J.R.G., Yang, S.F.: Philos. Mag. 90, 4453 (2010) [10Zie1] Ziegler, J.F., Biersack, J.P., Ziegler, M.D.: SRIM – The Stopping and Range of Ions in Matter. Lulu Press, Morrisville (2010) [10Zie2] Ziegler, J.F., Biersack, J.P., Ziegler, M.D.: Nucl. Inst. Methods Phys. Res. B. 268, 1818 (2010) [14C] CIAAW (Commission on Isotopic Abundances and Atomic Weights): 2013 Standard Atomic Weights. http://www. ciaaw.org/atomic-weights.htm (23 Aug 2014). To be published as [14 Mej] [14E] England, G.: Electronic data resource available at: http://www.gordonengland.co.uk/elements/u.htm (23 Aug 2014) [14Kno] The Elements Handbook at KnowledgeDoor (electronic data resource). Data on cohesive energies at http://www. knowledgedoor.com/2/elements_handbook/cohesive_energy.html (15 Aug 2014) [14Mej] Meija, J., et al. Atomic Weights of the Elements 2013. Pure and Applied Chemistry (to be published 2014) [14Mil] Miller, M.K., Forbes, R.G.: Atom Probe Tomography: The Local Electrode Atom Probe. Springer, New York (2014) [14Web] Web Elements: The Periodic Table on the Web (electronic data resource). Data on enthalpy of atomisation at: http:// www.webelements.com/periodicity/enthalpy_atomisation/ (15 Aug 2014). See “shaded table” option [14Wik] Wikipedia, Densities of the elements (data page), at http://en.wikipedia.org/wiki/Densities_of_the_elements_% 28data_page%29 (22 Aug 2014) [15H1] Haynes, W.M. (ed.), Lide, D.R. (ed., internet version): CRC Handbook of Chemistry and Physics, 95th Ed., Internet Version 2015; http://www.hbcpnetbase.com/ (15 August 2014). [15H2] See [15H1], Sect. 12, pp. 12–124 [15H3] See [15H1], Sect. 10, pp. 10–197 [15H4] See [15H1], Sect. 4, pp. 4–120, Table 12

Chapter 159

Post-field ionization R. G. Forbes

Post-field ionization (PFI) (also called “post-ionization”) is the field-induced ionization of an ion from charge state j (
1) into the charge state j+1. The PFI theory used in the context of field evaporation was developed, mainly by Kingham (see [82K]), from earlier theory relating to the field ionization of noble gases, as occurs in field ion microscopy. In principle, this PFI theory needs: (a) an expression for the field ionization rate-constant Pe(n,x,F(x)) of an ion in charge-state j that has its nucleus situated at distance x from the emitter’s electrical surface, with F(x) denoting the relevant ionizing field for this position; and (b) an expression for the speed v(x) of the ionic nucleus at position x. It is implicitly assumed that, at any position x, this field F(x) scales with the local field FL in the electrical surface. The total probability, Π et(FL), that PFI from j+ to ( j+1) + occurs is given formally by 2 Π et ðFL Þ ¼ 1  exp4

Z1

3 fPe =vgdx5

ð159:1Þ

0

In practice, the lower limit of the integral is determined by the critical distance xjcr at which the topmost occupied orbital in the j+ ion rises above the emitter Fermi level, thereby allowing PFI to take place into an empty emitter electron state above the Fermi level. Details of the various approximations used by Kingham are given in [82K]. For a large number of elements, Kingham [82K] plotted curves showing charge-state abundances as a function of field, for all relevant charge states. Parameters of interest are the local field values Fj,j+1 at which the probable abundances of both j+ and ( j+1)+ ions are 50%. These equal-abundance fields have been extracted from the Kingham diagrams and are shown above in Table 159.2. There is some reason to believe [92L, 14F] that Kingham’s approximations are less satisfactory than he thought, but it is currently not clear what effect any corrections would have. However, there is no doubt that PFI occurs, and there is no empirical evidence that his PFI predictions are seriously incorrect. Symbols and abbreviations Short form

Full form

PFI

post-field ionization

References [82K] Kingham, D.R.: Surf. Sci. 116, 273 (1982) [92L] Lam, S.C., Needs, R.J.: Surf. Sci. 277, 359 (1992) [14F] Forbes, R.G.: Unpublished work (2014)

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_159

1

Chapter 160

The “changeover field” in thermal-field shaping R. G. Forbes

At sufficiently high temperatures, a field emitter will change shape, as a result of the migration of surface atoms. As discussed in [14Mil], the direction of change, as indicated by the relevant electrical Gibbs function, depends in principle on the applied voltage. If the voltage is sufficiently small, then the surfaceenergy term dominates, and the emitter will tend to become blunter and to “ball up”; if the voltage is sufficiently large, then the energy term relating to the capacitance between the emitter and its surroundings (and to the work done by the high-voltage generator) dominates, and the emitter will tend to “reach out toward its surroundings,” by becoming sharper or by the formation of nanoprotrusions. The condition for changeover from blunting to sharpening is often formulating as the stress condition 

 1 1 þ , r1 r2

ε0 F2 > 2γ 0

ð160:1Þ

where r1 and r2 are the principal local radii of curvature. There is reason to think that this is not a general result (see [09F1], Sect. 2.4.2), but in practice it seems to work adequately for field emitters ([09S1], p. 18). For a field emitter apex of radius ra, Eq. 160.1 produces a formula for the changeover field (from blunting to sharpening) Fb!s:  Fb!s ¼ 2

γ0 ε0 r a

1=2 ð160:2Þ

Values of this changeover field for a tip radius of 100 nm are shown in the last column of Table 158.2 [https://doi.org/10.1007/978-3-662-53908-8_158] and are typically a few V/nm or less. Obviously, for a tip radius of 1 nm, the changeover fields would be higher by a factor of 10. Comparisons with predicted evaporation field values indicate that, for all except very small tip apex radii, in the vicinity of 1 nm, emitter sharpening is the expected TF-shaping tendency in atom-probe operating conditions. Symbols and abbreviations Short form

Full form

TF

thermal field

References [09F1] [09O] [09S1] [14Mil]

Forbes, R.G., Mair, G.L.R.: Liquid metal ion sources, Chapter 2 in [09O] Orloff, J. (ed) Handbook of Charged Particle Optics (2nd Edition). Boca Raton, CRC Press (2009) Swanson, L.W., Schwind, G.A.: Chapter 1 in [09O] Miller, M.K., Forbes, R.G.: Atom Probe Tomography: The Local Electrode Atom Probe. Springer, New York (2014)

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_160

1

Chapter 161

The position of the electrical surface R. G. Forbes

In qualitative terms, the emitter’s electrical surface is the “surface where the field seems to start.” Its importance is that (in simple surface models) distance z measured from the electrical surface is needed in order to define (the electrostatic components of) the potential energy structures in which electrons and ions move close above charged surfaces. In particular, outside a planar atomically structured surface of large extent, one needs the potential energy Ue of a hypothetical classical point electron (measured relative to the emitter Fermi level) to have the limiting form (for distances z somewhat less than the extent of the plane): U e ¼ ϕ þ eFz,

ð161:1Þ

where ϕ is the local work function and F is the (uniform) electrostatic field above the surface. In simple models of a planar charged surface, the electrical surface is at the centroid of the induced charge distribution [73L, 99F] and is co-located in position with the image plane (from which x in the Schottky expression –e2/16πε0x is measured) [73L]. To make simple theoretical expressions predict correctly, the electrical surface needs to be positioned correctly relative to the emitter. For the real atomically structured surfaces of metal elements, this positioning can be done exactly only for planar surfaces of large extent, in which case the electrical surface is outside (i.e., on the vacuum side) of the plane of the surface atom nuclei by a distance d called the repulsion distance. Since one-dimensional models are widely employed, values of d are of more relevance than might initially seem. The use of a classical array model (e.g., [98F]), in which each atom in a charged metal surface is replaced by a co-located point charge and polarizable dipole, provides a simple method of estimating dvalues. For metals with cubic space lattices, and for crystallographic faces that can be represented in terms of a simple rectangular or centered rectangular “net” (or surface lattice) of topmost surface layer atoms, this is based on the formula (e.g., [98F]) h
i d ¼ b= ε0 Asl 1 þ T hkl b=4πε0 c3sp ,

ð161:2Þ

where b is the effective ISQ atomic polarizability of a surface metal atom, Asl is the area associated with one atom in the surface lattice, csp is the space-lattice parameter, and Thkl is a quantity known as a structure factor. This factor is different for different space lattices and – for a given space lattice – is different for different crystallographic faces as specified by Miller indices (hkl). Thkl is defined by T hkl ¼

X
i

 c3sp =r 3i ,

ð161:3Þ

where ri is the distance, in the topmost surface layer, from a chosen “origin atom” to its ith neighbor. The summation is in principle performed over all atoms in the topmost surface layer.

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_161

1

2

R. G. Forbes

For the body-centered cubic (bcc) and face-centered cubic (fcc) space lattices, relevant crystallographic data and values of Thkl for some relevant low-order crystallographic faces are shown in Tables 161.1 and 161.2, respectively. The crystallographic data are taken from the well-known Atlas of Models of Crystal Surfaces compiled by Nicholas [65N]. Values of Thkl have been calculated using a computer program initially developed by the present author and Wafi [80F, 81W]; these calculations were repeated and extended to other surface lattices by Tey [99T].

Table 161.1 Crystallographic data for selected faces of the bcc space lattice. dx and dy are the lengths of the sides of the rectangular surface lattice cell, and Asl is the area associated with each surface lattice atom; csp is the space-lattice parameter. Origins of data are as described in the text. Data are arranged in order of decreasing values of the structure factor Thkl Face (hkl)

Surface lattice data Centered? dx/ccp

dy/csp

Asl/(csp)2

Asl/(csp)2

Structure factor Thkl

110 100 211 310 111 210 411 332

Yes No No Yes Yes No Yes No

√2 1 (√3)/2 √10 √6 √5 3 (√11)/2

(√2)/2 1 √(3/2) (√10)/2 2√3 √5 3/√2 √(11/2)

0.707 1.000 1.225 1.581 1.732 2.236 2.121 2.345

15.037595 9.033622 7.500860 5.035373 3.901170 3.720067 2.906882 2.546468

1 1 √2 1 √2 1 √2 √2

Table 161.2 Crystallographic data for selected faces of the fcc space lattice. Other details are the same as in Table 161.1 Face (hkl)

Surface lattice data Centered? dx/ccp

dy/csp

Asl/(csp)2

Asl/(csp)2

Structure factor Thkl

111 100 110 211 210 310

Yes Yes No No Yes Yes

(√6)/2 1 (√2)/2 √3 (√5) √10

(√3)/4 1/2 (√2)/2 (√6)/2 (√5)/2 (√10)/2

0.433 0.500 0.707 1.225 1.118 1.581

31.30936 25.55094 16.11101 9.901582 7.648053 5.035373

(√2)/2 1 1 (√2)/2 1 1

The result for the bcc (100) face, namely, 9.033622, is almost identical with the analytical result (9.033623  .000006) obtained much earlier by Topping [27T], by using ζ-function theory, and provides mutual validation of the computational and analytical approaches. The central difficulty with classical array model calculations is choice of a suitable value for b in formula (161.2). There is no physical reason to believe that the “effective polarizability” for a surface metal atom should be exactly equal to the polarizability of the same atom in free space, even in low applied fields (i.e., no reason to think that b/4πε0 αv). Further, there are no reliable independent estimates of b, and there are some reasons to think that b might be weakly dependent on field [97F] and that hyperpolarizability terms (and other higher polarizability terms) might need to be taken into account [81F]. Another difficulty is that tabulations of αv-values have in the past (and to some extent continue to have) limited accuracy. Nevertheless, simple approaches set b/4πε0 equal to αv. For aluminum, comparisons (shown in Table 161.3) may be made between good quantum-mechanical (QM) calculations (from which d-values can be obtained) and d-values found by means of formula (161.2). The latter are based on αv-values: (1) given by Miller and Bederson [77M] and (2) extracted from the literature by Tey . As can be seen, the QM and classical calculations are in all cases within 25 pm (better than 20%) of each other, with the classical results underpredicting the QM results. There is a need to update these calculations, using the updated estimates of αv given in Table 4.4, but results were not available at

161

The position of the electrical surface

3

the time of writing. Consequently, Tables 161.4 and 161.5 reproduce here selected results from the calculations of Tey [99T], which are presumed to normally underpredict the correct physical result by up to around 20% but to adequately display trends.

Table 161.3 Comparison of repulsion distances for three aluminum faces, as calculated by quantum mechanical (QM) and by classical models (for two different assumed values of polarizability volume αv)

Reference for QM model

Material and face

Repulsion distance (pm) at low fields, for: Classical model, for (103αv) ¼ 8.34 nm3 [98F] 6.8 nm3[99T] QM model

Lam and Needs [93L] Inglesfield [87I] Lam and Needs [93L]

Al (111) Al (100) Al (110)

167 159 152

150 152 149

143 144 139

Table 161.4 Repulsion distances, for selected bcc metals and crystallographic faces, calculated from formula (161.2) using values of space lattice parameter csp and polarizability volume (αv) shown and Thkl-values shown in Table 161.1. For comparison, a distance equal to half the nearest-neighbor distance (RNN) in the space lattice is shown. Results are shown in order of increasing αv-value At. No.

Gp

26 74 24 23 42 73 41 11 37

8 6 6 5 6 5 5 1 1

El. Fe W Cr V Mo Ta Nb Na Rb

csp (pm)

1000αv (nm3)

Repulsion distance (pm) for crystallographic faces: (110) (100) (211) (310) (111)

(210)

RNN/2 (pm)

286.64 316.50 288.46 302.82 314.68 330.26 330.07 429.06 561.00

8.4 11.1 11.6 12.4 12.8 13.1 15.7 24.1 47.3

143 157 150 156 160 165 169 208 266

123 135 140 1,434 144 143 154 172 212

124 137 125 131 136 143 138 186 243

152 167 163 169 172 176 183 219 276

143 157 155 159 162 165 173 204 256

145 159 161 165 167 169 179 205 254

155 170 175 179 180 180 193 217 267

Table 161.5 Repulsion distances for selected fcc metals and crystallographic faces. Other details are the same as in Table 161.4, except that Thkl-values are taken from Table 161.2 At. No.

Gp

46 79 29 78 13 82 28 47 77 45 20 38

10 11 11 10 13 14 10 11 9 9 2 2

El. Pd Au Cu Pt Al Pb Ni Ag Ir Rh Ca Sr

csp (pm)

1000αv (nm3)

Repulsion distance (pm) for crystallographic faces: (111) (100) (110) (210) (211)

(310)

RNN/2 (pm)

389.07 407.88 361.47 392.39 404.96 495.02 352.36 408.57 383.89 380.44 558.2 608.49

4.8 5.8 6.1 6.5 6.8 6.8 6.8 7.2 7.6 8.6 22.8 27.6

130 138 135 141 143 146 136 146 144 147 209 224

89 97 112 109 109 86 122 112 122 132 175 183

138 144 128 139 143 175 125 145 136 135 197 215

129 138 136 141 144 143 138 147 146 150 211 227

122 130 135 137 139 130 139 142 145 150 209 223

110 119 132 130 131 109 141 134 143 152 205 216

90 97 105 105 106 92 111 108 114 120 163 173

4

R. G. Forbes

It is possible in principle to use appearance energy spectroscopy [93E] to make an experimental estimate of d (e.g., see [97F]). Unfortunately, results are of limited accuracy, but they do confirm that the electrical surface is on the vacuum side of the plane of the surface atom nuclei, by a distance that is at least a significant fraction of the surface atom radius. Symbols and abbreviations Short form

Full form

bcc fcc QM ISQ

base-centered cubic face-centered cubic quantum mechanical international system of quantities

References [27T] [65N] [73L] [77M] [80F] [81F] [81W] [87I] [93E] [93L] [97F] [98F] [99F] [99T]

Topping, J.: Proc. R. Soc. Lond. A. 114, 67 (1927) Nicholas, J.F.: An Atlas of Model of Crystal Surfaces. Gordon and Breach, New York (1965) Lang, N.D., Kohn, W.: Phys. Rev. B. 7, 3541 (1973) Miller, T.M., Bederson, B.: Adv. At. Mol. Phys. 13, 1 (1977) Forbes, R.G., Wafi, M.K.: Surf. Sci. 93, 192 (1980) Forbes, R.G.: Surf. Sci. 108, 311 (1981) Wafi, M.K.: PhD thesis, University of Aston in Birmingham (1981) Inglesfield, J.E.: Surf. Sci. 188, L701 (1987) Ernst, N.: Appl. Surf. Sci. 67, 82 (1993) Lam, S.C., Needs, R.J.: J. Phys. Condens. Matter 5, 2101 (1993) Forbes, R.G.: Z. Angw. Phys. (Neue Folge). 202, 139 (1997) Forbes, R.G.: Ultramicroscopy. 73, 31 (1998) Forbes, R.G.: Ultramicroscopy. 79, 25 (1999) Tey, C.S.: BEng Project Report, University of Surrey (1999)

Chapter 162

Physical properties of the noble operating gases R. G. Forbes

For the operating gases used in the gas field ion source (GFIS) and field ion microscopy (FIM), thermodynamic parameters of interest are the first ionization energy I1 and the static atomic polarizability αISQ. For the noble operating gases, values of these parameters have been extracted in the same way as described above for the metal elements and are shown in Table 162.1. An experimental parameter of interest for each gas is its best image field Fbi: values are discussed in Chap. 163[https://doi.org/10.1007/978-3-662-539088_163]. Table 162.1 Relevant physical properties of the noble gases: first ionization energy I1, polarizability volume αv, ISQ polarizability αISQ, and polarization potential energy (Upol)bi at best image field (BIF). I1 values are taken from [15H3]; αvvalues are taken from [14S] and converted via formulae (158.3a[https://doi.org/10.1007/978-3-662-53908-8_158]) and (158.3d[https://doi.org/10.1007/978-3-662-53908-8_158]). (Upol)bi values are obtained from formula (162.1), using BIF values in column 5 of Table 163.1[https://doi.org/10.1007/978-3-662-53908-8_163] Operating gas

I1 (eV)

αv (au)

(1000 αv) (nm3)

αISQ (meV V
2 nm2)

bi U pol (meV)

He Ne Ar Kr Xe

24.59 21.56 15.76 14.00 12.13

1.38 2.67 11.07 17.075 27.815

0.205 0.396 1.640 2.530 4.122

0.142 0.275 1.139 1.757 2.862


144
178
203
182
183

Also shown in Table 162.1 is the polarization potential energy associated with the weak long-range field adsorption due to polarization forces, at the best image field for each gas, as given by the formula bi U pol

 
2 1 ¼
αISQ Fbi : 2

ð162:1Þ

The BIF values used are those shown in column 5 of Chap. 163[https://doi.org/10.1007/978-3-66253908-8_163], Table 163.1. For comparison, the value of kBT at 80 K is 6.9 meV. Symbols and abbreviations Short form

Full form

BIF GFIS ISQ

best image field gas field ion source international system of quantities

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_162

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References [14S] Schottky, W.: Phys. Z. 15, 872 (1914) [15H3] Haynes, W.M. (ed.), Lide, D.R. (ed., internet version): CRC Handbook of Chemistry and Physics, 95th Ed., Internet Version (2015); Sect. 10, pp. 10–197

Chapter 163

Field calibration issues R. G. Forbes

163.1

Introduction

For experimental processes involving high electrostatic fields, values are often needed for some field that characterizes the process, in particular the evaporation field in atom probe tomography [14Mil] and the ionizing field in the gas field ion source (GFIS) and field ion microscopy (FIM) [09F2]. Issues relating to the definition and calibration of nanoscale and sub-nanoscale fields (which in some contexts vary significantly over distances of less than 1 nm) have recently been discussed [14Mil] and are very complex. Usually, it is not practicable to apply macroscopic field determination methods to nanoscale situations. Consequently, indirect methods are used that are based on “fixed point arguments” and assume proportionality between field and applied voltage. For metal elements and for any given operating gas, field ion images look best over a narrow range of voltages and fields. Further, good theoretical reasons exist [14Mil] to think that this is a consequence of gas behavior that (for metal elements) is largely independent of the metal being imaged, though it may depend weakly on emitter temperature and (for very sharp emitters) on the emitter apex radius of curvature [61M]. Hence, for an emitter of moderate to large apex radius, for each operating gas (at a given emitter operating temperature), one assumes that a relatively well-defined best image field (BIF) exists. By comparing, for a given emitter of moderate apex radius, the best image voltages for each operating gas that can be used on that emitter, one can establish the relationships between the BIFs for the various operating gases. One then needs an “absolute” calibration for one of the gases. Historically, the calibration has been carried out for the helium field-ion imaging of tungsten (the He-on-W system). Originally, this calibration was done, by Müller and Young [61M], by means of the Murphy-Good theory of field electron emission (FE) [56Mur]. To a certain level of accuracy that was originally estimated [56D, 61M] as around
15%, but might be worse (since the inadequacies of Murphy-Good theory are now better understood – see [15F]), this theory enabled the barrier field corresponding to a given measured electron current density to be determined. One then needs to assume that the GFIS/FIM ionizing field is a field “of nearly the same kind” as the FE barrier field. (If fields are not “of the same kind,” then for a given applied voltage the fields have different values.) This equivalence is not guaranteed, because the two fields are specified in different ways, but appears to be a reasonable assumption for emitters of moderate apex radius. Then, for a given W specimen, by comparing the magnitude of the corresponding FE voltage with the best image voltage (BIV) for He imaging of this specimen, the BIF for He imaging can be established. The value originally found was 44 V/nm [61M], but subsequently this was often rounded to 45 V/nm. The BIF values for the other noble operating gases and hydrogen (H2) were initially determined, by Müller and Tsong [69M], partly by experiment (Ne, Ar, and H2) and partly by means of field ionization (FI) theory (Kr and Xe). This FI theory was originally developed by Gomer [61G] and is now known to be of limited accuracy. Nevertheless, textbook lists of BIF values are often derived from this hybrid list ([69M], p. 12). These hybrid list values commonly given, e.g., in [96M], are shown in column 2 of

R. G. Forbes (*) Advanced Technology Institute, University of Surrey, Guildford, UK e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_163

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R. G. Forbes

Table 163.1. A different list of values, found in [12G], derives from a list of field values in [78T] that appears to relate to the field adsorption properties of the noble gases rather than their field ionization properties.

Table 163.1 Values for best image field (BIF). Column 2 shows the values originally derived [69M], and often presented (usually rounded), until recently; (E) denotes an experimental value, (T) a theoretical estimate. Column 3 shows experimental results for relative values, all taken on a specific emitter [71B]. In columns 4–8, the helium BIF value is regarded as “calibrated,” either at one of the values commonly used or via experiments on different regions of a tungsten end form [77S], and the other values are obtained by using the column 3 entries. In columns 4–8, the H2 BIF estimates are obtained by rounding the Ar estimates to the nearest 0.5 V/nm Operating gas

[69M]

[71B]

He Ne Ar Kr Xe H2 1

V/nm 44 (E) 35 (E) ~22 (E) 15.1 (T) 12.2 (T) ~22 (E) 2

Relative 100% (E) 80% (E) 42% (E) 32% (E) 25% (E) 3

Old usual values 44 V/nm 45 V/nm

[77S] W(111)

W(211)

W(110)

All fields below are in [V/nm] 44.0 45.0 35.2 36.0 18.5 18.9 14.1 14.4 11.0 11.3 (18.5) (19) 4 5

50.1 40.1 21.0 16.0 12.5 (21) 6

46.5 37.2 19.5 14.9 11.6 (19.5) 7

45.2 36.2 19.0 14.5 11.3 (19) 8

Experimental measurements of relative BIV-values, for a given tungsten emitter, at 78 K, and for all the noble operating gases, were carried out by Boyes et al. [71B]. Results are recorded in Table 163.1, column 3, with the He BIV value being given as “100%.” The related BIF values that correspond to assumed He BIF values of 44 V/nm and 45 V/nm are shown in columns 4 and 5; for consistency, values are shown to a precision of 0.1 V/nm, although at this stage of discussion the absolute accuracy has to be assessed as “probably not better than
15%,” as discussed above. The values given in [14Mil] are rounded from the column 5 values given here. Issues relating to the calibration of evaporation fields now need discussion. Slow continuous field evaporation (FEV) of emitter layers can be observed in the FIM if the applied voltage (and related fields) is raised to sufficiently high values. The FEV flux (as measured in “emitter layers/s”) is a function of emitter temperature and of the evaporation field at the high-risk sites. For a given emitter temperature Te, the onset of FEV, as applied voltage and evaporation field are increased, can be defined by an onset flux criterion, which is usually taken as 1 layer/s or 0.01 layers/s. The corresponding onset evaporation field Fon is a function of temperature. Since the corresponding onset voltage Von can be compared with the best image voltage Vbi for imaging of the “recently field evaporated” emitter, a calibrated value of Fon for a given material at a given temperature can be obtained from the relevant BIF value Fbi, calibrated as described above, using the formula
Fon ¼ V on =V bi  Fbi :

ð163:1Þ

Lists of experimental onset fields derived in this way can be found in the literature, e.g., [66N, 78T, 82B], but it is not helpful to present them here. Note that, as in the ionizing field case, this approach implicitly assumes that the surface field appearing in FEV theory is a “field of the same kind” as the FE barrier field. This is almost certainly not true (this surface field is almost certainly greater than the FE barrier field), but the detailed physics of the situation is so complex that qualitative arguments are unreliable in terms of exactness, and good quantitative (quantum-mechanical) analyses are currently too difficult to be carried out successfully. In consequence, there is intrinsic unreliability over the calibration of evaporation fields as used in FEV theory. This is difficult to assess, but it is thought that it could in principle be as much as 20% or more, in addition to any uncertainty there may be over the calibration of FE barrier fields and best image fields. (In their original

163

Field calibration issues

3

work, Müller and Young [M61] were of the view that the surface field used to discuss FEV was greater than the field used to define the FE tunneling barrier, by a factor of 1.8, but the theory they used to reach this conclusion is itself now thought to be unreliable [14F].)

163.2

The Sakurai-M€ uller Approach

Due to the difficulties described above – and possibly stimulated by the work of Van Oostrom (see [65V], [69M], p. 71]) – Sakurai and Müller [77S] (SM) developed an alternative approach to field calibration, based on using the energy distribution associated with the free-space field ionization of deuterium (D2), krypton, or argon (depending on the metal involved). Details of their approach can be found in their paper. What their approach will measure is a field slightly outside the emitter surface, called here the external field. Sakurai and Müller applied their approach to both the “best image” condition and the onset of field evaporation (using the onset flux criterion of one layer/s) and determined fields above different regions of a tungsten end form. The helium BIF values given in columns 6–8 of Table 163.1 are the averages of the two sets of values recorded in Table 1. The values that SM found for onset evaporation fields (strictly, for external fields rather than the surface fields used in FEV theory), for six metals, for various different regions of the emitter surface, after the end form had been field evaporated in the presence of the stated operating gas, are shown in Table 163.2. A misprint in the labelling of the last column in Table 3 of [77S] has been corrected by using the corresponding table in [78T]. Table 163.2 Values of the onset evaporation field Fon, for a FEV onset flux of one layer/s and at the emitter temperature Te shown, for six metals. End forms were first field evaporated in the presence of an operating/imaging gas (first entry), and then a reference gas (second entry) was used to generate the free-space field ionization Metal

Gases used

Te (K)

W

He/D2

Mo

He/D2

Ir

He/D2

Rh

He/D2

Ni

He-Ne/Kr

78 21 78 21 78 21 78 21 78 21

FEV onset field Fon (V/nm) for: (001) (011) (111) 55 57 46 50 52 54 45 48 32 35

62 63 47 50 51 54 45 48 32 36

(112) 57 59 47 50

(113)

47 54 56 48 49 35 38

Sakurai and Müller were of the view [77S] that the accuracy of their determinations (of external field) was
1 V/nm, which is around
2%. Subsequently, Castilho and Kingham [84C, 86C] pointed out an incorrect assumption in SM’s treatment of energy distribution theory, and proposed an improvement. Sakurai et al. ([89S], p.85) accepted the need for the improvement, but considered that it did not significantly affect the accuracy of the SM results, and reaffirmed the accuracy of the SM results as
1 V/nm (around
2%). Tsong ([90T], p. 123), however, considered that the improvement might reduce the accuracy of the SM measurements to around
5%. The matter remains unresolved, but clearly this estimated accuracy (whether
2% or
5%) is significantly better than the presumed accuracy (
15%) of the calibration via the Murphy-Good theory of field electron emission, and supersedes the earlier calibration. Of course, all these accuracy estimates are estimates of the accuracy of measuring the external field. There remain unresolved questions as to what extent (a) the field involved in field ionization and (b) the surface field that that appears in FEV theory are “fields of the same kind” as the external field. The problem

4

R. G. Forbes

is that, due to the surface atomic structure and the related surface charge distribution, electrostatic fields vary significantly from point to point above real field emitters. The three fields discussed above are average fields taken in slightly different regions of space and in slightly different ways, and the presumption is that they are not equal. Currently, it remains impracticable to attach realistic numbers to these differences, and – as already emphasized – this is a significant source of uncertainty. Further difficulties arise when attempting to calibrate the evaporation fields used in modern atom probe tomography (APT), because the physical situation is different from that used in the SM calibrations. First, the emitter surface is clean, rather than covered by a layer of either the operating gas or the reference gas used to generate the energy distributions. It is known (e.g., [84K]) that the existence of a layer of strongly field-adsorbed gas on the specimen surface alters bonding energies and hence onset evaporation fields. Second, the operating fluxes, and hence the operating fields, used in modern APT are significantly higher than those used in SM calibrations. We do not yet clearly know how to link the two sets of conditions reliably. This issue is a topic of active research (see [14Mil]).

163.3

Calibration via Post-Field-Ionization

For metal elements, a third calibration method can be based on making measurements of the relative abundances of field evaporated ions in different charge states, in circumstances where one can be sure that the higher charge state is derived from the lower one by post-field-Ionization. One can then use the Kingham ion abundance diagrams [82K, 12G] to deduce a corresponding evaporation field. Since surface fields may vary across the surface of an operating field emitter, one may need to apply this technique selectively to regions or areas of the emitter surface where one might reasonably expect the surface field to be relatively uniform across the surface. This method has been applied in the context of liquid metal ion sources [86S], although with mixed results, and has had some use in APT, e.g., [11G]. The method probably deserves greater attention. Known problems with the method are that small errors have been found [92L, 14F] in Kingham’s mathematical and physical treatment, and possibly that the theory is applied in the context of a smooth classical conductor surface model, rather than an atomically structured model. In general, the implications of these problems for evaporation-field prediction are not clearly known, but currently there is no reason to think that the resulting corrections would be significantly large. Symbols and abbreviations Short form

Full form

BIF GFIS FIM FE BIV FEV SM APT FI

best image field gas field ion source field ion microscopy field electron emission best image voltage field evaporation Sakurai and Müller atom probe tomography field ion or field ionization

References [56D] [56Mur] [61G] [61M] [65V] [66N] [69M]

Dyke, W.P., Dolan, W.W.: Adv. Electr. Electron. Phys. 8, 89 (1956) Murphy, E.L., Good Jr., E.H.: Phys. Rev. 102, 1464 (1956) Gomer, R.: Field Emission and Field Ionization. Harvard University Press, Cambridge, MA (1961) Müller, E.W., Young, R.D.: J. Appl. Phys. 32, 2425 (1961) Van Oostrom, A.G.J.: PhD thesis, University of Amsterdam (1965) Nakamura, S.: J. Electron Microsc. (Japan). 15, 279ver (1966) Müller, E.W., Tsong, T.T.: Field Ion Microscopy: Principles and Applications. American Elsevier, New York (1969)

163

[71B]

Field calibration issues

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Boyes, E.D., Turner, P.J., Southon, M.J.: Proceedings of the 25th Anniversary Meeting EMAG Institute of Physics, p. 256. IOP, London (1971) [77S] Sakurai, T., Müller, E.W.: J. Appl. Phys. 48, 2618 (1977), and references therein. [78T] Tsong, T.T.: Surf. Sci. 70, 211 (1978) [82B] Biswas, R.K., Forbes, R.G.: J. Phys. D Appl. Phys. 15, 1323 (1982) [82K] Kingham, D.R.: Surf. Sci. 116, 273 (1982) [84C] De Castilho, C.M.C., Kingham, D.R.: J. Phys. 45, C9–77 (1984) [84K] Kellogg, G.L.: Phys. Rev. B29, 4304 (1984) [86C] De Castilho, C.M.C., Kingham, D.R.: Surf. Sci. 173, 75 (1986) [86S] Swanson, L.W.: Appl. Phys. A41, 223 (1986) [89S] Sakurai, T., Sakai, A., Pickering, H.W.: Atom-Probe Field Ion Microscopy and Its Applications. Advances in Electronics and Electron Physics, Supplement 20. Academic, Boston (1989) [90T] Tsong, T.T.: Atom Probe Field Ion Microscopy. CUP, Cambridge (1990) [92L] Lam, S.C., Needs, R.J.: Surf. Sci. 277, 359 (1992) [96M] Miller, M.K., Cerezo, A., Hetherington, M.G., Smith, G.D.W.: Atom Probe Field Ion Microscopy. Clarendon, Oxford (1996) [09F2] Forbes, R.G.: Gas field ionization sources, Chapter 3 in [09O] [11G] Gault, B., Loi, S.T., Araullo-Peters, V.J., Stephenson, L.T., Moody, M.P., Shrestha, S.L., Marceau, R.K.W., Yao, L., Cairney, J.M., Ringer, S.P.: Ultramicroscopy. 111, 1619 (2011) [12G] Gault, B., Moody, M.P., Cairney, J.M., Ringer, S.P.: Atom Probe Microscopy. Springer, New York (2012) [14F] Forbes, R.G.: Unpublished work (2014) [14Mil] Miller, M.K., Forbes, R.G.: Atom Probe Tomography: The Local Electrode Atom Probe. Springer, New York (2014) [15F] Forbes, R.G., Deane, J.H.B., Fischer A., Mousa, M.S.: Jordan J. Phys. 8, 125 (2015) 125; [arXiv 1504.06134v7]

Part VIII

Epigraphene

Chapter 164

Introduction to epigraphene and overview C. Berger, E. H. Conrad, and W. A. de Heer

164.1

Epitaxial Graphene and Transferred Graphene

Graphene, a single sheet of carbon atoms, and the basic building block of graphite (see Fig. 164.1) has been studied for more than half a century. Last century, academic graphene research focused primarily on surface science of epitaxial graphene on various metal surfaces, as well as on silicon carbide. Only some of its electronic properties were theoretically considered, but none were experimentally probed. In the past decade, initially fueled by its potential for electronics, graphene research has flourished, following two main distinct paths: graphene grown epitaxially on silicon carbide, or epigraphene,1 and graphene that is produced by a variety of methods and is designed to be transferred onto various substrates, known as transferred graphene. Basically, the two materials only differ due to the substrate that they are on, but this difference is fundamentally important. Much research has been devoted to producing large essentially perfect graphene sheets, which was considered by many to be an essential first step for graphene electronics. However, essentially all applications require graphene structures. Graphene electronics is an extreme case that requires highly reproducible graphene nanostructures in order to be technologically interesting. However, most nanolithographic pattering methods are detrimental to graphene. Consequently nanoelectronic graphene devices are not competitive with conventional nanoelectronics. Epigraphene is an exception, and is currently the only type of graphene that is suitable for graphene nanoelectronics [1, 2].

1

The term epitaxial graphene originally coined for graphene on SiC [1] is now widely used for graphene grown epitaxially – or not – on various metals. For this reason in this review, we refer to epitaxial graphene on SiC as epigraphene. C. Berger (*) School of Physics, Georgia Institute of Technology, Atlanta, GA, USA Institut Ne´el, CNRS - University Grenoble - Alpes, Grenoble, France e-mail: [email protected] E. H. Conrad School of Physics, Georgia Institute of Technology, Atlanta, GA, USA e-mail: [email protected] W. A. de Heer School of Physics, Georgia Institute of Technology, Atlanta, GA, USA TICNN, Tianjin University, Tianjin, China e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_164

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C. Berger et al.

Fig. 164.1 (a) Graphene is a one-atom thick two-dimensional honeycomb structure of carbon atoms. (b) Two Bernal stacked graphene layers are the constitutive building block of hexagonal graphite (c) Three Bernal stacked graphene layers. (d) ABC stacking of graphene layers makes the unit cell of rhombohedral graphite. A and B atoms correspond to the two sublattices forming the honey comb structure. The tight-binding γi parameters, corresponding to first, second, etc., neighbors, for electronic structure calculations are indicated (From Ref. [39])

Historically, the first examples of patterned epitaxial graphene for graphene-based electronics were published in 2004, in a paper titled: “Ultrathin epitaxial graphite and a route to graphene based electronics” [1]. The present review, finalized in the fall of 2015, follows the history and the developments of that seminal work, that, incidentally presents the first (monolayer) graphene transport measurements. In 2005, Novoselov et al. [3] invented a method now generally known as the “Scotch tape method”. In this method, adhesive tape is used to cleave (exfoliate) graphene flakes from bulk graphite and transfer them onto oxidized silicon wafers, to demonstrate their field effect properties. In 2004 the same group reported very similar properties in ultrathin graphite flakes transferred on oxidized silicon (using a different deposition method). The paper, titled “Field effect in atomically thin graphite” [4], carefully demonstrates that the measured properties were those of thin graphite (see also similar work by Zhang et al. in 2005 [5]). Nevertheless this paper is widely cited not only for demonstrating graphene properties, but also for the discovery of graphene. The controversial discovery claim was based on the authors presumption, that freestanding graphene should be expected to be chemically unstable, unaware at the time that in 1962 Boehm et al. [6] had already produced and identified freestanding graphene sheets. Boehm also coined the name “graphene” in 1986 [7, 8]. Transferred graphene was originally characterized as “freestanding” in Ref. [3] to distinguish it from other previously known forms of graphene directly grown on substrates including epigraphene. The name reflected the belief at that time that interactions with the SiO2 substrate were negligible. Later research found that substrate-induced disorder is significant. In contrast, epitaxial graphene on silicon carbide is widely used to demonstrate the intrinsic band structure of graphene [9–11] (see Fig. 164.2) that is not observable in transferred graphene (see Fig. 164.3 and Chap. 167[https://doi.org/10.1007/978-3-66253908-8_167]).

164

Introduction to epigraphene and overview

3

a

Binding energy E [eV]

b

c

d

e

Parallel wavevector k// [Å–1] Fig. 164.2 (a) Band structure E(k) of graphene, and zoom in close to the K point, showing the two inverted cones. (b–e) The π-bands near EF for 1–4 graphene layers, respectively, measured for epigraphene (Si-face) by Angle Resolved Photo-Emission Spectroscopy. The dashed lines are from a calculated tight-binding band structure, with band parameters adjusted to reproduce the measured bands. Red and orange lines are for ABAB and ABAC stacking, while blue lines are for rhombohedral ABC stacking (From Ref. [10])

a

2D exfoliated graphene

2D EG

2D exfoliated graphene

24 nm EG ribbon

Free-standing 5µ exfoliated graphene

~ 0.2nm 100 x 100nm z

E-EF (eV)

0

-1

-2

b z

~ 0.02nm

Intensity

2D EG

-1.0

400 x 400nm c

0.0

Parallel wavevector k [Å-1]

1.0

-0.4

0.2

Parallel wavevector k [Å-1] d

Fig. 164.3 Comparison of epigraphene with different exfoliated graphene materials. (a) AFM images of exfoliated graphene on SiO2 [40]. (b) An STM image of epigraphene grown on SiC-(0001) (Courtesy Philip First, Georgia Tech and Joseph Stroscio, NIST-CNST). Note the ten-fold increase in flatness of the epigraphene film. (c) A comparison of the ARPES measured Dirac cone for 2D epigraphene grown on SiC-(000-1) [9] (left), the band structure of a 2D exfoliated film (center) [41], and a 24-nm-wide epigraphene sidewall ribbon [38]. Note that the energy and momentum scales are the same in all images in (c) and (d). Top panels in (c) are measured E(k) and bottom panels are constant energy cuts through E(k) showing the momentum distribution curves (MDC) of the bands. The Δk broadening in exfoliated graphene gives a coherence length, Lc ¼ 2π/Δk of 1–3 nm. The momentum distribution curve width for epigraphene, including the 24 nm wide ribbons, is entirely due to instrument resolution giving Lc > 10 times longer than exfoliated graphene on SiO2. (d) Energy and momentum distribution curves and MDCs of the highest quality (suspended) exfoliated graphene [42]

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Epitaxial graphene is a graphene film that is directly grown on various crystalline surfaces. The carbon atoms of the graphene layer are orientationally registered and nearly commensurate with the atomic lattice of the substrate surface. The degree of chemical bonding of the graphene to the substrate varies from extremely weak to relatively strong, and the graphene properties are modified accordingly. In contrast, there is in general no coherent atomic registration for graphene films that are transferred onto surfaces, for example, on oxidized degenerately doped silicon wafers (graphene transferred on boron nitride single crystals is a notable exception but the registry is not controlled). Various transfer methods have been developed, either by drying graphene flake solutions [4, 6] or by direct mechanical transfer from graphite onto these surfaces (as first done by Novoselov et al. [12] in 2005). The Scotch tape method has a great advantage for two-dimensional electron gas (2DEG) investigations [12, 13], because the charge density of the graphene layer can be adjusted by electrostatic “back gating,” which cannot be done with epitaxially grown graphene. For back gating a parallel plate capacitor is made of a thin SiO2 dielectric sandwiched between a conducting silicon substrate and the graphene layer(s) that is transferred on it. For epigraphene, by virtue of its growth process directly from the silicon carbide crystal, such an insulating barrier does not exist. However, the transfer process has the disadvantage of considerable disorder inherent in the transfer. Epitaxial graphene on silicon carbide (epigraphene) was first identified in 1962 by Badami [14, 15], followed by van Bommel et al. [16] in 1973, in the investigations of the graphite layers that spontaneously grow on silicon carbide when silicon carbide crystals are heated to extremely high temperatures (>1000  C) in vacuum. The growth proceeds by sublimation of Si from the SiC surfaces, resulting in a carbon-rich surface that reconstructs to produce graphene. It is interesting, that graphitic layers on heated SiC crystals were already noted in investigations by G.E. Acheson, who also first synthesized silicon carbide in 1891 [17]. It is worth noting also that in 1907 H.J Round produced the first SiC light emitting diode and SiC diodes were used in the first radio receivers [18]. These are harbingers of SiC-based electronics. The invention of graphene-based electronics [19] (patented in 2003) was based on the earlier graphene research in combination with carbon nanotube electronics research. The choice of SiC as the substrate material was motivated by the strict requirements for high-end electronic materials (i.e., Si, Ge, GaAs, SiN, SiC). This requires a platform that is reliably nanopatternable, which demands that the substrate is a single crystal. Single-crystal, electronics grade SiC is commercially available, and it is currently extensively used in electronics. In the last decade, SiC-based electronics has developed significantly including hightemperature complementary metal-oxide-semiconductor (CMOS) technology [20]. As we will see in this review, epigraphene has been shown to satisfy requirements for electronics grade graphene. Moreover, various schemes to modify the properties of epigraphene using nanopatterning methods and by tuning the interaction with the SiC substrate have added significant flexibility as discussed below. In contrast, most transferred graphene and thin graphitic flake research currently focuses on chemical properties, para-electronics, and physical properties like super-capacitors and transparent and flexible conductors, in optoelectronic and photonic demonstrators and as ultrathin membranes [21, 22]. This shift in emphasis is primarily due to the inherent difficulties of reliably producing high-end electronics grade graphene-based materials by transferring graphene (grown epitaxially on metal surfaces or from graphite) onto various substrates as mentioned above. While there is still considerable research on fundamental graphene properties using small mechanically transferred graphene flakes, expectations that transferred graphene will significantly impact high-end electronics have recently faded. The current confusion of the definition of graphene is not merely one of semantics, but actually confounds graphene research with nanographite research (a several decades old, mature field).

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Introduction to epigraphene and overview

164.2

5

Definition of Graphene

Graphene was defined [7] by H-P Boehm in 1986, and the nomenclature was officially adopted[23] by the International Union of Pure and Applied Chemistry (IUPAC) in 1994. It reads as follows: Graphene is a single carbon layer of the graphite structure, describing its nature by analogy to a polycyclic aromatic hydrocarbon of quasi infinite size. Previously, descriptions such as graphite layers, carbon layers or carbon sheets, graphite monolayers have been used for the term graphene. Because graphite designates that modification of the chemical element carbon, in which planar sheets of carbon atoms, each atom bound to three neighbors in a honeycomblike structure, are stacked in a three-dimensional regular order, it is not correct to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed.

Consistent with this definition, “graphite” should be used when graphene layers are stacked in the graphitic (Bernal) structure (see Fig. 164.1), so that “few layer graphene” is incorrect and should be referred to as “thin graphite”. In practice, graphene (including transferred graphene) is usually supported on a substrate. The term “freestanding graphene” is often used to suggest the absence of substrate-induced perturbations. Some even have suggested [24] to redefine graphene accordingly: Graphene is a single atomic plane of graphite, which—and this is essential—is sufficiently isolated from its environment to be considered freestanding.

However in practice, graphene on a substrate is never freestanding. Substrates always affect the properties and quite significantly so in graphene transferred on SiO2 using the “Scotch tape” method, making this alternative definition ineffective. It makes more sense to adhere to the IUPAC definition of graphene and to apply “quasi-freestanding” relative to a property. For electronic properties, quasifreestanding implies that the electronic properties are essentially identical to those of an ideal graphene sheet. A recent publication in the authoritative journal Carbon suggests the usage of more precise definitions [25]. The adhesion of graphene to many substrates involving van der Waals forces and/or electrostatic forces usually minimally affects its chemical and electronic properties (see below). But the adhesion to the substrate can be strong, involving significant chemical bonding of the carbon atoms in the graphene layer to the substrate. In these cases the electronic structure (as well as planarity) will be significantly modified. Finally, graphene can also be functionalized, in which cases atoms or molecules are chemically bound to graphene carbon atoms, whereby the electronic structure is typically significantly modified. Consequently chemical functionalization and chemical bonding to a substrate are closely related. Below, examples of all three forms of graphene are presented in the context of epitaxial graphene on silicon carbide. Properties of “structured graphene” ribbons and islands are also discussed.

164.3

Graphite, Freely Suspended Graphene, and Graphene Isolated on Substrates

Until 1987, graphene was known as monolayer graphite, emphasizing its nature as a structural unit of graphite. Graphene was already known to be one of the most chemically and mechanically stable materials in nature, with a cohesive energy of 7 eV. This extreme stability of the individual graphene sheets results from the sp2 bond, as first described theoretically by Pauling [26]. Pauling demonstrated that the sp2 hybridization produces three extremely strong symmetrically arranged coplanar bonds (the sigma bonds), which explains why polycyclic aromatic hydrocarbons (including graphene) are flat and rigid: it requires energy to bend these structures. In addition to the in-plane sigma bonds, each carbon atom has an atomic pz orbital that extends above and below the plane. Overlap of these orbitals produces π-bands that are responsible for the electronic properties of graphene. Graphene is so stable that it requires temperatures exceeding 4000  C (as occur, for example, in electric arcs) to convert it into fullerenes, nanotubes, soot and other curved graphitic structures, as was experimentally demonstrated in the late 1989 in the famous experiments by Krätschmer et al. [27] and Ebbesen et al. [28].

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In contrast, the interlayer bonding of the graphene layers in graphite is extremely weak, on the order of 30 meV per carbon atom [29]. This small value (less than 1% of C-C bond energy in graphene) represents the difference in energy of a carbon atom in graphite compared to a carbon atom in a free graphene sheet. The weak adhesion explains why graphene layers are so easily peeled from a graphite crystal in the “Scotch tape method,” for example. This anciently known property underlies graphite’s name (graphite, from graphein, the Greek word for to write). Consequently, for all practical purposes, graphite’s exceptional chemical and mechanical stability is entirely due to graphene’s stability, and the added stability due to the crystal substrate is negligible. This explains the well-known fact that almost all chemical and physical properties of graphene and graphite are practically identical. Nowadays, the most common forms are aqueous graphene suspensions produced from exfoliated graphite[6, 30–32], chemical vapor deposition on various metal substrates (for a review, see [33]), epitaxial growth on SiC by Silicon sublimation [15, 34], and deposition on various substrates by mechanical exfoliation of graphite [3]. The suspensions of graphene flakes, produced and isolated by H-P Boehm in 1962, were identified with, for those times, novel electron microscopy methods, revealing that they indeed were graphene monolayers. These tour-de-force measurements were published in the most prominent German science journal of the time [6]. As a carbon chemist, Boehm knew that his work did not amount to the discovery of graphene nor proof of its stability. This work was performed mainly as an academic exercise to demonstrate that freestanding graphene flakes could be made and measured. Later, graphene was epitaxially grown on many single-crystal metal surfaces, by heating metal samples in the presence of carbon containing gasses (chemical vapor deposition (CVD)). In these experiments performed in ultrahigh vacuum, the atomic and electronic structure can be probed using a variety of surface science probes. In 1997 Gall et al. [33] recognized the quasi-freestanding nature of epitaxial graphene on various metal surfaces, as well as the fact that they were natural two-dimensional crystals. In their article titled “Two Dimensional Graphite Films on Metals and Their Intercalation,” the first sentence of the abstract reads: Two-dimensional graphite films (2DGF) on solids are wonderful objects, real nature-made two-dimensional crystals. . . . A special attention is paid to intercalation of 2DGF — a process when foreign atoms and even molecules (fullerenes C60 molecules) spontaneously penetrate between graphite film and metal substrate.

In this paper, and many other last century papers, the quasi-freestanding nature of the graphene layer is explicitly demonstrated, as it was by Forbeaux et al., in early investigations of epigraphene, who realized that the epitaxial graphene layers appeared to be “floating above the substrate” [35]. Several investigators pursued controlled mechanical exfoliation of graphene with explicit attempts to produce graphene by peeling layers from graphite. In 1999, Ruoff and coworkers published a paper titled: “Tailoring graphite with the goal of achieving single sheets” [36]. The process involved producing micronsized graphite islands on a substrate and mechanically peeling layers off with an atomic force microscope. The process produced ultrathin graphite flakes but not monolayers. In 2004 Novoselov and coworkers ultrasonicated islands produced by Ruoff’s method resulting in suspension of micron-sized flakes [4]. The suspensions were dried on oxidized silicon wafers. The electrical properties of micron-sized ultrathin graphite flakes were measured. After Novoselov and coworkers measured transport properties of graphene flakes produced by the “Scotch tape method” in 2005 [3], Novoselov et al. [12] and Zhang et al. [13] simultaneously published quantum Hall effect measurements in graphene. Graphene was first exfoliated chemically by separation of the layers through strong oxidation (graphite oxide, also called graphite paper), dispersion in aqueous solution followed by reduction [6]. Graphene can also be directly exfoliated in solution by ultrasonication in various solvents [31, 32] or using surfactants, similarly to carbon nanotubes and for stabilizing polymers [37], resulting submicron square (kBT, so that only the n ¼ m ¼ 0 mode will be occupied. A 100 nm wide ribbon will only have the m ¼ 0 modes occupied, and therefore it behaves like a one-dimensional wire, even at room temperature (see Chap. 170[https://doi.org/10.1007/978-3-66253908-8_170]). Symbols and abbreviations Short form

Full form

LDA MEG GW

local dipole approximation multilayer epitaxial graphene Green’s function of the Coulomb interaction W

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References 1.

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3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

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22. 23. 24. 25. 26. 27. 28. 29.

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Jpn. 67, 2857–2862 (1998) Khveshchenko, D.V.: Ghost excitonic insulator transition in layered graphite. Phys. Rev. Lett. 87, 2468021–2468024 (2001) Hwang, C., Siegel, D.A., Mo, S.K., Regan, W., Ismach, A., Zhang, Y.G., Zettl, A., Lanzara, A.: Fermi velocity engineering in graphene by substrate modification. Sci Rep-UK. 2, 590 (2012.) (594 pp) Ponomarenko, L.A., Gorbachev, R.V., Yu, G.L., Elias, D.C., Jalil, R., Patel, A.A., Mishchenko, A., Mayorov, A.S., Woods, C.R., Wallbank, J.R., Mucha-Kruczynski, M., Piot, B.A., Potemski, M., Grigorieva, I.V., Novoselov, K.S., Guinea, F., Fal’ko, V.I., Geim, A.K.: Cloning of Dirac fermions in graphene superlattices. Nature. 497, 594–597 (2013) Berger, C., Song, Z.M., Li, X.B., Wu, X.S., Brown, N., Naud, C., Mayou, D., Li, T.B., Hass, J., Marchenkov, A.N., Conrad, E.H., First, P.N., de Heer, W.A.: Electronic confinement and coherence in patterned epitaxial graphene. Science. 312, 1191–1196 (2006) Wu, X.S., Li, X.B., Song, Z.M., Berger, C., de Heer, W.A.: Weak antilocalization in epitaxial graphene: evidence for chiral electrons. Phys. Rev. Lett. 98, 266405 (2007) Sadowski, M.L., Martinez, G., Potemski, M., Berger, C., de Heer, W.A.: Landau level spectroscopy of ultrathin graphite layers. Phys. Rev. Lett. 97, 266405 (2006) Orlita, M., Faugeras, C., Plochocka, P., Neugebauer, P., Martinez, G., Maude, D.K., Barra, A.L., Sprinkle, M., Berger, C., de Heer, W.A., Potemski, M.: Approaching the Dirac point in high-mobility multilayer epitaxial graphene. Phys. Rev. Lett. 101, 267601 (2008) Faugeras, C., Nerriere, A., Potemski, M., Mahmood, A., Dujardin, E., Berger, C., de Heer, W.A.: Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study. Appl. Phys. Lett. 92, 011914 (2008) Song, Y.J., Otte, A.F., Kuk, Y., Hu, Y.K., Torrance, D.B., First, P.N., de Heer, W.A., Min, H.K., Adam, S., Stiles, M.D., MacDonald, A.H., Stroscio, J.A.: High-resolution tunnelling spectroscopy of a graphene quartet. Nature. 467, 185–189 (2010) Martin, J., Akerman, N., Ulbricht, G., Lohmann, T., Smet, J.H., Von Klitzing, K., Yacoby, A.: Observation of electronhole puddles in graphene using a scanning single-electron transistor. Nat. Phys. 4, 144–148 (2008) Chen, J.H., Jang, C., Xiao, S.D., Ishigami, M., Fuhrer, M.S.: Intrinsic and extrinsic performance limits of graphene devices on SiO2. Nat. Nanotechnol. 3, 206–209 (2008) Tan, Y.W., Zhang, Y., Bolotin, K., Zhao, Y., Adam, S., Hwang, E.H., Das Sarma, S., Stormer, H.L., Kim, P.: Measurement of scattering rate and minimum conductivity in graphene. Phys. Rev. Lett. 99, 246803 (2007) Morozov, S.V., Novoselov, K.S., Katsnelson, M.I., Schedin, F., Ponomarenko, L.A., Jiang, D., Geim, A.K.: Strong suppression of weak localization in graphene. Phys. Rev. Lett. 97, 016801 (2006) Das Sarma, S., Adam, S., Hwang, E.H., Rossi, E.: Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407–470 (2011) Dean, C.R., Young, A.F., Meric, I., Lee, C., Wang, L., Sorgenfrei, S., Watanabe, K., Taniguchi, T., Kim, P., Shepard, K.L., Hone, J.: Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 5, 722–726 (2010) Fujita, M., Wakabayashi, K., Nakada, K., Kusakabe, K.: Peculiar localized state at zigzag graphite edge. J. Phys. Soc. Jpn. 65, 1920–1923 (1996) Nakada, K., Fujita, M., Dresselhaus, G., Dresselhaus, M.S.: Edge state in graphene ribbons: nanometer size effect and edge shape dependence. Phys. Rev. B. 54, 17954–17961 (1996)

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30. Emtsev, K.V., Bostwick, A., Horn, K., Jobst, J., Kellogg, G.L., Ley, L., McChesney, J.L., Ohta, T., Reshanov, S.A., Rohrl, J., Rotenberg, E., Schmid, A.K., Waldmann, D., Weber, H.B., Seyller, T.: Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide. Nat. Mater. 8, 203–207 (2009) 31. Mahmood, A., Mallet, P., Veuillen, J.Y.: Quasiparticle scattering off phase boundaries in epitaxial graphene. Nanotechnology. 23, 055706 (2012) 32. Veuillen, J.Y., Hiebel, F., Magaud, L., Mallet, P., Varchon, F.: Interface structure of graphene on SiC: an ab initio and STM approach. J. Phys. D: Appl. Phys. 43, 374008 (2010)

Chapter 166

Silicon carbide and epitaxial graphene on silicon carbide C. Berger, E. H. Conrad, and W. A. de Heer

166.1

G.E Acheson: Silicon Carbide, Graphite, and Graphene

Silicon carbide is a synthetic compound, first mass-produced by E.G. Acheson in 1891 (who called it Carborundum) by heating aluminum silicate with carbon. This process was patented in 1893, and Acheson founded the Carborundum Company. Silicon carbide was immediately industrially interesting because of its extreme hardness, so that it was used as an abrasive. Interestingly, Acheson also discovered that when Carborundum was heated to a high temperature, it produced extremely pure graphite. He patented his graphite-making process in 1896 and founded the Acheson Graphite Company in 1899. The company initially produced graphite for incandescent light filaments and electrolysis anodes and electrodes for arc furnaces. Interestingly Acheson also discovered a way to produce ultrafine graphite colloidal suspensions in water that he produced in his Acheson Industries Company under the trade name Aquadag (DAG: Deflocculated Acheson’s Graphite). These “graphene-like” conducting inks continue to be used extensively in the electronics industry to produce conductive coatings inside electronic vacuum tubes and cathode ray tubes ever since the early days of radio and television. It is now used in electronic, automotive, aerospace, appliance, medical, metalworking, die casting, and energy storage industries [4].

166.2

Electronic-Grade Silicon Carbide

Crystalline silicon carbide is a wide band gap semiconductor that occurs in more than 150 crystalline forms (polytypes) (see, for instance, [7]). The most relevant polytypes for electronics and epigraphene are hexagonal 6H (band gap: 3.05 eV) and 4H (3.23 eV) and cubic β-3C (band gap: 2.36 eV) (see Fig. 166.1). The structures consist of SiC bilayers which stacking determines the polytype. The 4H-(aSiC ¼ 3.0805 Å and cSiC ¼ 10.0848 Å [8]) and 6H-hexagonal crystals consist of four and six SiC bilayers, respectively (see Fig. 166.1). The 4H commercial crystals are generally considered of higher quality. The hexagonal planes are polar, that is, the (0001) face is made only of Si atoms (the bulk terminated surface Si atoms have one dangling bond per atom), and the opposite (000-1) has carbon atoms only. Single-crystal wafers of these two polytypes with diameters up to 150 mm are produced by several companies. These crystals are produced by the physical vapor transport method (a modified version of the original Lely process), at elevated temperatures above 2000  C in a closed graphite crucible. SiC powder, placed in the hot zone of the growth cell (e.g., 2200  C), sublimes and recrystallizes in the colder zone (e.g., 2150  C) at a C. Berger (*) School of Physics, Georgia Institute of Technology, Atlanta, GA, USA Institut Ne´el, CNRS - University Grenoble - Alpes, Grenoble, France e-mail: [email protected] E. H. Conrad School of Physics, Georgia Institute of Technology, Atlanta, GA, USA e-mail: [email protected] W. A. de Heer School of Physics, Georgia Institute of Technology, Atlanta, GA, USA TICNN, Tianjin University, Tianjin, China e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_166

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SiC seed. Control of various defects (“micropipes” and screw dislocations) has plagued SiC electronics industry from the outset; however, improvements in the quality as well as reduction in cost have been dramatic in the past decade, and this trend is expected to continue.

Fig. 166.1 SiC-hexagonal (H) and cubic (C) polytypes. Red: carbon atoms, blue: silicon atoms. The unit cell comprises respectively of 2, 3, 4, and 6 Si-C bilayers. A, B, C refers to the stacking sequence (From Ref. [21])

Electronic-grade SiC is commercially available, produced as semi-insulating and degenerately n-doped SiC. For semi-insulating SiC, the Fermi level is pinned in the band gap, for example, by doping with vanadium. SiC is widely used in electronics, especially for discrete components like light-emitting diodes and high-voltage Schottky diodes. Recently, high-voltage (1200 V) MOSFETs have become commercially available, and high-temperature CMOS integrated circuits have been demonstrated [3].

166.3

Epitaxial Graphene Growth by Silicon Sublimation

Epitaxial growth of graphene on SiC is nonconventional. Epitaxial growth of graphene on metals typically involves the decomposition of a carbon-containing gas on single-crystal metal surface, after which the carbon atoms arrange into the graphene structure that registers with the crystalline metal surface. However, epitaxial graphene growth on SiC is different and typically does not involve an external source of carbon. Rather, silicon sublimes from the hot SiC surfaces, resulting in a carbon-rich surface, then forms a graphene layer on the SiC surface. Van Bommel et al. [2] was among the first to study this graphitization of SiC (as used by Acheson) as a surface science problem (see also [1]). The motivation for these early studies was to understand the surface phase transitions of clean SiC as a function of temperature. For this, 6H-SiC crystals were heated in ultrahigh vacuum, and their surfaces were measured with low-energy electron diffraction (LEED) and Auger electron spectroscopy as a function of annealing temperature. It was discovered that as temperature increases, a monolayer graphite layer grows and stable graphite film ultimately formed on the SiC surface [2]. This early work also showed that graphene grows differently on the two polar surfaces of hexagonal (4H/6H) SiC: the (000-1) carbon-terminated face (C-face) and the (0001) silicon-terminated face (Si-face) (see Fig. 166.1 and schematics Fig. 166.2d). In the Si-face, graphitization proceeded with an initial phase at 1000  C involving a carbon-rich reconstructed SiC surface with a 6√3 R30 crystal structure (buffer layer; see Chap. 167[https://doi.org/10.1007/978-3-662-53908-8_167]). This is followed by the formation of an epitaxial graphene layer at higher temperatures and ultimately thin (Bernal) graphite at 1500  C. The C-face, on the contrary, showed signs of different graphene-SiC orientations. While in the years 1975–2000 there were many studies of Si-face graphene, very few were conducted on C-face graphene because of its perceived disorder (for a review of the earlier work, see Hass et al. [9]). As discussed in Chap. 167[https:// doi.org/10.1007/978-3-662-53908-8_167], the C-face is in fact ordered but the multiple layers are non-Bernal stacked, which has important consequences for its electronic properties.

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a

c

d

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Multilayered epitaxial graphene

b

C-face

Si-face buffer layer graphene or thin graphite

Fig. 166.2 Schematics of the confinement controlled sublimation growth method [5]. Contrary to Si sublimation in vacuum (a), in the CCS method (b), the Si vapor is confined in a graphite enclosure provided with a calibrated leak. (c) Photograph of the inductive furnace used for the CCS. (d) Schematics of graphene growth on the two polar faces of 4H and 6H-SiC

It should be noted that graphene layer’s growth by silicon sublimation in ultrahigh vacuum (the growth method used in earlier studies) typically results in lower-quality films that have a so-called “Swiss” cheese nanostructure as shown in Fig. 165.1[https://doi.org/10.1007/978-3-662-53908-8_165]. For this reason, alternative graphitization methods have been developed [5, 10].

166.4

Confinement Controlled Sublimation (CCS)

In free sublimation of silicon in vacuum, the sublimation rate is controlled only by the temperature. If one considers a silicon carbide crystal in a background of silicon vapor, then equilibrium will be established when the rate of absorption of silicon atoms on the surface equals the sublimation rate. Consequently, this equilibrium temperature depends on the silicon vapor pressure at the SiC surface [11]; in equilibrium, the formation of graphene is arrested. Free silicon sublimation (in UHV) produces defective graphene layers because the dynamics controlling the formation of graphene at a given temperature cannot keep up with the rate at which free carbon is produced at the surface, resulting in poorly developed graphene layers. Consequently, either slowing down the rate of carbon liberation or increasing the temperature so that the graphene formation process is speeded up should produce better graphene. At the same time, growth over the entire sample surfaces will be uniform if the growth processes occur close to equilibrium. The confinement controlled sublimation method [5] is designed to provide growth conditions close to equilibrium. In this method, a small silicon carbide crystal is placed in a graphite ampoule that is supplied with a small calibrated hole (Fig. 166.2b). The assembly is placed in a vacuum chamber that it is uniformly heated (typically using a radio-frequency induction heater, as shown in Fig. 166.2c) to a given temperature (in the range of 1500–1700  C). The silicon that evaporates from the SiC surface will dwell inside the ampoule for relatively long times, before it can escape out of the hole. Consequently, a silicon background pressure builds up and growth occurs in quasi-equilibrium conditions. The rate of graphene formation is directly related to the rate at which the silicon escapes. By confining silicon, the growth temperatures can be increased. Ultimately, the quasi-equilibrium growth at elevated temperatures assures a uniform graphene layer extending over the entire crystal surface. Optimum growth conditions (temperatures, growth times, and hole size) are empirically determined (see Chap. 167[https://doi.org/10.1007/978-3-662-53908-8_167]).

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Growth in Ar Atmosphere (Edison Light Bulb Method)

The rate at which silicon is depleted from the surface, and therefore the graphene growth rate, can also be controlled by heating the silicon carbide crystals in an inert gas background. While the silicon sublimation is unchanged, these atoms must diffuse through the Ar gas in order to escape. This diffusion process results in a Si density gradient in the gas, where the Si density is greatest at the surface. Hence, close to the surface the number of atoms leaving the surface is approximately equal to those returning to it. As in the confinement-controlled sublimation method, the return flux of silicon atoms (that depends on the Ar pressure and temperature) and therefore the graphene growth rate can be adjusted. This method pioneered by Emtsev et al. [10] has been successfully applied to produce relatively uniform epigraphene/SiC at the full wafer scale [12–14]. While this method (which is similar to the way tungsten evaporation in incandescent light bulbs is controlled) appears to be similar to the CCS method (see, for instance, surface studies in Fig. 166.3a, b), there is a fundamental difference. Whereas in the CCS method growth occurs under essentially uniform conditions over the whole surface, in Ar growth, it does not, because it is determined by diffusion of silicon atoms in the Ar gas. Growth rates depend on the boundary conditions and therefore sensitively on the chamber geometry, location on the sample, and critically on Ar flow and convection. Typically, the growth temperature of a monolayer epigraphene on the Si-face ranges from 1100  C in UHV [6] to 1550  C in the CCS method (depending on the crucible hole size [5]), up to 1650  C [10] and 2000  C in 1 atm of argon [15].

Fig. 166.3 (a–b) Si-face epigraphene grown under 1 atm Ar pressure (From Ref. [10]). (a) AFM image with a nominal thickness of 1.2 monolayer covering the SiC steps, (b) LEEM image revealing macroterraces covered with graphene. Area covered with 1, 2, and 3 graphene layers has been identified by the presence of 1, 2, or 3 reflectivity minima, respectively. Two and three layers are located at the step edges. (c–e) Hydrogen intercalation after epigraphene growth on the Si-face (c) (left to right) E(k) dispersion measured in ARPES for: pristine buffer layer, after hydrogen intercalation, after annealing at 900 C. (d) Same as (c) for a monographene layer. (e) Schematics of the hydrogen buffer lifting from the SiC substrate

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Variations of the high-pressure growth have been implemented, for instance, by supplying Si with (di) silane gas [16] or by providing external carbon atoms from gas (chemical vapor deposition; see, for instance [17]) or solid carbon sources (molecular beam epitaxy [18]). In a recent development, higher mobility samples on the Si-face for quantum Hall effect metrology (see Chap. 168[https://doi.org/10.1007/ 978-3-662-53908-8_168]) were obtained by balancing both carbon etchant (H2) and carbon supply gases in a process combining chemical vapor deposition and SiC thermal decomposition [19, 20]. Symbols and abbreviations Short form

Full form

DAG MOSFET CMOS LEED CCS UHV ML AFM LEEM ARPES

deflocculated Acheson graphite metal-oxide semiconductor field-effect transistor complementary metal oxide semiconductor low-energy electron diffraction confinement controlled sublimation ultrahigh vacuum monolayer atomic force microscopy low-energy electron microscopy angle-resolved photoelectron spectroscopy

References 1. 2. 3. 4. 5.

6. 7. 8.

9. 10.

11. 12. 13. 14.

15. 16.

Badami, D.V.: Graphitization of alpha-silicon carbide. Nature. 193, 569–570 (1962) Van Bommel, A.J., Crobeen, J.E., Van Tooren, A.: LEED and Auger electron observations of the SiC(0001) surface. Surf. Sci. 48, 463–472 (1975) Clark, D.T., Ramsay, E.P., Murphy, A.E., Smith, D.A., Thompson, R.F., Young, R.A.R., Cormack, J.D., Zhu, C., Finney, S., Fletcher, J.: High temperature silicon carbide CMOS integrated circuits. Mater. Sci. Forum. 679–680, 726–729 (2011) H.N. America, Aquadag® water based graphite coating/additive, 2015. de Heer, W.A., Berger, C., Ruan, M., Sprinkle, M., Li, X., Hu, Y., Zhang, B., Hankinson, J., Conrad, E.H.: Large area and structured epitaxial graphene produced by confinement controlled sublimation of silicon carbide. Proc. Natl. Acad. Sci. 108, 16900–16905 (2011) Forbeaux, I., Themlin, J.M., Debever, J.M.: Heteroepitaxial graphite on 6H-SiC(0001): interface formation through conduction-band electronic structure. Phys. Rev. B. 58, 16396–16406 (1998) Saddow, S.E., Anant Agarwal, A.: Advances in silicon carbide – processing and applications. Artech House, Boston (2004) Bauer, A., Kräußlich, J., Dressler, L., Kuschnerus, P., Wolf, J., Goetz, K., Käckell, P., Furthmüller, J., Bechstedt, F.: High-precision determination of atomic positions in crystals: the case of 6H- and 4H-SiC. Phys. Rev. B. 57, 2647–2650 (1998) Hass, J., de Heer, W.A., Conrad, E.H.: The growth and morphology of epitaxial multilayer graphene. J Phys-Condens Mat. 20, 323202 (2008) Emtsev, K.V., Bostwick, A., Horn, K., Jobst, J., Kellogg, G.L., Ley, L., McChesney, J.L., Ohta, T., Reshanov, S.A., Rohrl, J., Rotenberg, E., Schmid, A.K., Waldmann, D., Weber, H.B., Seyller, T.: Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide. Nat. Mater. 8, 203–207 (2009) Lilov, S.K.: Study of the equilibrium processes in the gas phase during silicon carbide sublimation. Mater. Sci. Eng. B. 21, 65–69 (1993) Robinson, J.A., Hollander, M., LaBella, M., Trumbull, K.A., Cavalero, R., Snyder, D.W.: epitaxial graphene transistors: enhancing performance via hydrogen intercalation. Nano Lett. 11, 3875–3880 (2011) Yager, T., Lartsev, A., Yakimova, R., Lara-Avila, S., Kubatkin, S.: Wafer-scale homogeneity of transport properties in epitaxial graphene on SiC. Carbon. 87, 409–414 (2015) Dimitrakopoulos, C., Lin, Y.M., Grill, A., Farmer, D.B., Freitag, M., Sun, Y.N., Han, S.J., Chen, Z.H., Jenkins, K.A., Zhu, Y., Liu, Z.H., McArdle, T.J., Ott, J.A., Wisnieff, R., Avouris, P.: Wafer-scale epitaxial graphene growth on the Si-face of hexagonal SiC (0001) for high frequency transistors. J Vac Sci Technol B. 28, 985–992 (2010) Yakimova, R., Iakimov, T., Yazdi, G.R., Bouhafs, C., Eriksson, J., Zakharov, A., Boosalis, A., Schubert, M., Darakchieva, V.: Morphological and electronic properties of epitaxial graphene on SiC. Physica B. 439, 54–59 (2014) Tromp, R.M., Hannon, J.B.: Thermodynamics and kinetics of graphene growth on SiC(0001). Phys. Rev. Lett. 102, 106104 (2009)

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17. Strupinski, W., Grodecki, K., Wysmolek, A., Stepniewski, R., Szkopek, T., Gaskell, P.E., Gruneis, A., Haberer, D., Bozek, R., Krupka, J., Baranowski, J.M.: Graphene epitaxy by chemical vapor deposition on SiC. Nano Lett. 11, 1786–1791 (2011) 18. Moreau, E., Ferrer, F.J., Vignaud, D., Godey, S., Wallart, X.: Graphene growth by molecular beam epitaxy using a solid carbon source. Phys Status Solid A. 207, 300–303 (2010) 19. Michon, A., Vezian, S., Roudon, E., Lefebvre, D., Zielinski, M., Chassagne, T., Portail, M.: Effects of pressure, temperature, and hydrogen during graphene growth on SiC(0001) using propane-hydrogen chemical vapor deposition. J. Appl. Phys. 113, 203501 (2013) 20. Lafont, F., Ribeiro-Palau, R., Kazazis, D., Michon, A., Couturaud, O., Consejo, C., Chassagne, T., Zielinski, M., Portail, M., Jouault, B., Schopfer, F., Poirier, W.: Quantum Hall resistance standards from graphene grown by chemical vapour deposition on silicon carbide. Nat. Commun. 6, 6806 (2015) 21. Friedhelm, B., Abderrezak, B.: Structure, energetics, and electronic states of III–V compound polytypes. J. Phys. Condens. Matter. 25, 273201 (2013)

Chapter 167

Structure and band structure of epitaxial graphene on hexagonal silicon carbide C. Berger, E. H. Conrad, and W. A. de Heer

Since the early studies started in the 1960s [14, 16, 35], epigraphene production methods have improved significantly so that higher-quality material is now produced [34, 66]. The improved material, coupled with the ability to use a variety of modern surface science techniques, has allowed more detailed electronic and structural information to be uncovered. No other form of graphene has the crystallinity, epitaxial registry, and large-scale patternability that allow a broad range of surface analytical tools necessary to study and modify the properties of graphene. As an example Fig. 164.3[https://doi.org/10.1007/978-3-662-53908-8_ 164]shows a comparison of the surface roughness and K-point Dirac cone energy and momentum spread of various forms of graphene. AFM and STM images in Fig. 164.3a, b[https://doi.org/10.1007/978-3-66253908-8_164]show that the surface roughness is an order of magnitude larger in transferred graphene. Angle-resolved photoemission spectroscopy (ARPES) measurements show the dramatic difference between epigraphene and transferred graphene on SiO2 (see Fig. 164.3c, d[https://doi.org/10.1007/978-3662-53908-8_164]). For large-scale graphene grown by CVD on Cu, graphene studies are hindered by rotational disorder and the bandgap induced by substrate interactions [77]. At the time of writing, only epigraphene is sufficiently ordered to allow graphene’s characteristic band structure to be revealed. Graphene growth on the two 4H-(6H-)SiC polar surfaces is very different. Under identical conditions, graphene growth on the Si (0001)-face is both slow and orientationally well defined with SiC. On the carbon face, epigraphene grows fast and a graphene layer readily forms. Multilayers subsequently grow with a variety of orientations that are commensurate with the SiC substrate, as can be seen in the LEED patterns of Fig. 167.1b, c. The status quo of the electronic and crystalline structure epigraphene is reviewed next.

C. Berger (*) School of Physics, Georgia Institute of Technology, Atlanta, GA, USA Institut Ne´el, CNRS - University Grenoble - Alpes, Grenoble, France e-mail: [email protected] E. H. Conrad School of Physics, Georgia Institute of Technology, Atlanta, GA, USA e-mail: [email protected] W. A. de Heer School of Physics, Georgia Institute of Technology, Atlanta, GA, USA TICNN, Tianjin University, Tianjin, China e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_167

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Fig. 167.1 (a) The unit cell structure of 4H-SiC. Filled circles are carbon atoms and open circles are silicon atoms. (b) LEED pattern of monolayer graphene grown on the Si-face. The subscript “G” refers to coordinates in the graphene lattice constant. (c) LEED pattern of 10-layer graphene film grown on the C-face. The diffuse graphene rings are marked

167.1

Si-Face


> direction (see Fig. 167.1b) On the Si-face, graphene is rotated 30
with respect to the SiC < 1010 [35, 65]. Film thicknesses (up to about five layers) can be accurately controlled by adjusting growth conditions. The first graphene layer (the so-called buffer layer) is bound to the SiC and the π-bands are modified; instead of a Dirac point, a bandgap is observed at the K-point [78]. The second layer (i.e., the graphene layer on top of the buffer layer) shows the textbook graphene band structure. Subsequent layers show characteristic thin graphite behavior. The first ARPES graphene band structure measurements of the Si-face were performed by Rollings et al. [79] and by Ohta et al. [10]. They studied UHV-grown graphene films (one to four layers not counting the buffer layer). Figure 164.2b–e[https://doi.org/10.1007/978-3-662-53908-8_164] shows the ARPES spectrum at the graphene K-point as a function of film thickness. The linear π-bands (Dirac cone) are clearly observed for the monolayer film (Fig. 164.2b[https://doi.org/10.1007/978-3-662-53908-8_164]); note that the monolayer film is n-doped by ~0.45 eV due to the SiC substrate. The AB stacking (Bernal stacking) of the second layer, which causes the lifting of the degeneracy of the two graphene sublattices, is evident from the splitting of the π-bands (Fig. 164.2c[https://doi.org/10.1007/978-3-662-53908-8_164]). The bands are shifted to lower binding energy (~ 0.5 eV). Also note that a small bandgap has formed. This gap that lies well below the Fermi level can be varied from 0 to 0.25 eV by changing the doping level [80]. The gap originates from the perpendicular electric field due to the difference in doping of the two layers [81]. ARPES shows that the graphene stacking in thicker films is a mixture of Bernal and rhombohedral stacking (see Fig. 164.2d, e) [10, 82]. Electron–phonon, electron–electron, and electron–plasmon interactions are observed in detailed ARPES studies of epigraphene Si-face that has the required structural order. Disorder prevents these effects to be

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observed in other forms of graphene [83–85] (for a review, see Basov et al. [86] and refs. therein). For instance, Fig. 167.2 presents non-linearities close to the Dirac point and a kink in E(k) in epigraphene Si-face and potassium-doped quasi-free standing epigraphene. These have been explained by a band renormalization due to many-body interactions (electron–plasmon coupling, plasmarons; see Chap. 171 [https://doi.org/10.1007/978-3-662-53908-8_171]) [84]. Note that in another set of experiments, the kink feature was ascribed to a substrate-induced gap [87].

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Fig. 167.2 Renormalization of the band structure due to electron-plasmon interactions (a–b) Epigraphene Si-face (n- doped 1.1  1013 cm2). ARPES measured E(k) along a line through the K point and along the vertical double arrow in the inset of (b). The kink shape is outlined by the dashed line (b) same band but along the horizontal double arrow (in that direction the other band cannot be observed in ARPES). (c) Schematic picture of the renormalized band. (d–e) Same experiment but for potassium-doped (n ¼ 1.7  1013 cm2) quasifree standing epigraphene Si-face along the (c) vertical and (e) horizontal directions, showing the strongly modified band due to plasmaron (electron-plasmon coupling), (f) schematic picture of the renormalized band and (g) comparison with non-renormalized graphene

167.2

Buffer Layer

The existence of the buffer layer (also called the zeroth layer or nanomesh) was not known in the earlier literature. LDA calculations predicted its existence in 2007 [88, 89] and experimental verification soon followed [90, 91]. The buffer layer is a graphene layer that is bonded to the SiC. Little is however understood about its structure, stability, electronic properties, and the nature of the bonding. While LEED shows a 6√3 periodicity (Fig. 167.1b), early STM measurements showed only a 6  6 reconstruction

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(see Fig. 167.3a) [92–96, 97]. Later STM measurements, using a lower tunneling voltage of ~0.2 eV, revealed the 6√3 periodicity (Fig. 167.3b) [98]. This higher-order reconstruction is poorly ordered (with coherent domain sizes of only a few 6√3 unit cells, i.e., ~5 to 6 nm). This explains why surface X-ray diffraction (SXRD) finds no evidence of a 6√3 structure [99]. STM experiments also show groups of adatoms (possibly trimers) at the interface of UHV-grown buffer [90]. These adatoms may be responsible for the surface reconstruction, although other studies rule out any significant presence of Si within the interfacial layer [100].

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Fig. 167.3 (a) Atomically resolved STM images of the 6  6 structure at Utip ¼ 1.7 V (green dashed line marks the 6  6 cell) (From Ref. [35]). (b) STM at Utip ¼ 0.2 V showing the 6√3 cell (From Ref. [35]). (c) Differential conductance measurements obtained on the buffer and monolayer showing a band gap feature of ~0.8 eV on the buffer (From Ref. [90]). (d) ARPES intensity map of the SiC(0001) (6√3  6√3) R30 surface (hν ¼ 50 eV). Vertical dashed line marks the K-point of graphene. Two states g1 and g2 above the SiC valence band are also marked (From Ref. [78])

Riedl et al. [91, 101] demonstrated that the buffer layer is structurally a graphene layer. They showed that by intercalating hydrogen between the SiC and the buffer layer, the buffer layer transforms reversibly to a normal graphene layer (Fig. 166.3c[https://doi.org/10.1007/978-3-662-53908-8_166]). This newly formed graphene layer is simply vertically displaced by 2.1 Å along with the other graphene layers on top, if there are any, as shown by high-resolution X-ray reflectivity [102]. Moreover, when the hydrogen is intercalated in a monolayer graphene film, the monolayer graphene electronic structure transforms into that of an AB-stacked bilayer (Fig. 166.3d[https://doi.org/10.1007/978-3-662-53908-8_166]). The decoupling of the buffer from the substrate by hydrogen intercalation is an example of the ease that foreign atoms intercalate at the SiC–buffer layer interface. Intercalation and buffer layer decoupling have been demonstrated with Si [103], Ge [101, 104], O2 [105], H2O [106], Au [107], Li [108], Pt [109], F [110], and others. The crystallographic structure of the buffer layer is essentially that of graphene, but interactions with the substrate transform it into a semiconductor. Early band structure work [35, 78] on UHV-grown samples

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indicated a large band gap, and two non-dispersing surface states g1 and g2 are observed [78] located 0.5 eV and 1.6 eV below the Fermi level (see Fig. 167.3d): the distance from the valence band maximum to EF is ~2 eV indicating that the bandgap is at least 2 eV wide. However, STS measurements of the bandgap shown in Fig. 167.3c give a much smaller gap value of ~0.4 eV [90]. This discrepancy remains to be resolved. The large unit cell size of the buffer layer impedes an exact determination of its structure. Based on photoemission spectroscopy measurements of the C1s core level, it was argued [78] that one third of the carbon in the buffer layer is bonded to Si in the SiC below. A more detailed X-ray standing wave that enhanced XPS (XSW-XPS) measurement [100] indicates that of the two C1s peaks corresponding to the buffer, one (S1 at 284.75 eV binding energy) is attributed to C–C bonds in graphene and the other (S2 at 285.55 eV binding energy) is consistent with C–Si bonds. The S1 carbon is 2.39 Å above the last Si layer in the bulk SiC, while the S2 carbon is closer to the bulk at 2.07 Å. The distance of the buffer to the SiC surface is in agreement with transmission electron microscopy [111] and earlier X-ray reflectivity experiments that put a non-flat graphitic layer (0.16 Å rms thickness) 2.3 Å above the last SiC layer [112]. The in-plane lattice constant of the buffer layer is found [113] to be tensile strained relative to graphite. What is surprising is that when the buffer layer is covered with graphene, not only is the buffer layer’s strain reduced by more than half, but the buffer and monolayer lattice parameters are incommensurate with each other (epigraphene is compressed compared to graphite). Clearly more experimental work will be required to fully understand the buffer–SiC structure. Theoretical predictions of the structure of the buffer or monolayer on the Si-face have been similarly limited by the long computation time when dealing with a very large 6√3 unit cell [88, 89]. Calculations of a fully relaxed 6√3 graphene–SiC cell starting from a bulk terminated (0001) surface [114, 115] have shown that a superhexagonal mesh develops that is at least consistent with the 6  6 periodicity observed in STM [93, 98, 115]. While the calculated bands [114] show some features that are similar to the measured bands of Emtsev et al. [78] in Fig. 167.3d, there are a set of distorted π-bands that appear near the K-point. In the calculations, these bands are due to the π-bands of carbon atoms in the buffer layer that are not bounded to Si atoms in the SiC surface. The non-bonded carbon atoms form a superhexagonal network seen in STM (Fig. 167.3b). Whether or not the predicted superhexagonal distorted π-bands can be observed experimentally remains to be determined.

167.3

Growth Mechanism on the Si-Face

The growth of epigraphene is unusual because it proceeds by decomposition of a crystal rather than by adding atoms to a surface. Very few theoretical studies have addressed this question [116, 117]. STM studies [90, 92, 118, 119] agree that the top layer is continuous and that subsequent graphene layers grow below it. STM, AFM, LEEM, and cross-sectional transmission electron microscope (TEM) observations show fingerlike structures on the Si-face (Fig. 167.4a). Based on these observations, growth models have discussed graphene nucleation at step edges. The terraces recede to remove enough Si to form graphene. The key assumption is that the decomposition of a SiC step edge depends on the local curvature of the front, so that the growth is understood from a competition between capillary smoothing and a decomposition driven step-edge roughening (see Fig. 167.4c, d). This is described by a linear stability analysis of a step equation of motion as a function of growth process variables: temperature, background Si, and inert gas pressure [116]. It has been argued that epigraphene growth is diffusion controlled and therefore naturally leads to instabilities (such as the fingerlike features of Fig. 167.4a) instead of the advancement of straight steps [120]. However, simple step flow growth can occur for a step height of three SiC bilayers, which correspond almost exactly to the number of carbon atoms required to form a graphene layer [120]. As seen in section 167.12–167.14, patterned steps have been introduced to direct graphene growth at step edges.

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Fig. 167.4 Epigraphene growth model (Si-face). (a) 10 μm  10 μm atomic force microscopy image of Si-face epigraphene grown by the CCS method, showing step edge growth. (b) Graphene growth kinetic processes on a vicinal surface by step decomposition (c–d) Onset of step instability: once the thermal decomposition of SiC has started, a positive feedback mechanism promotes further decomposition and graphitization where it has already begun (From Refs. [116, 117])

Models were further developed [117] for graphene growth on nonplanar nanofaceted 6H–SiC substrates; the model parameters are the effective energy barriers for the nucleation and propagation of graphene at the SiC steps. The main result, in agreement with kinetic Monte Carlo simulations, is that the original nanofacet is fractured into several nanofacets during graphene growth, which is related to terrace width distribution [117]. Because the growth of epigraphene is driven by Si evaporation, atomic transport of silicon and carbon on graphene and in-between layers is critical to the understanding of multilayer growth processes. Results from density functional theory calculations show that Si atoms can move almost freely on graphene and between graphene layers, while C atoms have much larger diffusion barriers. The results provide an explanation of the high Si sublimation rates during the growth of epigraphene even after graphene layers are formed on the surface [121].

167.4

C-Face

The main difference between graphene on the Si- and C-face is as follows. Graphene grows very fast on the C-face compared to the Si-face. With the CCS method [34], five- to ten-layer films are typical and films thicker than 20 layers are easily grown, while mono-layer films are much harder to achieve [34, 122–125]. There is no evidence of a buffer layer on the SiC(000-1) surface. However, SiC interface reconstruction may occur, as the 2  2 and 3  3 reconstruction observed in UHV-grown samples [126]. Subsequent layers show a mostly ordered stacking with a distribution of relative rotations alternating around 0
and 30
rotations. These various rotations correspond to graphene–SiC commensurate structures. This is clearly shown in the C-face graphene LEED pattern in Fig. 167.1c, where diffuse intensity arcs are seen instead of the sharp hexagonal pattern of diffraction spots seen in Si-face graphene.

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167.5

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Epigraphene Microstructure on the C-Face

In well-formed multilayer samples [34], the top graphene layer is continuous and drapes over the steps on the SiC substrates, and no grain boundaries are observed in STM [127]. AFM and STM images show that the graphene film has pleats (also called folds, puckers, ridges, creases, rumples, or wrinkles in the literature) [49, 128]. The pleats are typically 1–10 nm high, are typically spaced 3–10 μm apart, and are thought to result from the differential expansion of the silicon carbide and graphene and the very weak coupling of the graphene to the substrate. The monolayer pleats can be easily displaced by an AFM tip, in a manner of nanoscale ironing, showing the weak graphene–substrate interaction [124]. Estimates of the coherent domain size from Raman, STM, and transport measurements indicate that graphene domains are large, 400–1000 nm [49, 53], with a lower limit of 300 nm as observed in surface X-ray diffraction (SXRD) [129] (resolution set by the SiC steps that destroy the X-ray coherence). The film roughness is also extremely small, with atomically flat terraces [128] (in contrast to the nm roughness typically observed in transferred CVD films) (see Fig. 167.5a, b, e).

Fig. 167.5 C-face epigraphene grown by the CCS method. (a) 2.6 nm  2.6 nm atomic resolution STM image corresponding to the blue square in (b). (b) 400 nm  400 nm STM image. Bottom full height scale: 0.1 nm. The RMS height variation is less than 0.02 nm of this large area. (c) Atomic Force Microscopy image showing extended flat regions bordered by continuous graphene pleats. Scale bar: 10 μm. (a) A 50 μm field of view LEEM image of a C-face graphene film with an average thickness of 3-layers. Contrast is due to local layer thickness marked in the figure. (e) 400 nm-long STM image across two regions of different orientations, showing that the top graphene layer is continuous and flat (rms along the profile line in red: 50 pm) (STM images: Courtesy Philip First, Georgia Tech and Joseph Stroscio, NIST-CNST)

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Epigraphene Growth on the C-Face

There is indication that graphene can also nucleate on C-face terraces [123, 124, 130], in contrast with Si-face graphene growth that is mostly promoted at step edges. Graphene is more readily formed where Si can escape easily from the SiC substrate, that is, at defects [130], screw dislocations in SiC [71], and holes in the graphene film acting as “volcanoes” [131]. Because of this, although large flat and uniform areas are possible (Fig. 167.5c), thickness uniformity is more difficult to achieve on the C-face, and thicker films tend to show more thickness variations as demonstrated by LEEM analysis [132] (Fig. 167.5d). Various schemes have been developed to realize a more uniform growth on the C-face. For large-area graphene, the key is to monitor the Si out-diffusion to grow graphene in near-equilibrium condition, either by confining the Si vapor in an enclosure (CCS growth [34, 49]; see Chap. 165), by applying a noble gas back pressure (similar to the Si-face in [66]), by limiting the Si escape with a graphite cap [124] or in between two SiC chips [133], or by maintaining a Si partial pressure with an external flux of Si (similar to Si-face work in [72]). Excess graphene was also etched during growth with H2[125]. Another approach is to functionalize the SiC surface prior to growth, and it was shown that nitrogen-seeded 4H–SiC surface induces more thickness uniformity on top of C-face narrow mesas [134]. From a device perspective, it is obviously advantageous to grow nanostructures at predefined locations. To this end structured growth methods have be developed, the most promising of which is to etch patterns into the SiC substrate prior to growth, which serve as template for graphene nanostructures [135, 136]. Preferential growth was also induced in pits and mesas [137] (see also improved uniformity on the Si-face of mesas [138]). Capping AlN [139] or removable SiN masks [140] have been successfully used to prevent or enhance graphene growth in the masked area.

167.7

Rotational Stacking on the C-Face

Unlike on the Si-face, graphene on the C-face is not Bernal stacked. It must be emphasized that this C-face graphene stacking is not “turbostratic graphite.” In the literature, turbostratic graphite refers to disordered graphitic materials composed of non-Bernal stacked platelets that are typically on the order of 10 nm in size [141]. These platelets are randomly distributed in an otherwise AB-stacked film [142, 143]. In contrast, in CCS-grown C-face graphene multilayers are ordered and very large (order of at least tens of microns). The first graphene layer that forms is rotationally aligned 30
relative to the SiC. A 7
rotation is occasionally observed [127]. Thicker layers exhibit well-ordered rotational stacking. SXRD experiments show that this stacking consists of alternating 30
and 0
 ~7
rotated graphene sheets approximately every other layer. Rotational angles around 0
correspond [144, 145] to commensurate structures between graphene and the SiC(000-1) surface. LEED pattern of the rotated layers produces arcs centered at 0
, which were mistakenly attributed to small disordered grains of HOPG graphite [16, 146]. These observations indicate that properly produced and annealed C-face multilayers are ordered, while otherwise produced multilayers exhibit disorder that can be extreme. For example, it has been reported that C-face graphene grows as small graphite crystallites similar to HOPG graphene [147]. However, the samples used in those studies were grown in argon at much higher temperatures (1800–2000
C). This turbostratic structure is most likely due to an amorphous SiC interface layer that forms at these high growth temperatures [148]. In C-face multilayered graphene, it was estimated that AB-stacked layers represent less than 19% of the layers in the film [144]. STM [141, 149], ARPES [144], μ-LEED [149], Raman spectroscopy [53], and electronic transport [49] all confirm these results. In STM, these commensurately stacked layers show up as moire´ patterns with large supercell sizes. Figure 167.6c–f shows STM images from C-face films showing moire´ patterns from three graphene layers commensurately stacked above each other. μ-LEED presents these commensurate rotations as diffraction patterns with a large supercell (see Fig. 167.6a, b). The supercell size varies over several micron length scales, but the top layer orientation is always 30
relative to SiC. This indicates that while the commensuration angle varies in the layers below, the top layer is continuous over very large areas.

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Fig. 167.6 (a) μ-LEED image of a (√57  √57)GR6.59
superlattice from a commensurately rotated two layer C-face graphene film (E ¼ 96 eV). The image is from a 1 μm area (From Ref. [149]). The principle diffraction rods from two rotated graphene sheets are marked. The inset shows a blow-up of the superstructure unit cell in graphene units. (b) A calculated LEED pattern from the same √57 structure commensurate (log scale). (c) STM topography of moire´ patterns on multilayer epigraphene (sample bias VS ¼ 0.5 V, tunnel current I ¼ 100 pA). (c) Two similarly sized moire´ patterns due to three graphene layers result in a large superlattice unit cell. Layers 1 (surface layer) and layers 2 and 3 have comparable rotation angles but in opposite directions. (d) High resolution image of a region in (c). (e) STM image of a different moire´ superlattice. (f) High resolution image from within the same area [141]

167.8

Epigraphene Electronic Structure on the C-Face

The electronic structure from C-face graphene is very different from Si-face graphene. Whereas ARPES of Si-face few layer graphene exhibits overlapping, interacting Dirac cones (see Fig. 164.2[https://doi.org/10. 1007/978-3-662-53908-8_164]), ARPES of C-face multilayer graphene exhibits multiple undistorted Dirac cones that are mutually displaced, corresponding to individual graphene layers of the rotational stacked film. Figure 167.7a shows the band structure from an 11-layer C-face film measured in ARPES [9]. Two rotated Dirac cones are clearly visible. Note also that the graphene Dirac point is very near EF. The limited mean free paths of the photoelectrons in the ARPES experiment only allow the top three layers to be probed. The data shows that that these three layers are undoped (since the Dirac points coincide with the Fermi level) and that the band structure of each layer corresponds to that of a free graphene sheet. (The band structure of bilayer graphene is only rarely observed.)

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Fig. 167.7 (a) ARPES measured band structure of an 11-layer C-face graphene film grown on the 6H SiC(000-1). The ARPES resolution was set at 7 meV at hν ¼ 30 eV. The scan in ky is perpendicular to the SiC SiC direction (i.e., graphene rotated 0
relative to SiC). Two linear Dirac cones are visible. (b) k-PEEM constant energy surface (BE ¼ 1.3 eV) from a 2ML C-face graphene film using a 7-μm field aperture. Two sets of rotated graphene Dirac cones are visible (relative rotation of 21.9
). The reciprocal lattice constants of the two BZ are g1 and g2. A third set of cones, on a different radius, are obtained by coherent diffraction of either the g2 set of cones by the principal lattice vector g1 (dotted line), or the g1 set of cones diffracted by the secondary lattice vector g2 (dotted line) (From Ref. [200])

Standard area-averaged ARPES cannot distinguish whether the two cones in Fig. 167.7a are due to a stack of two graphene sheets or from two uncorrelated graphene sheets that are laterally separated by a distance within the 50 μm ARPES beam diameter. k-PEEM (a version of micro-ARPES) only measures the band structure within the illuminated area. Figure 167.7b shows the k-PEEM from a two-layer C-face film using a 7 μm illumination aperture [150]. Besides the two mutually displaced (rotated) primary Dirac cones, a third set of Dirac cones is also visible. The third set of cones results from an Umklapp process that translates the Dirac cone of one layer by the reciprocal lattice vector of the second layer and vice versa (see Fig. 167.7b) as shown by Mathieu et al. [150]. The observation of this interaction proves that the rotated graphene sheets must be indeed stacked on top of each other. The signal specifically cannot be due to separate rotated grains in the beam. The observation that C-face graphene multilayers are electronically decoupled has motivated a number of theoretical studies [129]. Interesting effects are anticipated because the stacking that gives the moire´ pattern lifts the degeneracy between sublattices in a nontrivial way. In particular, a strong reduction of the Fermi velocity is predicted for small rotation angles, both with ab initio and tight-binding methods [151–155]. Interlayer couplings between the rotated layers may introduce a singularity in the energy spectrum due to geometric considerations [154], and observed peaks in the STS local density of states that scale with the rotation angle were interpreted as such (Van Hove singularities) [156, 157]. The fact that thick C-face graphene films are electronically similar to a stack of independent, mutually rotated graphene sheets warrants the accepted nomenclature multilayer epigraphene or MEG.

167.9

Raman Spectroscopy: Thickness Determination

Raman spectroscopy, which is sensitive to electron–phonon coupling, is a widely used technique to characterize graphene. The spectrum typically presents three peaks, labeled D, G, and 2D (see Fig. 167.8). Since the D peak is only Raman active when the lattice symmetry is broken, its presence is indicative of structural defects (e.g., point defects and edges). Figure 167.8a shows the Raman spectrum for thick MEG. Figure 167.8b shows the Raman spectrum of a C-face graphene monolayer before and after subtraction of the SiC Raman background signal (that is invisible in Fig. 167.8a due to the film thickness) [158]. The absence of the D peak attests to the quality of C-face epigraphene monolayers and MEG.

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a

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Intensity (a.u.)

2D

2700

2650

2750

G+A2u b

Intensity (a.u.)

2nd order SiC

1500

2000

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Energy (cm-1)

3000

Fig. 167.8 Raman spectroscopy of C-face epigraphene (laser excitation: 532 nm). (a) A 26-nm-thick multilayer epigraphene (average thickness determined by ellipsometry), showing the two main graphene Raman peaks (G and 2D) and a very low D peak, indicative of very low disorder and extended graphene sheet. Inset: 2D peak fitted by a single Lorentzian peak (FWHM ¼ 25 cm1, position ¼ 2702 cm1). (b) For thinner films the raw spectrum (blue) contains both the graphene and SiC contribution. The latter (black trace) is subtracted by a Nonnegative Matrix Factorization method [158] to reveal a pure graphene Raman spectrum (red)

The 2D peak profile evolves from a single Lorentzian in graphene to a characteristic shouldered wide peak in graphite. Therefore, the shape and width of the 2D peak are often used to determine the number of layers in thin (Bernal stacked) graphite films [159] as well as in Si-face graphene films, where graphene layers are Bernal stacked. However, on the C-face, the layers are electronically decoupled, and the 2D line shape does not evolve with increasing thickness but remains a simple Lorentzian peak [53] (see Fig. 167.8a) which profile cannot be used to determine the film thickness. The relative intensity of the graphene Raman peaks compared with those related to SiC increases with the number of layers, but these ratios are difficult to calibrate accurately [160, 161]. In LEEM, the interference of the incoming electrons with the electrons that are reflected from the SiC–graphene interface produces oscillations in the reflected electron intensity. The number of layers equals the number of oscillations [162]. While accurate, this method is complex and therefore cannot be used as a routine diagnostic tool. Auger spectroscopy provides an accurate measurement of very thin epigraphene layers by comparing the ratio of the Si peak intensity with that of C. For thicker layers, ellipsometry gives a very good estimate of the average number of layers [163]. For graphene monolayers, the position of the Lorentzian 2D peak depends on the electronic doping density and strain in graphene [164–167]. In quasi-free standing epigraphene on the Si-face, the 2D peak position is constant within about 1 cm1 for electron doping n < 5  1012cm2 and shifts by 4 cm1 for p-doped graphene [167]. Shifts in the 2D peak position for C-face monolayers have been attributed mainly to strain and to a much lesser extent to doping density [137]. Note that an unexpected Raman intensity enhancement is observed by collecting light through the SiC substrate, in a reverse configuration. The effect is explained in terms of dipole radiation at the dielectric surface [167].

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However, besides sensitive to strain and doping, shifts in Raman peaks in graphene are determined by a subtle interplay between the phonon and electron energy dispersions [168]. The 2D peak in Si-face epigraphene is blueshifted compared to exfoliated graphene [167] which indicates compressive strain in epigraphene. But, actually the lattice parameter a ¼ 2.456 Å of epigraphene Si-face [113] is larger than the theoretical value for graphene, indicating expansion. It would be instructive to know the lattice parameter of transferred graphene and compared to the free graphene value. Comparison with HOPG is more subtle because the 2D peaks are composed of four peaks reflecting the more complex graphite electronic band structure.

167.10

Epigraphene on Other Faces

There are very few epigraphene studies other than those on the (0001) and (000-1) faces, due to the lack of available substrates. Contrary to the Si- and C-faces, theses surfaces are nonpolar, i.e., they have an equal amount of silicon and carbon atoms, which is quite interesting regarding the difference in graphene growth and morphology between the 4H/6H-C- and Si-faces. As expected graphene was found to grow on the two perpendicular surfaces, so-called a-(11-20) and m-(1-100) faces. From XPS, LEED, LEEM, and in agreement with density functional theory calculations, it is concluded that there is no buffer on either face [170]. Differences were observed between the two faces. On the SiC(1-100), micro-LEED reveals multiple rotations similar to C-face graphene (although the stacking has not been studied), while on the SiC (11-20) face, graphene grows with a single orientation. ARPES shows the typical conical bands of graphene, with a negative charge density of 4  1012 cm2. This is unexpected since the graphene doping density in the absence of buffer (quasi-free standing graphene) was argued [171] to be due to spontaneous polarization in the polar Si- and C-faces. The charge density therefore could be attributed to the workfunction difference between graphene and silicon carbide. Transport properties confirm that lightly doped single layers can be grown on the (11–20) face [172]; however, the heavily doped substrate confines measurements to very low temperature.

167.11

Epigraphene on 3C-SiC

Graphene layers have also successfully been grown on cubic β-3C-SiC (Fig. 166.1[https://doi.org/10.1007/ 978-3-662-53908-8_166]), both on the hexagonal (111) and the cubic (001) face of commercial polycrystalline substrates or overlayers grown on silicon or 6H-SiC substrates [173–178]. Note that the commercial production of 3C-SiC substrates is limited. In contrast to the 4H and 6H-SiC, large single crystal 3C-SiC is not available. Studies on 3C-SiC are nevertheless interesting in several respects. In contrast to hexagonal SiC, 3C-SiC does not spontaneously electrically polarize (see section 167.10), so that graphene on 3C-SiC is found to be quasi-neutral (see Fig. 167.9b) [175, 179]. Step-free growth and large-area monolayer coverage have also been reported for 3C [178] (Fig. 167.9a). Since thin layers of 3C-SiC can be epitaxially grown on silicon, this has been proposed as a strategy for integration of SiC-based epigraphene with Si-based electronics (see Fig. 167.9c and Chap. 170[https://doi.org/10.1007/978-3-662-53908-8_170]).

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Structure and band structure of epitaxial graphene on hexagonal silicon carbide

b

Binding energy E (eV)

a

13

c

Parallel wavevector kx [Å-1]

Fig. 167.9 Epigraphene on 3C-SiC. (a) LEEM image of epigraphene on 3C-SiC(111), showing 98% monolayer coverage. The 3C-SiC substrates were grown by sublimation epitaxy on 6H-SiC, and epigraphene was grown at 2000
C under 1 atm Ar (From Ref. [178]). (b) ARPES of epigraphene on n-type 3C-SiC(111) showing quasi-neutrality after hydrogen intercalation (From Ref. [179]). (c) Epitaxial graphene formation on 3C-SiC/Si thin films, LEED pattern shows rotational order on 3C-SiC (100) compatible with C-termination, and Bernal stacking on 3C-SiC(111) compatible with Si-termination (From Ref. [174])

For 3C-SiC epilayers on silicon substrates, the polar Si-terminated 3C-SiC(111)/Si(111) surface grown in UHV shows graphene Bernal stacking with an interfacial buffer layer, similarly to the 4H- or 6H-SiC (0001) surface. Conversely, the C-terminated 3C-SiC(111)/Si(110) shows a non-Bernal stacking, with the absence of an interfacial buffer layer, consistent with a C-face termination. The quality of these graphene films is poor as shown by large Raman D peaks. The disorder results from Si diffusion through SiC grain boundary (due to a large ~ 20% lattice mismatch between Si and 3C-SiC) and the lower graphene growth temperature (limited by the Si melting point at 1414
C). Growing an epitaxial AlN layer on Si prior to SiC growth significantly reduces Si out-diffusion and helps grow higher-quality epigraphene [174].

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Graphene was also grown on the 3C-SiC(001) surface, which demonstrates that a hexagonal template is not required for the growth of graphene. LEED patterns show no evidence for a buffer layer (growth in Ar at 1800
C) [180].

167.12

Nanostructured Graphene

From the outset of epigraphene electronics research, it was clear that graphene nanostructures would be required [1, 2]. Moreover, these structures would necessarily need to be as defect-free and reproducible as possible, in order to serve as building blocks for electronic devices. Early calculations [61, 62] had already predicted that quantum confinement would play an important role in graphene ribbons. Depending on the edge structure, a graphene ribbon would be semiconducting or metallic. Those calculations predicted that all zigzag ribbons would be metallic, while armchair ribbons would alternate between being metallic or semiconducting, depending on their widths (see Chap. 167). Early work on exfoliated and on epitaxially grown graphene focused primarily on graphene nanoribbons produced by electron beam lithography and plasma etching. Epigraphene nanoribbons were found to be metallic exhibiting quantum confinement effects at cryogenic temperatures [49], which implied that edge scattering was reasonably coherent. Disorder in the ribbon was not large enough to cause localization. On the other hand, charge neutral exfoliated e-beam patterned nanoribbons were invariably found to become insulating at cryogenic temperatures, implying a band gap. In fact, the magnitude of the bandgap was determined to be consistent with Eg ¼ 1 eV nm/W as expected for the quantum confinement gap in specific armchair ribbons. However, it was soon found that the low temperature insulating behavior was due to a transport gap that opened due to charge puddles in the ribbons combined with edge disorder [181–186]. To improve edge order, “bottom-up growth” methods were developed to grow graphene nanoribbons [135, 187, 188]. Very narrow graphene ribbons have been grown at steps on Au(788) facets by catalyzing molecular precursors into linear polyphenylenes [187, 188]. While the edge order is essentially perfect [188] so that the armchair-edge ribbons are consistent with the predicted [62, 189] finite size band gap, scalability as required for electronics is still lacking. Moreover, the growth is limited to metal surfaces, and it is expected that the transfer process to semiconducting substrates will face the same problems as other transferred CVD graphene films. Hence, these efforts have largely been abandoned for large-scale electronics. Epigraphene, however, provides another solution by growing ribbons on lithographically patterned steps etched into the SiC substrate [135, 137, 190] and exploiting the fact that graphene growth proceeds first on the facet walls of natural step edges on the Si-face of SiC [191]. In order to produce nanoribbons, trenches are first etched in SiC that serve as a template for graphene growth. This allows ribbons and other nanostructures to be accurately defined on a substrate as required for nanoscale integrated circuits. The method allows thousands of parallel ribbons as narrow as 20 nm and with well annealed edges to be grown at once over mm2 area (see Fig. 167.10). No further (potentially damaging) post-growth processing of graphene is required. In this process, the ribbon width is defined by the trench depth that is very well controlled using standard plasma SiC etching processes [135].

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15

Fig. 167.10 (a) 6 μm field of view (FOV) of a sidewall graphene trench array. (b) An expanded 25 μm FOV of (a) shows a parallel array used for area averaged ARPES measurements. (c–f) Examples of epigraphene sidewall structures produced by the structured growth method [135], demonstrating its versatility: (c) an array of parallel ribbons grown on the step edges of a vicinal surface, (d) graphene grown in many orientations on the sidewalls of complex convoluted trenches, (e) rings grown on the sidewalls of pillars, and (f) a Hall bar with eight transverse voltage probes. The top images in (a–d) and the left image in (f) represent the AFM topography; the corresponding bottom and right images are electrostatic force microscopy images showing bright areas where graphene grows at the edges of the etched patterns (From. Ref. [190])

Epigraphene also has a distinct advantage because Si-face graphene is epitaxial with the SiC(0001) surface; therefore, the ribbon orientation is also predetermined. The graphene’s zigzag (ZZ) or armchair (AC) edges naturally align with the SiC step edge simply by etching steps in the SiC in a given SiC crystallographic orientation. When a trench in SiC is oriented perpendicular to the h-1100i direction, the graphene that grows has its AC edge parallel with the step edge. Trenches perpendicular to the h11-20i direction produce ZZ ribbons. For convenience, we will refer to these SiC step edges as AC-edge steps (or AC facet walls) and ZZ step edges (or ZZ facet walls) (see Fig. 167.11). Structured sidewall growth has been used to produce a wide variety of shapes (see Fig. 167.10c–f) [190]. Of particular interest are pillars (or circular pits) around which graphene rings are grown for quantum interference pattern experiments [190].

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c

G

G

e

G AC Edge

d b

_ SiC

Armchair Edge

_ SiC

ZZ Edge

f

K G

Zig-Zag Edge

Fig. 167.11 (a) Schematic definition of AC and ZZ graphene ribbons. (b) shows the orientation of the graphene Brillouin zone with respect to the ZZ and AC directions. (c) and (e) show a schematic of an AC edge step on SiC and the corresponding AFM image of an AC step edge array. (d) and (f) show a schematic of an ZZ edge step on SiC and the corresponding AFM image of an ZZ step edge array

The structured SiC chip is then heated to 1100
C to allow the vertical etched sidewalls to crystallize into the equilibrium facets onto which the graphene ribbons grow around 1500–1600
C. The exact temperature depends on the specifics of system, such as the Si escape leak in the furnace CCS method [34] or the faceto-face geometry in the current annealing growth [192, 193].

167.13

Armchair-Edge Sidewall Ribbons

The structure of AC sidewall ribbons has been studied extensively with a number of techniques. AFM shows that the trench walls for AC steps facet into planes with an average facet angle of 28–30
. Early TEM studies of graphene growth on natural AC step edges used exceptionally thick Si-face films (>4 layers) [191, 194]. The graphene was found to tend to nucleate at the bottom of the step edges so that graphene grows thicker on the step facet than on the (0001) surface (Fig. 167.12a). Several edge terminations are observed (see Fig. 167.12a, b).

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17

Fig. 167.12 High Resolution cross-sectional TEM images of graphene layers grown on SiC steps. (a, b) Views of different edge terminations of natural sidewall graphene. Graphene layers are observed as dark contrast lines (From Ref. [191]). (c) False-color image of a subfacet region near the top of a 30-nm-deep etched facet sidewall (armchair). The image is an overlay of a high-angle annular dark-field image (HAADF) (red) that enhances the SiC and a low-angle annular dark-field image (green) that enhances the graphene. (d) HAADF atomic resolution scanning TEM image of a ZZ-edge step facet on 4H-SiC (0001) with 5 graphene layers, cross sectioned along the [1–120] direction. Note the difference of the distance between the first graphene layer and the SiC (From Ref. [197])

Under certain CCS growth conditions, cross-sectional transmission electron microscopy measurements show mini facets near the top edge and bottom of the primary facet, where the sidewall merges into the (0001) surface on the top and bottom of the sidewall [111]. The composite scanning transmission electron microscopy (STEM) image of Fig. 167.12c shows that the graphene ribbon continuously drapes over the entire sidewall. The ribbon appears to be anchored to the edges (or mini terraces) at the mini facets. At those places, the SiC–graphene distance is slightly smaller than that of the SiC–buffer layer spacing. Note that nm-wide ribbons have been predicted at SiC step edges on 6H-SiC [117]. Ultimately, the graphene ribbon merges into the buffer layer on top (and often at the bottom) of the sidewall. ARPES from the sidewall ribbons gives additional information on both the electronic and topographical structure of these ribbons [195]. Since the facet wall normal is tilted relative to the (0001) plane, the graphene on the facet is tilted by the same angle (see Fig. 167.13a). The step edge the K-point of the facet graphene can be measured (see Fig. 167.13a) by appropriately rotating the sample. ARPES shows that the graphene that grows on the sidewalls has a different doping than the graphene on the (0001) surface. While the monolayer graphene on the (0001) is n-doped by ~0.45 eV, the graphene on the facet wall is only slightly p-doped (3 layers. Electron energy loss spectra in STEM indicates that the graphene on the sidewall is decoupled from the SiC (see Fig. 167.12d) [197]. Single graphene layers can be grown on ZZ sidewalls. Transport measurements made on ZZ ribbons produced by current annealing have been found to be metallic and even demonstrate ballistic transport properties [136]. However, ARPES measurements of arrays of ZZ ribbons do not show a Dirac cone, while a Dirac cone is observed for AC ribbons that are produced using the same CCS method. The absence of a Dirac cone in this case was originally attributed to bonding of the graphene layer to the ZZ sidewall facet to produce a buffer layer [198]. It is however also possible that, depending on the growth condition, the ZZ annealed sidewall is not straight because natural SiC ZZ steps have a known instability toward nanofaceting into local AC steps [199] (see Fig. 167.14a, b). A similar instability has been seen in patterned ZZ-edge steps in SiC [198], meaning that instead of a ZZ edge, a series of small AC nanofacets, 60
relative to the average ZZ step-edge direction, would form as shown in Fig. 167.14c. If ARPES requires that the sidewalls are well ordered, which could explain why the graphene signal was not observed using those methods, the short-order length scale necessary for the observation in PEEM indicates that the two different growth methods may lead to two different structures.

Fig. 167.14 Schematic of SiC step flow during H2 etching: (a) AC step edges and (b) ZZ-step edges (From Ref. [199])

Symbols and abbreviations Short form

Full form

STM CVD LDA LEED

scanning tunneling microscopy chemical vapor deposition local dipole approximation low-energy electron diffraction (continued)

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Short form CCS UHV ML AFM LEEM ARPES SXRD TEM XPS XSW-XPS HOPG μ-LEED MEG PEEM STS FWHM 2D FOV STEM k-PEEM ZZ AC

Full form confinement controlled sublimation ultrahigh vacuum monolayer atomic force microscopy low-energy electron microscopy angle-resolved photoelectron spectroscopy synchrotron radiation X-ray diffraction transmission electron microscopy X-ray photoemission spectroscopy X-ray standing wave (enhanced)-X-ray photoemission spectroscopy highly ordered (or oriented) pyrolytic graphite micro-low-energy electron diffraction multilayer epitaxial graphene photoemission electron microscopy scanning tunneling spectroscopy full width half maximum two-dimensional field of view scanning transmission electron microscopy k-resolved photoemission electron microscopy zigzag armchair

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Chapter 168

Electronic transport properties of epigraphene C. Berger, E. H. Conrad, and W. A. de Heer

As shown below epigraphene presents the characteristics expected for graphene. The large surface area and high structural quality allow for experiments that would not be possible with small flakes or rough substrates and for large-scale integration. In some instances specificities are observed, in particular, related to the original rotational stacking on the C-face. Here we only review electronic properties as they pertain to epigraphene, and the reader is referred to review articles for general graphene electronic properties that are beyond the scope of this article. As shown below epigraphene presents the characteristics expected for graphene. The large surface area and high structural quality allow for experiments that would not be possible with small flakes or rough substrates and for large-scale integration. In some instances specificities are observed, in particular, related to the original rotational stacking on the C-face. Here we only review electronic properties as they pertain to epigraphene, and the reader is referred to review articles for general graphene electronic properties that are beyond the scope of this article. As explained in the introduction, what made graphene attractive in the first place is its potential for electronics. Extremely high electronic mobility was anticipated from the onset [1], based on the roomtemperature ballistic conduction of the closely related carbon nanotubes [21]. By choosing the appropriate substrate, mobilities in the range of 100,000 cm2/Vs are achieved in 2D graphene on boron nitride [6], up to more than 106 cm2/Vs at room temperature in the neutral rotated epigraphene C-face layers [22] or for graphene on graphite at low temperature, and unrivaled room-temperature ballistic conduction up to 15 μm in epigraphene nanoribbons. Graphene offers also the possibility to vary the charge carrier, and thereby the conduction by electrostatic gating [1, 2, 3] and patterning by standard lithographic techniques are available.

168.1

Charge Density

The first graphene layer above the SiC interface is negatively charged, as shown in the ARPES measurements presented in Chap. 167[https://doi.org/10.1007/978-3-662-53908-8_167]. For the Si-face, the n-doping of about 1013 cm
2 as measured by photoemission spectroscopy [8, 10] is believed to arise, at least partially, from interface states associated with the SiC interface and the buffer layer [17]. Similar doping of a few 1012 cm
2 is found on the C-face [14] by photoemission in UHV. Because of screening on a length scale of about one layer, the charge density decreases from one layer to the next as observed in ARPES [14], in optical spectroscopy [23], and electron energy loss [24] spectroscopy experiments. More C. Berger (*) School of Physics, Georgia Institute of Technology, Atlanta, GA, USA Institut Ne´el, CNRS - University Grenoble - Alpes, Grenoble, France e-mail: [email protected] E. H. Conrad School of Physics, Georgia Institute of Technology, Atlanta, GA, USA e-mail: [email protected] W. A. de Heer School of Physics, Georgia Institute of Technology, Atlanta, GA, USA TICNN, Tianjin University, Tianjin, China e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_168

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precisely, a charge profile consistent with nl ¼ nle e-(l
1)/λ was determined in C-face multilayered epigraphene by mid-infrared pump-probe spectroscopy, where l is the graphene layer index from the SiC interface, nle ¼ 9.6  1012 cm
2 and λ ¼ 1.2 [23]. A full calculation can be found in Ref [25]. As a result, the layers away from the SiC interface in multilayer C-face are quasi-neutral and present the properties of ideal graphene close to the Dirac point, as close as 8 meV, that is, n ~ 5  109 cm
2 (see Sects. 168.3 and 169.2[https://doi.org/10.1007/978-3-662-53908-8_169]). For graphene exposed to air, the top layer shows sign of contamination by the environment that results in a counter-positive doping. The measured charge density changes sign from negative to positive for epigraphene monolayer C-face left in air typically within an hour; after that time it stabilizes [13]. It has been consistently observed that the effect is reversible by heating above 80–100  C. After air exposure, ambient-environment Kelvin probe microscopy of Si-face single-layer epigraphene indicates a highly uniform carrier concentration of the order of 1012 cm
2 with very small carrier fluctuations ~1010 cm
2 (corresponding to measured rms surface potential variation of 12 meV) [26]. On epigraphene Si-face, when the SiC interface is saturated with hydrogen and the buffer layer becomes the first graphene layer (see Sect. 167.2[https://doi.org/10.1007/978-3-662-53908-8_167]), a consistent p-doping is observed. The positive sign and the charge carrier doping level are explained by a polarization doping arising from the bulk spontaneous polarization of the pyroelectric SiC substrate [17]. This is because at the interface with graphene, this polarization is equivalent to a negative charge that is balanced by a positive charge in the graphene layer and to a lesser extent by a positive space charge in the SiC substrate depletion layer. When the epigraphene layer resides on the (non-H2-lifted) buffer layer, the presence of donor-like states associated with the SiC/buffer interface is believed to overcompensate the positive polarization doping yielding the measured n-doping of epigraphene Si-face. The polarization doping model was further confirmed by ARPES measurements of the charge densities of quasi-free standing graphene on 6H-SiC(0001), 4H-SiC(0001), and 3C-SiC(111) [18]. The SiC spontaneous polarization, and accordingly the epigraphene charge density, decreases from 4H to 6H and to 3C-SiC so that quasi-free standing graphene on 3C-SiC is quasi-neutral.

168.2

Square Resistance, Mobility, and Charge Density in Single Layers

In two-dimensional systems, transport is characterized by the square resistance defined by Rsq ¼ (V/I)W/L ¼ (ρ/t) where V is the voltage difference between the voltage probes; I the current through the sample; W, L, and t the sample width, length, and thickness, respectively; and ρ the material resistivity. An important property of graphene that sets it apart for ordinary metals is that the charge density can be varied by orders of magnitude, inducing a large change in Rsq. The square resistance of clean graphene, hereafter simply called resistivity, goes through a sharp maximum at charge neutrality (transport at charge neutrality goes beyond the simple one electron picture). The maximum resistivity value and peak sharpness as a function of charge density depend on the graphene structural quality and source of scattering. In the simplest picture of short-range scatterers, a conductivity independent of carrier density was expected because of the linear in energy density of states N(E) [27, 28]. The resistance maximum calls for other scattering mechanisms, including charge impurity scattering and resonant scattering (for a review of transport mechanisms, see, for instance, Ref. [28]). For “dirty” graphene samples, at energies away from the charge neutrality point, the conductivity rises linearly with the charge density n [28, 29] σ ¼ σ res + Ce(|n/nimp|). Here nimp describes the charge impurity concentration, and σres reflects the fact that graphene conducts even at zero carrier density. The sharpness of qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the conductance minimum can phenomenologically also be captured with σ ¼ eμ n2imp þ n2 [30]. Note that with the usual definition σ ¼ neμ, the mobility μ would reach unphysically large values at charge neutrality. Indiscriminate and improper use of mobility equations implies that the mobility is infinite at zero charge density, while in fact, the actually mobility (taking into account the charge disorder) is actually much more modest. In disordered samples zero charge density arises from compensated puddles of electrons and holes and transport proceeds by hopping from puddle to puddle.

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Electronic transport properties of epigraphene

3

When the graphene is not too close to charge neutrality, the mobility μ can nevertheless be determined from the measurement of σ ¼ 1/Rsq and n ¼ 1/(Beρxy) where ρxy is the transverse (Hall) resistivity in the linear regime of magnetic field B (μH ¼ ρxy/B . Rsq). Note that field effect mobilities are often reported, which are determined by modulating the charge density on either the Si or C faces (see also Sect. 170.1[https://doi.org/10.1007/978-3-662-53908-8_170]). For this, techniques include counter-doping in air [13], with molecules (such as tetracyanoquinodimethane [12]), with a charge-induced silicon nitride top dielectric coating [31], by metal intercalation at the interface (see Sect. 167.2[https://doi.org/10.1007/978-3-662-53908-8_167]), and lifting the buffer layer by hydrogen intercalation to saturate the dangling bonds on the SiC substrate [11]. In a more controllable way, the charge density can be varied by applying a voltage Vg to a top electrostatic gate (standard planar capacitor) as widely used for epigraphene high-frequency transistors (see Sect. 170.1[https://doi.org/10. 1007/978-3-662-53908-8_170]). For this, epigraphene is coated with a thin dielectric (Al2O3, HfO, SiN, etc.) plated with a metal (typical Au or Al) [32, 16, 33]. The (surface) charge variation Δn induced on graphene is Δn ¼ (ε0ε/td)Vg/ε, where ε and td are the dielectric constant and thickness of the dielectric, respectively. Examples of modulation of the resistance of epigraphene are given in Fig. 168.1. Top gating was also achieved, with a UV light photochemically sensitive polymer [34] and electrolytes [35]. The mobility is related to the slope of the transconductance dIsd/dVg for a graphene strip where a current Isd flows between source and drain contacts; this is the configuration of a field effect transistor (FET).

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Fig. 168.1 Top-gated graphene on Si and C-faces. (a) Top-gated Si-face graphene (40 nm SiOHx,(HSQ e-beam resist)), gate effect on the resistivity ρxx (300 K) and Hall effect ρxy (4K – 5T). Inset: image of the patterned Hall bar, with all graphene contacts, before and after top-gate deposition. On-off ratio ¼ 31 (From [50]). (b) Top-gated C-face graphene (monolayer with 40 nm alumina gate dielectric); 2 point conductivities. The two branches give FET mobility μFET ¼ 8700 cm2/(V.s) on the n-side, to be compared to Hall mobility μHall ¼ 7500 cm2/(V.s) at n ¼ 1.6  1012/cm2 (Vg ¼ 0 V), and μFET < 5000 cm2/(V.s) on the p-side. Inset: AFM image of a C-face monolayer graphene (scale bar 5 μm) over SiC steps. The white lines are graphene pleats characteristic of C-face epigraphene (From Ref. [41]). (c) Top-gated multilayer C-face graphene (40 nm HfO2) of mobility up to 5000 cm2/V.s. Inset: optical image of the multiple devices patterned on a single SiC chip (From Ref. [32])

Because deposition of a dielectric on graphene tends to reduce the mobility, attempts were made to back-gate epigraphene [36]. High-energy nitrogen implantation into SiC produces a thin conducting layer buried into the insulating SiC substrate, to which a voltage can be applied. However, interface states limit the gate efficiency, and efficient doping was observed only for quasi-free standing epigraphene (H2 passivated). Besides, the gate is inefficient at low temperature (the carriers in SiC are frozen in), and at room temperature, it relies on the Schottky-like contact between conducting SiC and graphene (“Schottky capacitor” regime) [36, 37]. For epigraphene on the Si-face, mobility values are somewhat limited and on the order of 1500 cm2/Vs at charge density of about 1013/cm
2, even for Hall bars patterned on single terraces. Reported mobilities increase dramatically by decreasing the charge density, as expected, with record low-temperature values of

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μ  30 , 000 cm2/Vs for n  5  1010 cm
2 [38, 39]. When the buffer layer is lifted by hydrogen intercalation and graphene becomes p-doped, higher mobilities are observed (roughly by a factor two). It is not clear what causes the increase in scattering when the buffer is present. As for the conductivity, high values can be reached with large charge density obtained with top gating or molecular doping: record low conductivity of 16Ω/sq. was reported by intercalating the ionic conductor FeCl3 [40]. Epigraphene on the carbon face shows higher mobilities despite contaminations and monolayers draping over multiple SiC steps [13, 16]. For charge densities of the order of a few 1012 cm
2, μ ¼ 20 , 000 cm2/Vs was reported early on [13] and up to 39,800 cm2/Vs by reducing the charge density to n ¼ 1.9  1011 cm (Fig. 169.4b[https://doi.org/10.1007/978-3-662-53908-8_169]). A top gate induces scattering. Nevertheless top-gated FET mobilities of 7000–8000 cm2/Vs are routinely found at room temperature [41] for n ~ 1.5  1012 cm
2 (see Fig. 168.1b, for instance).

168.3

Charge Density and Mobility in Multilayers

For multilayers on the C-face, the graphene layers retain the electronic structure of single-layer graphene, as discussed in Sect. 167.7[https://doi.org/10.1007/978-3-662-53908-8_167]. Mobility values of the quasineutral graphene layers in the middle of the stack are the highest measured in any 2D graphene system to date, reaching μ ¼ 106 cm2/Vs [22] for n ¼ 1010 cm
2 at room temperature and independent of temperature [5]. The mobility was estimated by infrared spectroscopy measurements in magnetic field (see Sect. 169.2 [https://doi.org/10.1007/978-3-662-53908-8_169]). Square resistance of about 200 Ω is commonly measured for about five layers MEG on the C-face, with mobility of 20,000 cm2/Vs or more [4]. Because of interlayer screening, a top gate addresses primarily the top layer [32] (see Fig. 168.1c). For graphene on the Si-face, Bernal-stacked layers have a quadratic band structure at the K and K0 points (see Sect. 167.1[https://doi.org/10.1007/978-3-662-53908-8_167]). The electric field perpendicular to the layers that builds up due to the intrinsic charge density difference causes a small gap to open [9]. This may explain the observation of massive carriers in thin epitaxial graphite in magneto-conductance measurements [42].

168.4

Scattering at SiC Steps: The Si-face

For single epigraphene layer on the Si-face, high charge density is associated with moderate mobility of the order of 1500 cm2/Vs. Several sources of scattering have been implicated including the substrate, substrate phonons, SiC steps, and single-layer-bilayer junctions. Hydrogenated quasi-freestanding graphene shows high mobility, roughly by a factor two. A significantly higher channel conductance is reported for devices patterned parallel to the intrinsic SiC step direction compared to across the SiC steps [43, 44]. Similar anisotropic transport has been measured by local four-point probe and scanning probe techniques [45–47]. The anisotropy was attributed to various mechanisms. This may be related to a reduction of the carrier concentration for graphene on the sidewall of steps [15, 43], to a n/p junction at the step edge [20], to the opening of a band gap at the step edge [20] (see Sect. 167.13[https://doi.org/10.1007/978-3-662-53908-8_167]), or to the presence of bilayer multilayers on the steps (see Fig. 167.12[https://doi.org/10.1007/978-3-662-53908-8_167]). Conversely a careful surface preparation carried before graphitization to reduce the SiC step height notably increases the mobility [19], and very homogeneous device-to-device electronic properties (carrier concentration and mobility) are achieved at the wafer scale when the devices are fabricated entirely on single terrace monolayer domains [7].

168.5

High Current Carrying Capability

One of the most remarkable properties of graphitic materials is their high current carrying capability. For instance, electromigration breakdown was reported for exfoliated graphene at current densities of 1.6 mA/μm (corresponding to 5  108 A/cm2). For epigraphene in vacuum, conductance increases for current densities up to ~1.3  109 A/cm2 due to local cleansing of the graphene channel. At higher current the

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5

sample glow reflects local heating above 1200  C and SiC decomposes. The graphene film breaks down at a critical current density on the order of 1.3
2  109 A/cm2 [48], to be compared to 3  109 A/cm2 for carbon nanotubes [49]. Symbols and abbreviations Short form

Full form

UV FET AFM LEED UHV ARPES MEG

ultra violet field-effect transistor atomic force microscopy low-energy electron diffraction ultrahigh vacuum angle-resolved photoelectron spectroscopy multilayer epitaxial graphene

References 1.

2. 3. 4.

5.

6. 7. 8.

9. 10. 11. 12. 13. 14. 15.

16. 17. 18. 19.

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20. Hicks, J., Tejeda, A., Taleb-Ibrahimi, A., Nevius, M.S., Wang, F., Shepperd, K., Palmer, J., Bertran, F., Le Fevre, P., Kunc, J., de Heer, W.A., Berger, C., Conrad, E.H.: A wide-bandgap metal-semiconductor-metal nanostructure made entirely from graphene. Nat. Phys. 9, 49–54 (2013) 21. Frank, S., Poncharal, P., Wang, Z.L., de Heer, W.A.: Carbon nanotube quantum resistors. Science. 280, 1744–1746 (1998) 22. Orlita, M., Faugeras, C., Grill, R., Wysmolek, A., Strupinski, W., Berger, C., de Heer, W.A., Martinez, G., Potemski, M.: Carrier scattering from dynamical magnetoconductivity in quasineutral epitaxial graphene. Phys. Rev. Lett. 107, 216603 (2011) 23. Sun, D., Divin, C., Berger, C., de Heer, W.A., First, P.N., Norris, T.B.: Spectroscopic measurement of interlayer screening in multilayer epitaxial graphene. Phys. Rev. Lett. 104, 136802 (2010) 24. Liu, Y., Willis, R.F.: Plasmon-phonon strongly coupled mode in epitaxial graphene. Phys. Rev. B. 81, 081406(R) (2010) 25. Min, H.K., Adam, S., Song, Y.J., Stroscio, J.A., Stiles, M.D., MacDonald, A.H.: Landau levels and band bending in few-layer epitaxial graphene. Phys. Rev. B. 83, 155430 (2011) 26. Curtin, A.E., Fuhrer, M.S., Tedesco, J.L., Myers-Ward, R.L., Eddy, C.R., Gaskill, D.K.: Kelvin probe microscopy and electronic transport in graphene on SiC(0001) in the minimum conductivity regime. Appl. Phys. Lett. 98, 243111 (2011) 27. Shon, N.H., Ando, T.: Quantum transport in two-dimensional graphite system. J. Phys. Soc. Jpn. 67, 2421–2429 (1998) 28. Das Sarma, S., Adam, S., Hwang, E.H., Rossi, E.: Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407–466 (2011) 29. Chen, J.H., Jang, C., Adam, S., Fuhrer, M.S., Williams, E.D., Ishigami, M.: Charged-impurity scattering in graphene. Nat. Phys. 4, 377–381 (2008) 30. Kim, S., Nah, J., Jo, I., Shahrjerdi, D., Colombo, L., Yao, Z., Tutuc, E., Banerjee, S.K.: Realization of a high mobility dual-gated graphene field-effect transistor with Al2O3 dielectric. Appl. Phys. Lett. 94, 062107 (2009) 31. Wehrfritz, P., Fromm, F., Malzer, S., Seyller, T.: Quasi-freestanding epitaxial graphene transistor with silicon nitride top gate. J. Phys. D: Appl. Phys. 47, 305103 (2014) 32. Kedzierski, J., Hsu, P.L., Healey, P., Wyatt, P.W., Keast, C.L., Sprinkle, M., Berger, C., de Heer, W.A.: Epitaxial graphene transistors on SIC substrates. IEEE Trans. Electr. Dev. 55, 2078–2085 (2008) 33. Sangwan, V.K., Jariwala, D., Filippone, S.A., Karmel, H.J., Johns, J.E., Alaboson, J.M.P., Marks, T.J., Lauhon, L.J., Hersam, M.C.: Quantitatively enhanced reliability and uniformity of high-kappa dielectrics on graphene enabled by selfassembled seeding layers. Nano Lett. 13, 1162–1167 (2013) 34. Tzalenchuk, A., Lara-Avila, S., Cedergren, K., Syvajarvi, M., Yakimova, R., Kazakova, O., Janssen, T.J.B.M., MothPoulsen, K., Bjornholm, T., Kopylov, S., Fal’ko, V., Kubatkin, S.: Engineering and metrology of epitaxial graphene. Solid State Commun. 151, 1094–1099 (2011) 35. Krach, F., Hertel, S., Waldmann, D., Jobst, J., Krieger, M., Reshanov, S., Schoner, A., Weber, H.B.: A switch for epitaxial graphene electronics: utilizing the silicon carbide substrate as transistor channel. Appl. Phys. Lett. 100, 122102 (2012) 36. Waldmann, D., Jobst, J., Speck, F., Seyller, T., Krieger, M., Weber, H.B.: Bottom-gated epitaxial graphene. Nat. Mater. 10, 357–360 (2011) 37. Jabakhanji, B., Consejo, C., Camara, N., Desrat, W., Godignon, P., Jouault, B.: Quantum Hall effect of self-organized graphene monolayers on the C-face of 6H-SiC. J. Phys. D: Appl. Phys. 47, 094009 (2014) 38. Jobst, J., Waldmann, D., Speck, F., Hirner, R., Maude, D.K., Seyller, T., Weber, H.B.: Quantum oscillations and quantum Hall effect in epitaxial graphene. Phys. Rev. B. 81, 195434 (2010) 39. Satrapinski, A., Novikov, S., Lebedeva, N.: Precision quantum Hall resistance measurement on epitaxial graphene device in low magnetic field. Appl. Phys. Lett. 103, 173509 (2013) 40. Bointon, T.H., Khrapach, I., Yakimova, R., Shytov, A.V., Craciun, M.F., Russo, S.: Approaching magnetic ordering in graphene materials by FeCl3 intercalation. Nano Lett. 14, 1751–1755 (2014) 41. Guo, Z.L., Dong, R., Chakraborty, P.S., Lourenco, N., Palmer, J., Hu, Y.K., Ruan, M., Hankinson, J., Kunc, J., Cressler, J. D., Berger, C., de Heer, W.A.: Record maximum oscillation frequency in C-face epitaxial graphene transistors. Nano Lett. 13, 942–947 (2013) 42. Jouault, B., Jabakhanji, B., Camara, N., Desrat, W., Tiberj, A., Huntzinger, J.R., Consejo, C., Caboni, A., Godignon, P., Kopelevich, Y., Camassel, J.: Probing the electrical anisotropy of multilayer graphene on the Si face of 6H-SiC. Phys. Rev. B. 82, 085438 (2010) 43. Giannazzo, F., Deretzis, I., Nicotra, G., Fisichella, G., Spinella, C., Roccaforte, F., La Magna, A.: Electronic properties of epitaxial graphene residing on SiC facets probed by conductive atomic force microscopy. Appl. Surf. Sci. 291, 53–57 (2014) 44. Schumann, T., Friedland, K.J., Oliveira, M.H., Tahraoui, A., Lopes, J.M.J., Riechert, H.: Anisotropic quantum Hall effect in epitaxial graphene on stepped SiC surfaces. Phys. Rev. B. 85, 235402 (2012) 45. Yakes, M.K., Gunlycke, D., Tedesco, J.L., Campbell, P.M., Myers-Ward, R.L., Eddy, C.R., Gaskill, D.K., Sheehan, P.E., Laracuente, A.R.: Conductance anisotropy in epitaxial graphene sheets generated by substrate interactions. Nano Lett. 10, 1559–1562 (2010) 46. 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47. Nagase, M., Hibino, H., Kageshima, H., Yamaguchi, H.: Local conductance measurements of double-layer graphene on SiC substrate. Nanotechnology. 20, 445704 (2009) 48. Hertel, S., Kisslinger, F., Jobst, J., Waldmann, D., Krieger, M., Weber, H.B.: Current annealing and electrical breakdown of epitaxial graphene. Appl. Phys. Lett. 98, 212109 (2011) 49. Moser, J., Barreiro, A., Bachtold, A.: Current-induced cleaning of graphene. Appl. Phys. Lett. 91, 163513 (2007) 50. Li, X.B., Wu, X.S., Sprinkle, M., Ming, F., Ruan, M., Hu, Y.K., Berger, C., de Heer, W.A.: Top- and side-gated epitaxial graphene field effect transistors. Phys Status Solid A. 207, 286–290 (2010)

Chapter 169

Transport properties of epigraphene in magnetic field C. Berger, E. H. Conrad, and W. A. de Heer

169.1

Low-Field (Anti)-weak Localization

As in any metallic diffusive system, quantum interference effects are observed at low temperature. These are corrections to the classical conductivity arising from interference phenomena, when the electronic wave function keeps its phase for multiple scattering events (phase coherence length Lϕ>> mean free path l ). These corrections have characteristic functional forms, which magnetotransport data can be fitted to in order to extract relevant transport parameters. In particular, weak localization involves an enhanced probability for an electron to be coherently scattered back to its starting point in a loop trajectory. The enhancement originates from interferences between the clockwise and anticlockwise trajectories. As a result, the resistance is up to twice as much as with no interference, and any mechanism producing incoherent scattering (temperature) or dephasing (magnetic field, spin scattering, spin–orbit) will destroy the interference and restore the classically lower resistance. Therefore, a decrease of resistance is expected in a magnetic field (i.e., negative magnetoresistance that peaks at zero field). Graphene adds an interesting twist to it. Because the character of the wave function in graphene cannot be changed by long-range scattering (only short-range scattering can locally destroy the equivalence of the A and B sublattices), 180
backscattering of electrons is forbidden and the resistance is low. Dephasing the wave function in a magnetic field can restore backscattering, yielding a positive magnetoresistance (so-called weak anti-localization) [14]. Weak anti-localization in graphene was first observed in epigraphene grown on the C-face [3] for a highmobility sample (μ ¼ 11,600 cm2/Vs). As seen in Fig. 169.1, the magnetoresistance can be fitted very accurately to weak anti-localization theory with only one temperature-dependent parameter, ascribed to electron–electron scattering. Besides providing yet more evidence that multilayer epigraphene behaves like a stack of mono layers, these measurements are consistent with a dominant scattering at low temperature that preserves the pseudo-spin, most probably from long-range potentials arising from charges in the substrate.

C. Berger (*) School of Physics, Georgia Institute of Technology, Atlanta, GA, USA Institut Ne´el, CNRS - University Grenoble - Alpes, Grenoble, France e-mail: [email protected] E. H. Conrad School of Physics, Georgia Institute of Technology, Atlanta, GA, USA e-mail: [email protected] W. A. de Heer School of Physics, Georgia Institute of Technology, Atlanta, GA, USA TICNN, Tianjin University, Tianjin, China e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_169

1

2

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-4

5 10 15 20 25 30 35

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-6

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4 0

0

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8 10 12 14 16 18

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Fig. 169.1 Weak antilocalization in multilayer epigraphene (C-face) (a) Low-field magnetoresistance for a sample of 100 μmx1000 μm at various temperatures. Inset: magnetoresistance peak near B ¼ 0 at 1.4 K. The electron mobility is 11600 cm2/V.s, and the transport time τ ¼ 0.26 ps. (b) Low-field resistance (open circles) at 4.2 K after subtracting the high temperature background resistance. Solid line is a fit to the model of weak antilocalization, showing excellent agreement with the data. The only temperature dependent parameter is the phase coherence time τϕ potted in the inset that is consistent with electron-electron scattering time (From Ref. [3])

On the Si-face, detailed analysis of low-field magnetoresistance and temperature dependence shows evidence for strong electron–electron interaction effects, giving logarithmic dependence. This is difficult however to detangle from the logarithmic dependence arising from the Kondo effect. Even by adding magnetic impurities studies so far are not conclusive [15].

169.2

Landau Level Spectroscopy on the C-Face

As the magnetic field increases, the energy levels bundle up in discrete (quantized) Landau levels. A simple picture is that the electron energy is minimized for orbits that are a multiple of the Fermi wavelength λ. An exact calculation for a standard 2D electron gas (2DEGs) gives EN ¼ ħωc(N + 1/2) with the angular frequency ωc ¼ eB/m* and N is the band index. Because graphene dispersion relation E(k) is not quadratic but linear, the energy of the Landau levels varies as the square root of magnetic field and N : EN ¼ c∗ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ℏeBjN j where c* is the effective Fermi velocity. For a review of graphene in magnetic field, see Ref. [16]. The square root dependence is characteristic of graphene, and there is no ½ offset. The Landau index level N can take positive and negative values (the electrons and hole levels being identical). The N ¼ 0 level is special. It is field independent, pinned at E0 ¼ 0, and it is equally composed of holes and electron states. The filling factor reflects the number of filled Landau levels. pffiffiffiffiffiffiffiffiffi The first direct observation of the characteristic BjN j energy dispersion in graphene was made in multilayered epigraphene by infrared magneto-spectroscopy [4]. Infrared light is absorbed (see Fig. 169.2a) when its frequency matches inter-level separation (according to specific optical absorption rules, namely, only transition LL –(N+1) ! LN and LL–N ! LN+1 are allowed). Only quasi-neutral graphene can be probed in the infrared light and magnetic field range accessible. In C-face epigraphene, the energy versus field plot in Fig. 169.2b displays textbook graphene behavior, and the slope gives c* ¼ 1.1  106m/s, very close to the expected value for graphene (we refer the reader to [17] and [8] for a discussion of the renormalization of the Fermi velocity due to electron/hole excitation effects and substrate-screening effects). Electron–phonon coupling also manifests itself in the magneto-Raman in epigraphene C-face. The position and width of the Raman G band at 196 meV undergo oscillations (avoided crossings) at magnetic field values for which the G band energy crosses the optically active inter-Landau level transitions [18].

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a

b

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Transition energy (meV)

Magnetic field B [T] 0

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16

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L-5(-6) L6(5) L-4(-5) L5(4) L-3(-4) L4(3) L-2(-3) L3(2) L -1(-2) L 2(1)

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substrate L0(-1) L1(0) 0

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B [T1/ 2 ]

Fig. 169.2 Landau level magneto-spectroscopy. (a) Temperature dependence of the transmission spectra taken at B ¼ 0.8 T, showing the L1(0) to L0(1) transition up to room temperature. Successive spectra are shifted vertically by 0.15 for clarity. The Lorentzian fits to the data (blue curve) indicate no peak shift or widening up to room temperature (From Ref. [5]). (b) Position of the absorption lines as a function of the square root of the magnetic field. Dashed lines are calculated energy of the transitions between Landau levels. The transitions Lm(n) to Ln(m) are labeled corresponding to the diagram (color coded) in the inset

It is significant that the E1!E0 transition is observed at magnetic field as low as B0 ¼ 40 mT [5]. To resolve Landau levels requires that the levels are minimally broadened by disorder. This simply means that an electron needs to complete a cyclotron orbit before being scattered. Because the cyclotron radius is inversely proportional to B, this translates into the criterion, μB0 >1. The low B0 value gives extremely high mobility for the neutral MEG layers: μ > 250,000 cm2/Vs, and from a direct measurement of the level broadening, a value of μ ¼ 106 cm2/Vs was estimated at room temperature [5, 12]. Moreover, the level broadening varies linearly with energy [12], which provides some insight about carrier scattering; in particular, it rules out extrinsic scattering mechanisms, such as resonant scatterers or charge impurities, in the epigraphene layers which are protected from the environment. A great advantage of graphene compared to conventional 2DEGs is that the electron gas is exposed and not buried at the interface between two semiconductors. It is therefore readily accessible to direct imaging and spectroscopy. Local spectroscopic measurements of the Landau levels were performed using highresolution scanning tunneling spectroscopy (STS) on the top C-face layer at very low temperature (10 mK) and in magnetic field (up to 15 Tesla) [6] (see Fig. 169.3). The Landau levels correspond to peaks in the STS local density of states (dI/dV spectra), and the graphene behavior is confirmed. The splitting of the four quantum states that make up a degenerate graphene Landau level (two levels per valley, two per spin) is studied in great detail as the magnetic field is increased (Fig. 169.3b). Splitting due to broken valley degeneracy occurs first, followed by spin degeneracy as the field increases. Most unexpectedly, states with non-integer Landau level filling factors of 7/2, 9/2, and 11/2 are also observed suggestive of new manybody states in graphene. The graphene layers below the probed top surface may also influence STS results, by serving as a charge reservoir but also by screening interactions between top-layer electrons. They may also have a role in the observed fractional filling factor [6] (see also [13]).

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Fig. 169.3 Landau level tunneling spectroscopy. (a) Scanning Tunneling Spectroscopy at low temperature in 5T of multilayer epigraphene (C-face) showing graphene Landau level peaks in the local density of states. Insert 5  5 nm STM image. The scale is in pm (From Ref. [24]). (b) High-resolution Landau level spectroscopy of the fourfold states that make up the N ¼ 1 Landau level above 11 Tesla. The large energy separation between peaks corresponds to valley splitting (ΔEV); the spin splitting is indicated by up (down) arrows in each valley (From Ref. [6])

Real space mapping of the two-dimensional spatial distribution of the electronic states of a Landau level was achieved for the first time on a 2DEGs by using scanning tunneling spectroscopy on the top C-face epigraphene layer. The local density of state mapping of the zeroth Landau level shows extraordinary fine details giving much insight into the nature of the Landau levels in graphene [10]. In particular, unlike disordered patterns found in conventional quantum Hall systems, an organized pattern of localized states and extended states is observed in epigraphene C-face. STS measurements reveal local splitting of the zeroth Landau level corresponding to the local top bilayers AA, AB, or BB stacking arising for the C-face rotational stacking [10]. This observation has important implications for transport phenomena. Spatial modulation of the sublattice symmetry and redistribution of charges between layers [13] may account for observations of fractal-like structure in magnetoresistance measurements of this material [2].

169.3

High-Field Shubnikov–de Haas Oscillation and Quantum Hall Effect

When the magnetic field is increased, the Fermi energy EF crosses the successive Landau levels EN; the density of states maximizes for EF ¼ EN resulting in resistance oscillations that are periodic in 1/B (Shubnikov–de Haas oscillations). The oscillations are very well developed in epigraphene on both the pffiffiffiffiffi Si-face [1] (Fig. 169.4c) and on the C-face [2] (Fig. 169.4a). The charge density n (EF ¼ ħvF πn ) can be determined from the period of the oscillations (slope of the index N versus 1/B; see Fig. 169.4a). In the plot of Fig. 169.4a (top inset), the zero intercept with the N axis is a signature of graphene (no ½ offset) even for MEG. The temperature dependence (Lifshitz–Kosevich equation) gives access to the separation between levels that is also characteristic of graphene in multilayer C-face. The Landau levels smoothly merge into equidistant levels at low field, when the cyclotron orbit size is larger than the ribbon width and confinement effects dominate the energy quantization (particle in a box effect) [2].

Transport properties of epigraphene in magnetic field

10Ω Magnetic field B [T]

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Fig. 169.4 Magneto-transport in epigraphene C-face (a, b) and Si-face (c, d). (a) Multilayer C-face Hall bar (1 μm  5 μm, mobility ¼ 12,500 cm2/V.s, charge density ¼ 4.5  1012 cm2). Shubnikov de Haas oscillations are observed in the magnetoresistance (main panel), as outlined once a background is subtracted (bottom panel). The level index is plotted as a function of 1/B, where B is the position of the magnetoresistance maxima (From Ref. [25]). (b) Monolayer C-face at low charge density (n ¼ 1.9  1011 cm2) and high mobility (39800 cm2/V.s). The ν ¼ 2 ρxy plateau and vanishingly small ρxx are observed as low as 3 T at 4K. Inset quantum Hall effect observed at 200 K, well above liquid nitrogen temperature (From Ref. [11]). (c) Shubnikov-de Haas oscillation in ρxx and corresponding ρxy for monolayer Si-face at high charge density (From Ref. [1]). (d) QHE for metrology in Si-face epigraphene. At lower charge density, quantization is observed above 3T (main panel). The relative deviation ΔRH/RH of the Hall resistance RH to h/(2e2) and of Rxx are plotted in the top and bottom panel, respectively. It shows a standard uncertainty around 1  109 (From Ref. [7])

At high field or very low charge density, similarly to other 2D electron gases, the resistance oscillations develop into the quantum Hall effect (QHE). The resistance becomes vanishingly small at the oscillation minima, concomitant with plateaus in the transverse conductance that are quantized in units of e2/h : σ xy ¼ νe2/h (e2/h ¼ 1/25, 812.807 Ω1). The zero resistance comes from the physical separation of forward and backward moving charges at each edge of the sample. Simply put, since the opposite travel direction cannot be reached, the electrons cannot be scattered and the resistance vanishes. The particularity of graphene is in the unique sequence of plateaus at filling factors ν ¼ 4(N + 1/2) ¼ 2 , 6 , 10 for N ¼ 0, 1, 2, . . . instead of ν ¼ 2N , N ¼ 1 , 2 , 3, . . . (without spin splitting) in normal 2DEGs. The factor 4 in graphene reflects spin and valley degeneracy. The second particularity of graphene is the large separation between Landau levels, for instance, ΔE ¼ EN ¼ 1  E0 ¼ 36 √ B(meV) ~ 400K at 1 Tesla, to be compared to ΔE ¼ 1.7B(meV) ~ 20K in GaAs/AlGaAs 2DEGs heterostructures. This allows to observe this quantum effect at much lower magnetic field [7, 11] (see Fig. 169.4b) and much higher temperature than the sub-Kelvin temperature range of QHE in 2DEGs. In graphene the QHE was observed even at room temperature [19]; see also inset of Fig. 169.4b for single-layer epigraphene C-face. This is particularly sought for in metrology applications for resistance standards based on the quantized e2/h plateaus working at a few Tesla (see Fig. 169.4d) and

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potentially at liquid nitrogen temperature, instead of the current sub-Kelvin range. Large-area highmobility graphene is however required, which epigraphene can provide [7, 20, 21]. The first observation of the QHE in epigraphene was on high-mobility graphene on the C-face [9, 11]. Environmental positive counter doping [9] or top gate controlled [11] was used to observe the QHE in low magnetic field (ν ¼ 2 plateau below 3 Tesla; see Fig. 169.4b). Progress was rapidly made also on the Si-face with proper charge density compensation (see Sect. 168.1) [20, 21] with a measured quantum Hall resistance quantization accuracy of 3  109 at 300 mK [7, 20], rivaling with the best 2DEG standards. The relative discrepancy between the quantized Hall resistances in the graphene sample and in a reference GaAs was found as low as (2  4)  1010, which demonstrates that epigraphene can substitute GaAs QHE resistance standard [7, 22]. This result demonstrates the structural integrity and uniformity of epigraphene over hundreds of micrometers. A particular type of disorder is however necessary to observe the QHE to insure that states in the bulk of graphene are localized, so that the states at both edges are well decoupled. It turns out that the QHE for epigraphene Si-face shows bilayer inclusions [23], by coupling (or channeling) of states from both edges. Symbols and abbreviations Short form

Full form

LL 2DEG STS STM QHE 2D MEG

Landau level two-dimensional electron gas scanning tunneling spectroscopy scanning tunneling microscopy quantum Hall effect two-dimensional multilayer epitaxial graphene

References 1.

Berger, C., Song, Z.M., Li, T.B., Li, X.B., Ogbazghi, A.Y., Feng, R., Dai, Z.T., Marchenkov, A.N., Conrad, E.H., First, P. N., De Heer, W.A.: Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics. J. Phys. Chem. B. 108, 19912–19916 (2004) 2. Berger, C., Song, Z.M., Li, X.B., Wu, X.S., Brown, N., Naud, C., Mayou, D., Li, T.B., Hass, J., Marchenkov, A.N., Conrad, E.H., First, P.N., de Heer, W.A.: Electronic confinement and coherence in patterned epitaxial graphene. Science. 312, 1191–1196 (2006) 3. Wu, X.S., Li, X.B., Song, Z.M., Berger, C., de Heer, W.A.: Weak antilocalization in epitaxial graphene: evidence for chiral electrons. Phys. Rev. Lett. 98, 266405 (2007) 4. Sadowski, M.L., Martinez, G., Potemski, M., Berger, C., de Heer, W.A.: Landau level spectroscopy of ultrathin graphite layers. Phys. Rev. Lett. 97, 266405 (2006) 5. Orlita, M., Faugeras, C., Plochocka, P., Neugebauer, P., Martinez, G., Maude, D.K., Barra, A.L., Sprinkle, M., Berger, C., de Heer, W.A., Potemski, M.: Approaching the Dirac point in high-mobility multilayer epitaxial graphene. Phys. Rev. Lett. 101, 267601 (2008) 6. Song, Y.J., Otte, A.F., Kuk, Y., Hu, Y.K., Torrance, D.B., First, P.N., de Heer, W.A., Min, H.K., Adam, S., Stiles, M.D., MacDonald, A.H., Stroscio, J.A.: High-resolution tunnelling spectroscopy of a graphene quartet. Nature. 467, 185–189 (2010) 7. Lafont, F., Ribeiro-Palau, R., Kazazis, D., Michon, A., Couturaud, O., Consejo, C., Chassagne, T., Zielinski, M., Portail, M., Jouault, B., Schopfer, F., Poirier, W.: Quantum Hall resistance standards from graphene grown by chemical vapour deposition on silicon carbide. Nat. Commun. 6, 6806 (2015) 8. Basov, D.N., Fogler, M.M., Lanzara, A., Wang, F., Zhang, Y.B.: Colloquium: graphene spectroscopy. Rev. Mod. Phys. 86, 959–994 (2014) 9. Wu, X.S., Hu, Y.K., Ruan, M., Madiomanana, N.K., Hankinson, J., Sprinkle, M., Berger, C., de Heer, W.A.: Half integer quantum Hall effect in high mobility single layer epitaxial graphene. Appl. Phys. Lett. 95, 223108 (2009) 10. Miller, D.L., Kubista, K.D., Rutter, G.M., Ruan, M., de Heer, W.A., Kindermann, M., First, P.N., Stroscio, J.A.: Realspace mapping of magnetically quantized graphene states. Nat. Phys. 6, 811–817 (2010) 11. Hu, Y., Ruan, M., Guo, Z.L., Dong, R., Palmer, J., Hankinson, J., Berger, C., de Heer, W.A.: Structured epitaxial graphene: growth and properties. J. Phys. D: Appl. Phys. 45, 154010 (2012)

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12. Orlita, M., Faugeras, C., Grill, R., Wysmolek, A., Strupinski, W., Berger, C., de Heer, W.A., Martinez, G., Potemski, M.: Carrier scattering from dynamical magnetoconductivity in quasineutral epitaxial graphene. Phys. Rev. Lett. 107, 216603 (2011) 13. Min, H.K., Adam, S., Song, Y.J., Stroscio, J.A., Stiles, M.D., MacDonald, A.H.: Landau levels and band bending in few-layer epitaxial graphene. Phys. Rev. B. 83, 155430 (2011) 14. McCann, E., Kechedzhi, K., Fal’ko, V.I., Suzuura, H., Ando, T., Altshuler, B.L.: Weak-localization magnetoresistance and valley symmetry in graphene. Phys. Rev. Lett. 97, 146805 (2006) 15. Jobst, J., Kisslinger, F., Weber, H.B.: Detection of the Kondo effect in the resistivity of graphene: artifacts and strategies. Phys. Rev. B. 88, 155412 (2013) 16. Goerbig, M.O.: Electronic properties of graphene in a strong magnetic field. Rev. Mod. Phys. 83, 1193–1243 (2011) 17. Orlita, M., Potemski, M.: Dirac electronic states in graphene systems: optical spectroscopy studies. Semicond. Sci. Technol. 25, 063001 (2010) 18. Faugeras, C., Amado, M., Kossacki, P., Orlita, M., Sprinkle, M., Berger, C., de Heer, W.A., Potemski, M.: Tuning the electron-phonon coupling in multilayer graphene with magnetic fields. Phys. Rev. Lett. 103, 186803 (2009) 19. Novoselov, K.S., Jiang, Z., Zhang, Y., Morozov, S.V., Stormer, H.L., Zeitler, U., Maan, J.C., Boebinger, G.S., Kim, P., Geim, A.K.: Room-temperature quantum hall effect in graphene. Science. 315, 1379–1379 (2007) 20. Tzalenchuk, A., Lara-Avila, S., Kalaboukhov, A., Paolillo, S., Syvajarvi, M., Yakimova, R., Kazakova, O., Janssen, T.J. B.M., Fal’ko, V., Kubatkin, S.: Towards a quantum resistance standard based on epitaxial graphene. Nat. Nanotechnol. 5, 186–189 (2010) 21. Pallecchi, E., Lafont, F., Cavaliere, V., Schopfer, F., Mailly, D., Poirier, W., Ouerghi, A.: High electron mobility in epitaxial graphene on 4H-SiC(0001) via post-growth annealing under hydrogen. Sci. Rep. UK. 4, 4558 (2014) 22. Ribeiro-Palau, R., Lafont, F., Brun-Picard, J., Kazazis, D., Michon, A., Cheynis, F., Couturaud, O., Consejo, C., Jouault, B., Poirier, W., Schopfer, F.: Quantum Hall resistance standard in graphene devices under relaxed experimental conditions. Nat. Nanotechnol. 10, 965–U168 (2015) 23. Chua, C., Connolly, M., Lartsev, A., Yager, T., Lara-Avila, S., Kubatkin, S., Kopylov, S., Fal’ko, V., Yakimova, R., Pearce, R., Janssen, T.J.B.M., Tzalenchuk, A., Smith, C.G.: Quantum hall effect and quantum point contact in bilayerpatched epitaxial graphene. Nano Lett. 14, 3369–3373 (2014) 24. First, P.N., de Heer, W.A., Seyller, T., Berger, C., Stroscio, J.A., Moon, J.-S.: Epitaxial graphenes on silicon carbide. MRS Bull. 35, 296–305 (2010) 25. de Heer, W.A., Berger, C., Wu, X., First, P.N., Conrad, E.H., Li, X., Li, T., Sprinkle, M., Hass, J., Sadowski, M.L., Potemski, M., Martinez, G.: Epitaxial graphene. Solid State Commun. 143, 92–100 (2007)

Chapter 170

Towards electronic devices based on epigraphene C. Berger, E. H. Conrad, and W. A. de Heer

170.1

High-Frequency Transistors

Digital electronics requires that the gate-modulated current through the transistor channel be switched between on and off values, with a large Ion/Ioff ratio and small Ioff for minimum loss. Because graphene does not have a bandgap, the conductance is nonzero at all gate voltage and the channel current cannot be turned off (for a review, see, for instance, [24]). This means that Ion/Ioff is limited to values of a few tens (Fig. 168.1[https://doi.org/10.1007/978-3-662-53908-8_168]), to be compared to at least 104 in CMOS technology, and that poor current saturation is observed at high bias voltage [25]. Nevertheless, graphene can be used for amplification at high frequency, owing to its intrinsic low dimensionality, high carrier mobility, and large carrier velocity. Epigraphene field-effect transistors have shown fast progress. For radio-frequency transistors, the two most important small-signal figures of merit are the cutoff frequency fT (the maximum frequency for current amplification, i.e., at which the current gain is unity) and the maximum oscillation frequency fmax (i.e., the maximum frequency for power gain). The intrinsic properties of epigraphene are quite promising in view of the transconductance gm ¼ dIsd/ dVg and high carrier velocities [26]. The transconductance describes the efficiency of the gate voltage Vg to modulate the channel current Isd and directly relates to the intrinsic cutoff frequency fT ¼ gm/(2πCG), excluding parasite resistance or capacitance, with CG the gate capacitance. Large transconductance up to 2 mS/μm and output current above 5 mA/μm have been reported in epigraphene Si-face [27]. Higher carrier velocities can be achieved with high saturation velocity and high mobility. As a substrate SiC compares favorably with SiO2 because optical phonon, argued to be the main source of hot carrier scattering, has a higher energy [25]. Following this line of argument, THz operation is predicted on SiC substrates. The highest cutoff frequency (after removal of parasitic effects) in epigraphene made by conventional scalable process is fT ¼ 280 GHz on the Si-face (Lg ¼ 40 nm) [27], to be compared with record fT ¼ 427GHz (Lg ¼ 67 nm) for a transferred gate on exfoliated graphene [28], and with world record 0.5-THz fT in SiGe heterojunction bipolar transistors [29]. (Note that the cutoff frequency depends on the gated length Lg.) However, use in any practical circuit requires high values of the power gain fmax, which still remains much lower than fT in most graphene devices (see Fig. 170.1c). High fmax values (fmax ¼ 70 GHz for Lg ¼ 100 nm) were only very recently demonstrated (see Fig. 170.1b). This was realized with high-mobility epigraphene C-face (room-temperature FET mobility μ ¼ 6,000 cm2/Vs; fT ¼ 110GHz) and by optimization of the device dual-gate design (shown in Fig. 170.1a), with low contact and gate resistances [23]. C. Berger (*) School of Physics, Georgia Institute of Technology, Atlanta, GA, USA Institut Ne´el, CNRS - University Grenoble - Alpes, Grenoble, France e-mail: [email protected] E. H. Conrad School of Physics, Georgia Institute of Technology, Atlanta, GA, USA e-mail: [email protected] W. A. de Heer School of Physics, Georgia Institute of Technology, Atlanta, GA, USA TICNN, Tianjin University, Tianjin, China e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_170

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G S

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power gain U1/2

current gain |H21|

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Fig. 170.1 High frequency epigraphene transistors. (a) Scanning electron microscopy image of a symmetric dual gate transistor, featuring a graphene channel between source (S) and drain (D) modulated by a gate (G) fabricated on C-face graphene. (b) High frequency characteristics of a 100 nm gated channel. The cutoff frequency is fT¼ 110 GHz for the current gain (obtained by extrapolation of theoretical slope of 20 dB/decade to |H21| ¼ 1, where |H21| ¼ ∂Ids /∂Igs, with Igs the gate source current) and fmax ¼ 70 GHz for the power gain U ¼ 1/2 (From Ref. [23]). (c) State-of-the-art graphene high-frequency electronics (stars) compared with high electron mobility transistors (From Ref. [26]). Red stars: C-face epigraphene FET [23]. Vertical bar indicates record fT in transferred graphene [28]

Note that multilayer graphene is not as efficiently gated because of electronic interlayer screening that results in a constant conductance in parallel (as shown in Fig. 170.1c). On the Si-face, better performances are obtained when the entire channel lies within a single graphene terrace, avoiding step edge scattering (Sect. 170.4) [30]. Another challenge for any graphene-based transistor is to develop gate dielectrics that preserve high mobility and charge homogeneity in graphene. With no dangling bonds to adhere to, dielectric coating on chemically passive graphene requires a nucleation layer or a roughened top graphene layer [31]. Atomic layer deposition (ALD) or evaporation of high K dielectrics (Al2O3, HfO2, SiO2)[32] or Si3N4 [27] have best RF performance. Progress is also being made with less perturbing coating, like boron nitride (a substrate with no dangling bonds where graphene retains a high mobility) or polymers [21]. The latter, however, may induce unwanted hysteretic behavior. Good results (in terms of low leakage, highcapacitance gate dielectrics, and no damage to graphene) have been reported for oxides grown by ALD on graphene seeded by self-assembled molecular layers of perylene-3,4,9,10-tetracarboxylic-3,4,9,10dianhydride (PTCDA) [20]. The PTCDA molecules show long-range order that is not perturbed by defects in the epigraphene or SiC atomic steps [33]. A chemical route using solution-based self-assembling nanodielectrics has been processed on epigraphene Si-face and seems promising [34]. Contact resistance to graphene is an interesting fundamental problem. The question of how to inject from a 3D to a 2D material while matching energy and momentum is difficult considering that at charge neutrality the graphene Fermi surface is reduced to points in k-space. Similarly to dielectric coatings, metal-to-graphene non-wettability issues are solved by using an adhesion layer (Ti, Cr). The lowest reported contact resistance on epigraphene is less than 100 Ωμm [23] for gold-plated high work function metal Pd or Pt, similarly to carbon nanotubes. Frequency multiplication and mixing have also been developed for epigraphene. This is based on the nonlinearity of graphene FETs near the Dirac point: the I(Vg) has a voltage square ambipolar behavior at zero bias, unlike in other semiconductor transistors, that greatly suppresses odd-order harmonics in epigraphene-FET devices [35]. Epigraphene-based frequency mixers show excellent linearity [35]. Moreover the observed low phase noise and low 1/f noise in epigraphene-FETs [36] are an important consideration for nonlinear circuits. Ultra-wideband detection (2–110 GHz) was also demonstrated in

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epigraphene-FETs. Their performance is comparable to or better than state-of-the-art FET-based direct millimeter-wave detection without applied dc biases [37].

170.2

Spintronics

Spintronics devices use electronic spin instead of charge to process information. Fundamental to this vision is the possibility of efficient spin propagation over long distances, but despite several decades of intense research, spin transport efficiencies have remained low in metals and semiconductors. Carbon-based materials however are good candidates owing to small spin–orbit coupling, and results on high-mobility multilayer C-face epigraphene (μ ¼ 17,000 cm2/Vs) indeed present a breakthrough in the field [38]. Spin transport efficiencies reach 75%, spin signals are in the MΩ range, and spin diffusion lengths exceed 300 μm (spin lifetimes >100 ns), which is significantly larger than any other material. For these measurements, the devices were provided with two-terminal high-impedance tunnel contacts (evaporated cobalt on alumina) acting as spin polarizer and analyzer (see Fig. 170.2b). The spin signal is measured by the difference ΔR in the resistance when the two ferromagnetic electrodes have parallel or antiparallel magnetization. The MΩ range signal, as shown in Fig. 170.2a, is to be compared to the few tens of Ohms generally reported in other materials [39]. Similarly, much larger relative spin signals are also measured in C-face epigraphene with ΔR/R  10% [38]. Micrometer long spin diffusion lengths on C-face epigraphene were also inferred from the resonance width in spin resonance experiments. In that case, the transition between Zeeman-split levels probed by microwave radiation in magnetic field was detected electrically [40].

Fig. 170.2 Spintronics. (a) Resistance versus magnetic field at 1.4 K presenting a large resistance change ΔR ¼ 1.7 MΩ when the magnetization of the two Co electrodes is parallel or antiparallel. High tunnel resistances are important for efficient spin injection (From Ref. [38]). (b) Scanning electron micrograph of the two-terminal lateral spin valve. The two Al2O3/Co electrodes (red) are deposited on a 10-μm-wide epigraphene channel grown on the C-face

On the Si-face, sub-μm spin relaxation length and 1–2 ns spin relaxation time were determined from measurements in a nonlocal configuration and in Hanle spin precession measurements. In the former experimental configuration, a spin-polarized current is sent between two contacts. The spin accumulation generated at the injection contact diffuses and is detected at two remote spin sensitive voltage contacts

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[41]. Hanle precession experiments yield an order of magnitude lower diffusion coefficient but higher spin relaxation time on monolayer epigraphene compared to quasi-freestanding epigraphene (hydrogenated buffer). This was tentatively explained by localized states in the buffer layer [42].

170.3

Large-Scale Integration: Integration with Si

Epigraphene is the only graphene platform where large-scale transistor fabrication was demonstrated. Hundreds of devices [19] were produced on mm size SiC chips as early as 2008 (an example is given in Fig. 168.1c[https://doi.org/10.1007/978-3-662-53908-8_168]) and more than 10,000 2 years later [8] (see Fig. 170.3a). Wafer size patterning of high-frequency transistors was demonstrated on a 100 mm wafer (see Fig. 170.3b) in 2011 [5]. An integrated circuit was fabricated on a single SiC chip with a graphene FET that operates as a broadband radio-frequency mixer at frequencies up to 10 GHz with thermal stability up to 400 K [43].

Fig. 170.3 Wafer scale graphene transistor integration. (a) Integration of 10,000 sidewall epigraphene transistors on a 4  6 mm SiC chip, with Al2O3 gate dielectric (From Ref. [8]). (b) 100 mm wafers scale FETs utilizing hydrogenated Si-face graphene and HfO2 gate dielectric (From Ref. [5])

As SiC is a large bandgap semiconductor widely used in the high power electronics industry, it is interesting to develop schemes to integrate the electronic properties of epigraphene and SiC. One such scheme is to utilize the semiconducting SiC as the transistor channel and graphene as electrodes [22]. A variation of the technique consists in using a quasi-freestanding hydrogenated epigraphene bilayer as the gate, so that the entire device can be carved in one step from epigraphene on SiC (the monolithic waferscale electronics scheme is presented in Fig. 170.4). It is expected that this will allow for high currents, high operation speed, and high operation temperatures. Current on–off ratios exceeding 104 were indeed observed [44].

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Source-drain voltage Vsd [V] Fig. 170.4 Combined graphene-SiC field effect transistors. (a–d) Semiconductor SiC forms the transistor channel that is provided with graphene ohmic source and drain contacts on the Si-face (made of monolayer graphene + buffer, see (b)). Hydrogenated graphene (bilayer graphene, see (c)) produces the FET Schottky-like gate. The device geometry is shown in the electron micrograph of (d) (From Ref. [44]). (e) The SiC/SiOx interface forms the transistor channel on the C-face, as sketched in the inset. Contacts are provided by multilayer epigraphene. Inset (bottom) AFM image of the device, the channel is in between the bright graphene pads. Current on-off ratios of more than 106 are demonstrated at room temperature (From Ref. [45])

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In another promising design [45], the channel between coplanar multilayer graphene source and drain consists of the accumulation layer at the interface of semi-insulating SiC and a surface silicate that forms after high temperature annealing (Fig. 170.4d). The current flow over the one-dimensional C-face graphene/SiC barrier exhibits on–off ratio over 106, with current densities up to 35 A/m. Significantly, transport is dominated by tunneling at low temperatures, while it is dominated by thermal activation above the Schottky barrier at high temperatures. Tunneling FETs are in fact much sought after to overcome the transconductance thermal limitation. Another approach is to integrate epigraphene to Si-based electronics. The first graphene-on-silicon (GOS) strategy takes advantage of the heteroepitaxy growth of 3C–SiC on Si to produce epigraphene-onSiC covered Si substrate (3C–SiC is the only SiC polytype known to grow on Si) [10, 11, 12]. Epigraphene growth on SiC/Si substrates was discussed in Sect. 167.11. FETs were produced on GOS with SiC layers on both Si(111) and Si(110) substrates. Besides the usual epigraphene top gates [46], back gates have also been realized by using the thin (less than 100 nm) heteroepitaxial SiC film on Si as the dielectric [47]. Modulation of the current in the graphene channel is observed. Despite non-negligible leakage currents to the Si substrate through the granular SiC, a room-temperature logic inverter was demonstrated [48]. In another strategy [49], thin monocrystalline silicon layers are transferred onto previously graphitized SiC substrates using well-established industrial silicon-on-insulator (SOI) wafer bonding and smart-cut techniques. The transferred crystalline silicon layer bonded on top of SiC/epigraphene is ready for siliconCMOS device implementation. It is connected to the sealed epigraphene layer beneath it by metallic vias managed in the submicron thin Si layer. The key advantage of the technique is that epigraphene is grown and structured prior to bonding. The process is therefore compatible with epigraphene high temperature growth and preserves epigraphene high structural quality integrity with no degradation. The process produces monolithic integration of graphene-on-SiC/silicon 3D stacked layers and is fully compatible with very-large-scale integration technology (see Fig. 170.5a, b).

a

Si-CMOS bonded to SiC wafer

SiC epitaxial graphene patterned devices

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170.4

Fig. 170.5 (a) Concept of Si-SiC wafer bonding. The top Si wafer supports the CMOS platform and the SiC wafer the epigraphene electronic devices. The devices on top and bottom wafers are connected by metal vias through the thin Si wafer. (b) Realization of the bonding after SiC graphitization with an intermediate Al2O3 bonding layer (From Ref. [49])

Bandgap

The two main schemes to create a gap in gapless graphene include narrowing the channel width W to open a confinement gap and locally functionalizing graphene (sp3-like covalent bonding). The order of magnitude of the confinement gap Eg ¼ 1 eV nm/W (see Sect. 165.9[https://doi.org/10.1007/978-3-662-53908-8_ 165]) means patterning at the tens nm scale or below for any practical application. This is usually done by lithography and oxygen plasma etching of 2D graphene, which tends to create disordered edges that severely reduce mobility (see Sect. 170.5).

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Bandgaps are reported in several all-graphene structures. Epigraphene grown on minifacets a few nm wide that border the sidewall ribbons, as described in Sect. 167.12[https://doi.org/10.1007/978-3-66253908-8_167] [7], has been associated with the ~0.5 eV wide bandgap observed by ARPES [18] (see Fig. 167.13[https://doi.org/10.1007/978-3-662-53908-8_167]). Buckled epigraphene also presents a bandgap larger than 0.7 eV from ARPES measurements [50]. Buckling arises in this case from a submonolayer concentration of nitrogen seeded on SiC that pins epigraphene to the SiC interface as graphene grows by thermal decomposition. The buffer layer is also a well-known all-graphene semiconductor, with a bandgap of at least 1 eV according to early band structure measurements [3, 6]. Recent ARPES measurements put the distance between the Fermi level in the gap and the top of the conduction band closer to 0.5 eV [51] (see Sect. 167.2[https://doi.org/10.1007/978-3-662-53908-8_167]). For semiconducting graphene, seamless connection to graphene provides optimum carrier injection that can be provided in this case by the ballistic ribbon grown on the sidewall facets, as described in Sects. 167.12 [https://doi.org/10.1007/978-3-662-53908-8_167] and 170.5. Transport measurements confirm the semiconducting nature of the buffer layer [40]. Other seamless planar junctions have been proposed between semiconducting functionalized graphene and graphene structures. These include, for instance, locally converting an epigraphene channel through oxidation between graphene contacts [52], fluorination [53], and covalent chemistry with nitrophenyl groups [54], where a bandgap was demonstrated [55]. The formation of covalent carbon–oxygen/fluorine or molecule bonds locally changes the electronic structure and the transport properties of the epigraphene from metallic to semiconducting [54]. Large on–off ratios up to 105 and current saturation at high bias voltage are measured [53]. Remarkably ferromagnetic behavior was observed at room temperature by functionalization epigraphene with nitrophenyl groups. The interpretation is that magnetic products may be produced when two groups are grafted on the A sublattice, leaving two unpaired spins in the B sublattice [56]. Although quite promising, progress may be hindered by inhomogeneous graphene functionalization that consequently reduces the mobility. Graphite oxide, which is graphene functionalized with epoxy and hydroxyl groups, was fabricated by direct oxidation of epigraphene, either by the Hummers’ method [52] or through milder oxidation [57]. Nanopatterning under a biased conducting AFM tip also leads to local graphene oxidation [58]. Interestingly epigraphene (both Si- and C-face) resists the very harsh chemical treatment and does not exfoliate so that multilayer graphene oxide is produced directly on chips. In that case, the layers are very well ordered and exhibit excellent interlayer registry and little amount (10ps

~1ps

b

171.1

Thermalization initial relaxation

Pump excitation

a

Fig. 171.1 Pump probe spectroscopy. (a) Band structure and carrier distribution after optical excitation. The pump photons (red) excite carriers that rapidly thermalize establishing a new hot thermal distribution that slowly cools down (From Ref. [5]. (b) After optical excitation an optical probe probes the carrier distribution. (Left) For neutral (gapless) graphene, all transitions are allowed. (Right) For doped graphene, only excitations larger than twice the Fermi level can create an electron-hole pair (Fermi blockade)

Ultrafast Optical Spectroscopy

Ultrafast time-resolved optical pump-probe spectroscopy has been used to study the dynamic response and the hot-carrier relaxation and cooling dynamics in epigraphene with femtosecond resolution. In this technique, an ultrafast optical pump pulse excites electrons and holes to high energies, while a probe pulse, whose frequency can be tuned from the visible [13] through the infrared [5] to the THz frequencies [14, 15], probes the dynamics response (see Fig. 171.1). The electron dynamic response is an important property for all photodetectors and photovoltaic devices that rely on the conversion of light into free electron–hole pairs. Best performances can be achieved if the photoexcited carriers transfer their excess energy into the production of additional electron–hole pairs (carrier multiplication) through carrier–carrier scattering processes rather than production of heat (emission of phonons). Similarly the ultimate performance of high-speed electronic devices will depend on the energy exchange between large electric fields induced hot carriers and the lattice. Epigraphene is particularly well suited for ultrafast optical experiments due to its large area and homogeneity. Up to cm-scale surface areas provide sample sizes that are large enough even for the typically large probe spot sizes at frequencies below 300 GHz. The signal is enhanced by the multiple layers in C-face epigraphene without compromising the graphene characteristics since each layer behaves electronically like a monolayer graphene. Finally, transmission experiments benefit from the transparency of the SiC substrate over broad frequency window from the visible to the THz range. In ultrafast time-resolved THz spectroscopy experiments, an ultrafast optical pump excitation generates electron–hole pairs in a nonequilibrium state, while a broadband single-cycle THz probe pulse probes the

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dynamic THz response of the hot-carrier relaxation and cooling dynamics. The high-energy nonequilibrium electrons and holes thermalize with the background of cold carriers due to very efficient carrier–carrier scattering which forms a single hot-carrier Fermi–Dirac distribution within ~100 to 200 fs, as observed in epigraphene [5, 13–16]. The hot-carrier distribution is characterized by an elevated transient carrier temperature and a transient Fermi level. As the hot carriers relax and cool, both the transient carrier temperature and Fermi level shift return to equilibrium. The THz carrier dynamics are the result of an interplay between efficient carrier–carrier scattering, which maintains a thermalized hot-carrier distribution, and carrier–optical–phonon scattering, which removes the energy from the hot carriers to the lattice [17, 18]. This dynamics is shown to depend critically on the doping density, ranging from a few picoseconds at doping density n > 1013 cm2 to hundreds of picoseconds at doping densities n < 1010 cm2, due to the vanishing density of states at the Dirac point. In MEG, the low-energy dynamics is governed by a unique cooling pathway enabled by interlayer energy transfer via screened Coulomb interactions between Dirac electrons, with the highly doped layers near the SiC substrate acting as a heat sink for the quasi-neutral top layers [14]. In a special semiconducting form of epitaxial graphene, in which an energy gap of up to 0.7 eV was engineered by buckling [7], the relaxation of the dynamics is enhanced by up to two orders of magnitude, which is attributed to direct electron–hole recombination via optical phonon emission over a broad range of carrier temperatures[15]. These experiments, consistent with results on other forms of graphene [9–11] [19, 20], show that carrier–carrier scattering is highly efficient in a wide range of photon wavelengths and produces secondary hot electrons that can drive currents. This multiple hot-carrier generation is therefore interesting for highly efficient broadband conversion of light into electronic energy for optoelectronic applications. Applying an external magnetic field leads to a significantly longer relaxation [21], which is attributed to a reduction of electron–electron scattering. This is because in a magnetic field, the energy levels bunch into unequally spaced Landau levels (see Sect. 169.2[https://doi.org/10.1007/978-3-662-53908-8_169]); therefore, inter-level carrier–carrier scattering processes (Auger processes) are not allowed because they cannot conserve energy. This result is in sharp contrast with normal 2D electron gases, where the formation of equidistant Landau levels in magnetic field increases scattering. Graphene’s zeroth Landau level is special because the three LL0, LL1, and LL1 Landau levels are equally spaced so that Auger processes are allowed [8, 22]. Neutral C-face layers provide an ideal system to study carrier–carrier scattering processes involving the LL0 level, and strong Auger processes have been observed by addressing the levels individually with circularly polarized light [22]. Ultrafast optical spectroscopy also gives insight into the electronic structure. Consistent with ARPES measurements [1], the upper limit for a potential bandgap is found to be below 1 meV in C-face graphene [5]. The doping density in the successive layers in MEG was also evaluated, corresponding to the energies of Pauli blocking (EF ~ 350 meV, 210 meV, 135 meV, 90 meV) [5] (see Fig. 171.1b). Also the polarization of the THz emitted light by coherently controlled photocurrents (see below) indicates that there is some coupling between the graphene layers in MEG although the electronic structure of each layer is that of graphene [23]. Coherently controlled photocurrents have been produced in MEG [24]. The method uses two phaselocked beams at frequency ω and 2ω. Quantum interference between single-photon and two-photon absorption breaks the lattice symmetry, so that the photoinjected carriers have an anisotropic distribution in k resulting in a net current flow. The current flow direction is controlled by the polarization of the pump beam. The transient current is detected by the electromagnetic pulse at the THz frequencies that it generates. Note that this all-optical injection of current could provide a noncontact way of injecting directional current in graphene. Quantitative studies of the magnitude of the effect show that current decay time in graphene is longer compared to common semiconductor-like GaAs.

171.2

THz Generation

Graphene exhibits a large nonlinear optical response due to its linear energy dispersion that leads to harmonic generation at THz frequencies. However, second-order nonlinear effects important for applications like frequency difference or rectification processes are forbidden by the centrosymmetric nature of graphene. Generation of coherent THz radiation (0.1–4 THz and projected up to 60 THz) via a second-order nonlinear

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effect was nonetheless achieved in multilayer epigraphene on the C-face where it is induced by the anisotropy of the in-plane photon momentum [25]. This dynamical photon drag effect relies on the transfer of photon momentum to the carriers by the ponderomotive electric and magnetic forces. Interestingly, the effect is related to the usually neglected next-nearest-neighbor coupling of C atoms in graphene and to the asymmetry between the electron and hole dynamics. These properties are particularly interesting for the generation of ultra-broadband terahertz pulses in compact room temperature THz sources.

171.3

Photocurrent

The electrical response of epigraphene under illumination was studied for both Si- and C-faces. Similarly to the classical Hall effect, the crossed AC electric and magnetic fields of circularly polarized light can create a voltage, what is called the circular AC Hall effect. Graphene centrosymmetric structure prevents other helicity-driven photocurrent effects, and the circular AC Hall effect was observed for the first time in epigraphene Si-face, owing to the large area available for the terahertz (THz) laser radiation [26]. In one report [27], a significant increased photocurrent on the Si-face compared to the C-face (and CVD graphene) is attributed to the presence of the buffer layer, although the mechanism is unclear. In an attempt to increase photocurrents, asymmetric contact configurations were applied on top of C-face and Si-face epigraphene (Au/epigraphene/Al [28] and Ti/epigraphene/Pd [29]). The enhanced photoresponse is attributed to the difference in built-in electric fields at the two epigraphene/metal interfaces. Thicker layers show stronger response [28, 29]. In another implementation, an epigraphene strip was locally modified by laser illumination (LEG) creating epigraphene/LEG/epigraphene Schottky junctions. In the LEG strip, epigraphene is converted into a poor conductor (possibly graphene oxide), and the device shows nanosecond photoresponse, promising for photodetectors [30]. In the same line, enhanced photosensitivity of epigraphene was also reported after electrochemical oxidation in nitric acid [31]. This is attributed to the formation of deep traps at the electrooxidized epigraphene interface, which release charge carriers under illumination and prolong the lifetime of the photocarriers. The SiC substrate can also induce photocurrent resonance. This was observed in the spectral region where SiC has a negative dielectric constant. As SiC is a wide-bandgap semiconductor in its own right, epigraphene was also used as the (transparent) contact to probe the photo-generated charge carriers in the semi-insulating 4H-SiC substrate [32], with best response in the ultraviolet.

171.4

Plasmonics

An important motivation for plasmonics is to merge the fields of photonics and electronics using nanoscale confined electromagnetic fields. Graphene presents the advantage that its plasmonic properties (frequency, propagation direction) are highly tunable by changing its carrier density [33, 34] and structural characteristics, such as the graphene nanostructure dimension, packing density, or number of stacked layers, or by applying a magnetic field. Also owing to the low ohmic loss of the material, long lifetimes and high degree of optical field confinement are observed. Like for other metal surface, collective charge density oscillations of the electron gas (plasmons) can propagate at the surface of graphene. These electromagnetic waves have their own, strictly two-dimensional, band-dispersion relation that is different in graphene than in ordinary metals [4, 35]. Plasmons can couple to light (creating surface plasmon–polaritons that can convert light into electronic signals), to elementary charge (to create plasmarons), to interband electron–hole (e–h) pair excitation (to create plexciton), and to phonons. All the plasmon coupling mechanisms mentioned above have been observed in epigraphene. The first observation of plasmons in graphene was realized in epigraphene Si-face by high-resolution pffiffiffi electron-energy-loss spectroscopy (EELS). The predicted dispersion relation ωp / q at small wave vector q was confirmed as well as a kink in the dispersion in the vicinity of the Fermi wave vector [6, 35]. This dip in the plasmon dispersion was shown to be an intrinsic property of pristine epigraphene and does not depend on defect concentration and on the number of graphene layers or temperature. It is attributed to the decay of plasmons due to resonant coupling between plasmons and e–h pair excitations [36]. At higher q an unusual damping of the plasmon mode is observed, because of the combined effect of phase space limited backscattering for electrons in graphene and enhanced electron–electron elastic scattering [35]. In an unexpected application, epigraphene was used to demonstrate that coating materials with graphene can enhance radiative

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heat transfer between materials in the near field [23]. This exploits the tunability of graphene plasmons that can match the frequency of phonon–polariton or plasmon–polariton resonances in a given material. Best heat transfer is indeed expected when resonances in the opposing bodies match each other. This effect may be interesting for energy conversion devices [37]. Plasmons in highly charged epigraphene on the Si-face strongly interact with the surface phonons of the SiC polar substrate [6]. In this system, the plasmon and phonon energy bands show avoided crossings. Despite electronic screening from one layer to the next, the plasmon–phonon coupling extends to multilayers. Bound states of plasmons and electrons–holes (plasmarons) can play a strong role in renormalizing the bands around the Dirac energy [2, 3]. In particular, for potassium-doped quasi-freestanding epigraphene (hydrogenlifted buffer layer), ARPES measurements show that the energy band dispersion close to the Dirac point is reconstructed in a nontrivial way with four distinct bands instead of the usual pair [2] (see Fig. 167.2b[https:// doi.org/10.1007/978-3-662-53908-8_167]). This was interpreted as evidence for many-body effects (electron– electron, electron–plasmon, and electron–phonon couplings) in the dynamics of quasiparticles. Surface plasmons manifest themselves as resonance absorptions in the optical transmission spectra. Excitation of plasmons was shown to dramatically modify the magneto-optical response [38], in particular the giant Faraday rotation observed for the first time in epigraphene [39]. Despite the inefficiency of plasmon excitation and detection by light due to the large wave vector mismatch of light with graphene plasmons, light–matter interactions were demonstrated in graphene nanostructures via confined plasmons. In this case, electromagnetic radiation can excite plasmon resonances in graphene, even in nanostructures having dimensions much smaller than the incident light wavelength. These structures can be either intentionally patterned or arise naturally, such as the step-terrace microstructure of epigraphene on the Si-face or the tapered monolayers structures grown on the C-face [20]. In magnetic fields, plasmons can couple with the cyclotron resonance (inter-Landau level transition) to form a hybrid mode. Infrared magnetospectroscopy measurements have taken advantage of large arrays of sub-100 nm patterned quasi-neutral ribbons (EF < 17 meV) of high mobility (μ > 50,000 cm2/Vs) on epigraphene C-face to study this hybrid mode in detail. The observed energy shift exhibits a peculiar energy–magnetic field scaling that distinguishes it from conventional 2DEGs and highly doped graphene [40]. Complementary to the spectroscopic results above, coupling of plasmons and light has enabled plasmon fields imaging in real space on epigraphene monolayers [34] (see Fig. 171.2) or multilayer [41] C-face nanoribbons [34]. Strong optical field confinement (plasmon to incident light wavelength reduction by a factor more than a hundred) [40] and long propagation distances are observed [34], and the time evolution of the electric field distribution over the surface [42] could be detected in the THz regime.

Fig. 171.2 Plasmons launched and imaged with SNOM. (a) Schematics of the experimental configuration. An infrared laser light illuminates a metalized AFM tip (yellow). (b) The near-field amplitude image (color scale) is acquired for a tapered epigraphene ribbon (12 μm long). (c) Calculated local density of optical states (LDOS) at a distance of 60 nm from the graphene surface [34]

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Important to the field of plasmonics is the possibility of plasmon tuning, also demonstrated in epigraphene. The plasmon wavelength can be varied in epigraphene over a wide spectral range by slightly changing the incident light wavelength [34], owing to the strong dependence of the dielectric constant of SiC on the wavelength, and the sensitivity of plasmon to the dielectric environment. The dependence of the plasmon dispersion on the carrier density (proportional to n1/4) was measured on a top-gated epigraphene Si-face [43], where plasmon transport was studied by time-resolved electrical measurements of a charge pulse traveling in a plasmon mode. Change in the plasmon velocity was also realized by varying the magnetic field, charge density, and top-gate screening effect in epigraphene on the Si-face [43]. Symbols and abbreviations Short form

Full form

MEG LL LEG CVD EELS AFM LDOS 2DEG ARPES 2D

multilayer epitaxial graphene Landau level laser-modified epigraphene chemical vapor deposition electron energy-loss spectroscopy atomic force microscopy local density of states two-dimensional electron gas angle-resolved photoelectron spectroscopy two-dimensional

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Part IX

Fullerenes on Surfaces

Chapter 172

Introduction to fullerenes on surfaces C. Cepek and A. Goldoni

Fullerenes (see Fig. 172.1 for a sketch of them) are fascinating spherical molecules exhibiting outstanding chemical, electrochemical, and photophysical properties, which have made them one of the most studied chemical compounds during the last 25 years. In addition to the many applications in the field of nowadays nanotechnology, fullerenes have recently emerged as important components and have found extensive applications in nanobiotechnology and nanomedicine. Now they are considered potential drugs for antitumor therapy [13M1, 12C, 13D]. As a result, there is a good understanding of the electronic properties [04G] and covalent chemistry [05H, 07L] of these carbon allotropes, since a detailed understanding of such molecular systems is crucial for further development of new fullerene-based materials suitable for application in the fields of organic nanodevices, molecular scale electronic, medicine, or biology. Supramolecular chemistry of fullerenes has also been developed to a great extent, and because of their singular geometry, these almost spherical molecules have been used as both hosts and guests in a wide variety of supramolecular ensembles [05G]. Therefore, coverage of solid surfaces with mainly C60, C70, and, more recently, with organic-C60 heterojunctions is a broad scope area that has received the attention of the scientific community during the latest years. This interest is based on the fact that the presence of molecules usually modifies the surface properties and reconstructions as well as the effects of the bonding with the substrate. These effects may change the molecular mechanisms resulting in new materials with enhanced properties suitable for the preparation of devices in molecular electronics or for the study of emerging nanoscience and nanotechnology.

C. Cepek (*) CNR-IOM, Laboratorio Nazionale TASC, Trieste, Italy e-mail: [email protected] A. Goldoni Elettra Sincrotrone Trieste, Trieste, Italy e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_172

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Fig. 172.1 The major isomers of fullerenes, C60, C70 C76, C78, C80, C82, C84, and their group symmetry

In addition to its remarkable propensity for self-assembly, the fullerene family of molecules is associated with a rich and complex set of physicochemical properties. Therefore, the coverage of solid surfaces with fullerenes offers the possibility of transferring the fascinating properties of these molecular carbon allotropes (involving chemical, electrochemical, and photophysical properties) to solid surfaces [07B]. The chemical and physical methods available allow transfer of fullerenes in a controlled way to the substrate, giving rise to ordered structures, where electronic interactions between the molecules with the solid surface or with other closed molecules are responsible for the two-dimensional (2D) supramolecular organizations. In this regard, the design and development of new C60-coated surfaces showing unprecedented electronic properties require detailed understanding of the phenomena occurring at the atomistic scale at the interface between the solid surface and the overlayer. To unravel the fascinating aspects occurring in these new materials, a wide variety of studies have been carried out on different solid substrates also using a huge number of organic-C60 heterojunctions interacting with them. The fullerene adsorption problem has thus far stimulated and underpinned advances in a variety of subfields of condensed matter physics and surface science including, but certainly not limited to, organic-inorganic heterointerfaces, self-assembly and selforganization, single-molecule spectroscopy and molecular orbital imaging, the manipulation and controlled positioning of individual molecules using scanning probes, and the physics of correlated electrons in molecular assemblies. Thus, important topics such as those devoted to band dispersion in ordered systems, charge transfer, molecular orientation, nanoelectrodes, self-assembling monolayers (SAMs) and multilayers, and the most recent heterojunctions at the nanometer scale for application in molecular electronics, sensing, or catalysis are topics where the topological and electronic interactions occurring at the interface between the substrate and the molecules are critical. Needless to say, to have good expertise in all of these topics as well as in

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their applications, such as light conversion, or to discuss their manipulations (electric and chemical measurements, charge transport, etc.) is almost impossible for a single research group; therefore, multidisciplinary studies are required for the rational development and applications of these modified surfaces. A different supramolecular approach to that known in solution or three-dimensional (3D) crystals, which currently represents a major challenge in science, is the engineering of organic molecular films on atomically well-defined solid surfaces, mainly involving some coinage metals (typically Au, Cu, or Ag but also Pt and Ni), semimetals (graphite), or oxides (e.g., TiO2), usually in ultrahigh vacuum (UHV). The aim is to achieve good control of the self-ordering of the adsorbed molecules on the substrate with the final goal of obtaining new nanostructured functional materials for the preparation of novel and smaller devices. This bottom-up approach, which is mainly based on the characterization of samples by using modern microscopy techniques [scanning tunneling microscopy (STM), atomic force microscopy (AFM), and transmission electron microscopy (TEM)] and electron spectroscopies, requires a good understanding of the interactions occurring between the substrate and the adsorbed molecules as well as the ones between the molecules in the presence of the interacting solid surface. Thus, the 2D or 3D arrangement is the result of combinations of weak noncovalent intermolecular forces (such as van der Waals or dispersive forces) with molecule-substrate interactions, where crystalline symmetry of the surface may play a leading role. In this regard, molecule-substrate interactions should determine adsorption geometry and conformation at low surface coverage. Only when molecules are able to form strong directional bonds, such as H-bonds, and the corrugation of the potential energy for the adsorbed species is small as compared to the energy gain from intermolecular interactions, supramolecular structures formed on surfaces are mainly determined by intermolecular forces (although the substrate influence may still be important). On the other hand, in some specific systems, such as the Au(111) surface, there is a strong selectivity in the adsorption site of the adsorbates, which, in turn, determines the final morphology of the organic monolayer. Therefore, supramolecular chemistry is an important tool for the development and understanding of the emergent nanoscience and nanotechnology at surfaces. Herein, we review different strategies followed for the incorporation of fullerene molecules onto solid surfaces, which mainly involve: (i) The selective adsorption of fullerene and fullerene derivatives on metal or semiconductor surfaces, where substrate reconstructions frequently occur or disappear (ii) The generation of a regular network on the surface substrates, which, in turn, is used as a template for the further controlled organization of fullerenes, thus avoiding the strong tendency of fullerenes to rearrange the substrate atomic structure (iii) The formation of superlattices and heterojunctions at a nanometer scale by mixing fullerenes with other electronically complementary molecules Our aim is to provide an overview of the recent experimental advances in elucidating the physical and chemical properties of the fullerene-substrate interfaces and make a comprehensive presentation of the still relatively few examples known on surface-supported 2D supramolecular networks involving fullerenes. The intention is also to highlight some open questions and, in particular, to place the work in the broader context of developments in nanoscience, showing some paradigmatic cases that illustrate the importance of the bottom-up approach for the controlled generation of ordered C60 carbon nanostructures. Fullerene surface science has produced a variety of fascinating (and sometimes controversial) results, and the field remains a cornerstone of nanometer scale physics and chemistry. In summary, fullerenes, probably the most studied molecules during the last 25 years, are called to play a leading role in the development of 2D supramolecular organizations formed by the assembly of pristine and chemically modified molecules that can preserve the outstanding chemical, electrochemical, and photophysical properties that they exhibit. Many examples are reported here, showing how the fullerene can be combined simply by adsorption on metal and semiconductor surfaces, changing the original properties of the substrates and in many cases the substrate morphologies (reconstruction or deconstruction). Molecular and supramolecular assemblies based on noncovalent interactions have been explored in an attempt to control surface properties. Adsorption of simple fullerene layers, co-adsorption of fullerenes with other organic molecules, or realization of templates (atomic or molecular) needed to form heterogeneous interfaces for donor-acceptor interaction or to adsorb fullerene molecule in defined positions, with

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given symmetry, or in a chiral way, allow the researchers to obtain several new systems, using the bottomup approach, with novel chemical, electrochemical, and photophysical properties. The bottom-up strategy is an attractive and promising approach for the construction of fullerenes nanoarchitectures. Symbols and abbreviations Short form

Full form

UHV STM TEM 3D AFM 2D SAM

ultrahigh vacuum scanning tunneling microscopy transmission electron microscopy three-dimensional atomic force microscopy two-dimensional scanning auger electron microscopy

References [04G]

Gunnarsson, O.: Alkali-Doped Fullerides: Narrow-Band Solids with Unusual Properties. World Scientific Publishing Co., Singapore (2004) [05G] Guldi, D.M., Zerbetto, F., Georgiakilas, V., Prato, M.: Acc. Chem. Res. 38, 38 (2005) [05H] Hirsch, A.: The Chemistry of Fullerenes. Wiley-VCH, Weinheim (2005) [07B] Bonifazi, D., Enger, O., Diederich, F.: Chem. Soc. Rev. 36, 390 (2007) [07L] Langa, F., Nierengarten, J.-F.: Fullerenes: Principles and Applications. RSC Publishing, Cambridge, UK (2007) [12C] Chen, Z., Mao, R., Liu, Y.: Curr. Drug Metab. 13, 1035–1045 (2012) [13D] Dellinger, A., Zhou, Z., Connor, J., Madhankumar, A.B., Pamujula, S., Sayes, C.M., Kepley, C.L.: Nanomedicine. 8, 1191–1208 (2013) [13M1] Montellano, A., Da Ros, T., Bianco, A., Prato, M.: Nanoscale. 3, 4035–4041 (2013)

Chapter 173

Band dispersion of solid C60 C. Cepek and A. Goldoni

The C60 molecules crystallize in a weakly bounded face-centered-cubic (fcc) solid with a lattice constant of 14.2 Å, corresponding to about 10 Å of separation between the centers of adjacent molecules [91H]. The molecules are orientationally disordered above 260 K (C60 spins almost like a free rotor) [94A], while below 230 K the “free” rotations are stopped and the molecules can only swing between two orientations (merohedral disorder) [92D]. The band structure in solid C60 compounds (Fig. 173.1) is far from being understood due to the experimental and theoretical challenges involved. C60 fullerides are interesting systems because both the electron-phonon and electron-electron interactions are large on the energy scale of the expected narrow bandwidth. Orientational disorder, temperature-dependent phase transitions, very small Brillouin zone, weak molecular interaction, and strong electron-phonon coupling have combined effects that are difficult – if not impossible – to disentangle and all together imply a level of complexity that, at best, has made difficult the application of theoretical models and the elucidation of experimental results [04G].

C. Cepek (*) CNR-IOM, Laboratorio Nazionale TASC, Trieste, Italy e-mail: [email protected] A. Goldoni Elettra Sincrotrone Trieste, Trieste, Italy e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_173

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Molecular levels

LDA bands in Solid fcc C60 t 1g

6

2.0 gg hu t2u hg

t 1u 1.0

2 t1g tlu

0

hu

LUMO+1 LUMO

HOMO gg+hg HOMO–1

–2

gu t2u

–4

hg

–6

ttu ag

–8

Energy (eV)

BINDING ENERGY (eV)

4

0.0

hu

–1.0 gg+hg –2.0

–3.0

–4.0

Γ

Wavevector

Χ

W

L

Γ

Κ

Wavevector

Fig. 173.1 C60 molecular levels with the corresponding symmetry and degeneracy (left) and the calculated band structure of the fcc solid C60 (right) (Adapted from [93E]. Copyright 1993 VCH publishing)

Symbols and abbreviations Short form

Full form

fcc HOMO LUMO

face-centered cubic highest occupied molecular orbital lowest unoccupied molecular orbital

References [91H] Heney, P.A., Fischer, J.E., McGhie, A.R., Romanow, W.J., Denenstein, A.M., McCauley Jr., J.P., Smith III, A.B., Cox, D.E.: Phys. Rev. Lett. 66, 2911 (1991) [92D] David, W.I.F., Ibberson, R.M., Dennis, T.J.S., Hare, J.P., Prassides, K.: Europhys. Lett. 18, 219 (1992) [93E] Erwin, S.C.: In: Billups, W.E., Ciufolini, M.A. (eds.) Buckminsterfullerenes, p. 217. VHC Publishers, New York (1993) [94A] Axe, J.D., Moss, S.C., Newmann, D.A.: Solid State Phys. 48, 149 (1994), and references therein [04G] Gunnarsson, O.: Alkali-Doped Fullerides: Narrow-Band Solids with Unusual Properties. World Scientific Publishing Co., Singapore (2004)

Chapter 174

Fullerenes on metals and semiconductors: interaction with the substrate C. Cepek and A. Goldoni

One way to reduce the number of experimental parameters influencing the band structure is to adsorb the fullerene on metal substrates, where at least the molecule could be orientationally fixed in positions. The nature of the interaction between fullerenes and metal single crystal surfaces has been the subject of a number of reports [93M, 97T, 97T1, 00C, 01C, 01C1, 05T, 08T]. The ability to tune both the Fermi level position and the stoichiometry of an adsorbed C60 monolayer (ML) has played an important role in elucidating the bonding mechanisms and associated electronic properties of adsorbed fullerenes. However, until 2003, no clear statements about the band dispersion of ordered C60/metal films on metal substrates were described, mainly because of the extremely narrow bandwidths and small surface Brillouin zone (BZ). The first unambiguous example was shown by Yang et al. [03Y] for a monolayer of doped C60 on Ag(111). The authors showed angle-resolved photoemission data of the band dispersion for an alkalidoped C60 monolayer and a detailed comparison with theory. Compared to the maximum bare theoretical bandwidth of 170 meV, the observed 150-meV dispersion is within the range of renormalization by electron-phonon coupling. This dispersion is a fraction of the integrated peak width, revealing the importance of many-body effects. After that, Brouet et al. [04B] compared the dispersion of one monolayer of C60 on Ag(111) and Ag(100) as shown in Fig. 174.1. A dramatic change in the electronic structure of two C60 monolayers, even after doping with potassium to half filling of lowest unoccupied molecular orbital, was observed. The Fermi surface symmetry, the bandwidth, and the curvature of the dispersion at Γ point are different. Orientations of the C60 molecules on the two substrates are known to be the main structural difference between the two monolayers, and band-structure calculations [04B] for these orientations confirm the experimental data, indicating that the molecular orientations play a key role in the electronic structure of fulleride ML on metal substrates.

C. Cepek (*) CNR-IOM, Laboratorio Nazionale TASC, Trieste, Italy e-mail: [email protected] A. Goldoni Elettra Sincrotrone Trieste, Trieste, Italy e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_174

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Fig. 174.1 Band dispersion and Fermi surfaces of “K3C60” on Ag(111) (left) and Ag(100) (right) [04B] (Copyright 2004 American Physical Society)

That the molecular orientations are important for the fullerides band dispersions was shown by Goldoni et al. [06G] measuring a film of K6C60 on Ag(100). Several studies indicate that at saturation doping, e.g., six electrons/molecule, the alkali metal fullerides form band insulators. The crystal structure of K6C60 is a body-centered cubic, the lowest unoccupied molecular orbital (LUMO)-derived bands are completely filled, and there is no room for molecular motions. K6C60 is therefore a very lucky case, in which merohedral disorder and electron-electron interactions do not play a role in the photoemission spectra. The authors showed that band dispersion in K6C60(110) films at 40 K survives in spite of the strong electron-phonon coupling expected in fullerides that should give rise to polaron formation. Figure 174.2 shows the momentum dependence and the total bandwidth of the dispersing bands contributing to the highest occupied molecular orbital (HOMO), and lowest unoccupied molecular orbital features agree quite well with one-electron band-structure calculations. Therefore, apart the orientation, also the electronelectron correlations are important in the band dispersion renormalization observed in the fullerene monolayers.

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Fig. 174.2 Dispersion of K6C60 along the ΓN (top) and ΓHN (bottom) directions [06G] (Note the good comparison with bulk band-structure calculations [91E]. Copyright 2006 American Physical Society)

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Further evidence of the band dispersion of a monolayer on Cu substrates was reported by Tamai and coworkers [05T, 06T, 08T], revealing the presence of an extra photoemission peak dispersing in the HOMO-LUMO gap, which has been interpreted as a signature of a strong hybridization between the copper and the carbon electronic states. This interface state, similar to the one later identified on C60/Cu (111) [08T], shows a one-dimensional dispersion along the chains on Cu(553) [06T]. In contrast, no significant momentum dependence is detected for emission from the lowest unoccupied molecular orbital. The LUMO displays similar phonon features, as in C60/Cu(111), but it does not peak toward the Fermi level for all considered potassium doping, and its photoemission line shape is broader than in any other monolayer system investigated so far. This behavior is not easily reconciled with existing theory and indicates that the one-dimensional character of the chains affects the electronic structure of the monolayer in an intricate way. The interaction between C60 molecules and metallic surfaces is also supported by STM studies [04L , 04S], showing a significant influence of the underlying metal on the electronic structure of the absorbed C60 and by density functional theory (DFT) calculations [04L, 04W , 04W1]. Apart from the hybridization between the metal states and the π-orbitals at the C60 cage and the observation of band dispersion, a significant charge transfer from the substrates to C60 is usually observed on Au, Ag, and Cu metals, with reported values ranging from 0.2 to 2 e/C60 [93M, 97T, 00C, 01C, 01C1, 04L, 04W, 05T, 08T]. Figure 174.3 shows some STM experiment at low temperature on Au(111) where different C60 orientations are experimentally observed due the small interaction with the substrate, in agreement with DFT calculations. The effects of charge transfer (and the lack of it) for individual C60 molecules adsorbed onto Au(111) and Ag(100) where the interaction is more intense were also calculated. STS indicated an increase of the HOMO-LUMO gap of 0.6 eV, as well as suppressed LUMO splitting, for C60 molecules on Au(111) compared with Ag(100), which allow inferring that the C60 intramolecular Coulomb energy is 0.6 eV higher for C60 on Au(111) than for C60 on Ag(100). This difference is explained as the result of increased screening for C60 on Ag(100) relative to Au(111) due to an increase in the electronic density of states at EF when C60 is adsorbed onto Ag(100). Such an interpretation is supported by local density approximation (LDA) calculations, which indicated that negligible charge is transferred from Au(111) to adsorbed C60, while about 0.2 electrons are transferred to C60 adsorbed onto Ag(100).

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Fig. 174.3 (Left) experimental topographs and scanning tunneling spectroscopy images of a single C60 molecule on Au(111). (a) Topograph taken at 2.5 V; (b–d) dI/dV maps taken at V ¼ 2.2 V, 1.0 V, and 1.7 V; (e) topograph taken at 2.0 V. Right column: simulated topographs and spectroscopic images obtained from LDA calculation. Constant current topographs are visualized as 3D rendered surfaces, while spectral maps are visualized as 2D projections. (Right) integrated differential electron density of C60 on (a) Au(111) and (b) Ag(100) surfaces, obtained through DFT calculation. Differential electron density is integrated along direction perpendicular to the page. Blue color represents an increase in electron density, while red represents a decrease in electron density (Adapted from [04L]. Copyright 2004 American Physical Society)

Slightly different results were obtained by Wang and Cheng [04W1] with an electronic charge transfer of 0.5 and 0.2 electrons per molecule from the Ag(111) and Au(111) substrates to C60, respectively. Their analysis also indicated on the basis of the electron density difference and density of states that the interaction between C60 and the noble metal surfaces is primarily covalent, with some ionic character. This picture is in contrast with the common notion developed from experiments that the interaction between C60 and noble metal surfaces is predominantly ionic. The data reported by Tamai et al. [08T] seem to shed light on the issue of the observed charge transfer difference between DFT calculations and experiments at the C60/noble metal interfaces. So far, in all photoemission studies of C60 monolayers on metal surfaces, the intensity close to the Fermi level has been interpreted as emission from the partially occupied C60 LUMO, and the contribution of the substrate was neglected. Based on these assumptions, different methods have been developed to calibrate the occupancy of the C60 LUMO due to charge transfer [97T, 00C]. However, the evidence of Tamai et al. [08T] of electronic hybridization at the interface and the fact that the Shockley surface state is visible in the first C60 Brillouin zone suggested that this approach should overestimate the charge transfer. DFT calculations of the charge transfer from the metal to the molecules generally yield smaller values than the ones obtained experimentally based on photoemission spectra. In the case of C60/Cu(111), the charge state of the molecule calculated in DFT is 0.8 e/molecule [04W]. The experimental value reported by Tsuei et al. [97T1] upon evaluating the integrated intensity close to EF is 1.5–2 e/C60, while using the method of Cepek et al. [00C] on the data of Tamai et al. [08T], the charge transfer is about 3 e/C60. The significant disagreement between experiments and theory can be explained by the fact that in the presence of strong

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hybridization, the occupied states close to the Fermi level were not actually due to a full electron transfer to the molecule because there is also a significant weight coming from the Cu atoms. The above results demonstrate that an absolute determination of the C60 charge state in strongly hybridized monolayer systems is not straightforward. The local atomic arrangements at the C60-metal contact affect not only the stability of the structure and the strength of the bonding but also the electronic structure and transport properties of the supported molecule. Many factors affect the electronic structures of the supported C60, in particular the interface reconstruction (discussed in Chap. 176[https://doi.org/10.1007/978-3-662-53908-8_176]) and the fixed inter-C60 orientations due to bonding with surface atoms (discussed in the Chap. 177[https://doi.org/10. 1007/978-3-662-53908-8_177]). Also the fullerene-on-silicon systems have played a pivotal role in the development of roomtemperature molecular manipulation protocols [10M]. While the interaction of fullerene molecules with clean and adsorbate-covered silicon surfaces forms a key focus, adsorption on germanium [94X, 00G], III–V semiconductors [06C, 10M], and SiC [13B] surfaces was also covered. Contrary to the case of metals, actually no band dispersion and electron transfer have been reported for semiconductor substrate although the ordered structures and fixed orientation were observed on some of them. The possible reasons can be searched in the screening of the electron correlation due to the metal substrates; the strong covalent bonding with Si, Ge, and SiC semiconductor surfaces; and the orientational disorder (GaAs, InP). The mainly covalent bonding (instead of the expected ionic bonding observed on metals) was detected by photoemission [00P, 00G], X-ray diffraction [98K], and scanning tunneling microscopy (STM) and spectroscopy (STS) [92L, 92W] measurements. Symbols and abbreviations Short form

Full form

BZ ML LUMO HOMO STM LDA 2D DFT

Brillouin zone monolayer lowest unoccupied molecular orbital highest occupied molecular orbital scanning tunneling microscopy local density approximation two-dimensional density functional theory

References [91E] [92L] [92W] [93M] [94X] [97T]

Erwin, S.C., Pederson, M.R.: Phys. Rev. Lett. 67, 1610 (1991) Li, Y.Z., Chander, M., Patrin, J.C., Weaver, J.H., Chibante, L.P.F., Smalley, R.E.: Phys. Rev. B. 45, 13837 (1992) Wang, X.D., Hashizume, T., Shinohara, H., Saito, Y., Nishina, Y., Sakurai, T.: Jpn. J. Appl. Phys. 31, L983 (1992) Modesti, S., Cerasari, S., Rudolf, P.: Phys. Rev. Lett. 71, 2469 (1993) Xu, H., Chen, D.M., Creager, W.N.: Phys. Rev. B. 50, 8454 (1994) Tjeng, L.H., Hesper, R., Heessels, A.C.L., Heeres, A., Jonkman, H.T., Sawatzky, G.A.: Solid State Commun. 103, 31 (1997) [97T1] Tsuei, K.-D., Yuh, J.-Y., Tzeng, C.-T., Chu, R.-Y., Chung, S.-C., Tsang, K.-L.: Phys. Rev. B. 56, 15412 (1997) [98K] Kidd, T., Aburano, R.D., Hong, H., Gog, T., Chiang, T.-C.: Surf. Sci. 397, 185 (1998) [00C] Cepek, C., Sancrotti, M., Greber, T., Osterwalder, J.: Surf. Sci. 454, 467 (2000) [00G] Goldoni, A., Cepek, C., De Seta, M., Avila, J., Asensio, M.C., Sancrotti, M.: Phys. Rev. B. 61, 10411 (2000) [00P] Pesci, A., Ferrari, L., Comicioli, C., Pedio, M., Cepek, C., Schiavuta, P., Pivetta, M., Sancrotti, M.: Surf. Sci. 454, 832 (2000) [01C] Cepek, C., Fasel, R., Sancrotti, M., Greber, T., Osterwalder, J.: Phys. Rev. B. 63, 125406 (2001) [01C1] Cepek, C., Vobornik, I., Goldoni, A., Magnano, E., Selvaggi, G., Kroeger, J., Panaccione, G., Rossi, G., Sancrotti, M.: Phys. Rev. Lett. 86, 3100 (2001) [03Y] Yang, W.L., Brouet, V., et al.: Science. 300, 303 (2003) [04B] Brouet, V., et al.: Phys. Rev. Lett. 93, 197601 (2004) [04L] Lu, X., Grobis, M., Khoo, K.H., Louie, S.G., Crommie, M.F.: Phys. Rev. B. 70, 115418 (2004)

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[04S] [04W] [04W1] [05T] [06C] [06G] [06T] [08T] [10M] [13B]

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Silien, C., Pradhan, N.A., Ho, W., Thiry, P.A.: Phys. Rev. B. 69, 115434 (2004) Wang, L.-L., Cheng, H.-P.: Phys. Rev. B. 69, 045404 (2004) Wang, L.-L., Cheng, H.-P.: Phys. Rev. B. 69, 165417 (2004) Tamai, A., Seitsonen, A.P., Fasel, R., Shen, Z.-X., Greber, T., Osterwalder, J.: Phys. Rev. B. 72, 085421 (2005) Cherkashinin, G., Krischok, S., Himmerlich, M., Ambacher, O., Schaefer, J.A.: J. Phys. Condens Matter. 18, 9841 (2006) Goldoni, A., Petaccia, L., Zampieri, G., Lizzit, S., Cepek, C., Gayone, E., Wells, J., Hofmann, P.: Phys. Rev. B. 74, 045414 (2006) Tamai, A., Seitsonen, A.P., Greber, T., Osterwalder, J.: Phys. Rev. B. 74, 085407 (2006) Tamai, A., Seitsonen, A.P., Baumberger, F., Hengsberger, M., Shen, Z.-X., Greber, T., Osterwalder, J.: Phys. Rev. B. 77, 075134 (2008) Moriarty, P.J.: Surf. Sci. Rep. 65, 175 (2010), and reference therein Bocquet, F.C., Ksari, Y., Lin, Y.P., Porte, L., Themlin, J.-M.: Phys. Rev. B. 88, 125421 (2013)

Chapter 175

Ordered fullerenes on metal surfaces: monatomic steps on vicinal surfaces and reconstruction on metals C. Cepek and A. Goldoni

Fullerenes have been deposited onto metal surfaces since the early 1990s, and the nature of the interaction between fullerenes and metal single crystals surfaces has been the subject of a numbers of STM and X-ray photoelectron diffraction reports (XPD) [90B, 97M, 01W, 04L, 04P, 08Z, 09L]. The molecular orientation of fullerenes on surfaces is an important parameter directly related to both the interfacial interaction between the substrate and the molecules and the molecule–molecule interaction. This molecules differ significantly from the elemental or simple molecular adsorbates because of their three-dimensional character and because of the modulation of the valence charge distribution over the molecular cage. Several possible interaction mechanisms between fullerene and the host surface might induce substrate reconstructions, might choose some optimal orientations, and might undergo structural distortions, in order to enhance the binding with the surface. Adsorption on noble metal surfaces implies in general a lower interaction, with charge transfer from the metal surface to the cages, and the molecules desorb but typically do not decompose. In particular, it has been observed that at room temperature, C60 molecules diffuse fast on coinage metals, like Ag, Cu, and Au. In this case, the molecules can assume one single orientation [96F, 99F] or can flip between two inequivalent orientations, like on Ag(100) [01C, 02G]. STM has extensively used to distinguish the C60 species; however, since the STM image is a convolution of the surface electronic and geometric structure, it is often controversial as to whether the contrast is related simply to a difference in geometrical height (due to surface reconstruction) or to electronic effects (a spatially nonhomogeneous density of states due to different adsorption sites or cage orientations). On the other hand, XPD has proven to be a powerful means to determine the orientation of the C60 cage at surfaces when the molecules can assume only one or two molecular orientations on the surface [96F, 99F, 01W, 01C, 03M]. On (111) surfaces presenting hexagonal symmetry, like the Au(111), Cu(111), Al(111), Pt(111), etc., the ordered C60 monolayer systems have been found from both, XPD and STM, that the molecular C60 cage is sitting on a hexagon. However, XPD showed that the molecules on Cu(111) are adsorbed with the six ring toward the surface, in two azimuthally equivalent orientations [96F]. A low-temperature STM study of C60 on Cu(111) showed that the spatial distribution and the STS spectral width of the LUMO-derived states are particularly sensitive to the adsorbate–substrate contact [04S]. On these substrates, the molecules move fast on terraces at room temperature and will end up being selectively anchored at the lower step edges on the face-centered-cubic (fcc) areas [90B, 98B]. Only after complete decoration of the step edges, close-packed C60 islands grow. At higher coverage, the C60 layer grows out from the step chains and across the terraces, which is energetically favored over the closing of the step chain segments into extended 1D molecular chains. This observation has suggested the possibility to employ vicinal surfaces, with a periodic arrangement of monatomic steps, as a template to obtain ordered C. Cepek (*) CNR-IOM, Laboratorio Nazionale TASC, Trieste, Italy e-mail: [email protected] A. Goldoni Elettra Sincrotrone Trieste, Trieste, Italy e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_175

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arrays or chains of fullerene molecules. In stepped and reconstructed gold surfaces [vicinal to the (111) face], a rectangular array of preferred adsorption sites arises from the perpendicular intersection of two nanoscale patterns of different origin: step edges and dislocation lines from the remaining herringbone reconstruction on the (111) facets. This characteristic property of vicinal surfaces has been skillfully utilized by Fasel and coworkers [06X] for preparing C60 nanostructures with long-range order and uniform size by using Au(11 12 12) surfaces. This nanostructure consists of line of 7 nm wide on the (111)-oriented terraces separated by a periodic array of (100) monatomic steps. After deposition of 0.1 monolayer of C60 on the gold surface at room temperature, a highly regular 2D superlattice of short molecular chains, formed mostly by four or five C60 units, was observed, as shown in Fig. 175.1. A similar nanochain arrays was observed on Cu(553).

Fig. 175.1 STM image of the superlattice obtained after formation of a highly regular 2D array of C60 nanochains on the Au(11 12 12) template surface after deposition of 0.1 ML of C60. The inset shows a highresolution image of two short chains (Adapted from [06X]. Copyright 2006 American Chemical Society)

Interestingly, the nanochain superlattice contains fullerene molecules adsorbed exclusively on the fcc areas of the step edges of the substrate. This organization has been accounted for by the possibility of a certain charge transfer degree from the electron-rich step edge to the electron deficient C60. At the same time, Neel and coworkers [06N] have used the faceting propensity of Au(433) vicinal surfaces that form regular 4-nm-wide terraces separated by groups of 1.4 nm terraces and the capacity of C60 to modify the atomic structure of some metal surfaces, in order to produce long and narrow fullerene stripes. By combining C60 adsorption on this Au vicinal surface and subsequent heating to 500 K, there is the formation of a faceted surface with a decoration of alternating metal and fullerene stripes, several hundreds of nanometers long, having an average width of six to eight adjacent molecular chains. Again, a similar experiment was performed on Cu. Combining STM and XPD experiments [04T], it has been found that, by using (111) vicinal surfaces, like Cu(221), it is possible to grow long-ordered one-dimensional chains of C60 molecules aligned along the steps of this vicinal template. By STM a unit cell with two distinctly imaged molecules is found. At least in one of the two species, the molecules have a well-defined orientation as determined by XPD. Another topic that has been amply discussed in the literature is the effect of metal surface reconstruction upon fullerene adsorption. For example, while C60 molecules have not been observed to decorate preferentially the elbows of the herringbone Au(111) reconstruction, the use of fullerene derivatives, like phenylC61-butiric acid methyl ester (PCBM), which show more interaction with the substrates, should use the dislocation pattern arising from the herringbone reconstruction to produce 1D template even for flat (nonvicinal) surfaces [07E]. PCBM, typically used in many heterojunctions, adsorb preferentially at the elbows, forming a regular array of single molecules. At low coverage, because of the influence of the “side tail” of PCBM, the herringbone reconstruction of Au(111) acts, thus, as an efficient template that dictates

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the resulting structure. The organization process starts with adsorption of individual PCBM molecules at the elbows of the reconstruction but for larger coverage continues with the formation of 1D wires formed by double rows of PCBM molecules nucleated exclusively at the fcc areas of the reconstruction, which give rise to a 2D nanosized spiderweb of PCBM nanowires. Anyway, also for fullerenes strongly interacting with the substrate systems, the adsorption often leads to significant changes in the subtle energetic balance governing surface structure and, thus, to a significant modification of the substrates atomic geometry known as surface reconstruction. Actually the adsorption on transition metal like Pt, Ta, Rh, and Pd is characterized by a strong predominantly covalent bonding, where the strength of the interaction is able to catalyze the fullerene cage decomposition prior to the desorption of the monolayer [see, e.g., Refs. 93R, 93S, 94J, 94R, 96C, 97M, 99P]. For fullerene adsorption on these clean metal surfaces, surface reconstruction seems to be the rule rather than the exception when the interaction has mainly a covalent character. For example, Pd(110) [01W] and Ni(110) [97M] surfaces show large mass transport associated with fullerene adsorption; the strong interaction between these d-band metals and the π-systems of C60 promotes the creation of a long-range ordered array of vacancy islands that permit a closer interaction between the metal surface and the lateral π-electrons of the C60 cage that otherwise would not be in close proximity of any surface atoms. There is even ample evidence supporting surface reconstruction for the much less reactive noble metal surfaces [97M, 01C, 03A, 08H], including close-packed ones where the interaction is less strong [04P, 08Z, 09L]. The molecular orientation can depend on the C60 coverage, like in the case, for example, of Cu(100) [10W], Ni(110) [97M], and Pd(110) [01W], where different short-range ordered phases are observed as a function of C60 coverage. At low coverages, due to the lack of intermolecular interactions, a larger number of local C60–metal contact configurations is observed than at monolayer coverage [08L, 03L, 04S]. On Pd (110) [01W] XPD analysis showed that C60 molecules are generally oriented in the same way, facing a pentagon–hexagon bond toward the substrate, and the height difference seen by STM (evidenced in the images by a sharp bright-dim contrast) is due to a thermally activated bonding transition, where the C60 molecules accommodate in microscopic pits resulting in a higher C–Pd coordination. Surfaces showing well-ordered uniform arrays of anchoring sites are excellent templates for the preparation of ordered molecular nanostructures by site-selective nucleation and a further self-assembly of the adsorbed molecules. When the substrate reconstruction due to the fullerene molecules leads to large modifications of the substrate, the produced surface reconstructions are visible by STM, as, for example, in the case of C60 adsorption on Au(110) [93G] or on Pd(110) [01W], while other experimental techniques, like surface X-ray diffraction, are needed when the reconstruction involve only few substrate atoms localized at the C60/substrate interface, as in the case of C60 on Pt and Au [05F, 00P1]. In particular, on the Au(110)-p(6x5) surface, it was found that the C60 adsorption is accompanied by important displacements of the underlying Au atoms, while in the case of adsorption on Pt(111), the reconstruction, due to the presence of the fullerene molecules, consists on the creation of an ordered surface vacancy lattice: the C60 molecules are located on top of the vacancies, and 12 covalent bonds are formed between the carbon atoms and the six platinum surface atoms around the vacancies (Fig. 175.2).

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a

b dz

Δ1

dz12

Δ2

dz23

Δ3

dz34

Δ4

dz45

Δ5

Fig. 175.2 (a) Vacancy site structure, showing three layers of Ag(111). The mirror plane of the molecule is parallel to the mirror plane of the substrate (dashed line). There are two such parallel orientations of the molecules, one as shown and one rotated 180 . The top hexagon is surrounded by three hexagons and three pentagons – 180 rotation interchanges these (as well as some others that are not visible). (b) Side view of the vacancy structure, viewed from the bottom of (a), along the dashed line, including the atoms in the box on (a). The buckling is magnified and the atoms are shown with a reduced size for clarity (After [09L]. Copyright 2009 American Physical Society)

Moreover, it has also been shown that metallic nanostructures, as a consequence of the strain-relief patterns and dislocation networks characteristics of some solid surfaces, like the Au(111) herringbonereconstructed surface or Ag(111), favors the initial nucleation in preferential regions. Actually, a wide variety of surface defects, such as steps or impurities, can also act as nucleation sites for anchoring molecules. Recently, spatially resolved local electronic structure and molecular orientation of a C60 ML on Ag(001) were measured by STM and STS [02G, 03H]. The spatial mapping of the spectral density of single C60 molecules on Ag(100) demonstrated the need for explicitly including the substrate interaction and the STM tip trajectory to understand the observed C60 local electronic structures [03L]. Bright-dim molecules were observed in the ordered ML [02G, 03H]. STM observed orientation only on the dim molecules. XPD found the presence of two inequivalent prevailing molecular orientations of the C60 cage, as well as a considerable fraction of rotationally not-ordered molecules (bright) [01C]. These data were better understood considering the behavior of a C60 monomer and then the effects of additional C60–C60 interactions and a modified C60–Ag environment. Comparison of C60 monomer and ML behavior showed that these effects lead to a nearly rigid shift of the single-molecule electronic structure and a slight broadening of STS spectral features. Such comparisons allowed Grobis et al. [02G] to conclude that

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the coexistence of the observed bright and dim C60 molecules in the ordered ML on Ag(001) most likely originates from the underlying Ag surface reconstruction. Symbols and abbreviations Short form

Full form

STS ML XPD PCBM STM LDA 2D DFT 1D LUMO

scanning tunneling spectroscopy monolayer X-ray photoelectron diffraction phenyl-C60butyric acid methyl scanning tunneling microscopy local density approximation two-dimensional density functional theory one-dimensional lowest unoccupied molecular orbital

References [90B] [93G] [93R] [93S] [94J] [94R] [96C] [96F] [97M] [99F] [99P] [00P1] [01C] [01W] [02G] [03A] [03L] [03H] [03M] [04L] [04P] [04S] [04T] [05F] [06N] [06X] [07E] [08L] [08H] [08Z] [09L] [10W]

Barth, J.V., Brune, H., Ertl, G., Behm, R.J.: Phys. Rev. B. 42, 9307 (1990) Gimzewski, J.K., Modesti, S., Gerber, C., Schlittler, R.R.: Chem. Phys. Lett. 213, 401 (1993) Ruckman, M.W., Xia, B., Qiu, S.L.: Phys. Rev. B. 48, 15457 (1993) Sellidj, A., Koel, B.E.: J. Phys. Chem. 97, 10076 (1993) Jiang, L.Q., Koel, B.E.: Chem. Phys. Lett. 223, 69 (1994) Rudolf, P., Gensterblum, G.: Phys. Rev. B. 50, 12215 (1994) Cepek, C., Goldoni, A., Modesti, S.: Phys. Rev. B. 53, 7466 (1996) Fasel, R., Aebi, P., Agostino, R.G., Naumovic, D., Osterwalder, J., Santaniello, A., Schlapbach, L.: Phys. Rev. Lett. 76, 4733 (1996) Murray, P.W., Pedersen, M.Ø., Lægsgaard, E., Stensgaard, I., Besenbacher, F.: Phys. Rev. B. 5, 9360 (1997) Fasel, R., Agostino, R.G., Aebi, P., Schlapbach, L.: Phys. Rev. B. 60, 4517 (1999) Pedio, M., Hevesi, K., Zema, N., Capozi, M., Perfetti, P., Gottebaron, R., Pireaux, J.J., Caudano, R.: Surf. Sci. 437, 249 (1999) Pedio, M., Felici, R., Torrelles, X., Rudolf, P., Capozi, M., Rius, J., Ferrer, S.: Phys. Rev. Lett. 85, 1040 (2000) Cepek, C., Fasel, R., Sancrotti, M., Greber, T., Osterwalder, J.: Phys. Rev. B. 63, 125406 (2001) Weckesser, J., Cepek, C., Fasel, R., Barth, J.V., Baumberger, F., Greber, T., Kern, K.: J. Chem. Phys. 115, 9001 (2001) Grobis, M., Lu, X., Crommie, M.F.: Phys. Rev. B. 66, 161408(R) (2002) Abel, M., Dmitriev, A., Fasel, R., Lin, N., Barth, J.V., Kern, K.: Phys. Rev. B. 67, 245407 (2003) Lu, X., Grobis, M., Khoo, K.H., Louie, S.G., Crommie, M.F.: Phys. Rev. Lett. 90, 096802 (2003) Hsu, C.-L., Pai, W.W.: Phys. Rev. B. 68, 245414 (2003) Abel, M., Dmitriev, A., Fasel, R., Lin, N., Barth, J.V., Kern, K.: Phys. Rev. B. 67, 245407 (2003) Lu, X., Grobis, M., Khoo, K.H., Louie, S.G., Crommie, M.F.: Phys. Rev. B. 70, 115418 (2004) Pai, W.W., Hsu, C.-L., Lin, M.C., Lin, K.C., Tang, T.B.: Phys. Rev. B. 69, 125405 (2004) Silien, C., Pradhan, N.A., Ho, W., Thiry, P.A.: Phys. Rev. B. 69, 115434 (2004) Tamai, A., Auwarter, W., Cepek, C., Baumberger, F., Greber, T., Osterwalder, J.: Surf. Sci. 566–568, 633 (2004) Felici, R., Pedio, M., Borgatti, F., Iannotta, S., Capozi, M., Ciullo, G., Stierle, A.: Nat. Mater. 4, 688 (2005) Neel, N., Kroger, J., Berndt, R.: Appl. Phys. Lett. 88, 163101 (2006) Xiao, W., Ruffieux, P., Mansour, K., Groning, O., Palotas, K., Hofer, W.A., Groning, P., Fasel, R.: J. Phys. Chem. B. 110, 21394 (2006) Ecija, D., Otero, R., Sanchez, L., Gallego, J.M., Wang, Y., Alcamı, M., Martın, F., Martın, N., Miranda, R.: Angew. Chem. Int. Ed. 46, 7874 (2007) Larsson, J.A., Elliott, S.D., Greer, J.C., Repp, J., Meyer, G., Allenspach, R.: Phys. Rev. B. 77, 115434 (2008) Huang, C.-P., Su, C.-C., Ho, M.-S.: Appl. Surf. Sci. 254, 7712 (2008) Zhang, X., Yin, F., Palmer, R.E., Guo, Q.: Surf. Sci. 602, 885 (2008) Li, H.I., Pussi, K., Hanna, K.J., Wang, L.-L., Johnson, D.D., Cheng, H.-P., Shin, H., Curtarolo, S., Moritz, W., Smerdon, J.A., McGrath, R., Diehl, R.D.: Phys. Rev. Lett. 103, 056101 (2009) Wong, S.-S., Pai, W.W., Chen, C.-H., Lin, M.-T.: Phys. Rev. B. 82, 125442 (2010)

Chapter 176

C60 monolayer on semiconductors C. Cepek and A. Goldoni

The field of fullerene adsorbed on semiconductor surfaces is currently still active as reviewed by a recent report [10M]. From the very beginning, the observation in STM and AFM images on various faces of Si substrates of isolated fullerene molecules “scattered” across the surface in the place where they have landed assuming many molecular orientations were considered as the big difference with noble metals – there is no tendency for the molecules to migrate on step edges nor to form close-packed islands on atomic terraces [92L, 92W ] (see Fig. 176.1). This behavior provided the first indications of the presence of a relatively strong, predominantly covalent, fullerene-silicon surface interaction. Moreover, on these Si surfaces, the adsorption site is not always the same.

Fig. 176.1 Occupied state STM image of C60 adsorbed on Si(111)-(7  7). The arrows indicate a reduction in density of states near the molecules (After [94C]. Copyright 1994 American Physical Society)

STM resolved the internal electronic structure, and it has revealed the presence on many different adsorption sites, where the fullerenes have multiple orientations and multiple bonding configurations with the surrounding silicon adatoms [00P2, 99H]. From Si surfaces the molecules do not desorb, but at high temperature they are highly distorted, and at T > 800 K the molecules fragment and react with the Si atoms of the substrate to form SiC [00P].

C. Cepek (*) CNR-IOM, Laboratorio Nazionale TASC, Trieste, Italy e-mail: [email protected] A. Goldoni Elettra Sincrotrone Trieste, Trieste, Italy e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_176

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The observed changes with the C60 coverage and the sensitivity of the fullerene adsorption site to the details of the sample preparation are highlighting the difficulties that are inherent in the precise determination of the bonding sites of this large adsorbate on Si surfaces [94C, 99K, 08H]. The strong C60-Si(111) interaction evident from the STM studies of individual molecules for sub-ML and ML coverage was originally postulated to arise from a charge transfer mechanism driven by the donation of electrons from the partially filled adatom surface states into the LUMO states of the adsorbed C60 molecules [92W]. This proposal that the C60/Si(111)-(7  7) interaction was dominated by a surfacemolecule charge transfer analogous to that observed for many fullerene-on-metal systems – i.e., a transfer of charge from silicon dangling bonds to a “state that looks very much like the LUMO” – was to gain particular currency in the mid-1990s. In the charge transfer model (as for metal-fullerene systems) first discussed by Ohno et al. [91O], among others, there is little or no polarization of charge. On the other hand, lack of charge transfer in the C60/Si(111)-(7  7) system was evidenced by valence band photoemission [99C, 00P, 09G]. Also, near-edge X-ray absorption fine structure (NEXAFS) studies at the carbon K edge have shown, for C60 molecules covalently bonded to the Si(111)-(7  7) surface, a 0.1 eV shift of the π*LUMO-derived transition peak toward higher energy [00B, 01S]. Instead a shift toward lower energy would be expected if partial occupation of the LUMO was occurring due to charge transfer from the surface, so the NEXAFS results support the absence of ionic bonding strongly suggested by photoemission. Similar results were obtained for Si(100) [93K, 93W, 95C, 95G, 96H, 99D, 05C]. In both cases, Si(111) and Si(100), these surfaces covered by one monolayer of C60 do not show reconstruction. Also on Si(100), the C60 molecule is adsorbed without any preference between step edges or nucleation into islands at defect sites, distributed randomly at the place they land with little traveling. After the ML appearance, a sort of local (4  3) superstructure forms that transforms to a (4  4) C60 superstructure after annealing at 650  C. DFT calculations suggest an antiferromagnetic ground state for this (4  4) superstructure, which apparently is in agreement with the vanishing of the Si dimers surface state near the Fermi level observed in photoemission and STS [09L1]. In the case of the Ge(100) and Ge(111) surfaces, the interface formation with C60 molecules has been largely studied via microscopic [94X, 96K, 97D, 96W, 97W, 99K, 98K] and diffraction techniques that provide many information on the growth mode, morphology, and stability of the C60 film. On Ge(111)-c(2  8), the adsorption of C60 apparently behaved in a significantly different manner to the Si surfaces. While on Si surfaces, the ML is not well ordered but simply displays a local order, Xu, Chen, and Creager [94X] determine that 1 ML coverage of C60 on the Ge(111) surface annealed at 250–400  C shows a low-energy electron diffraction (LEED) pattern forming a (3√3  3√3)R30 . However, STM images of this phase indicated that the molecular periodicity as measured from the tunneling microscope images was twice that observed in the LEED pattern. The proposal that the LEED pattern originated from a Ge(111) reconstruction was, however, questioned by Goldoni et al. [00G, 00G1]. Their Ge3d synchrotron radiation core-level photoemission data strongly suggested that the order arose not from the underlying Ge surface but from the presence of four inequivalent molecules within a (2  2)-C60 superlattice bonded to an unreconstructed (i.e., (1  1)) Ge(111) substrate, as shown in Fig. 176.2. Later, high-resolution STM data [08F] clearly show the variation in molecular orientation, which gives rises to the (2  2) order. STM at submolecular resolution allowed distinguishing differently oriented molecules [08F]. In the 3√3  3√3R30 phase, the molecules are arranged in rhomboidal groups of four molecules, named tetramers. The (2  2) periodicity in the domains of homogeneously oriented tetramers is due to the alternating orientation of the molecules within the tetramer, accounting for the observed 3√3  3√3R30 low-energy electron diffraction pattern (see Fig. 176.2). The symmetry of the molecular lattice suggests that the molecules interact only with the first layer of substrate atoms. The orientation of each molecule is mainly determined by the configuration of the substrate atoms in the adsorption site, even though a contribution from the intermolecular interaction is likely present. Moreover, the earlier surface X-ray diffraction data of Kidd et al. [98K] lends considerable support to Goldoni et al. arguments. In that paper it was showed that roomtemperature adsorption of C60 on the Ge(111)-c(2  8) surface lifted the c(2  8) reconstruction, producing a (1  1) periodicity at the C60/Ge(111) interface (deconstruction). On the other hand, the valence band photoemission data are very reminiscent of the changes in HOMO line shape observed for C60 adsorption on Si(111) and Si(100). Importantly, as also observed for C60 adsorbed on Si(111) and Si(100), no filling of a LUMO-derived band is observed in the ultraviolet photoemission spectroscopy (UPS) data [00G,

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00G1]. Taken together, these observations strongly point toward a covalent interaction between C60 and Ge (111), which is already present for room-temperature adsorption (i.e., annealing at higher temperatures is not required to drive covalent bond formation as in Si). Anyway, compared to Si surfaces the interaction with Ge, although looks similar from the point of view of the electronic properties, is rather different from the point of view of the strength of bonding. C60 desorbs from Ge(111), at high temperatures, which recovers its original c (2  8) reconstruction, while C60 brakes on the Si surfaces forming SiC [00P, 01P, 02G1].

Fig. 176.2 (a) The C60 adsorption sites on the Ge(111) surface in the (3√3  3√3)R30 phase in the model of Goldoni et al. [00G]. The big circles indicate the position of the C60 molecules and different colors indicate different sites (After [00G]. Copyright 2000 American Physical Society) (b) High-resolution STM image of the (3√3  3√3)R30 phase where the four C60 different molecules are visible (After [08F]. Copyright 2008 American Physical Society)

On the other hand, before the desorption of C60 on the Ge(111), annealing at 500  C transforms the (3√3  3√3)R30 into another reconstruction called (√13  √13)R14 . In this phase the interaction with Ge is significantly stronger than in the low-temperature phase, and neighboring molecules are oriented with all the molecules having the same adsorption configuration, so that charge-rich regions face charge-poor regions with a hexagon facing the substrate. The symmetry of the molecular lattice suggests that the C60-Ge interaction involves also the atoms of the second layer of the substrate. Figure 176.3 shows the STM [08F] and X-ray diffraction [03T] experiments on (√13  √13)R14 phase. Using grazing incidence X-ray diffraction, Torrelles et al. [03T] investigated the structure of the C60/Ge(111) interface for the (√13  √13)R14 phase. They showed that the substrate reconstructs to form pits of 1 nm diameter, hosting C60 molecules, which are bonded to six Ge atoms in the topmost bilayer and three Ge atoms in the underlying bilayer. This model is in good agreement with the strong increase in the C-Ge valence band peak observed in the UPS measurements [03B] and with the threefold rather than sixfold rotational symmetry of the Ge (111) substrate inferred from STM data [08F].

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Fig. 176.3 (Top) C60/Ge(111)-(√13  √13)R14 phase with high-resolution STM (7.0  7.4 nm2, 2.0 V, 1.8 nA) in which the molecular orbitals are visible. In the inset, the details of a single molecule STM image are shown (left). Sketch of the arrangement of C60 with respect to the (1  1) substrate lattice (black crosses) as deduced by LEED and STM (right) (After [08F]. Copyright 2008 American Physical Society) (bottom) structure of the C60/Ge(111) (√13  √13)R14 phase determined from the x-ray diffraction measurements (After [03T]. Copyright 2003 ESRF)

Although, as compared with adsorption on Si and Ge, there have been rather fewer studies of the interaction of fullerenes with III-V and other compound semiconductor surfaces (like SiC), this area of research has provided key insights into the influence of a substrate on, for example, the electronic structure of adsorbed molecules. Indeed, important observations and analysis of ordered overlayers on GaAs(110) indicated an highly mobility of C60 on this surface [10M, 11N]. The presence of ordered islands already at the very beginning of the C60 adsorption led Li et al. [92L] to argue that C60 molecules have mainly weak van der Waals interactions with the substrate. They also highlighted that no internal structure was observed in the adsorbed molecules due to molecular rotation, which, unlike the case for adsorption on Si and Ge surfaces, is not “quenched” due to strong bonding. Also the growth of C60 fullerene films on InP(001)-(2  4) was studied by spectroscopic and microscopic techniques [01C2, 05E, 06C]. The molecules were found weakly bonded to the substrate, leading to three-dimensional cluster formation of C60 at the initial stages of deposition. Surprisingly, low-energy electron diffraction and scanning tunneling microscopy measurements reveal that further molecular deposition forms a well-ordered single domain film with a face-centered cubic (111) orientation. Structural inhomogeneities and indium clusters, which are the most prevalent defects of the InP(001)-(2  4) surface, do not disturb the C60 growth. The interaction of C60 with the Si-rich 6H–SiC(0001)-(3  3) reconstruction was studied by Bouquet et al. [13B]. By analyzing the C60 adsorbed on (3  3) and on hydrogen-terminated (3  3), they found that in the case of hydrogen-terminated Si, C60 is electronically decoupled from the substrate. Upon annealing a C60 thick film deposited on hydrogenated (3  3) up to 670 K, there is a hint for a possible hydrogen transfer to the C60 molecules. The initially physisorbed molecules then adopt covalent bonding with Si, forming the contact layer. Part of the substrate is already found uncovered at this temperature. By further annealing up to 860 K, all H atoms have desorbed. Finally, at 1100K, the remaining covalently bound C60 has desorbed. Unexpectedly, the structural damages caused by H and C60 deposition and by the successive annealing steps do not prevent a final restoration of the initial SiC (3  3) reconstruction at about 1100K. Moreover, scanning tunneling microscopy studies of the fullerene C60 molecule adsorbed on the silicon carbide SiC(0001)-3  3 surface [13O], combined with density functional theory (DFT) calculations, show that chemisorption of individual C60 molecules occurs through the formation of one bond to one silicon adatom only, in contrast to multiple bond formations on other semiconducting surfaces. Three stable adsorption sites with respect to the Si adatoms of the surface unit cell were found. Comprehensive DFT calculations give different adsorption energies for the three most abundant sites showing that van der Waals forces between the C60 molecule and the neighboring surface atoms need to be considered. The C60

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molecules were observed to form small clusters even at low coverage indicating the presence of a mobile molecular precursor state and non-negligible intermolecular interactions. Symbols and abbreviations Short form

Full form

AFM ML NEXAFS LEED STM DFT LUMO UPS HOMO

atomic force microscopy monolayer near-edge x-ray absorption fine structure low-energy electron diffraction scanning tunneling microscopy density functional theory lowest unoccupied molecular orbital ultraviolet photoelectron spectroscopy highest occupied molecular orbital

References [91O] [92L] [92W] [93K] [93W] [94C] [94X] [95C] [95G] [96H] [96K] [96W] [97D] [97W] [98K] [99C] [99D] [99H] [99K] [00B] [00G] [00G1] [00P] [00P2] [01C2] [01P] [01S] [02G1] [03B] [03T] [05C] [05E]

Ohno, T.R., Chen, Y., Harvey, S.E., Kroll, G.H., Weaver, J.H., Haufler, R.E., Smalley, R.E.: Phys. Rev. B. 44, 13747 (1991) Li, Y.Z., Chander, M., Patrin, J.C., Weaver, J.H., Chibante, L.P.F., Smalley, R.E.: Phys. Rev. B. 45, 13837 (1992) Wang, X.D., Hashizume, T., Shinohara, H., Saito, Y., Nishina, Y., Sakurai, T.: Jpn. J. Appl. Phys. 31, L983 (1992) Kawazoe, Y., Kamiyama, H., Maruyama, Y., Ohno, K.: Jpn. J. Appl. Phys. Part 1. 32(3B), 1433 (1993) Wang, X.D., Hashizume, T., Shinohara, H., Saito, Y., Nishina, Y., Sakurai, T.: Phys. Rev. B. 47, 15923 (1993) Chen, D., Chen, J., Sarid, D.: Phys. Rev. B. 50, 10905 (1994) Xu, H., Chen, D.M., Creager, W.N.: Phys. Rev. B. 50, 8454 (1994) Chen, D., Sarid, D.: Surf. Sci. 329, 206 (1995) Gunster, J., Mayer, T., Brause, M., Maus-Friedrichs, W., Busmann, H.G., Kempter, V.: Surf. Sci. 336, 341 (1995) Hunt, M.R.C.: J. Phys. Condens. Matter. 8, L229 (1996) Klyachko, D., Chen, D.M.: J. Vac. Sci. Technol. B. 14, 974 (1996) Wirth, K.R., Zegenhagen, J.: Surf. Sci. 351, 13 (1996) Dunphy, J.C., Klyachko, D., Xu, H., Chen, D.M.: Surf. Sci. 383, L760 (1997) Wirth, K.R., Zegenhagen, J.: Phys. Rev. B. 56, 9864 (1997) Kidd, T., Aburano, R.D., Hong, H., Gog, T., Chiang, T.-C.: Surf. Sci. 397, 185 (1998) Cepek, C., Schiavuta, P., Sancrotti, M., Pedio, M.: Phys. Rev. B. 60, 2068 (1999) De Seta, M., Sanvitto, D., Evangelisti, F.: Phys. Rev. B. 59, 9878 (1999) Hou, J.G., Jinlong, Y., Haiqian, W., Qunxiang, L., Changgan, Z., Hai, L., Wang, B., Chen, D.M., Qingshi, Z.: Phys. Rev. Lett. 83, 3001 (1999) Kobayashi, K., Yamada, H., Horiuchi, T., Matsushige, K.: Appl. Surf. Sci. 140, 281 (1999) Butcher, M.J., Jones, F.H., Cotier, B.N., Taylor, M.D.R., Moriarty, P., Beton, P.H., Prassides, K., Tagmatarchis, N., Comicioli, C., Ottaviani, C., Crotti, C.: Mat. Sci. Eng. B. 74, 202 (2000) Goldoni, A., Cepek, C., De Seta, M., Avila, J., Asensio, M.C., Sancrotti, M.: Phys. Rev. B. 61, 10411 (2000) Goldoni, A., Cepek, C., De Seta, M., Avila, J., Asensio, M.C., Sancrotti, M.: Surf. Sci. 454–456, 514 (2000) Pesci, A., Ferrari, L., Comicioli, C., Pedio, M., Cepek, C., Schiavuta, P., Pivetta, M., Sancrotti, M.: Surf. Sci. 454, 832 (2000) Pascual, J.I., Go´mez-Herrero, J., Rogero, C., Baro´, A.M., Sa´nchez-Portal, D., Artacho, E., Ordejo´n, P., Soler, J.M.: Chem. Phys. Lett. 321, 78 (2000) Chao, Y., Svensson, K., Radosavkic, D., Dhanak, V.R., Siller, L., Hunt, M.R.C.: Phys. Rev. B. 64, 235331 (2001) Pesci, A., Cepek, C., Sancrotti, M., Ferrari, L., Capozi, M., Perfetti, P., Pedio, M.: Surf. Sci. 482–485, 829 (2001) Sakamoto, K., Kondo, D., Takeda, H., Sato, T., Suga, S., Matsui, F., Amemiya, K., Ohta, T., Uchida, W., Kasuya, A.: Surf. Sci. 493, 604 (2001) Goldoni, A., Larciprete, R., Cepek, C., Masciovecchio, C., El Mellouhi, F., Hudej, R., Sancrotti, M., Paolucci, G.: Surf. Rev. Lett. 9, 741 (2002) Bertoni, G., Cepek, C., Sancrotti, M.: Appl. Surf. Sci. 212, 52 (2003) Torrelles, X., Lee, T.-L., Bikondoa, O., Rius, J., Zegenhagen, J.: ESRF Highlights. 2003, 75 (2003) Cheng, C.-P., Pi, T.-W., Quang, C.-P., Wen, J.-F.: J. Vac. Sci. Technol. B. 23, 1018 (2005) Eremtchenko, M., Doring, S., Temirov, R., Schaefer, J.A.: Phys. Rev. B. 71, 045410 (2005)

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Cherkashinin, G., Krischok, S., Himmerlich, M., Ambacher, O., Schaefer, J.A.: J. Phys. Condens Matter. 18, 9841 (2006) [08F] Fanetti, M., Gavioli, L., Cepek, C., Sancrotti, M.: Phys. Rev. B. 77, 085420 (2008) [08H] Huang, C.-P., Su, C.-C., Ho, M.-S.: Appl. Surf. Sci. 254, 7712 (2008) [09G] Gangopadhyay, S., Woolley, R.A.J., Danza, R., Phillips, M.A., Schulte, K., Wang, L., Dhanak, V.R., Moriarty, P.J.: Surf. Sci. 603, 2896 (2009) [09L1] Lee, J.Y., Cho, J.-H., Kang, M.H.: ChemPhysChem. 10, 334 (2009) [10M] Moriarty, P.J.: Surf. Sci. Rep. 65, 175 (2010), and reference therein [11N] Nishinaga, J., Horikoshi, Y.: J. Cryst. Growth. 323, 135 (2011) [13B] Bocquet, F.C., Ksari, Y., Lin, Y.P., Porte, L., Themlin, J.-M.: Phys. Rev. B. 88, 125421 (2013) [13O] Ovramenko, T., Spillebout, F., Bocquet, F.C., Mayne, A.J., Dujardin, G., Sonnet, P., Stauffer, L., Ksari, Y., Themlin, J.-M.: Phys. Rev. B. 87, 155421 (2013)

Chapter 177

Directing fullerene adsorption via supramolecular templates C. Cepek and A. Goldoni

Chirality is a concept that has fascinated chemists and physicists from the very beginning. Nature uses chirality for the construction of biologically active molecules, which eventually gave place to life. In this regard, the development of chirality on surfaces opens the way to an alternative procedure for the preparation of new chiral compounds and enantio-selective reactions. Furthermore, chiral surfaces show enantio-specific properties of interest, such as, for instance, electron-molecule interactions, polarizationdependent photoemission, and nonlinear optical response. Fullerene C60, because of its intrinsically symmetric nature, is not a good candidate for organization in complex structures, in particular, chiral symmetry breaking. Despite the fact that the chirality of fullerenes has always been considered a fundamental issue, the lack of a general stereo-selective synthetic methodology has restricted the use of enantiopure fullerene derivatives. However, Marco-Martinez and coworkers [13M] have described an asymmetric organo-catalytic synthesis onto fullerenes to obtain new, stable, and versatile chiral carbocyclic derivatives. C60 fullerene has thus been successfully used as a benchmark to develop a novel organo-catalytic system to promote the enantio-selective [ 3 + 2] cyclo-addition of allenoates. The sector rule for the absolute configuration of chiral C60 derivatives has been amended. Density functional theory calculations strongly support the experimental findings for the assignment of the absolute configuration of the new stereo-centers. The use of the curved double bond of fullerene cages as a two-π-electron component in a variety of stereo-selective cyclo-addition reactions represents a challenging goal. As stated below, Xu et al. [06X1] (see Chap. 178[https://doi.org/10.1007/978-3-662-53908-8_178]) have also shown that C60, when coadsorbed with symmetric acridine-9-carboxylic acid (ACA, C2V symmetry) on an epitaxially ordered Ag(111) surface, forms a chiral phase as shown in Fig. 177.1 [05X, 06X1].

C. Cepek (*) CNR-IOM, Laboratorio Nazionale TASC, Trieste, Italy e-mail: [email protected] A. Goldoni Elettra Sincrotrone Trieste, Trieste, Italy e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_177

1

2

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a

b

[101]

[011] [110] 10 2

8 –2

–2 8

2 10

pm 500

0 Fig. 177.1 Proposed models and STM images of the intermixed C60-ACA supramolecular structures for the R and S chiral surfaces. A unit cell is indicated in each panel for reference purposes, along with the matrix notation of the domain (Reproduced with permission from Ref. [05X]. Copyright 2005 American Chemical Society)

On the other hand, this can also be achieved by functionalizing fullerene with added specific groups. Elaboration of fullerenes into the molecular design of host molecules for enantiomeric separation of chiral fullerenes and larger carbon nanoclusters is one of the subjects worth studying. By using a C1-symmetric N-methylporphyrin as an asymmetrically distorted π-electronic component, it was developed the first chiral host heterocyclic porphyrin dimer, containing an asymmetrically distorted N-alkylporphyrin as the first host molecule capable of sensing chiral fullerene C76 capable of discriminating the enantiomers of C76 and also determining its enantiomeric purity by visualization of the relative enantiomeric abundance [06S]. Thus, it was found that the optically inactive, C60-containing poly(phenylacetylene)s bearing crown ether pendants as the amino acid binding site can be transformed into a predominantly one-handed helical conformation upon complexation with optically active amino acids, and the achiral C60 pendants arrange in a helical array with the desired helix sense along the polymer backbone via chiral, non-covalent bonding interactions [04N]. This method will be applicable to other induced helical polymers with the desired pendant in a one-handed helical array (see Fig. 177.2).

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3

Fig. 177.2 Synthesis of poly(1m-co-2n) and schematic representation of macromolecular helicity induction on poly(1m-co-2n) upon complexation with L-alanine. The achiral fullerene and crown ether pendants represented by yellow and blue rings for clarity arrange in a helical array along the one-handed helical polymer backbone induced by non-covalent chiral interactions with L-alanine [04N]. The helix sense is tentative (Copyright 2004 Royal Society of Chemistry)

Another simple way to have chiral systems with fullerenes is to create a chiral host for adsorbing the fullerene molecules. For example, a new hierarchical self-assembling molecular template, which can sizeselectively immobilize fullerene molecules, was fabricated from 1,3,5-tris(10-carboxydecyloxy)benzene (TCDB) and triangle-shaped macrocycles [10S]. It was observed that the two-dimensional hydrogenbonded achiral TCDB network affected by the 3NN-Macrocycle becomes a chiral network. Host and guest molecules both form chiral arrangements with hexagonal empty pores. In addition, fullerenes and other molecules such as coronene can be entrapped in the empty pores or on the 3NN-Macrocycle molecules. This method provides a facile approach to molecularly chiral designed surfaces and the study of fullerene molecular arrays on the single-molecule level. Also, the self-assembly of C60 and pentacene molecules into acceptor/donor heterostructures results in well-ordered and, despite the high degree of symmetry of the constituent molecules, chiral structures [13S]. Pentacene was deposited on Cu(111) up to monolayer coverage, producing the random-tiling phase. Atop this pentacene phase, post-deposited C60 molecules cause rearrangement of the pentacene molecules into domains based on chiral supramolecular “pinwheels.” These two molecules are the highest-symmetry achiral molecules so far observed to coalesce into chiral heterostructures. The chiral pinwheels (composed of one C60 and six pentacene each) may share pentacene molecules in different ways to produce structures with different lattice parameters and degree of chirality. High-resolution scanning tunneling microscopy results, and knowledge of adsorption sites allows the determination of these structures to a high degree of confidence. The measurement of chiral angles identical to those predicted is a further demonstration of the accuracy of the models. van der Waals density functional theory calculations reveal that the pentacene molecules around each C60 are torsionally flexed around their long molecular axes and that there is charge transfer from C60 to pentacene in each pinwheel. In general, therefore, fullerene chiral systems on surfaces have been achieved by following two different strategies: (i) Adsorption of chiral molecules on an achiral surface (direct-transfer chirality) [06S]. (ii) Adsorption of achiral molecules, which became chiral when confined on a solid surface due to the symmetry breaking imposed by the substrate (surface-confined chirality) [10S, 13S]. It is important to note, however, that in this second case, even though the adsorbed molecules become chiral, the surface phase often remains achiral.

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The aforementioned results pave the way for the application of fullerenes in fields where chirality is a key issue such as in biomedical applications, as well as in the thus far less-explored materials science where chirality has recently been shown to impact some physical properties [10H] or organic electronics, and nanoscience, where control of the order and morphology at the nanometer scale are critical issues for achieving better device efficiencies (Figs. 177.3, 177.4, and 177.5).

Fig. 177.3 (a) STM image (28
28nm2, I ¼ 299 pA, V ¼ 649 mV) of the TCDB adlayers on a highly ordered pyrolytic graphite (HOPG) surface. (b) Large-scale STM image (55
55nm2, I ¼ 293 pA, V ¼ 700 mV) of the TCDB networks modulated by 3NN-Macrocycle on a HOPG surface. (c) High-resolution STM image of the type R TCDB/3NN-Macrocycle adlayer (14
14nm2, I ¼ 335 pA, V ¼ 553 mV). (d) High-resolution STM image of the type S TCDB/3NN-Macrocycle adlayer (18
18nm2, I ¼ 467 pA, V ¼ 700 mV). (e) R-type molecular model for the two-component network. (f) S-type molecular model for the two-component network. (g) High-resolution image of the R-type TCDB/3NN-Macrocycle/ coronene networks. A bright circular molecule is observed in the pore, which corresponds to the coronene (13
13nm2, I ¼ 1016 pA, V ¼ 591 mV) (After [10S]. Copyright 2010 WileyVCH Verlag GmbH)

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5

Fig. 177.4 (Left) C60/pentacene/Cu(111) 10
10 nm2 STM topograph (Vgap ¼ 2 V, IT ¼ 1 nA), showing a small hexagonal domain with a large lattice parameter. An individual pentacene molecule is indicated with a dotted box. (Center) Model of the C60/pentacene heterostructure based on a tiling of both chiralities of pinwheels of pentacene molecules, with the unit cell of the structure indicated. (Right) Computed charge density for the unsupported (no Cu(111)) pinwheel structure at the average height of C atoms in the pentacene network; red indicates positive charge accumulation relative to the reference constituent molecules. Electron accumulation is reported in blue (After [13S]. Copyright 2013 American Chemical Society)

Fig. 177.5 (Top) STM image of a small ordered C60 island on Ag:Si(111)-(√3
√3)R30 surface [10M]. Copyright 2010 Elsevier (bottom) STM image of a C60 thin film on the Ag:Si(111)-(√3
√3)R30 surface showing regions of bare surface (top righthand corner), 1 ML coverage, and a two-layer island. Note the high density of defects in the monolayer (After Nakayama et al. [99N]. Copyright 1999 American Physical Society)

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Fig. 177.6 Molecular structure of TPTC single-layer network. (a) Molecular structure of TPTC and arrangements for hydrogen-bonded TPTC dimers with either the long axes of molecules mutually parallel or with one molecule rotated by 60 . (b) Molecular schematic of a section of TPTC network that highlights the hexagonally ordered network of pores. The pore–pore separation (16.6 Å) is shown at the top left. (c) Five possible arrangements of molecules that surround each pore within the TPTC network. The arrangements contain three (pore a), four (pores b, c), five (pore d), or six (pore e) molecules. Examples of each of these pore types are labeled in (b). (d) STM image of an area of TPTC network about 24 h after deposition of C60. The locations of C60 are clearly visible as the bright spots in the image; the underlying TPTC network structure is not visible. Scale bar 10 Å (After [11B]. Copyright 2011 Nature Publishing)

Apart from chirality, there has been an explosion of interest in hydrogen-bonded supramolecular assemblies at surfaces (and, more recently, the question of generating covalently bonded networks has started to be addressed in pioneering experiments by, for example, Grill et al. [07G]). Sanchez et al. [09S] have published an excellent review article on the use of supramolecular assemblies (among other methods) to control the ordering of fullerene on solid surfaces. 2D molecular self-assembly at surfaces usually mediated by weak, non-covalent interactions guides to the formation of nano-scaffold networks with a wide variety of different forms and potential functionalities [02C, 03T1, 04D, 04W2, 05B, 05W, 08H1]. These templates capable of trapping guest molecular species on substrates may have different structures [03T2, 04G1, 04S1, 06S1, 07W, 08M, 09I], for example, close packed [03T2, 08C, 08L1, 09A] or porous [08B, 07S, 06T1]. In many cases the guest molecular species have shown to play a quite different and complex role than the simple passive occupation of voids in the network; instead, in most cases they keenly promote changes of the host-adsorbed molecular framework between different 2D configuration [07W1, 08B1]. One of the first examples was done on the Ag:Si(111) -(√ 3
√3)R30 surface, which has proven to be an excellent substrate for the assembly of intricate and highly ordered supramolecular assemblies and templates [10M]. For example, an ultrathin film of C60 molecules was prepared on a Ag:Si(111) -(√ 3
√3)

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7

R30 substrate [10M] in ultrahigh vacuum, and the use of a scanning tunneling microscope provides excellent controllability for reversible switching between the unbound and bound states of two or three adjacent C60 molecules in the film at room temperature by changing the polarity of an electric field that is locally applied to any designated position. Using a combination of adsorbed perylene tetra-carboxylic di-imide (PTCDI) and melamine molecules, Theobald et al. [03T2] exploited hydrogen-bonded interactions to form a 2D honeycomb network on the Ag:Si(111)-(√3
√3)R30 surface. Subsequent deposition of C60 molecules on this hydrogen-bonded template led to the formation of fullerene heptamers trapped inside the nanoscale pores formed by the PTCDI-melamine network. Following their demonstration of C60 confinement within the pores of a PTCDI-melamine network [03T2], the same group [05T1] went on to study the possible trapping of aggregates of larger C84 fullerenes. They found that, monitoring the nucleation of C84 clusters within the pores, the growth of the clusters requires a rearrangement of the adsorbed PTCDI-melamine molecules, leading to a transition between several types of cluster ordering. The important result of this work was that growth of fullerene clusters in a confined geometry leads to new molecular structures. The further demonstration that nonplanar guest molecules may be used to promote the formation of supramolecular bilayers opens up a wide range of new possibilities for the formation of functional three-dimensional supramolecular architectures. Moreover, the reversible nature of the growth process highlights the delicate balance of interactions required for perpendicular growth and provides an example of a responsive system in which guest exchange leads to changes in dimensionality. Similar work was done by Blunt et al. [11B] (Fig. 177.6) where an adsorbed monolayer of the molecule p-terphenyl-tetracarboxylic acid (TPTC) on HOPG forms an extended array of hexagonal pores separated by 16.6 Å and stabilized by in-plane hydrogen bonding. C60 can be trapped in these hexagonal voids. Furthermore, it was found that the trapping of C60 and growth of the second layer of the supramolecular framework are codependent, which confirms a cooperative addition of host and guest species. Significantly, the growth of the bilayer network may be reversed subsequently by the addition of coronene, a planar molecule that displaces the C60 and destabilizes the bilayer structure, which leads to reversion to a monolayer arrangement. Overall, this system provides an example of a reversible transformation between a planar and a nonplanar supramolecular network, an important step toward the controlled self-assembly of functional, three-dimensional, surface-based supramolecular architectures. The use of a nonplanar guest that, when trapped in a two-dimensional framework on a surface, promotes a new mode of supramolecular growth into the third dimension perpendicular to the surface. It is also interesting to consider why similar systems into which C60 is introduced as a guest do not lead to bilayer or multilayer growth. A possible explanation is that such stacking is energetically unfavorable and inhibits fullerene-mediated multilayer formation in trimesic acid and related supramolecular arrays [04G1, 07Z]. Therefore, in general, organic molecules previously deposited on a substrate can be used as new templates for the formation of 2D-ordered fullerene superstructures. On the other hand, planar as well as concave host organic molecules, namely, involving macrocyles, have been successfully used to accommodate fullerenes (C60 and C70) and fullerene derivatives in which the presence of alkyl chains or functional groups has a strong impact on the induced order. Compared to the fullerene monolayers on metal and semiconductor, where modification of the substrate induced by fullerenes may be provoked, the different strategies followed in the construction of hierarchical assemblies of fullerene arrays clearly show that it is first necessary the decoration the solid surface with suitable organic molecules acting as templates. These 2D superlattices are thus new scenarios for testing, for instance, nonconventional enantiomeric synthesis (chiral surface) or unraveling the fundamental electron transfer process in intermixed layers for the production of optoelectronic devices at a nanometer scale. Not only molecular templates but also atomic monolayer, as the hexagonal BN monolayer grown on Ni (111), may be good template where C60 can grow with some peculiar properties. Muntwiler at al. [05M] have shown that the monolayer of h-BN on Ni(111) plays a crucial role, being an ultimately thin, atomically flat, metal-insulator interface, on the adsorbed C60 monolayer. It provides the charge to C60 monolayer by tunneling, and it does not bind the C60 molecules strongly. This charge redistribution is triggered by the onset of molecular rocking motion, i.e., by orientation-dependent tunneling between the LUMO of C60 and

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the substrate: in parallel to the orientational phase transition, the occupancy of the LUMO – in the cold state almost empty – changes by 0.4  0.1 electrons. Therefore, there is the observation of a temperature-driven change in C60 molecular orbital binding energies parallel to the work function and a strong change in LUMO occupancy of C60 on h-BN/Ni(111) that coincide with the onset of molecular rocking. The charge transfer is triggered by an anisotropic tunneling matrix element of the C60 LUMO with the underlying substrate. The magnitude of the charge transfer is an indication for strong electron-phonon interactions. This effect might open the door for the application of the orientation dependence of the tunneling across molecules for electronic and spintronic switches. Symbols and abbreviations Short form

Full form

ACA ML TCDB HOPG STM DFT 2D PTCDI LUMO TPTC NN

acridine-9-carboxylic acid monolayer 1,3,5-tris (10-carboxydecyloxy) benzene highly ordered (or oriented) pyrolytic graphite scanning tunneling microscopy density functional theory two-dimensional perylene tetracarboxylic diimide lowest unoccupied molecular orbital p-terphenyl-tetracarboxylic acid 1-nitronaphtalene

References [99N] [02C] [03T1] [03T2] [04D] [04G1] [04N] [04S1] [04W2] [05B] [05M] [05T1] [05W] [05X] [06S] [06S1] [06T1] [06X1] [07G] [07S] [07Z] [07W] [07W1] [08B] [08B1] [08C] [08L1] [08H1] [08M] [09A] [09I]

Nakayama, T., Onoe, J., Takeuchi, K., Aono, M.: Phys. Rev. B. 59, 12627 (1999) Carroll, R.L., Gorman, C.B.: Angew. Chem. Int. Ed. 41, 4378 (2002) Thomas, G., Kamat, P.V.: Acc. Chem. Res. 36, 888 (2003) Theobald, J.A., Oxtoby, N.S., Phillips, M.A., Champness, N.R., Beton, P.H.: Nature. 424, 1029 (2003) Daniel, M.-C., Astruc, D.: Chem. Rev. 104, 293 (2004) Griessl, S.J.H., et al.: J. Phys. Chem. B. 107, 11556 (2004) Nishimura, T., Ohsawa, S., Maeda, K., Yashima, E.: Chem. Commun., 646 (2004) Stepanow, S., et al.: Nat. Mater. 3, 229 (2004) Wassel, R.A., Gorman, C.B.: Angew. Chem. Int. Ed. 43, 5120 (2004) Balzani, V.: Small. 1, 278 (2005) Muntwiler, M., Auwärter, W., Seitsonen, A.P., Osterwalder, J., Greber, T.: Phys. Rev. B. 71, 121402(R) (2005) Theobald, J.A., Oxtoby, N.S., Champness, N.R., Beton, P.H., Dennis, T.J.S.: Langmuir. 21, 2038 (2005) Whitesides, G.M.: Small. 1, 172 (2005) Xu, B., Tao, C., Cullen, W.G., Reutt-Robey, J.E., Williams, E.D.: Nano Lett. 11, 2207 (2005) Shoji, Y., Tashiro, K., Aida, T.: J. Am. Chem. Soc. 128, 10690 (2006) Schull, G.: Adv. Mater. 18, 2954 (2006) Tahara, K., et al.: J. Am. Chem. Soc. 128, 16613 (2006) Xu, B., Tao, C., Williams, E.D., Reutt-Robey, J.E.: J. Am. Chem. Soc. 128, 8493 (2006) Grill, L., Dyer, M., Lafferentz, L., Persson, M., Peters, M.V., Hecht, S.: Nat. Nanotechnol. 2, 687 (2007) Stepanow, S., et al.: Angew. Chem. Int. Ed. 46, 710 (2007) Zhou, H., et al.: J. Am. Chem. Soc. 129, 13774 (2007) Wahl, M., Stohr, M., Spillmann, H., Jung, T.A., Gade, L.H.: Chem. Commun., 1349 (2007) Wu, D., Deng, K., He, M., Zeng, Q., Wang, C.: ChemPhysChem. 8, 1519 (2007) Blunt, M.O., et al.: Science. 322, 1077 (2008) Blunt, M., et al.: Chem. Commun., 2304 (2008) Chen, W., et al.: J. Am. Chem. Soc. 130, 12285 (2008) Li, M., et al.: Angew. Chem. Int. Ed. 120, 6819 (2008) Heimel, G., Romaner, L., Zojer, E., Bredas, J.-L.: Acc. Chem. Res. 41, 721 (2008) Madueno, R., Raisanen, M.T., Silien, C., Buck, M.: Nature. 454, 618 (2008) Adisoejoso, J., et al.: Angew. Chem. Int. Ed. 48, 7353 (2009) Ivasenko, O., et al.: Chem. Commun., 1192 (2009)

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[09S] [10H] [10M] [10S] [11B] [13M] [13S]

9

Sanchez, L., Otero, R., Gallego, J.M., Miranda, R., Martın, N.: Chem. Rev. 109, 2081 (2009) Hizume, Y., Tashiro, K., Charvet, R., Yamamoto, Y., Saeki, A., Seki, S., Aida, T.: J. Am. Chem. Soc. 132, 6628 (2010) Moriarty, P.J.: Surf. Sci. Rep. 65, 175 (2010), and reference therein Shen, Y.-T., Deng, K., Zeng, Q.-D., Wang, C.: Small. 6, 76 (2010) Blunt, M.O., Russell, J.C., del Carmen Gimenez-Lopez, M., Taleb, N., Lin, X., Schroder, M., Champness, N.R., Beton, P.H.: Nat. Chem. 3, 74 (2011) Marco-Martinez, J., Marcos, V., Reboredo, S., Filippone, S., Martin, N.: Angew. Chem. Int. Ed. 52, 5115 (2013) Smerdon, J.A., Rankin, R.B., Greeley, J.P., Guisinger, N.P., Guest, J.R.: ACS Nano. 7, 3086 (2013)

Chapter 178

Co-adsorbed fullerene systems and the formation of heterojunction layers at a nanometer scale C. Cepek and A. Goldoni

One further step is the construction of molecular self-assembled devices by using co-adsorbed systems, which offer even broader possibilities for structure and property control. Only recently fullerenes have been mixed with other appealing molecules, which nicely complement them from a geometric and electronic point of view. In these systems, it has been shown that the adlayer structures formed depend on the ratio of the molecular components and their degree of coverage, resulting in a variety of different molecular structures and properties. The peculiar electrochemical and photophysical properties of fullerene molecules as electron acceptor make them promising candidates for the construction of two- and three-dimensional organic-based materials, in particular solar cells, when assembled with donor molecules. Therefore, the rational design of co-adsorbed systems results in outstanding achievements such as the generation of chiral surfaces, also described for other classes of organic molecules, or the organization of intermixed layers of electron donor and acceptor components. As an outstanding example of the above concepts, Vilmercati et al. [06V, 09V] have shown that co-adsorbing C70 and Zn-tetra-phenyl porphyrin (Zn-TPP) on Ag(111) induces the self-assembly of electron-rich flat aromatic molecules at the curved surface of C70, thus enhancing the chromophore interaction and forming a supramolecular multilayer donor-acceptor structure. While the ground-state electronic spectra almost reflect a simple summation of Zn-TPP and C70 components, the excited-state electrons at the porphyrin macrocycle can rapidly delocalize to the fullerene. The excited charge transfer time scale is faster than 1–2 fs. Another example was shown by Konarev et al. [10K], where a two-dimensional organic metal based on fullerene and N-methyldiazabicyclooctane cation and triptycene was formed, in which fullerene radical anions are closely packed in a hexagonal 2D array. This is the first 2D metal among the reported fullerene conductors, and it exhibits a metallic state down to 1.9 K, which can be explained by the 2D character of the electronic structure. Moreover, the Williams group [06X1] have shown, by using a co-adsorbed system formed by acridine-9carboxylic acid and fullerene C60 on Ag(111), that the formation of the intermixed structures depends on the balance between C60-ACA-Ag(111) interactions. Thus, upon changing the initial ACA coverage, two different C60:ACA cooperative structures were formed (a chiral intermixed structure and a chainlike C60 structure). The chiral C60:ACA structure was obtained at critical local coverage of 0.4 ML of ACA, whereas the chain C60:ACA structure was related with a ACA dimer phase. Thus, important organization patterns, such as chirality or 1D chains, can be tuned as a function of the coverage of the predeposited ACA structures. In a recent study, it was carried out the growth of a self-assembled lateral superlattice of 2-[9-(1,3-dithiol2-ylidene)anthracen-10(9H)-ylidene]-1,3-dithiole (exTTF) as an electron donor and PCBM as an electron acceptor on Au(111) under UHV conditions at variable temperature [07O]. The superlattice areas were determined to be 10–20 nm in width. The aim of this work was to use the nanometer-scale pattern provided by the well-known “herringbone” reconstruction of Au(111) surface as a template to steer the growth of the C. Cepek (*) CNR-IOM, Laboratorio Nazionale TASC, Trieste, Italy e-mail: [email protected] A. Goldoni Elettra Sincrotrone Trieste, Trieste, Italy e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_178

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molecular species into 1D molecular nanostructures with sizes in good agreement with the exciton diffusion lengths (10–20 nm), as required for highly efficient photovoltaic solar cells. The results reveal that the lateral segregation of donor/acceptor blends into a long-range-ordered superlattice where the appropriate morphology is feasible. PCBM, which upon vacuum deposition on Au(111) leads to a coverage-dependent transition from substrate-controlled to (weak) H-bond-controlled self-assembly, was deposited from two separate glass crucibles resistively heated at 400 and 500 K, respectively, onto the Au(111) substrate, which was held at room temperature. Addition of 0.6 ML of exTTF on top of the PCBM-based nanoscale spider-web structure results in the formation of two distinct areas observed by STM at room temperature: (i) A well-ordered area of exTTF where the elbow-free herringbone reconstruction underneath can be recognized as a long-period corrugation of the molecular rows. (ii) A disordered area reminiscent of the high-coverage PCBM phase. This singular nanoscale phase segregation has been accounted for by the low tendency of exTTF and PCBM to mix, the high mobility of PCBM molecules at room temperature (used in the experiment), and the stronger interaction of exTTF with the gold surface, in contrast to PCBM, which behaves as a 2D gas. Thus, the morphology and phase separation remain almost intact upon increasing the coverage, forming exTTF and PCBM stripes of around 20 nm, which compares well with typical exciton diffusion lengths. These morphological features fulfill the requirements for the construction at the nanometer scale of efficient photovoltaic solar cells, and in a broader sense, they are of interest for the study of other optoelectronic devices where morphology between photo- and electro-active donor and acceptor species plays a leading role. It is of interest the development of molecular systems that imitate the reaction center in natural plants. Porphyrin and fullerene donor-acceptor complexes have been extensively studied for their photoinduced charge transfer characteristics. Porphyrins are good light absorbers and, when combined with fullerenes, optimal donors. Fullerenes are excellent charge acceptors and optimal electron transporters. Thus, the electronic structure of ground states and a few charge-transfer excited states of many porphyrinfullerene molecular constructs were analyzed using density functional theory at the all-electron level using large polarized basis sets. The donors are based on porphyrins, and the acceptor molecules are C60-based and C70-based systems [99B, 01K, 03W, 05B1, 06V]. Many of these complexes are experimentally studied, which are both bonded and nonbonded (with a face-to-face interaction between the porphyrin and the fullerene) systems. For nonbonded systems the close contact of fullerenes and porphyrins arises from favorable van der Waals attraction of the curved π surface of fullerenes to the almost planar π surface of porphyrins [99B, 03W, 05B1, 06V]. In contrast to the covalently dyads or porphyrin-fullerene conjugates (shown in Fig. 178.1) [00S, 01K, 02S, 03K, 04H, 14K], these kinds of systems may have a truly non-covalent association of chromophores, which closely mimic the tetrapyrrolic special pairs and antenna pigments of biological photosynthetic reaction centers. Therefore, fullerenes are spontaneously attracted by porphyrins and metalloporphyrins, so they can easily form self-assembled supramolecular systems.

Fig. 178.1 Structure of the C60-zinc chlorine electron donor-acceptor conjugate (After [14K]. Copyright 2014 Wiley-VCH Verlag GmbH)

These new 2D organic nanostructures represent outstanding and alternative realistic possibilities for the preparation of nanoelectronic devices. The examples collected above clearly reveal that the preparation of well-organized organic donor/acceptor nanojunction arrays is feasible as shown in several investigations carried out on different donors and C60 as a paradigmatic case of electron acceptor molecule. For example, a well-ordered organic donor/acceptor hetrojunction array formed by self-assembly of fullerene C60 on the

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Co-adsorbed fullerene systems and the formation of heterojunction layers at a nanometer. . .

3

molecular nanotemplate formed by nanostripes of p-sexiphenyl (6P) (as an electron donor) on Ag(111) has been reported by Chen et al. [08C1]. In this case, STM studies reveal the formation of C60/6P arrays with a well-defined 2D arrangement. A further annealing process on the molecular superstructure formed by the C60/6P at 380 K leads to the insertion of C60 linear chains between the 6P nanostripes, thus resulting in the formation of a periodic lateral nanostructure constituted by C60 and 6P molecules. Further donor/acceptor overlayer heterojunctions can be formed with other acceptor organic molecules, like coronene, phthalocyanines, graphene, etc. [07Y, 11Y, 14K, 14S]. For example, supramolecularly assembled fullerenes, including C60, C70, a C60-C60 dumbbell dimer, a C60-C70 cross-dimer, and a C60 triangle trimer, have been realized on the coronene-modified Au(111) surface. STM images clearly demonstrated details of the electrochemical structural change of the coronene adlayer, of the internal structure and packing arrangement of those fullerenes on a clean Au(111) surface, and those of supramolecular assemblies on the coronene-modified Au(111) surface. Epitaxial growth of fullerenes on the Au(111) surface was found to be strongly influenced by the underlying coronene adlayer: the control of adlayer structure is very important for the film formation. Especially the C60 assembly on the coronene-modified Au(111) surface provided a unique nanostructure of the honeycomb array. The trapping reaction of C60 molecules into cavities in the honeycomb array suggested the presence of a special electronic state. Thus, the coronene adlayer plays an important role not only in the control of the donating ability of the Au surface but also in the selective recognition of the difference in shape and/or electronic structure of fullerenes (Fig. 178.2).

Fig. 178.2 (a) Proposed model for the honeycomb array. (b) Schematic illustration of electron donation from coronene molecules to the Au substrate. (c) Schematic illustration of a trapped C60 molecule in the honeycomb cavity. (Bottom) Typical STM images, obtained at 0.82 V of C60 honeycomb arrays on a coronene-modified Au(111) surface (After [07Y]. Copyright 2007 American Chemical Society)

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C. Cepek and A. Goldoni

Moreover, in some cases the obtained overlayer structures have new electronic properties, like metallicity in the second or third organic layer separated by the metallic substrate. For example, the metallicity was put forward for organic fullerene heterojunctions in several cases. For instance, Niederhausen et al. [12N] investigated C60 (sub)monolayer films, which were prevented from direct electronic coupling with the Ag(111) substrate by a two-layer thick α-sexithiophene (6T) spacer. The authors unambiguously showed that an integer charge transfer from the metal to a fraction of the C60 layer is caused by the interface dipole, while the 6T bilayer remains neutral. Regarding organic-organic heterojunctions, it is commonly believed that interfaces between different organic materials are generally dominated by very weak van der Waals interaction, an assumption that was proven to be incorrect by the abovementioned work [12N] and also by a recent work of Stadtmüller and coworkers [12S]. In the latter the authors demonstrated the evidence for a partly chemisorptive bonding between single monolayers of copper(II)-phthalocyanine (CuPc) and 3,4,9,10-perylene-tetracarboxylicdianhydride (PTCDA) that are stacked on Ag(111). In particular they revealed a gradual filling of the LUMO orbital of 1 ML PTCDA/Ag(111), already partly filled by the adsorption on the metal surface, upon further CuPc adsorption. The LUMO of the CuPc molecules was involved in the charge transfer to the PTCDA. Finally, a charge transfer from the metal to the hexaaza-triphenylene-hexacarbonitrile (HATCN) layer was observed when the HATCN layer was deposited atop of a monolayer of tris(8-hydroxyquinolinato)aluminum (Alq3) on Ag(111) [11A]. These works suggest that doped organic molecular layers, decoupled from the metal surface, can be assembled without the use of dopants, such as alkali atoms, just by forming the suitable heterojunctions on metal substrates or when the interaction between the organic molecules has also a chemisorption character. Recently, Caputo et al. [14C], growing an heterojunction multilayer film made by subsequent depositions of C60 and picene layers on Ag(111), showed that it is possible to obtain a metallic system without any further doping. Moreover, exploiting the huge difference of the electron affinities between the two molecular systems, it was also shown that doping the heterojunctions with potassium, a fulleride metallic state is observed independently on dopant concentration. This may open the way toward novel molecular heterojunction structures that may create new electronic phases in strongly correlated molecular materials. Symbols and abbreviations Short form

Full form

TPP 2D ACA ML 1D exTTF

tetra-phenyl porphyrin two-dimensional acridine-9-carboxylic acid monolayer one-dimensional 2-[9-(1,3-dithiol-2-ylidene)anthracen-10(9h)-ylidene]-1,3dithiole phenyl-c60butyric acid methyl scanning tunneling microscopy 3,4,9,10-perylene-tetracarboxylic-dianhydride lowest unoccupied molecular orbital

PCBM STM PTCDA LUMO

References [99B] [00S] [01K] [02S] [03K]

Boyd, P.D., et al.: J. Am. Chem. Soc. 121, 10487 (1999) Sun, D., Tham, F.S., Reed, C.A., Chaker, L., Burgess, M., Boyd, P.D.: J. Am. Chem. Soc. 122, 10704 (2000) Konarev, D.V., et al.: Chem. Eur. J. 7, 2605 (2001) Schuster, D.I., Jarowski, P.D., Kirscher, A.N., Wilson, S.R.: J. Mater. Chem. 12, 2041 (2002) Kesti, T., Tkachenko, N., Yamada, H., Imahori, H., Fukuzumi, S., Lemmetyinen, H.: Photochem. Photobiol. Sci. 2, 251 (2003) [03W] Wang, Y.-B., Lin, Z.: J. Am. Chem. Soc. 125, 6072 (2003) [04H] Hasobe, T., et al.: J. Phys. Chem. B. 108, 12865 (2004) [05B1] Basiuk, V.A.: J. Phys. Chem. A. 109, 3704 (2005)

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[06V]

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Vilmercati, P., Castellarin-Cudia, C., Larciprete, R., Cepek, C., Zampieri, G., Sangaletti, L., Pagliara, S., Verdini, A., Cossaro, A., Floreano, L., Morgante, A., Petaccia, L., Lizzit, S., Battocchio, C., Polzonetti, G., Goldoni, A.: Surf. Sci. 600, 4018 (2006) [06X1] Xu, B., Tao, C., Williams, E.D., Reutt-Robey, J.E.: J. Am. Chem. Soc. 128, 8493 (2006) [07O] Otero, R., Ecija, D., Fernandez, G., Gallego, J.M., Sanchez, L., Martın, N., Miranda, R.: Nano Lett. 7, 2602 (2007) [07Y] Yoshimoto, S., Tsutsumi, E., Narita, R., Murata, Y., Murata, M., Fujiwara, K., Komatsu, K., Ito, O., Itaya, K.: J. Am. Chem. Soc. 129, 4366 (2007) [08C1] Chen, W., Zhang, H.L., Huang, H., Chen, L., Shen Wee, A.T.: Appl. Phys. Lett. 92, 193301 (2008) [09V] Vilmercati, P., Castellarin-Cudia, C., Gebauer, R., Ghosh, P., Lizzit, S., Petaccia, L., Cepek, C., Larciprete, R., Verdini, A., Floreanos, L., Morgante, A., Goldoni, A.: J. Am. Chem. Soc. 131, 644 (2009) [10K] Konarev, D.V., Khasanov, S.S., Otsuka, A., Maesato, M., Saito, G., Lyubovskaya, R.N.: Angew. Chem. Int. Ed. 49, 4829 (2010) [11A] Amsalem, P., Niederhausen, J., Frisch, J., Wilke, A., Br€ oker, B., Vollmer, A., Rieger, R., Müllen, K., Rabe, J.P., Koch, N.: J. Phys. Chem. C. 115, 17503 (2011) [11Y] Yu, D., Park, K., Durstock, M., Dai, L.: J. Phys. Chem. Lett. 2, 1113 (2011) [12N] Niederhausen, J., Amsalem, P., Wilke, A., Schlesinger, R., Winkler, S., Vollmer, A., Rabe, J.P., Koch, N.: Phys. Rev. B. 86, 081411(R) (2012) [12S] Stadtmüller, B., Sueyoshi, T., Kichin, G., Kr€ oger, I., Soubatch, S., Temirov, R., Tautz, F.S., Kumpf, C.: Phys. Rev. Lett. 108, 106103 (2012) [14C] Caputo, M., Panighel, M., Petaccia, L., Struzzi, C., Alijani, V., Coreno, M., de Simone, M., Fratesi, G., Di Santo, G., Goldoni, A.: Phys. Rev. B, 001400(R) (2014, in press) [14K] Kirner, S., Sekita, M., Guldi, D.M.: Adv. Mater. 26, 1482 (2014) [14S] Satoh, N., Katori, S., Kobayashi, K., Matsushige, K., Yamada, H.: Jpn. J. Appl. Phys. 53, 05FY03 (2014)

Part X

Surfaces at Metal-Electrolyte Interfaces

Chapter 179

Introduction to surfaces at metal-electrolyte interfaces M. Nowicki and K. Wandelt

Surfaces at Metal-Electrolyte Interfaces This Part is divided into an introductory chapter (comprising 15 sections) followed by 55 data chapters. After an introductory text, in Sects. 179.1 to 179.4 some basic properties of metal surfaces, aqueous electrolytes and them requirement for the experimental techniques sensitive to the metal surface in contact with a solution are recalled. In Sects. 179.5–179.7 the standard models of the “electrochemical doublelayer” are reviewed. Subsequently (Sects. 179.8–179.11) a comprehensive list of in situ as well as ex situ methods is given without any description of how they work (Tables 179.1–179.3). This would go beyond the scope of this Part. Instead selected references giving a basic introduction to the various techniques are also included in Tables 179.1–179.3. Next, sample preparation methods are shortly described (Sects. 179. 12–179.14). Finally, concluding remarks follow (Sect. 179.15). In Chaps. 180–197, we will present and discuss in detail results obtained for the interaction of simple anions with copper single crystal electrodes, namely, Cu(100), Cu(111), and Cu(110), immersed in the respective aqueous electrolyte solution in order to demonstrate a present state of “electrochemical surface science.” Copper has been termed “the metal of the twenty-first century,” in particular due to its ubiquitous role in the production of modern electronic devices (e.g., the electrochemical “Damascene Process” of onchip wiring). In particular, the interaction of halide ions (Cl
, Br
, I
), and molecular perchlorate (ClO4
) and sulfate (SO42
) anions with these copper surfaces will be discussed in great detail. The last Chaps. 198–233 consist of a broad, but still not exhaustive, compilation of results for electrified single crystal silver, gold, and platinum surfaces (198–208, 209–222, 223–233), respectively in contact with chloride, bromide, iodide, perchlorate, and sulfate anion containing solutions. Interfaces are the locations of gradients, and gradients are a driving force for processes. These processes, of course, depend on the properties of the two phases on either side of the interface as well as on external parameters like temperature, pressure, electric potential, etc. Due to mutual interactions between the atoms and molecules across the interface, it appears intuitively clear that the properties of both phases immediately next to the interface are different from those further away in the bulk regions of both phases. For instance, adsorption of molecules from a gas phase on a solid surface changes their density, their degrees of freedom, as well as their electronic properties decisively, and their interaction with the surface changes also the properties of the surface atoms. Likewise the electrostatic attraction between a metal electrode and ions from a surrounding aqueous electrolyte causes “electro-adsorption” which in the extreme case results in an extensive discharging of the ions and the sacrifice of their hydration sphere on the one side, and, for instance, structural changes of the metal surface on the other side.

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_179

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Reference for the adsorption-induced changes of the solid surface are its properties prior to interaction with anything, thus its properties in vacuum. It is the incredible success story of the so-called surface science approach, i.e., a research strategy based on the use of well-defined single-crystal surfaces under ultrahigh vacuum (UHV) conditions ( 2 (at intermediate potentials, see Chap. 183[https://doi.org/10.1007/978-3-662-53908-8_183] and Figs. 181.2c and 183.2[https://doi.org/ 10.1007/978-3-662-53908-8_183]). Due to the higher density of adsorption sites on the Cu(111) surface already, bromide forms such incommensurate structures and even chloride at very high potentials. c(p × 2)-I

c(2 x 2)-Br

c(2 x 2)-Cl

a

b

c

d

e

f

Cu(100)

Cu(111)

c(p × √3)-Cl √

c(p × √ √3)-Br

c(p × √3)-I √

Fig. 181.2 In situ STM images of a Cu(100) electrode surface covered at positive potentials with (a) a c(2  2)Cl , (b) a c (2  2)Br , and (c) a uniaxially incommensurate c(p  2)I – anion layer, and in situ STM images of a Cu(111) electrode surface covered at positive potentials with (d) a uniaxially incommensurate c(p  √3)Cl , (e) a uniaxially incommensurate c (p  √3)Br , and (f) a uniaxially incommensurate c(p  √3)I – anion layer. The size of the images can be deduced from the nearest-neighbor distance of copper, 0.256 nm

Symbols and abbreviations Short form

Full form

STM

scanning tunneling microscopy

Chapter 182

Hydrohalic acid interaction with copper surfaces: Cu(100) – chloride and bromide M. Nowicki and K. Wandelt

A cyclic voltammogram of Cu(100) in 10 mM HCl solution is shown in Fig. 182.1. The double-layer regime between the hydrogen evolution reaction (HER) at the cathodic limit and the copper dissolution reaction (CDR) at the anodic end is surprisingly structureless and shows no clear chloride adsorption and only a weak, broad cathodic desorption feature around
200 mV (RHE). The only cathodic peak near +200 mV corresponds to the copper redeposition reaction:

Fig. 182.1 Steady state cyclic voltammogram of Cu (100) in 10 mM HCl solution. The voltammogram is limited at high (anodic) potentials by the oxidative copper dissolution and at low (cathodic) potentials by the decomposition of the electrolyte and hydrogen evolution. The current wave in negative scan direction near E ¼ +200 mV corresponds to the copper redeposition. At the bottom, the potential regimes of different chloride coverage and order are indicated

Cu2þ þ e
⇄Cuþ Cuþ þ e
⇄Cu



In situ STM images, however, prove that chloride does adsorb spontaneously within the double-layer regime forming a highly ordered structure as shown in Figs. 181.2a[https://doi.org/10.1007/978-3-66253908-8_181] and 182.2a. Comparison of this structure with that of the bare Cu(100) surface taken immediately after Cl
desorption (Fig. 182.2b) reveals that the adsorbate lattice has a √2-times wider, centered and 45 rotated unit cell, termed (√2  √2)R45 - or in short c(2  2) structure. The chloride species, thus, form a commensurate surface lattice and reside in fourfold hollow sites of the Cu(100) surface as verified by X-ray diffraction studies (see Chap. 184[https://doi.org/10.1007/978-3-662-53908-8_ M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_182

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184]). The surface coverage of the chloride layer is 0.5 ML, and the nearest Cl-Cl distance is √2aCu ¼ 0.362 nm (larger than the Van der Waals bonding distance).

Fig. 182.2 In situ STM images of a chloride covered Cu(100) electrode surface. (a) Atomically resolved c(2  2 )-Cl structure, (b) correlation of the c(2  2) structure (upper half) with the bare Cu(100) lattice (lower half), (c) large-scale morphology of the chloride covered Cu(100) surface, note the long, straight, and orthogonal step-edges, (d) step-edges stabilized by densely packed Cl
rows (After Ref. 7).

The specific adsorption of the chloride ions is also accompanied by a significant change of the surface morphology as can be seen in panels c and d of Fig. 182.2. Compared to the frizzy structure of step edges of adsorbate-free copper surfaces (see, e.g., Fig. 180.2[https://doi.org/10.1007/978-3-662-53908-8_180]), chloride adsorption leads to a strict alignment of the steps in [010] and [001] direction, i.e., in the direction of densely packed chloride rows (Fig. 182.2d). In fact, the edges are stabilized by chloride rows at the upper step edge and may run straight and kink-free for hundreds of nanometers until they meet another step in orthogonal direction. This impressive ordering and step faceting is observed after cycling the surface several times between high and low potentials and is the result of significant copper mass transport in the course of the so-called electrochemical annealing (see Sect. 179.13[https://doi.org/10.1007/978-3-66253908-8_179]). During the positive scan low-coordinated, i.e., particularly reactive, Cu atoms are dissolved as CuCl2
complexes, which are decomposed and redeposited in the reverse scan at energetically favorable sites, i.e., vacancies and kinks, which eventually lead to the formation of defect-free step edges. Also bromide anions adsorb specifically on the Cu(100) surface up to a coverage of θBr ¼ 0.5 ML. The cyclic voltammogram in 10 mM HBr solution as shown in Fig. 182.3 looks very similar to that in Fig. 182.1. Like chloride, bromide forms a c(2  2) structure (Fig. 181.2a, b[https://doi.org/10.1007/978-3-662-53908-8_181]) in both the electrolyte and UHV [1–4]. The appearance of the c(2  2) structure happens already at less positive potentials than chloride; the adsorption of bromide is thus less kinetically hindered due to its lower hydration energy. Bromide adsorption/desorption overlaps actually with the hydrogen evolution reaction, i.e., the HER

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Hydrohalic acid interaction with copper surfaces: Cu(100) – chloride and. . .

3

Current density [mA/cm2]

begins already on the bromide-covered surface, suggesting also a strong copper-bromide bond. Unlike with chloride, it is not possible to register in situ STM images of the bromide-free surface in the bromide-containing electrolyte. The hydrogen evolution reaction is actually enhanced on the Br covered Cu(100) surface due to the so-called Frumkin effect [5] according to which the high density of specifically adsorbed negative ad-species increases the concentration of cations, here protons, in the diffuse Helmholtz layer.

Cu dissolution 0.00

Cu redeposition H2 evolution

-0.05

-800

-600

-400

-200

0

Potential E vs Ag/AgBr [mV]

200

Fig. 182.3 Steady-state cyclic voltammogram of Cu (100) in 10 mM HBr solution

Figure 182.4 shows again (a) the large-scale morphology and (b) the atomic c(2  2) structure of a Cu (100) surface at anodic potentials, with perfectly stabilized steps aligned in the [010] and [001] directions (panel c), parallel to densely packed bromide rows of the c(2  2) adlayer structure. Even though bromide is larger than chloride, the bromide anions still fit into a c(2  2) structure on this Cu(100) surface. Occasionally, step edges cross each other leading to the so-called triple points of double-step height (arrows in panel a).

Fig. 182.4 In situ STM images of Cu(100) in 10 mM HBr solution: (a) large-scale morphology with extended terraces and orthogonal step-edges in [001] and [010] direction; arrows indicate “triple points” of double-step height, (b) c(2  2)-Br structure on Cu(100); (c) steps are aligned along densely packed Br
anion rows. Kinks like the one seen in (c) are energetically less favorable and therefore rare.

A careful inspection of the step edges on an fcc(100) surface covered with a c(2  2) adlayer reveals step configurations as illustrated in Fig. 182.5a in the case of a monoatomically high island. Both the island and the surrounding terrace are covered by the c(2  2) adlayer. Depending on the translational phase relation between the adsorbate rows on the island and the adjacent terrace, one finds “out-of-phase” (A,A0 ) and “inphase” (B) steps. In case of “out-of-phase” steps, two different configurations are conceivable for the adparticles nearest to up-step edges, namely, coordinated to four Cu atoms (A) or three Cu atoms (A0 ). In the former case (A), the nearest distance between up- and down-step adparticles is larger than in the latter case (A0 ), in which the adparticles assume a quasi-hexagonal arrangement. For sterical and probably electrostatic reasons, configuration A turns out to be the more stable, i.e., more abundant, configuration. The existence of both configurations, A and B, can be verified by STM (Fig. 182.5b, c). This anticipated energetic anisotropy of the near-step atomic arrangement, indeed, manifests itself in the anodic corrosion behavior of the surface if

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the potential is increased. Figure 182.6 shows a sequence of STM images of the same surface area (see hole in the center) of a bromide covered Cu(100) surface which clearly shows a pronounced unidirectional growth of grooves in the [001] and [010] direction with B-type edges which are the most stable ones. The same anisotropic behavior is found during copper redeposition upon lowering the electrode potential.

Fig. 182.5 (a) Hard-sphere model of the c(2  2)-Br covered Cu(100) surface with rectangular Cu-island in the center (brighter) illustrating the two translational phase relations B and A/A0 between Br rows on the island and the surrounding terrace, respectively. Both situations are verified in the experimental STM images in panels (b) and (c) (From Ref. [6])

Fig. 182.6 Sequence of in situ STM images showing the clear unidirectional preference of B-type steps (see Fig. 182.5) upon dissolution of Cu(100) in hydrobromic acid. The same behavior is observed upon Cu-redepositon. T refers to differently high terraces. The white and black circles indicate stable defects serving as markers (Adapted from Ref. [6])

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Hydrohalic acid interaction with copper surfaces: Cu(100) – chloride and. . .

5

Symbols and abbreviations Short form

Full form

STM HER CDR RHE UHV ML fcc

scanning tunneling microscopy hydrogen evolution reaction copper dissolution reaction reference hydrogen electrode ultrahigh vacuum monolayer face-centered cubic

References 1. Nakamura, C.Y., Altmann, E.I.: Scanning tunneling microscopy study of the reaction of Br2 with Cu(100). Surf. Sci. 398, 281 (1998) 2. Nakamura, C.Y., Zheng, G., Altmann, E.I.: Atomic-scale mechanisms of the halogenation of Cu(100). Surf. Sci. 401, 173 (1998) 3. Nakamura, C.Y., Altmann, E.I.: Erratum to “Scanning tunneling microscopy study of the reaction of Br2 with Cu(100)”. Surf. Sci. 416, 488 (1998) 4. Fishlock, T.W., Pethica, J.B., Egdell, R.G.: Observation of a nanoscale chessboard superstructure in the Br–Cu(100) adsorbate system. Surf. Sci. 445, L47 (2000) 5. Frumkin, A.: Wasserstoffüberspannung und Struktur der Doppelschicht. Z. Phys. Chem. A 164, 121 (1993) 6. Obliers, B., Anastasescu, M., Broekmann, P., Wandelt, K.: Atomic structure and tip-induced reconstruction of bromide covered Cu(110) electrodes. Surf. Sci. 573, 47 (2004) 7. Pham, D.T., Keller, H., Breuer, S., Huemann, S., Hai, N.T.M., Zoerlein, C., Wandelt, K., Broekmann, P.: Chimia 63, 115 (2009)

Chapter 183

Hydrohalic acid interaction with copper surfaces: Cu(100) – iodide M. Nowicki and K. Wandelt

Iodide anions are significantly larger than chloride or bromide ions. As a consequence, they do no longer fit into a simple c(2
2) structure on Cu(100) but form a series of different phases, which as a function of electrode potential and iodide concentration in solution differ in surface coverage [1]. A representative cyclic voltammogram of Cu(100) in 10 mM HClO4 containing 1 mM KI is shown in Fig. 183.1. The exponential increase of an anodic current (gray curve) starting at 5 mV (Ag/AgI) in the positive potential sweep arises from the anodic copper dissolution reaction (CDR), while the pronounced peak in the reverse potential sweep is due to Cu redeposition (CRD) of the previously dissolved copper material. At the cathodic end of the extended double-layer regime (25 mV and 360 mV), the onset of the hydrogen evolution reaction (HER) in the potential range between 420 and 600 mV is superimposed by two additional current features (arrows) which are attributed to surface phase transitions on the basis of the STM data presented in the following.

Fig. 183.1 Steady-state cyclic voltammogram of Cu (100) in 1 mM KI containing 10 mM HClO4 solution, CDR copper dissolution reaction, CRD copper redepositon reaction, HER hydrogen evolution reaction. The two arrows mark current waves associated with structural phase transitions within the adsorbed iodide layer as verified by the in situ STM images and models shown in Figs. 183.2, 183.3, 183.4, 183.5, 183.6, 183.7, 183.8, 183.9, and 183.10 (From Ref. [1])

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_183

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At positive electrode potentials near the onset of the copper dissolution reaction, the specifically adsorbed iodide anions form a distorted “pseudo”-square structure which is commensurate only in one of the [011] directions resulting in an additional one-dimensional height modulation perpendicular to this commensurate direction (Figs. 181.2c[https://doi.org/10.1007/978-3-662-53908-8_181] and 183. 2a, b). Every spot in these STM images is assigned to an individual iodide particle. Parallel to the commensurate direction, the nearest interatomic distance of 5.1  0.1 Å is exactly twice the nearest substrate spacing of aCu ¼ 2.56 Å. In contrast to that, the nearest neighbor distance between iodide particles of adjacent “commensurate” adsorbate rows is significantly smaller, namely, 3.7  0.1 Å. To elucidate the symmetry elements of the iodide lattice especially regarding the first and the second coordination sphere, a so-called correlation image (Fig. 183.2d) has been calculated from Fig. 183.2a. As a result in the first coordination sphere, every iodide particle is surrounded by four next neighbor iodide particles forming a centered rectangular unit cell with a smaller lateral edge of 2aCu (Fig. 183.2d) and a longer side, which is labeled p with p ˃ 2aCu. Apart from these four next neighbors, there are two further iodide particles within the second coordination sphere in a next nearest neighbor distance of 2aCu ¼ 5.1  0.1 Å.

Fig. 183.2 In situ STM images of the uniaxially incommensurate iodide structure on Cu(100) at positive potentials, (a) 12.6
12.6 nm, IT ¼ 30 nA, UB ¼ 3 mV, E ¼ 100 mV (Ag/AgCl); (b) 5.7
5.7 nm, IT ¼ 30 nA, UB ¼ 3 mV, E ¼ 100 mV; (c) 12
12 nm, IT ¼ 100 nA, UB ¼ 2 mv, E ¼ 300 mV; (d) correlation image of (b) showing the incommensurate iodide unit cell at positive potentials. I, II in panel (c) indicate different domains and α the rotational angle between their densely packed anion rows (From Ref. [1])

183

Hydrohalic acid interaction with copper surfaces: Cu(100) – iodide

3

As a result of this reduced symmetry of the iodide layer on the fourfold symmetric substrate, two rotational domains rotated by 90 against each other must exist. Such rotational domains (I, II) are indeed observed in Fig. 183.2c. To a rough approximation, this structure can be regarded as a distorted c(2
2) phase which is expanded parallel to only one of the c(2
2) unit-cell vectors. A schematic hard-sphere model comparing the original c(2
2) as observed with chloride and bromide and the derivative c(p
2) is presented in Fig. 183.3. The p-vector decreases (increases) linearly with increasing (decreasing) electrode potential in terms of a so-called electro-compression (electro-decompression) process within the potential range between 400 and 5 mV (Ag/AgI).

Fig. 183.3 Structure models of the hypothetical c(2
2)-I structure on Cu(100) and two incommensurate structures defining the lattice vectors 2aCu and p1 > p2 > 2aCu and the related angles β1, β2 between iodide anion rows (From Ref. [1])

The iodide adlayer in Fig. 183.2a, b corresponds to a saturation coverage of Θ ¼ 0.46 ML (at E ¼ 100 mV) which is rather close to 0.5 ML, i.e., the theoretical value for the c(2
2) structure. Changing the potential to 430 mV, the coverage decreases to Θ ¼ 0.38 ML. Accordingly, the (average) next-nearest neighbor (NND) distance increases, while the interatomic spacing along the commensurate direction remains unaffected. However, a pronounced nonuniform spacing of iodide particles along the non-commensurate direction at more negative potentials makes a precise determination more difficult (Fig. 183.4) compared to the more uniformly compressed adlayer at saturation coverage (Fig. 183.2a, b). Figure 183.4 represents the uniaxially incommensurate (UIC) iodide structure in a less compressed state at E ¼ 450 mV. Clearly visible are two kinds of alternating building blocks (denoted A and B in Fig. 183.4) separated by a somewhat larger distance. While building block A consists of three atomic rows of iodide particles, building block B consists of a narrow double row. Interestingly, the interatomic spacing within both building blocks is quite different which is particularly obvious in the line scan in Fig. 183.4b.

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Fig. 183.4 Domain wall structure of the iodide anion layer on Cu(100) at more negative potentials: (a) 5.3
5.3 nm, IT ¼ 30 nA, UB ¼ 3 mV, E ¼ 450 mV (Ag/AgCl), (b) height profile along the white line in (a) showing the discontinuous separation of iodide rows along the incommensurate direction (From Ref. [1])

This iodide structure with discontinuous inter-atomic spacings occurring at less positive potentials can strictly speaking no longer be described by a c(p
2) unit cell; just for the sake of convenience, however, we will continue to denote this structure as c(p
2)-I. Not only the atomic structure but also the surface morphology is strongly affected by the presence of the UIC iodide structure. This is demonstrated in Fig. 183.5, which correlates the step orientation to the symmetry properties of the atomic lattice. Most surprisingly, the energetically favorable step orientations do not coincide with the commensurate directions of the c(p
2) structure (Fig. 183.5b) running parallel to the wave crests of the long-range superstructure. In fact, step edges running parallel to the wave crests have never been observed. Instead, the oriented step edge in Fig. 183.5b encloses an angle of β ¼ 40  2 with the commensurate [011] direction. It is simply again the direction parallel to the close-packed anion rows, which determines the energetically most favorable step arrangement.

Fig. 183.5 Gross morphological features of an iodide covered Cu(100) surface: (a) 29
29 nm, IT ¼ 10 nA, UB ¼ 2 mV, E ¼ 200 mV (Ag/AgCl); (b) 16.04
16.04 nm, IT ¼ 10 nA, UB ¼ 2 mV, E ¼ 300 mV; (c) 15.7
15.7 nm, IT ¼ 10 nA, UB ¼ 2 mV, E ¼ 300 mV. I and II mark different domains, note in panel (c) that only step-edges between equal domains are straight; α and β are defined in Figs. 183.2 and 183.3. White lines in panel (b) accentuate the translational phase relation between the upper and the lower terrace (Adapted from Ref. [1])

This observed stabilization effect of iodide anions on the substrate steps is further substantiated in Fig. 183.5c by comparing the atomic structure of two adjacent terraces. Those steps which separate two equivalent rotational domains (I) on two adjacent terraces appear defect-free. Furthermore, the long-range corrugation of equivalent rotational domains on two adjacent terraces is usually in phase (see white lines in

183

Hydrohalic acid interaction with copper surfaces: Cu(100) – iodide

5

Fig. 183.5b). An out-of-phase behavior has never been observed. In contrast, step edges, which separate two different rotational domains on adjacent terraces, exhibit a pronounced fluctuation (I and II in Fig. 183.5c). The presence of two rotational domains on one and the same terrace has also impact on the surface morphology. The directions of anions stabilized steps often deviated by an angle α which arises from a characteristic angle defined by the close-packed adsorbate rows of two different rotational domains (Figs. 183.2c and 183.5a). The fact that the adsorbate lattice symmetry changes with increasing or decreasing electrode potentials obviously means that the direction of non-commensurate iodide rows changes. This influences also the preferential step orientation. Hence, the presented step orientation in Fig. 183.5a is characteristic only for the given electrode potential (see Fig. 183.3 for p1, p2 giving β1 < β2). By sweeping the electrode potential in negative direction, the iodide coverage shrinks and the structure becomes uniaxially expanded. At very negative potentials, i.e., from 450 to 550 mV, a further phase transition leads to the formation of a new ordered commensurate iodide structure, which remains stable even under massive hydrogen evolution. A desorption of iodide from the Cu(100) surface, however, could not be observed under the given conditions of iodide concentration and pH value of the solution (see however below). Figure 183.6a shows a high resolution STM image of this new iodide layer, which is characterized by close-packed rows of spots which are separated by a larger distance. Each spot is assigned to an individual iodide particle. A quantitative analysis of the unit cell is again based on a Fourier spectrum (Fig. 183.6b) and results in an interatomic distance of a ¼ 5.1  0.1 Å within the close-packed rows and an interatomic distance of b ¼ 8.0  0.1 Å between these rows. Both lattice vectors  enclose  an angle of γ ¼ 3 1 109.5  2 . These values are best described by the matrix notation as Cu(100)-I, or simpler, but 0 2 not fully correct, by a so-called (2
√10) unit cell in “quasi”-Wood notation (see Fig. 183.7). An alternative route to describe this adsorbate structure consists in assuming a rectangular c(6
2) unit mesh (Fig. 183.6a). Because of the reduced symmetry of this adsorbate lattice, two rotational domains of this structure are again observable in the STM experiments, and the corresponding Fourier analysis is in full agreement with LEED data of c(6
2) structures in the literature [2]. Ex situ LEED studies in UHV of dissociative iodine adsorption on Cu(100) reveal a superstructure for an iodine coverage of Θ ¼ 0.33 ML, which is identical to the two-domain Fourier spectrum of the c(6
2)-I structure (Fig. 183.6c) at negative electrode potentials in the electrochemical environment.

Fig. 183.6 Determination of the c(6
2)-I structure on Cu(100) at negative potentials close to the onset of hydrogen evolution: (a) 3.3
3.3 nm, IT ¼ 10 nA, UB ¼ 5 mV, E ¼ 440 mV (Ag/AgCl); (b) Fourier spectrum of the iodide structure; (c) two-domain power spectrum of the c(6
2)-I phase (From Ref. [1])

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M. Nowicki and K. Wandelt

Fig. 183.7 Structure models and parameters of the c(6
2)- or equivalent (2
√10)-unit cells of the iodide superstructure at negative potentials (Adapted from Ref. [1])

Figure 183.7 represents a hard-sphere model of the c(6
2)-I layer including the main symmetry elements of this structure and the most important interatomic spacings. Characteristically, the two kinds of iodide species form two identical sub-lattices shifted against each other by a translation vector c ¼ 3.8  0.1 Å (Fig. 183.7). Another approach to understand this iodide structure is to assume characteristic building blocks of iodide “zigzag” chains (see lower left corner). While one of the two iodide species resides in a fourfold hollow, the second one is placed in an interstitial site. The phase transition from the c(p
2)-I to the c(6
2)-I structure is kinetically hindered which allows to follow this process by STM. This kinetic hindrance is also the origin of the wide coexistence range of both phases on the potential scale (450 to 600 mV). In the initial stage of this phase transition, narrow stripes of the c(6
2)-I structure are formed, with the smallest building block being the abovementioned iodide zigzag row as demonstrated in Fig. 183.8a. Series of sequential STM images (Fig. 183.8b, c) show that the c(6
2) stripes broaden perpendicular to the wave crests of the incommensurate c(p
2) structure. The c(6
2)-I areas are imaged significantly darker or “deeper” than the c(p
2)-I phase due to an electronic effect. The final stage of the phase transition is characterized by larger areas of the c(6
2)-I phase which, however, are often still separated by narrow stripes of the c(p
2)-I structure all revealing the same width which corresponds exactly to one periodicity of the long-range superstructure (denoted l# in Fig. 183.8b). Interestingly, the widths of the c(6
2)-I patches (denoted l in Fig. 183.8b) are also multiples of l#.

183

Hydrohalic acid interaction with copper surfaces: Cu(100) – iodide

7

Fig. 183.8 In situ STM images showing the transition from the c(p
2)- to the c(6
2)-phase of an iodide layer on Cu(100). (a) Initial stage of the phase transition, 72
72 nm, IT ¼ 1 nA, UB ¼ 6 mV, E ¼ 450 mV (Ag/AgCl); (b) and (c) advanced stages of this phase transition: (b) 13
13 nm, IT ¼ 1 nA, UB ¼ 7 mV, E ¼ 460 mV; (c) 15.2
15.2 nm, IT ¼ 1 nA, UB ¼ 5 mV, E ¼ 460 mV. The width l of the c(6
2) stripes corresponds to multiples of the wave length l# of the c(p
2) superstructure (Adapted from Ref. [1])

This type of a single c(p
2)-I stripe often serves as a domain boundary separating two rotational domains of the c(6
2)-I phase (Fig. 183.8c). Such an arrangement remains extraordinarily stable even at extreme negative potentials within the potential regime of hydrogen evolution. Step edges often play a major role for phase transitions. This becomes confirmed by the high resolution STM image in Fig. 183.9 showing the atomic adsorbate structure on adjacent terraces close to a step edge. Relatively large domains of the c(6
2)-I phase are separated by narrow stripes of the c(p
2)-I structure continuing across a step (accentuated by dotted lines in Fig. 183.9b). The orientation of the step edges corresponding to the narrow c(p
2)-I domains (indicated by two white arrows in Fig. 183.9b) significantly differ from the step alignment characteristic for the neighboring c(6
2)-I phases. While for the latter case a preferential step alignment parallel to a quite open [0 1 2] direction seems to be the most stable configuration, the preferential step orientation of the c(p
2)-I phases corresponds to the close-packed rows of the iodide lattice as already described above (Fig. 183.5).

Fig. 183.9 Morphological features of the transition from the c(p
2)- to the c(6
2)-phase of an iodide layer on Cu(100); (a) 40.5
40.5 nm, IT ¼ 1 nA, UB ¼ 1 mV, E ¼ 565 mV (Ag/AgCl), (b) 14.4
14.4 nm, IT ¼ 1 nA, UB ¼ 1 mV, E ¼ 565 mV. The angle β is defined in Fig. 183.3 and refers to the c(p
2)-phase crossing the step (arrows) (Adapted from Ref. [1])

These observations support a scenario in which the phase transition from the c(p
2)-I to the c(6
2)-I phase initially starts at the bottom of a step edge by the formation of a small patch of the c(6
2)-I phase which grows along the [011] directions across the lower terrace up to the next step edge, which is rearranged such that the c(p
2)-I phase on the next lower terrace becomes again locally destabilized,

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M. Nowicki and K. Wandelt

and transforms into a small patch of c(2
6) structure which grows along the [011] direction, etc. This leads to narrow stripes running straight across steps and terraces as observed in Fig. 183.9a. The c(6
2)-I structure is stable down to very low potentials; no desorption of iodide is observed. A lower coverage can only be realized by adsorbing a priori less iodide [3]. This can be achieved by injecting very small doses of a low concentration iodide solution into an iodide-free KClO4 solution. As a result, also domains of a p(2
2)-I structure (θI ¼ 0.25 ML) are formed as shown in Fig. 183.10. This structure, of course, does not form distinguishable rotational domains on a Cu(100) surface; however, translational domains are possible as visible in Fig. 183.10c, which exhibits a so-called heavy domain wall (hdw), in which in the ideal case, the iodide anions would occupy positions like Cl and Br in a c(2
2) structure. In reality, due to the larger size of the iodide anions which does not allow this density, this domain wall will laterally be somewhat “relaxed.” The p(2
2)-I structure is a consequence of the large size of the iodide anions and their very strong interaction with the Cu(100) substrate.

Fig. 183.10 Coexistence of the uniaxially incommensurate c(p
2) iodide phase and the low coverage p(2
2)-I phase on Cu(100) after a dosing experiment: (a) 20.7
20.7 nm, IT ¼ 2 nA, UB ¼ 18 mv, E ¼ 280 mV (Ag/AgCl); (b) 11.5
11.5 nm, IT ¼ 2 nA, UB ¼ 18 mV, E ¼ 200 mV; (c) 4
4 nm, IT ¼ 2 nA, UB ¼ 18 mV, E ¼ 200 mV (Adapted from Ref. [3])

Symbols and abbreviations Short form

Full form

STM LEED UHV CDR HER UIC

scanning tunneling microscopy low-energy electron diffraction ultrahigh vacuum copper dissolution reaction hydrogen evolution reaction uniaxially incommensurate

References 1. Broekmann, P., Spaenig, A., Hommes, A., Wandelt, K.: Influence of uniaxially incommensurate adlayers on the surface morphology: Iodide on Cu(100). Surf. Sci. 517, 123 (2002) 2. Andryushechkin, B.V., Eltsov, K.N., Shevlyuga, V.M., Bardi, U., Cortigiani, B.: Structural transitions of chemisorbed iodine on Cu(100). Surf. Sci. 497, 59 (2002) 3. Hommes, A., Spaenig, A., Broekmann, P., Wandelt, K.: Low coverage p(2
2) iodide phase on Cu(100). Surf. Sci. 547, 239 (2003)

Chapter 184

Hydrohalic acid interaction with copper surfaces: XRD of chloride, bromide, and iodide on Cu(100) M. Nowicki and K. Wandelt

The STM results presented above as well as early X-ray diffraction studies [2–4] provided mainly information about the in-plane structure of the halide layers including order-disorder phase transitions. Detailed analysis of in situ X-ray diffraction data, however, yields also information about the out-of-plane structure, for instance, adsorption-induced relaxation effects perpendicular to the substrate surface. Such relaxation phenomena are experimentally well established for clean as well as adsorbate covered metal and semiconductor surfaces under UHV conditions [1] and theoretically well understood as a consequence of charge redistribution due to the broken symmetry at clean surfaces and the bond formation between the surface and an adsorbate. These data thus provide important information about the bonding mechanism between adsorbates and substrates. At metal-electrolyte interfaces, besides these two aspects, the electrification of the interface due to an applied potential is a further reason to expect relaxation effects, which are different than in UHV. In fact, it is the balance between the mere charging of the electrode surface and the accompanying “electrosorption” of ionic species, which makes the elucidation of relaxation effects at electrified electrode surfaces particularly challenging. Very detailed XRD analyses have been published for the interaction of all three halides, Cl, Br, and I, with Cu(100) surfaces as a function of electrode potential. As an example, Fig. 184.1a shows two symmetrically inequivalent so-called crystal truncation rods (CTRs) obtained from a Cu(100) surface at +260 mV and +95 mV (RHE) in 10 mM HCl solution. Their analysis not only confirms the presence of a c (2
2)Cl adlayer structure as already seen in in situ STM images but also reveals information about the surface roughness due to a statistical distribution of uncorrelated up- and down-steps, the adsorbate and the surface layer occupancy, as well as the first two interlayer spacings, i.e., between the adsorbate and the first Cu layer and the first and second Cu layer, respectively [5].

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_184

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a

Intensity [arb. units]

1000 100

XPD

Data Cl/Cu(100)-c(2x2) Clean Cu(100)

b Cl

top view

Cu

dad-layer

(2,0,L)

d12

10 1

c

d23

(2,2,L) Z

0.1

Side View 0.5 1.0

1.5

2.0

2.5

3.0

3.5

Wavevector qz[2π/c]

Fig. 184.1 (a) Plot of the intensity distribution of the (2,0,L) and (2,2,L) crystal truncation rods (CTRs) as a function of the momentum transfer perpendicular to a c(2
2)Cl-covered Cu(100) surface. The filled circles represent the experimental values, and the solid red line represents the best fit to the structure model shown in panel (b). The solid black line shows the calculated intensity based on an uncovered relaxed Cu(100) surface under UHV conditions. The CRT data were collected for a period of t > 40 min (From Ref. [5])

While the bare Cu(100) surface in UHV exhibits a 1% inward relaxation [6], the interlayer spacing between the first and second layers of the Cu(100) electrode in HCl electrolyte at +95 mV (RHE) is 2.2% larger than the Cu bulk interlayer spacing. This is not unexpected for two reasons. Firstly, at +95 mV, the copper surface is positively polarized causing a depletion of negative charge between the outer Cu layers. As a consequence, the electrostatic repulsion between the Cu cores increases which leads to a weakening of the Cu-Cu bond and an expansion perpendicular to the surface. Secondly, the presence of the adsorbed electronegative Cl species is expected to affect the charge redistribution even further. It is, in fact, a fundamental question what the charge state of the adsorbed Cl species actually is, also as a function of electrode potential. An answer to this question can be obtained by comparing the Cu-Cl bond length between the first Cu layer and the Cl ad-particles with known bond lengths in bulk CuCl and CuCl2 compounds [5]. While the Cu-Cl bond length of the c(2
2)Cl-Cu(100) system in the electrochemical environment is determined to be 2.61 Å, the Cu-Cl bond lengths in CuCl (nantokite) and CuCl2 (tolbachite) are 2.48 Å and 2.26 Å, respectively [7–9]. Finally, chloride adsorption on Cu(100) in UHV results also in a c(2
2)Cl structure, which is characterized by a Cu-Cl bond length of 2.41 Å [10–12]. Hence, from all these bond lengths, 2.61 Å is the longest, which supports the notion that the adsorbed chloride anions on Cu (100) largely retain their full negative charge upon adsorption in the electrochemical environment, in contrast to the behavior of iodide (see below) but in accord with chloride being the most electronegative of the three halides Cl, Br, and I. For comparison, we first jump to XRD results obtained for iodide which have been analyzed similarly as those of the c(2
2)Cl-Cu(100) system. In contrast to chloride, however, iodide forms a series of wellordered monolayer phases of different coverage on Cu(100) due to its larger size and electrocompressibility as described in the previous Chap. 183[https://doi.org/10.1007/978-3-662-53908-8_ 183]. XRD data obtained again at +95 mV (RHE) (in order to be comparable with those for chloride discussed above as well as to avoid CuI surface compound formation described in Chaps. 190[https://doi. org/10.1007/978-3-662-53908-8_190] and 191[https://doi.org/10.1007/978-3-662-53908-8_191]) identify the formation of a higher-order commensurate c(2
5)-I structure at the Cu(100) electrode surface which is qualitatively in agreement with a c(p
2)-I structure with p ¼ 2.5 (see Chap. 183[https://doi.org/10.1007/ 978-3-662-53908-8_183]). The best fit to the experimental XRD data is obtained with the model shown in Fig. 184.2 which is characterized by positional relaxations both perpendicular and parallel to the surface [5]. At this iodide coverage, a uniform compression of the anion layer would locate the atoms 2 and 20 at the near-bridge positions indicated by the dotted circles. The best fit to the XRD data, however, suggests a

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Hydrohalic acid interaction with copper surfaces: XRD of chloride, bromide, and iodide on Cu(100)

3

lateral shift by 0.20 Å toward the energetically more favorable nearest hollow site (full atoms 2, 20 ). As a result, the fit value for the distance between the two iodine atoms 1 and 2 becomes 3.81 Å, which is 11% smaller than in marshite, the most common CuI phase with zinc blende-like structure, hinting to a less ionic state of the iodine [13, 14]. The (average) bond length between first-layer Cu atoms and the adsorbed iodine particles (sitting actually in inequivalent surface sites) is found to be 2.51 Å. Moreover, the topmost Cu layer is relaxed 3% inward compared to the ideal bulk layer spacing. A similar inward relaxation was measured after bromide adsorption on Pt(111) [15]. However, in contrast to the expansion of the outer Cu layers by 2.2% upon adsorption of chloride, iodide adsorption causes a 3% compression. x

Top view

y

2 1

3

z

Side view

1

2

3

x

Fig. 184.2 Top and side view of the c(5
2)I-Cu(100) structure model. The solid rectangle represents the c(5
2) unit cell. The dashed circles indicate the positions of iodide anions prior to relaxation (see text). The labels 1, 2, and 3 mark iodide species in fourfold, quasi-bridge, and bridge-sites, respectively (From Ref. [5])

These results support the notion of a different bonding mechanism between these two halides and copper. Both the elongated Cu-Cl bond and the expansion of the outer Cu-Cu bond interlayer spacing upon chloride adsorption indicate a largely ionic bond between metal and the chlorine particles, while the reduced Cu-I bond length and the Cu-Cu interlayer compression upon I adsorption are consistent with a more covalent Cu-I bond. The less ionic the anions, the smaller they are, and the more charge they dump between the outer metal layers, which reduces the core-core repulsion. It is the chloride-induced Cu-Cu interlayer expansion and, hence, Cu-Cu bond weakening, which explains the increased Cu surface mobility (in the form of easily detaching CuCl2 complexes) and the chloride-driven “electrochemical annealing” effect. In turn, it is the iodide-induced stabilization of the Cu-Cu bond together with the strongly covalent Cu-I bond which (in contrast to Cl) leads to the formation of stable Cu-I surface compounds as described in Chaps. 190[https://doi.org/10.1007/978-3-662-53908-8_190] and 191[https://doi.org/10.1007/978-3-66253908-8_191]. Very similar XRD measurements have also been carried out with adsorbed bromide on Cu(100) in 10 mM KBr containing dilute sulfuric acid solution (Fig. 184.3). Though chloride and bromide form the same two-dimensional c(2
2) surface lattice, the detailed analysis of XRD data yields significantly different out-of-plane results [16]. Compared to chloride, adsorbed bromide leads to a decrease of the separation between the Br adlayer and the first Cu layer with increasing electrode potential. While at negative potential (150 mV vs. RHE), the Br-Cu layer spacing is found to be 8.3% larger than the spacing between parallel Cu bulk layers (see Fig. 184.4a), this value decreases to 5.6% at 50 mV and 4.2% at +50 mV (RHE), which indicates strengthening of the Br-Cu bond. Yet, even at +50 mV, the resulting Br-Cu bond length is 4.4% longer than in bulk CuBr, which can be understood in terms of the different coordination of the bromide ions: on the Cu(100) surface the Br particles sit in fourfold hollow sites, while in CuBr, they are tetrahedrally surrounded by four Cu atoms.

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Fig. 184.3 Top and side view of the p(2
2)Br-Cu(100) structure. The side view shows a series of layers and their interlayer distances, used in the fitting procedure of XRD data (not shown). The rectangles represent reduced unit cells commonly used in XRD. The arrows define the crystallographic directions (From Ref. [16])

b

1.09 Br c(2x2)/Cu(100)

Cu1 - Cul distance [a/2]

Halide - Cul distance [a/2]

a

1.08 1.07 1.06 1.05 1.04 –200

–150

–100

–50

0

Potential E vs RHE [mV]

50

100

Br c(2x2)/Cu(100)

1.03

1.02

1.01

–200

–150

–100

–50

0

50

100

Potential E vs RHE [mV]

Fig. 184.4 Plots of potential dependent interlayer spacings between (a) the c(2
2)-Br anion overlayer and the first Cu-layer, and (b) the first and second Cu layer (From Ref. [16])

The spacing between the first two copper layers underneath the Br adlayer is always expanded (compared to the bulk spacing). The maximum (average, see below) Cu-Cu interlayer expansion of 3.2% at 150 mV decreases to 1.1% at +50 mV (see Fig. 184.4b). At first sight, this contraction with increasing potential is surprising, because a mere positive polarization of the electrode, i.e., charge withdrawal, should result in a stronger repulsion between the Cu cores and, hence, in a Cu-Cu expansion. It is obviously the presence of the bromide adlayer which overcompensates this effect by increasing charge transfer from bromide into the Cu surface. Beyond the average interlayer distance between the first two Cu layers, this analysis of the c(2
2)BrCu(100) XRD data was carried one step further than the previously described one for Cl-Cu(100) and I-Cu (100), in that the consideration of a buckling of the second Cu layer was found to improve the fit quality significantly [16]. This buckling arises from the fact that every other Cu atom in the second layer has a different distance, and thereby interaction, with the adsorbed halide in the fourfold hollow sites on the first Cu layer. The above interpretation of the different bonding of chloride and bromide on Cu(100) was examined and supported by density functional theory (DFT) calculations [16]. The calculations were performed using the Vienna ab initio simulation program (VASP) [17–19]. The surfaces are simulated by parallel slabs of metal atoms of the proper symmetry, which are periodically repeated with a “vacuum spacing” of 20.5 Å between them. Changes of the electrode potential were achieved by varying the total charge within the unit cell, and

184

Hydrohalic acid interaction with copper surfaces: XRD of chloride, bromide, and iodide on Cu(100)

5

the solvent is explicitly taken into account by placing a small number of water molecules in the unit cell. Electroneutrality of the electrolyte itself is preserved by adding the appropriate number of counter-ions (here Ca2+) in the unit cell (see Fig. 184.5). First for the vacuum case, the calculations confirm that both, chloride and bromide, adsorb most stable in the fourfold hollow sites of the Cu(100) surface. The Br-Cu (Cl-Cu) interlayer spacing is found to be 1.83 Å (1.67 Å), which is 0.8% larger (8.1% smaller) than the optimized Cu-Cu bulk layer spacing. The spacing between the first two copper layers is increased by 0.3% (Br) and 0.6% (Cl) compared to the Cu bulk value, i.e., the Cu-Cu interaction is weakened more with adsorbed Cl than with Br. Consideration of the outer space charge layer with water molecules and counterions leads to a weakening of the Br-Cu bond and a decrease of the Br-Cu and Cu-Cu interlayer spacing with increasing potential in agreement with the experimental findings. By contrast, in the case of chloride, the theoretical calculations do not reproduce the experimental trend. While the measured Cl-Cu distance is almost independent on the electrochemical potential, the calculations give a similar trend as with Br [16].

Fig. 184.5 Side view of the model used for the simulation of the Helmholtz layer at a Cu(100) electrode surface in an X anion containing solution (X ¼ Cl, Br). Ca2+ cations are used as counter ions in the calculation (see Ref. [16])

Symbols and abbreviations Short form

Full form

STM XRD UHV RHE DFT VASP

scanning tunneling microscopy X-ray diffraction ultrahigh vacuum reference hydrogen electrode density functional theory vienna ab initio simulation package

References 1. 2. 3. 4.

Heinz, K., Starke, U.: Surface crystallography. In: Wandelt, K. (ed.) Surface and Interface Science, vol. 2, p. 489. WileyVCH, Weinheim (2012) Ocko, B.M., Magnussen, O.M., Wang, J.X., Adzic, R.R., Wandlowski, T.: The structure and phase behavior of electrodeposited halides on single crystal surfaces. Physica B 221, 238 (1996) Magnussen, O.M., Ocko, B.M., Adzic, R.R., Wang, J.X.: X-ray diffraction studies of ordered chloride and bromide monolayers at the Au(111)-solution interface. Phys. Rev. B 51, 5510 (1995) Wang, J., Ocko, B.M., Davenport, A.J., Isaacs, H.S.: In situ x-ray-diffraction and -reflectivity studies of the Au(111)/ electrolyte interface: Reconstruction and anion adsorption. Phys. Rev. B 46, 10321 (1992)

6

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5.

Huemann, S., Hai, N.T.M., Broekmann, P., Wandelt, K., Zajonz, H., Dosch, H., Renner, F.: Surface redox chemistry of adsorbed viologens on Cu(100). J. Phys. Chem. B 110, 24955 (2006) Lind, D.M., Dunning, F.B., Walters, G.K., Davis, H.L.: Surface-structural analysis by use of spin-polarized low-energy electron diffraction: An investigation of the Cu(100) surface. Phys. Rev. B 35, 9037 (1987) Monier, C.J., Kern, R.: Natl. Bur. Stand. 359, 30 (1955) Hull, S., Keen, D.A.: High-pressure polymorphism of the copper(I) halides: A neutron-diffraction study to 10 GPa. Phys. Rev. Condens. Matter. 50, 5868 (1994) Burns, P.C., Hawthorne, F.C.: Tolbachite, CuCl2, the first example of Cu2+ octahedrally coordinated by Cl. Am. Mineral. 78, 187 (1993) Jona, F., Westphal, D., Goldmann, A., Marcus, P.M.: A low-energy electron diffraction intensity analysis of Cu(00l)c (2
2)-Cl. J. Phys. C 16, 3001 (1983) Patel, J.R., Berremann, D.W., Sette, F., Citrin, P.H., Rowe, J.E., Cowan, P.L., Jach, T., Karlin, B.: Substrate surface relaxation for Cl and S on Cu(001). Phys. Rev. B 40, 1330 (1989) Q-Wang, L., Schach von Wittenau, A.E., Ji, Z.G., Wang, L.S., Huang, Z.Q., Shirley, D.A.: c(2
2)Cl/Cu(001) adsorbate geometry and substrate-surface relaxation using low-temperature angle-resolved photoemission extended fine structure. Phys. Rev. B 44, 1292 (1991) Cooper, M.A., Hawthorne, F.C.: A note on the crystal structure of marshite. Can. Mineral. 35, 785 (1997) Petrillo, C., Moze, O., Ibberson, R.M.: High resolution neutron powder diffraction investigation of the low temperature crystal structure of molecular iodine (I2). Physik. 180, 639 (1992) Lucas, C.A., Markovic, N.M., Tidswell, I.M., Ross, P.N.: In situ X-ray scattering study of the Pt(1 1 1)-solution interface: Ordered anion structures and their influence on copper underpotential deposition. Physica B 221, 245 (1996) Saracino, M., Broekmann, P., Gentz, K., Becker, M., Keller, H., Janetzko, F., Bredow, T., Wandelt, K., Dosch, H.: Surface relaxation phenomena at electrified interfaces: Revealing adsorbate, potential, and solvent effects by combined x-ray diffraction, STM and DFT studies. Phys. Rev. B 79, 115448 (2009) Kresse, G., Hafner, J.: Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251 (1994) Kresse, G., Furthmüller, J.: Efficiency of ab-initio total energy calculations for metals and semiconductors using a planewave basis set. Comput. Mater. Sci. 6, 15 (1996) Kresse, G., Furthmüller, J.: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996)

6. 7. 8. 9. 10. 11. 12.

13. 14. 15. 16.

17. 18. 19.

Chapter 185

Hydrohalic acid interaction with copper surfaces: Cu(111) – chloride M. Nowicki and K. Wandelt

Figure 185.1 shows a cyclic voltammogram of a Cu(111) surface in 10 mM HCl solution with the anodic Cl adsorption peak at 755 mV and the cathodic desorption peak at 980 mV (vs. Hg/Hg2SO4). The latter overlaps with the exponentially increasing hydrogen evolution current. It is evident that the area of the Cl desorption peak – even after subtraction of the exponential background (dashed trace) – is larger than that of the Cl adsorption peak. This effect arises from a superposition of the anion desorption and a concurrent hydrogen evolution current due to the so-called Frumkin effect (see Chap. 182[https://doi.org/10.1007/978-3662-53908-8_182] and Ref. [1]). The negative charge of the still chloride-covered surface facilitates reduction of H+ ions and causes hydrogen evolution before this process starts on the bare metal surface. Inasmuch as chloride desorbs, this process subsides with decreasing chloride coverage, until at more negative potentials, the exponential current increase due to hydrogen evolution on the bare copper surface sets in.

Current density [µA/cm2]

5

0

–5

–10

Cu(111)-Cl –15 –1.1

–1.0

–0.9

–0.8

–0.7

–0.6

Potential E[V] vs Hg/HgSO4

–0.5

Fig. 185.1 Cyclic voltammogram of Cu(111) in 10 mM HCl solution recorded with a scan rate of 10 mV/s. The dashed trace is obtained after correction for the hydrogen evolution current on bare Cu (111) (From Ref. [8])

The assignment of the pair of peaks in the cyclic voltammogram to the adsorption and desorption of chloride anions is supported by the appearance and disappearance of new structures on the surface as M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_185

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M. Nowicki and K. Wandelt

observed by in situ STM. This is demonstrated by panels b–e in Fig. 185.2 [2]. These images are recorded in a potentiodynamic imaging mode, i.e., the potential of the sample is scanned while imaging. Thus, the y-coordinate of each scan (see panel d) not only represents the geometric position in the slow scan direction but also a continuous variation of the electrode potential. Specifically, while taking image b (from left to right), the potential changes along the part b (full line) of the CV in panel a. Likewise, while scanning image c from left to right, the potential changes along the dotted section c in panel a and so on. The dotted/ full arrows below/above the panels b–e indicate both the scan direction of the potential and the evolution of the STM image. In the left part of panels b and e, the anion-free Cu(111) surface is seen with atomic resolution. In the rightmost part of panels b and e, a distinctly different, i.e., more coarse, structure is clearly seen which is the onset/remnant of the structure seen in panels c and d, respectively. Since the change to/from this more coarse structure from/to the bare Cu(111) lattice coincides with the rise of the adsorption and the desorption peak (i.e., at the transitions between the full and the dotted line parts of the CV), the more coarse structure on the right-hand side of panels b and e must be associated with the formation/decay of the anion adlayer, which dominates in panels c and d. Thus, potentiodynamic imaging may provide information about the kinetics of adsorption /desorption, e.g., as a function of the potential sweep rate. b

c

Cu (111) 30

Current density j/mA cm–2

20

Chloride absorbate

a

adsorption

10

c

b

0 –10

d

–20 –30 –40

e

–50 –60 –1.2

–1.1

–1.0

Desorption –0.9

–0.8

–0.7

–0.6

–0.5

–0.4

Potential E [V] / V Cu (111)

e

Chloride adsorbate

d

Fig. 185.2 (a) Cyclic voltammogram of Cu (111) in 10 mM HCl solution. (b–e) In situ STM images registered potentiodynamically during scanning of the electrode potential along the corresponding parts b, c, and d, e in anodic and cathodic direction, respectively (see text) (From Ref. [2])

185

Hydrohalic acid interaction with copper surfaces: Cu(111) – chloride

3

Since potentiodynamic imaging is more prone to distortions, as seen in Fig. 185.2d, an analysis of the respective structure in panels b–e is better done with images registered from the adsorbate-covered and anion-free surface at constant potential, respectively. Potentiostatic images of the bare and adsorbatecovered Cu(111) surface were already shown in Figs. 180.3[https://doi.org/10.1007/978-3-662-53908-8_ 180] and 181.2[https://doi.org/10.1007/978-3-662-53908-8_181], respectively. From the relative orientation of the observed close-packed rows and from the distances between the bright dots, assigned to the ad-particles, the structure of the adsorbate layer is identified as a (√3  √3)R30 -Cl superstructure which at very positive potentials undergoes uniaxial compression into a c(p  √3) phase (see Fig. 181.2d[https://doi. org/10.1007/978-3-662-53908-8_181]). There are, in principle, several possibilities to determine also the adsorption site of the individual ad-particles. The most intuitive way would be to register the surface before and after adsorption of the anions and to superimpose the two images. Thermal drift between the two measurements, however, makes this approach unreliable. A more trustworthy assignment can be achieved if at certain potentials, the bare substrate and the adsorbate structure are visible in one and the same image and the partial adsorbate coverage, e.g., in the form of islands, exhibits the same structure as at full monolayer. In this case, an extrapolation of the adsorbate grid onto the substrate lattice discloses the adsorption sites. Yet, another possibility consists in the quasi-spectroscopic imaging mode, as demonstrated by the three panels a–c in Fig. 185.3. These three images are all registered from the adsorbate-covered surface, but under different (constant) tunneling conditions, here different bias voltages, namely, (a) –420 mV, (b) –480 mV, and (c) –520 mV [2]. At these different bias voltages, electrons tunnel into different orbitals of the surface constituents, in (a) dominantly into empty states of the adsorbate and in (c) dominantly into empty states of the copper substrate. For panel b, the bias voltage is chosen such that the image shows contributions of both. A Fourier transformation of this image, a division of the low frequency and the high frequency part, and their back transformation enable a separation of both the adsorbate and the substrate contribution as shown in panels d–f in Fig. 185.3. The low frequency part represents the adsorbate lattice, while the high frequency part corresponds to the substrate surface grid. Since both partial images now originate from one and the same measurement, namely, panel b, their superposition yields clearly the position of the ad-particles with respect to the substrate lattice, namely, in the present case – not unexpectedly – the threefold hollow sites (like in UHV [3–6]) as illustrated in Fig. 185.3g.

Fig. 185.3 (a–c) In situ STM images of a chloride covered Cu(111) surface taken with the different indicated tunneling parameters emphasizing (a) the (√3  √3)R30 chloride overlayer and (c) the underlying Cu(111) substrate surface. Panel (b), including contributions from both the chloride overlayer and the Cu substrate, enables after (e) Fourier filtering a decomposition in both contributions from (d) the chloride overlayer on the one hand and (f) the (1  1) lattice of the underlying Cu(111) substrate on the other hand. Since the latter originate from the same image (b) their superposition yields the absolute adsorption site of the Cl anions, namely – not unexpectedly – the threefold hollow sites as sketched in panel (g) (From Ref. [2])

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M. Nowicki and K. Wandelt

Strictly speaking, none of the above results neither the CV signals nor the STM images nor their suggestive correlation says something about the chemical nature of the adsorbed species assigned to the coarse structure in Fig. 185.2c and panel a of Fig. 185.3. A chemical analysis of the surface composition might be done in situ by X- or UV-photon spectroscopy (see, e.g., [7]) or still has to draw largely on ex situ measurements since a similarly sensitive routine in situ equivalent to photoelectron spectroscopy has not emerged yet. Figure 185.4 shows XPS and Fig. 185.5 UPS and LEIS spectra of a Cu(111) electrode which was removed from the electrolyte in the potential regime of the (√3  √3)R30 superstructure and transferred, without contact to air, in the UHV spectrometer chamber [8, 9]. The XPS survey spectrum shows the characteristic copper valence band (VB), 3p and 3s lines, as well as clearly the spin-orbit split Cl2p3/2,1/2 doublet [e.g., 10]. The top UPS (HeI) spectrum (1) in Fig. 185.5 belongs to the well in UHV prepared Cu(111) surface. After air-free transfer into hydrochloric acid solution and back-transfer into the UHV chamber, a series of alternating UPS and LEIS spectra was registered beginning with the central UPS and ending with the LEIS spectrum at the lower right side after a total He+ ion dose of approximately 1940 μAs. The UPS spectrum (2) and the following first LEIS spectrum (3) show clear chloride signals. Since LEIS is not a nondestructive method, the repeated ion bombardment causes successive sputter removal of the adsorbed chloride; as a consequence, the chloride signals decrease, while the copper signals increase, so that after the total ion dose of 1940 μAs, all chloride is sputtered away and the clean copper surface remains (see spectra (4) and (5)). The slight dissimilarity between spectrum (1) and (4) can be explained in terms of the different roughness of both surfaces, well annealed in (1) versus ion bombarded in (4). Thus, the chemical nature of the adsorbed phase, though intuitively expected to be chloride, is verified by these XPS, UPS, and LEIS measurements. The XPS spectrum and the LEIS spectrum (3), however, convey further important information. The XPS lines belong to just one single chloride species; there is no spectral hint to the existence of two (or more) inequivalent chloride species. This excludes that during the emersion and transfer process, remnants of the liquid electrolyte, i.e., KCl, dried on the surface, which would result in a separate chloride signal. Moreover, the first LEIS spectrum (2) does not show any trace of oxygen, which clearly excludes adhering or occluded water. Both these observations substantiate the hope that such ex situ measurements do provide (at least some) relevant information about the status of the metal/electrolyte interface before transfer into UHV. Cl2p3/2

Intensity

Cl2p1/2

XPS

202 201 200 199 198 197 196

Cu3p CI2p

200

VB

Cu3s

100

0

Electron binding energy [eV]

Fig. 185.4 XPS spectrum taken after emersion of a chloride covered Cu(100) electrode showing the copper 3d valence band (VB), and the Cu(3p), Cu(3s) core levels as well as the spin-orbit split Cl2p emission. In the inset, the latter shows no indication of more than one adsorption state of chloride, e.g., from dried remnants of adhering solution during the emersion and transfer into the XPS spectrometer

185

Hydrohalic acid interaction with copper surfaces: Cu(111) – chloride

Intensity (arb units)

1

LEIS Cl Cu

x20

Intensity (arb units)

UPS

5

2 3

4 5

0 2 4 6 8 10 400 600 800 1000 Energy Eb (eV) Energy Ekin (eV)

Fig. 185.5 A sequence of UPS and LEIS spectra registered (1) from a clean Cu(111) surface in UHV, and (2–5) from the same surface after emersion from hydrochloric acid solution. The spectra 2–5 are taken in chronological order (see text) (From Ref. [9])

Symbols and abbreviations Short form

Full form

STM UHV UV UPS LEIS XPS

scanning tunneling microscopy ultrahigh vacuum ultraviolet ultraviolet photoelectron spectroscopy low-energy ion spectroscopy X-ray photoelectron spectroscopy

References 1. 2.

Frumkin, A.: Wasserstoffüberspannung und Struktur der Doppelschicht. Z. Phys. Chem. A 164, 121 (1993) Broekmann, P., Wilms, M., Kruft, M., Stuhlmann, C., Wandelt, K.: In-situ STM investigation of specific anion adsorption on Cu(111). J. Electroanal. Chem. 467, 307 (1999) 3. Goddard, P.J., Lambert, R.M.: Adsorption-desorption properties and surface structural chemistry of chlorine on Cu(111) and Ag(111). Surf. Sci. 67, 180 (1977) 4. Crapper, M.D., Riley, C.E., Sweeney, P.J.J., McConville, C.F., Woodruff, D.P.: Investigation of the Cu(111) (√3  √3) R30 -Cl structure using SEXAFS and photoelectron diffraction. Surf. Sci. 182, 213 (1987) 5. Molai, K., Hashizuma, T., Lu, H., Jeon, D., Sakurai, T., Pickering, H.W.: STM of the Cu(111)1  1 surface and its exposure to chlorine and sulfur. Appl. Surf. Sci. 67, 246 (1993) 6. Walter, W.K., Manolopoulos, D.E., Jones, R.G.: Chlorine adsorption and diffusion on Cu(111). Surf. Sci. 348, 115 (1996) 7. Barrett, S.B., Lucas, C.A., Raval, R.: Photon spectroscopies. In: Wandelt, K. (ed.) Surface and Interface Science, vol. 1, p. 311. Wiley-VCH, Weinheim (2012) 8. Kruft, M., Wohlmann, B., Stuhlmann, C., Wandelt, K.: Chloride adsorption on Cu(111) electrodes in dilute HCl solutions. Surf. Sci. 377–379, 601 (1997) 9. Stuhlmann, C., Wohlmann, B., Park, Z., Kruft, M., Broekmann, P., Wandelt, K.: Chloride adsorption on Cu(111) electrodes: electrochemical behavior and UHV transfer experiments. In: Wandelt, K., Thurgate, S. (eds.) Solid-Liquid Interfaces, Macroscopic Phenomena – Microscopic Understanding Topics in Applied Physics, vol. 85, p. 199. Springer, Heidelberg (2003. ISBN:3-540-42583-7) 10. Breuer, S., Phan, D.T., Huemann, S., Gentz, K., Zoerlein, C., Hunger, R., Wandelt, K., Broekmann, P.: Organic layers at metal/electrolyte interfaces: molecular structure and reactivity of viologen monolayers. New J. Phys. 10, 125033 (2008)

Chapter 186

Hydrohalic acid interaction with copper surfaces: Cu(111) – bromide M. Nowicki and K. Wandelt

As mentioned above, bromide binds more strongly to copper than chloride. As a consequence, desorption of bromide occurs at more negative potentials than chloride, in fact already in the hydrogen evolution regime (Fig. 181.1[https://doi.org/10.1007/978-3-662-53908-8_181]). It is thus impossible to image the uncovered Cu(111) surface in bromide-containing electrolyte. In the whole accessible potential range, the surface is covered by a highly ordered bromide layer. In contrast to chloride, the larger bromide anions never form a commensurate (√3
√3)R30 structure but uniaxially compressed c(p
√3) structures with 2.62 < p < 2.83 between the anodic and cathodic limit, respectively [1, 2]. Due to the incommensuracy, the bromide particles reside in inequivalent surface positions resulting in the wavy superstructure seen in Figs. 181.2e[https://doi.org/10.1007/978-3-662-53908-8_181] and 186.1b, which shows the most compressed situation. The commensurate (√3
√3)R30 structure is even at most negative potentials never reached. At the cathodic (anodic) limit, the bromide layer is 5.6% (9%) compressed in [110] directions compared to the hypothetical ideally hexagonal (√3
√3)R30 arrangement. In the state of highest compression, the shortest Br-Br distance is only 4.0 Å [3] which is longer than the Pauling distance between two singly charged bromide ions (3.9 Å) as well as the van der Waals distance between two neutral bromide atoms (3.7 Å), which supports the notion that even in the most compressed phase, the adsorbed bromide particles retain largely their ionic character. Figure 186.1a includes a step edge on the surface. This step edge is totally defect-free and has the same orientation as a high symmetry direction of the bromide adlayer, namely, the direction of the densely packed Br rows. Interestingly, this preferred step direction is explicitly not the commensurate √3-direction but a direction parallel to a diagonal of the c(p
√3) unit cell. Thus, the packing density of the bromide particles appears to be more important for the stabilization of step edges than the commensurability along a symmetry direction. As a consequence, the step edge in Fig. 186.1a does not run parallel but at an angle of 55 off the direction of the wave crests. This angle varies with the potential, i.e., the parameter p.

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_186

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Fig. 186.1 In situ STM images of a bromide coverd Cu(111) surface showing the uniaxially incommensurate c(p
√2)Br superstructure. The step in (a) runs along and is stabilized by a close packed row of Br anions. (a) 15.4
15.4 nm, IT ¼ 1 nA, UB ¼ 20 mV, E ¼ 215 mV; (b) 8.3
8.3 nm, IT ¼ 1 nA, UB ¼ 20 mV, E ¼ 215 mV (From Ref. [2])

The condition of step edges running parallel to the direction of densely packed bromide rows manifests itself – like in the case of the Cu(100) surface – also in the anodic corrosion morphology of the bromidecovered Cu(111) surface. Figure 186.2 shows a bromide-covered Cu(111) surface in the anodic potential regime resulting from a combination of local corrosion – and (accompanying) deposition processes. The steps are running parallel to the densely packed Br rows and not parallel to the densely packed Cu rows [2].

Fig. 186.2 In situ STM images of the morphology of a bromide covered Cu(111) surface at positive potentials. (a) 285
285 nm, IT ¼ 1 nA, UB ¼ 46 mV, E ¼ 120 mV (Ag/AgCl); (b) 112
112 nm, IT ¼ 1 nA, UB ¼ 46 mV, E ¼ 120 mV. Note the orientation and the anisotropy of extending islands (a) and depressions (b) of monoatomic height/depth (From Ref. [2])

Symbols and abbreviations Short form

Full form

STM

scanning tunneling microscopy

186

Hydrohalic acid interaction with copper surfaces: Cu(111) – bromide

3

References 1. Broekmann, P., Wilms, M., Kruft, M., Stuhlmann, C., Wandelt, K.: In-situ STM investigation of specific anion adsorption on Cu(111). J. Electroanal. Chem. 467, 307 (1999) 2. Broekmann, P.: Atomare Struktur und Dynamik von Kupfer/Elektrolyt- Grenzflächen. Ph.D. Thesis, University of Bonn (2000) 3. Inukai, J., Osawa, Y., Itaya, K.: Adlayer Structures of Chlorine, Bromine, and Iodine on Cu(111) Electrode in Solution: In-Situ STM and ex-Situ LEED Studies. J. Phys. Chem. B 102, 10034 (1998)

Chapter 187

Hydrohalic acid interaction with copper surfaces: Cu(111) – iodide M. Nowicki and K. Wandelt

A cyclic voltammogram of Cu(111) in 10 mM HClO4 + 0.1 mM KI solution is displayed in Fig. 187.1 [1]. The extra shoulder (arrow Des.) superimposed on the exponentially growing hydrogen evolution current in cathodic scan direction corresponds to the onset of the iodide desorption, which compared to chloride and bromide is shifted to even more negative potentials due to a stronger copper-adsorbate interaction. In the reverse, i.e., anodic, scan direction peak Ads. and peak P with the pre-shoulder (see inset) correspond to the re-adsorption of iodide and a phase transition within the adsorbed iodide layer, respectively, as concluded from STM-derived structure data shown in the following figures. At very negative potentials (
500 mV vs. Ag/AgI), iodide forms a hexagonal (√3  √3)R30 structure (Fig. 187.2a) with a nearest-neighbor distance of 4.4  0.15 Å (¼√3aCu
Cu). This structure is rather perfect as revealed by the 2D Fourier transformation in Fig. 187.2b; the hexagon is ideal, and the individual spots (inset) are sharp and circular, indicating a narrow distribution of nearest-neighbor distances. This structure corresponds to a coverage of θI ¼ 0.33 ML and was found in both UHV [2–7] and solution [1].

–20

Des.

1.5 1.0

–40

I [µA/cm2]

Current density [µA/cm2]

P

Ads.

0

P

0.5 0.0 –0.5 –1.0

–60

–1.5

–300 –250 –200 –150 –100 –50

Potential E vs. Ag/AgI [mV]

–80 –700

–600

–500

–400

–300

–200

–100

Potential E vs. Ag/AgI [mV]

0

Fig. 187.1 Cyclic voltammogram of Cu (111) in a 0.1 mM KI containing HClO4 solution; scan rate dE/dt ¼ 10 mV/s. Besides the iodide adsorption (Ads.) and iodide desorption (Des.) peak the cyclic voltammogram indicates a phase transition within the adsorbed iodide layer (P) as verified by in situ STM (From Ref. [1])

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_187

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Fig. 187.2 In situ STM images of the commensurate (a) and incommensurate (c) iodide layer on Cu(111) in 0.05 mM KI containing HClO4 solution at different electrode potentials. (a) (√3  √3)R30 -I structure close to the onset of hydrogen evolution; 10.4  10.4 nm, IT ¼ 1 nA, UB ¼ 14 mV, E ¼
510 mV (Ag/AgCl); (b) two-dimensional Fourier spectrum of (a); (c) uniaxially compressed iodide layer at more positive potentials, 15  15 nm, IT ¼ 1.9 nA, UB ¼ 4 mV, E ¼
139 mV; (d) two-dimensional Fourier spectrum of (c). The inset in (d) is an enlargement of the white rectangle showing a splitting into two sub-spots in contrast to the inset in (b) (From Ref. [1])

However, changing the potential toward more positive values causes a uniaxial compression of the iodide overlayer leading to a wavy superstructure seen in Fig. 187.2c (and Fig. 181.2f[https://doi.org/10. 1007/978-3-662-53908-8_181]). Like in the case of chloride and bromide on Cu(111) in the direction of the brighter wave crests, the ad-particles are in registry with the substrate (commensurate direction), while the adlayer is compressed in the direction perpendicular to the wave crests (incommensurate direction). As a result, along this direction, ad-particles occupy no longer equivalent adsorption sites. In the interval from
510 to
139 mV (Ag/AgI), the interatomic distance shrinks from 0.44 to 0.42 nm. This is also reflected in the Fourier transformation displayed in Fig. 187.2d. The hexagon is slightly distorted, and the spots are split into a broadened main spot and a satellite spot. The broadening indicates a broader distribution of interatomic distances, and the spot splitting d* reflects directly the periodicity of the long-range wavy superstructure. This “electro-compression” occurs within the potential range
300 to
100 mV and explains peak P in the CV (Fig. 187.1). Within the potential range
168 to
114 mV, the distance between adjacent wave crests decreases from 39.4  0.15 Å to 37.1  0.15 Å, respectively. The concomitant symmetry reduction of the iodide overlayer compared to the substrate causes the appearance of three equivalent rotational domains [1]. Two possible mechanisms can be considered to explain the transition from a commensurate (√3  √3) R30 to a uniaxially incommensurate (p  √3)R30 structure, namely, (i) the insertion of domain walls or

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Hydrohalic acid interaction with copper surfaces: Cu(111) – iodide

3

(ii) the uniform and continuous uniaxial compression of the adlayer. In the first case, commensurate domains are separated by narrow dislocation lines of shorter nearest-neighbor distances (heavy domain walls). In this case, the total bond energy of the commensurate domains overcompensates the reduced bond energy of all dislocated ad-particles within the domain walls. In the second case, all nearest-neighbor distances along the incommensurate direction shrink uniformly leading to a continuous displacement of ad-particles out of hollow sites and thus the spatially periodic occupation of energetically most and least favorable adsorption sites, respectively. The iodide layer on Cu(111) behaves according to the first, the domain-wall mechanism. For instance, at
114 mV (Ag/AgI), while the average nearest-neighbor distance has shrunk to 3.9  0.15 Å (compared to 4.4  0.15 Å in the ideal (√3  √3)R30 structure), the nearest-neighbor distance within the darker valleys is identical to that of an ideal (√3  √3)R30 structure, while it is found to be only 3.7  0.15 Å within the brighter wave crests (Fig. 187.2c). Figure 187.3a shows a hard-sphere model of a uniaxially compressed (√3  √3)R30 structure with a straight superheavy domain wall (shdw), in which the iodideiodide distance would be equal to aCu-Cu ¼ 2.56 Å. Since this is absolutely unrealistic, such a domain wall may partially relax by some local atom displacement and meandering as sketched in Fig. 187.3b, c, in agreement with the experimental observation (see Fig. 187.2c) [1]. This behavior is not peculiar to the copper/ electrolyte interface but has also been found for iodine adsorption on Cu(111) in UHV [7]. Shdw

NND√3-Domäne = 0.44 nm

a

√3aCu √3aCu

√3aCu √3aCu

NNDshdw = 0,256 nm

Shdw

b

√3aCu √3aCu

NNDshdw = 0,256 nm

c

√3aCu √3aCu

NNDshdw > 0,256 nm

Fig. 187.3 Schematic hard-sphere models of (a) an ideal superheavy domain wall (shdw); (b) a meandering shdw and (c) a partially relaxed shdw within a (√3  √3)R30 iodide layer on Cu(111) (From Ref. [1])

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Symbols and abbreviations Short form

Full form

UHV STM ML

ultrahigh vacuum scanning tunneling microscopy monolayer

References 1. Obliers, B., Broekmann, P., Wandelt, K.: Uniaxial compression of iodide adlayers on Cu(1 1 1) studied under electrochemical conditions. J. Electroanal. Chem. 554–555, 183 (2003) 2. Citrin, P.H., Eisenberger, P., Hewitt, R.C.: SEXAFS studies of iodine adsorbed on single crystal substrates. Surf. Sci. 89, 28 (1979) 3. Citrin, P.H., Eisenberger, P., Hewitt, R.C.: Adsorption Sites and Bond Lengths of Iodine on Cu{111} and Cu{100} from Surface Extended X-Ray-Absorption Fine Structure. Phys. Rev. Lett. 45, 1948 (1980) 4. DiCenzo, S.B., Wertheim, G.K., Buchanan, D.N.E.: XPS studies of adatom-adatom interactions: I/Ag(111) and I/Cu(111). Surf. Sci. 121, 411 (1982) 5. DiCenzo, S.B., Wertheim, G.K., Buchanan, D.N.E.: Epitaxy of CuI on Cu(111). Appl. Phys. Lett. 40, 888 (1982) 6. Andryushechkin, B.V., Eltsov, K.N., Shevlyuga, V.M.: Domain-wall mechanism of “(n√3n√3)R30 ” incommensurate structure formation in chemisorbed halogen layers on Cu(1 1 1). Surf. Sci. 470, L63 (2000) 7. Andryushechkin, B.V., Eltsov, K.N., Shevlyuga, V.M.: Atomic scale observation of iodine layer compression on Cu(1 1 1). Surf. Sci. 472, 80 (2001)

Chapter 188

Hydrohalic acid interaction with copper surfaces: Cu(110) – bromide M. Nowicki and K. Wandelt

Bromide adsorbs at
520 mV (vs. Ag/AgBr) and desorbs at about
560 mV [1]. The desorption peak is superimposed by the exponentially increasing hydrogen evolution current, but before the re-adsorption at 40 mV higher potential (Fig. 188.1), it is possible to register an STM image as shown in Fig. 188.2a. The atomically resolved image (Fig. 188.2b) reveals the expected rectangular unit cell with interatomic distances of 0.362  0.01 nm in [001] and 0.265  0.01 nm in [ 1 10] direction in agreement with crystallographic data. At potentials above the adsorption peak, the STM image in Fig. 188.2c shows the atomic structure of the bromide adlayer; every spot is assigned to a specifically adsorbed bromide particle. Looking under grazing angle at this image clearly reveals a wavy superstructure with wave valleys and wave crests running in [001] direction, in contrast to earlier results by Wan and Itaya [2]. The adsorbed particles forming a quasi-hexagonal structure are imaged with different brightness. Both observations indicate that the bromide particles are located in inequivalent adsorption sites, which is clearly supported by the power spectrum of this structure (Fig. 188.2d) showing the outer (quasi-)hexagon, which indicates the symmetry of the atomic structure, as well as weaker spots inside the hexagon from a long-ranged superstructure. The lattice parameters of this superstructure can be determined using the (1  1)-Cu(110) structure for internal calibration. Parallel to the [001] direction, the nearest interatomic distance is 0.720  0.01 nm, while it is 0.384  0,01 nm in [ 1 10] direction. This results in a c(3  2) unit cell with respect to the unit cell of the bare Cu(110) surface. The (3  2) periodicity as well as the concomitant inequivalence of adsorption sites is also clearly revealed by height profiles along the [001] and [ 1 10] direction displayed in Fig. 188.3. The c(3  2) structure corresponding to a coverage of θBr ¼ 0.67 ML is illustrated in Fig. 188.4 which gives relevant distances and refers to the profiles 1 and 2 in Fig. 188.3b, c.

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_188

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–500

–400

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Potential [mv] E vs. Ag/AgBr [mV]

–300

–200

Potential [mV] E vs. Ag/AgBr

100

Fig. 188.1 Representative cyclic voltammogram of Cu(110) in 10 mM HBr solution. The inset shows in anodic direction the onset of the anodic copper dissolution followed by the copper redepositon in the reverse potential sweep, dE/dt ¼ 10 mv/s. The arrow 1 marks the potential at which Fig. 188.5 was registered (From Ref. [1])

Fig. 188.2 In situ STM images of (a) a bromide covered Cu(110) surface, 16.5  16.5 nm, IT ¼ 30 nA, UB ¼ 150 mV, E ¼
480 mV (Ag/AgCl); (b) a bare Cu(110) surface region at very negative potential, 3.52  3.52 nm, IT ¼ 1 nA, UB ¼ 7 mV, E ¼
619 mV (Ag/AgCl); (c) the atomic structure of the bromide adlayer at positive potentials, 8.5  8.5 nm, IT ¼ 4 nA, UB ¼ 150 mV, E ¼
203 mV (Ag/AgCl); (d) power spectrum of panel (c) (From Ref. [1])

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Hydrohalic acid interaction with copper surfaces: Cu(110) – bromide

a

3

2

1

b

c

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z-corrugation [nm]

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0.06

2 0.04

0.02

0.00 0

1

2

3

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0

2

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distance [nm]

Fig. 188.3 (a) In situ STM image of the long-range superstructure of bromide on Cu(110), 5.08  5.08 nm, IT ¼ 4 nA, UB ¼ 133 mV, E ¼
203 mV. The white square indicates the unit cell, and the white circle marks a structural defect. (b) and (c) show line scans along the white lines 1 and 2 in panel (a) showing a twofold and fourfold periodicity (From Ref. [1])

0.384 nm 0.410 nm

[001]

0.724 nm

[110] Br in different adsorption sites Cu

Fig. 188.4 Schematic hard-sphere model of the bromide adlayer on Cu (110) at positive potentials giving relevant distances and the two possible unit cells ( full and dashed line rectangle). The arrows indicate the directions of twofold and fourfold periodicity along the white lines in Fig. 188.3 (From Ref. [1])

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A further very interesting property of the c(3  2)-Br-covered surface was discovered when scanning the surface with different imaging parameters [1]. Figure 188.5a shows an image which was obtained after the central dark part had been scanned before with higher bias voltage and a slower scan rate, respectively, a longer residence time per tip position. Imaging this obviously damaged part of the surface 30 min later again yields a regular structure of parallel furrows of mostly similar width and separation as illustrated by the height profile in Fig. 188.5c taken along the line in panel b. These furrows are the result of a tip-induced electrocorrosion process (well below the copper dissolution potential) as described in detail by Xie and Kolb [3], followed by some “electro-annealing” process afterward. All furrows in Fig. 188.5b run in [001] direction and have, except the leftmost, a width of 2.048  0.13 nm, which corresponds to eight times the Cu-Cu interatomic distance in the [ 1 10] direction. Based on these experimental findings, a structure model as shown in Fig. 188.6 was proposed. Five, four, three, two, and one Cu atoms are missing in [110] direction in the first, second, third, fourth, and fifth Cu layers. As a consequence, the two side walls of each furrow form Cu(100) facets, which are again covered with bromide, but in this case forming a c(2  2) structure as known from Cu(100) (see Chap. 182[https://doi.org/10.1007/978-3-662-53908-8_182]). The fact that the desorption of bromide from Cu(100) occurs at more negative potentials than from Cu(110) indicates a stronger Cu-Br interaction on Cu(100) than on Cu(110). Thus, the c(2  2)-Br-covered (100) facets forming the side walls of the furrows are energetically more stable than the c(3  2)-Br-covered Cu(110) area. The locally tunneling electrons of certain energy just provide the necessary activation energy for the transformation from the c(3  2)-Br-covered Cu(110) surface to a c(2  2)-Br-covered Cu(100) facet. These results are not only very much in line with the tendency of adsorbate-induced and thermally activated faceting of fcc(110) surface well known from adsorption experiments under UHV conditions but also nicely lead over to the electrosorption of chloride on Cu(110) described in detail in the following chapter.

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Hydrohalic acid interaction with copper surfaces: Cu(110) – bromide

5

Fig. 188.5 In situ STM images of the tip-induced surface modification of the bromide covered Cu(110) surface at E ¼
230 mV (Ag/AgCl), see arrow 1 in Fig. 188.1. (a) 49.1  49.1 nm, IT ¼ 10 nA, UB ¼ 100 mV; (b) 14.49  14.49 nm, IT ¼ 1 nA, UB ¼ 102 mV; (c) height profile along the line in (b) (From Ref. [1])

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Fig. 188.6 (a) Schematic hard-sphere model explaining the result of an “electroannealing process” on the bromide covered Cu(110) surface by the formation of bromide covered Cu(100) facets. (b) Cross section of the hard-sphere model in (a) showing possible adsorption sites within the furrows (From Ref. [1])

Symbols and abbreviations Short form

Full form

UHV STM ML fcc

ultrahigh vacuum scanning tunneling microscopy monolayer face centered cubic

References 1. Obliers, B., Anastasescu, M., Broekmann, P., Wandelt, K.: Atomic structure and tip-induced reconstruction of bromide covered Cu(1 1 0) electrodes. Surf. Sci. 573, 47 (2004) 2. Wan, L.-J., Itaya, K.: In situ scanning tunneling microscopy of Cu(110): atomic structures of halide adlayers and anodic dissolution. J. Electroanal. Chem. 473, 10 (1999) 3. Xie, Z.-X., Kolb, D.M.: Spatially confined copper dissolution by an STM tip: a new type of electrochemical reaction? J. Electroanal. Chem. 481, 177 (2000)

Chapter 189

Hydrohalic acid interaction with copper surfaces: Cu(110) – chloride M. Nowicki and K. Wandelt

As mentioned before, the bare Cu(110) surface is characterized by an anisotropic atomic structure with rectangular unit cell (a ¼ 2.56 Å, b ¼ 3.62 Å) as well as an electronic surface state at 2.5 eV binding energy [2]. Its reactivity toward chlorine has already been studied in UHV including STM measurements [1], which revealed severe restructuring of the surface [3]. First results about the interaction of a Cu(110) surface with chloride ions in hydro-chloric acid solution obtained with in situ STM were published by Wan et al. [4] and Li et al. [5], who also showed massive restructuring of the surface. Later, based on RAS measurements Barritt et al. [2] discussed the modification of the electronic properties of the Cu(110) surface once brought in contact with hydrochloric acid solution. These separate STM and RAS measurements led to the picture that no substantial differences seem to exist between a Cu(110) sample immersed in aqueous HCl solution or being exposed to chlorine gas under UHV conditions. Most recently combined measurements with in situ STM and RAS in conjunction with cyclic voltammetry within the same electrochemical cell [6, 7] revealed rather detailed information about the potential dependent reaction of chloride ions with a Cu(110) electrode surface in 10 mM HCl solution. Figure 189.1 displays a CV curve acquired with a Cu(110) sample immersed in 10 mM HCl solution [6]. The arrows indicate the direction of the CV scan (scan rate dV/dt ¼ 2 mV/s), and the scan interval is limited from about 600 to –300 mV (Ag/AgCl) in order to avoid both the anodic dissolution of the metal and the cathodic hydrogen evolution. In the potential scan along the positive (negative) direction, two peaks A, B (C, D) are detected with the same separation of 30 mV between B and C and A and D, respectively. The significant increase of the anodic current with increasing potential, in particular beyond peak B, indicates some ongoing charge transfer reaction which is found to be more pronounced the slower the potential is scanned [7]. In the negative scan direction, it is the “product” of this slow process at high potentials, which decays and gives rise to the pronounced peak C. The presence of the two peaks in both scan directions at similar electrode potentials suggests that the chloride anions are involved in two different electrochemically induced processes at the sample surface, either two different adsorption (A, B) and desorption (C, D) states or one adsorption (desorption) A (D) process and a further surface reconstruction (deconstruction) starting with B (ending with C). Combined in situ STM and RAS results have been interpreted in terms of the second explanation, as detailed in the following.

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_189

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- 550 - 600

- 450 - 500

- 300

- 550

Current density

< 600

Potenal [mV]

- 550 - 500

- 600 - 550

- 450

- 500

- 300

- 350

Fig. 189.1 Cyclic voltammogram and selected in situ STM images of a Cu(110) surface in 10 mM HCl solution. A and B indicate chloride adsorption/reconstruction processes, C and D the corresponding deconstruction/desorption processes whose effects on the surface structure are displayed in the STM images. The numbers 1–12 along the CV refer to the potential regime in which the image with the respective number has been registered. The leftmost image (4 nm  4 nm, IT ¼ 8 nA, UB ¼ 33 mV; E ¼ 605 mV (Ag/AgCl)) is dominated by bare Cu(110) regions, while all other images (81 nm  81 nm, IT ¼ 1.4 nA, UB ¼ 30 mV, E given next to each image) show drastic structural changes with increasing and re-decreasing potential (see text) (Composed from data in Ref. [6])

The leftmost STM image in Fig. 189.1 shows the Cu(110) surface with atomic resolution at a constant electrode potential of 605 mV. At this potential, no ions are adsorbed on the surface as suggested by the CV. The structure visible in this panel, specifically the rectangular unit cell with a ¼ 2.54  0.04 Å and b ¼ 3.66  0.04 Å, agrees with the crystallographic parameters of the Cu(110) surface and previous results for the bare Cu(110) surface in UHV [8], as well as with those shown in Figs. 180.3[https://doi.org/10.1007/ 978-3-662-53908-8_180] and 188.2. Thus, at such a negative value of the electrode potential (605 mV), the surface is clean and not affected by the presence of the solution. Some noisy, white spots with atomic dimensions and heights of the order of about 1 Å visible in the image are found to float on the surface, as judged from consecutive images. These mobile atomic-sized particles are assigned to [CuCl2] species formed with highly reactive low-coordinated Cu atoms at defect sites (the basis of “electro-annealing”; see Sect. 179.13[https://doi.org/10.1007/978-3-662-53908-8_179]) or being a residue from the mass transport inherent in the restructuring process at high potentials hypothesized above and verified below. Selected STM images from a series of 12 images taken while the electrode potential is varied through a full CV cycle are shown along with the CV in Fig. 189.1 [7]. The increasing numbers along the CV indicate the starting electrode potential of the associated STM image, while during acquisition of each image, the potential continues to change, so that each STM image of Fig. 189.1 directly shows the effect of the potential variation in a range of about 50 mV (see vertical arrows and potential values next to each image).

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Hydrohalic acid interaction with copper surfaces: Cu(110) – chloride

3

Image 1 of the clean Cu(110) surface exhibits a terrace of width ˃70 nm and a spotty appearance due to the enhanced formation of mobile [CuCl2] species in this potential range. At the bottom of panel 2 and the top of panel 3 corresponding to the onset of the first CV peak A, a restructuring process of the surface is visible. It starts from the step edges (arrow in panel 2) and evolves into the terraces with the formation of long dark channels (up to several tens of nanometers), aligned along the [100] crystallographic direction. In contrast to rather “frizzy” step edges of the bare surface, these erosion channels exhibit sharp boundaries, stabilized due to adsorption of chloride anions like at steps on the Cu(100) surface discussed in Chap. 182 [https://doi.org/10.1007/978-3-662-53908-8_182]. The same observation, reported for a Cu(110) surface subjected to high exposures of molecular Cl2 in UHV [3], was interpreted in terms of a surface faceting with the formation of (210) planes. This suggests that a similar faceting of the Cu(110) surface occurs also in solution at potentials ˃ 510 mV. At even higher potential values (470/480 mV), i.e., close to the onset of the second anodic current peak B in the CV, the development of extended directional bright stripes well aligned along the [100] direction is observed (panel 3). These stripes always start after or at least in coincidence with the previous copper restructuring and channel formation and extend onto copper terraces, preferentially from initial nucleation sites close to steps and channel edges. Most of them are positioned adjacent to a channel. At even higher potentials, passing the second anodic current peak (B) in the CV, the number and density of stripes increases until near the end of the positive scan (300 mV, panel 6) where the faceting process slows down; the stripes are up to several tens of nanometers long and have a width in the range of 2–3 nm. Some stripes have overgrown the lower ones. From height profiles perpendicular to the stripes and channels, an inclination angle of 18  3 is obtained, consistent with the formation of (210) facets [6]. After emersion of the sample at this stage and air-free transfer into UHV ex situ XPS Cl2p, spectra prove the presence of chloride on the surface. LEED images taken under the same experimental conditions show that the (1  1) pattern measured for the clean Cu(110) surface is modified by additional stripes in the [110] direction, in agreement with results of Stickney [9]. Panels 7–12 in Fig. 189.1 show STM images acquired in the reverse CV scan., i.e., along the negative direction [6]. The surface morphology remains basically unchanged until the first current peak C is reached (panel 10). Only in panel 11 an abrupt change is clearly visible at around 500 mV (onset of the desorption peak D), in that the stripes disappear and wide copper (110) terraces reappear, with “fuzzy” borders showing again mobility at the surface. A few channels are still visible implying a different kinetics of the healing process of the surface when going to negative potentials compared to the positive sweep. Finally, in panel 12 at potential values between 550 and 600 mV, the original clean copper surface including some mobile spots is completely regenerated. This evolution of the surface morphology due to chloride adsorption and concomitant restructuring as a function of the applied potential not only produces a pronounced structural anisotropy of the sample surface but is expected to perturb also the electronic states at the metal/liquid interface. This is detectable with RAS using linearly polarized light which in this case measures the anisotropy of the sample reflectance along the  and [001] directions, respectively [10]. Indeed, RAS spectra taken at E ¼ 600 mV and orthogonal [110] E ¼ 300 mV, respectively, are very different and their difference spectrum ΔRAS(E) as shown in Fig. 189.2 is an optical fingerprint for the Cl-induced restructuring of the surface [6]. This ΔRAS signal can be used to follow the restructuring process by varying the electrode potential. As a result Fig. 189.3 displays the ΔRAS signal measured at fixed photon energy of 2.5 eV, i.e., the peak maximum position, as a function of the electrode potential; the numbers along the curve refer to the same numbers along the CV and the panels in Fig. 189.1. In the positive scan direction, the signal starts to rise at the onset of the first adsorption peak A in the CV (550 mV), and the slope changes once the second peak B has been passed at about 425 mV. In the negative scan, the ΔRAS intensity stays basically constant until 480 mV and then drops rather sharply following the evolution of the morphology changes as displayed by the STM images in Fig. 189.1. Also this optical tracking indicates that the process is slower during the formation of the chloride-induced stripes, than during their decay in the opposite, i.e., negative direction, where also a more abrupt morphological change is seen in the STM image. It is interesting to note that during the positive scan, the flank of the ΔRAS plot has still an appreciable nonzero slope at 300 mV, indicating that the underlying adsorbate-induced restructuring process is slowly going on at this electrode potential.

M. Nowicki and K. Wandelt

RAS x 10-3

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∆RAS x 10-3

3

5 1.5

2 1 0

-1

2.0

4 eV

3

2

2.5

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4.0

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Fig. 189.2 Real part of the reflectance anisotropy spectrum (RAS) of a Cu(110) surface measured in situ in 10 mM HCl solution at E ¼ 605 mV (repeatedly, dotted traces) and at E ¼ 300 mV ( full line). The difference ΔRAS (green area) is plotted against photon energy in the inset

Fig. 189.3 Plot of the intensity of the ΔRAS signal (see inset) at the fixed photon energy of 2.5 eV as a function of electrode potential (vs. Ag/AgCl). The numbers 1–12 along the hysteresis loop refer to the numbers along the cyclic voltammogram and the corresponding STM images in Fig. 189.1. The two arrows indicate the scan direction of the electrode potential (From Ref. [6])

The different kinetics of the forward and backward surface process becomes best visible when switching the electrode potential abruptly and repeatedly from 500 to 550 mV and vice versa (Fig. 189.4). With the disappearance of the Cl-induced stripes (500 mV ! 550 mV), the ΔRAS signal suffers a fast reduction, while the reverse chloride-induced surface restructuring (550 mV ! –500 mV) follows a slower process with a more complex time dependence: an initial steep rise is followed by a slower further rise.

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Hydrohalic acid interaction with copper surfaces: Cu(110) – chloride

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-500 mV

-500 mV

-550 mV

-550 mV

Fig. 189.4 ΔRAS signal from a Cu(110) electrode surface in 10 mM HCl solution as a function of time between repeated potential steps from E ¼ 500 mV to E ¼ 550 mV, and from E ¼ 550 mV back to E ¼ 500 mV. The corresponding STM images (81 nm  67.8 nm) display the accompanying structural changes upon decreasing and re-increasing the potential. The different slope of the ΔRAS decrease and re-increase is reflected in the STM images (From Ref. [6])

Consistently, for increasing electrode potential, all three techniques (CV, in situ STM, and RAS) suggest a two-step process in the chloride adsorption-induced restructuring of the Cu(110) surface: (i) the cyclic voltammogram in Fig. 189.1 shows two successive current peaks followed by a relatively high current level at positive potentials; (ii) the series of STM images 1–6 in Fig. 189.1 shows a rather spontaneous formation of grooves and stripes of monolayer thickness when crossing the first CV adsorption peak A, followed by a further growth of the stripes in width, length, and, in particular, height when passing the second peak B and beyond; and (iii) finally, also the variation of the ΔRAS intensity in Fig. 189.3, namely, the obvious change in slope after ~2/3 of the maximum ΔRAS intensity (at 300 mV), has been reached near 420 mV and indicates a change in kinetics. All three observations as a function of increasing electrode potential are in line with an adsorbateinduced reconstructive faceting of the Cu(110) surface [6, 7] as already addressed for bromide in the previous chapter. At potentials below 550 mV, chloride anions start to react with individual, particularly low-coordinated Cu surface atoms, forming mobile [CuCl2] complexes, which appear as mobile bright spots in the STM images. At 550 mV this reaction is enhanced leading first to the formation of grooves, i.e., the consumption of surface copper atoms and thus the occurrence of missing copper rows (dark in the STM images), followed by the formation of added rows and stripes (bright) of predominantly monoatomic height. The latter first grow in number and length until higher (brighter) layers start to appear. In particular, the thickening seems to be a slower process which continues even at 300 mV as suggested by the relatively high current in the CV cycle above peak B as well as by the nonzero slope of the ΔRAS signal in positive direction at 300 mV. This continuation of the reconstruction process above the second anodic current peak is in line with the large “desorption/decay” peak C in the subsequent negative scan, showing a faster Cl desorption and Cu deconstruction of the surface (consistently with the ΔRAS cycle). Symbols and abbreviations Short form

Full form

UHV STM ML RAS XPS LEED

ultrahigh vacuum scanning tunneling microscopy monolayer reflection anisotropy spectroscopy X-ray photoelectron spectroscopy low-energy electron diffraction

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References 1.

Meyer, E., Hug, H.J., Bennewitz, R.: Introduction to scanning tunneling microscopy. In: Scanning Probe Microscopy Springer Series of Advanced Texts in Physics. Springer, Berlin/Heidelberg (2004) 2. Barritt, E.E., Smith, C.I., Martin, D.S., Gentz, K., Wandelt, K., Weightman, P.: Evidence for the observation of surface states at the Cu(110)/electrolyte interface. Europhys. Lett. 92, 57005 (2010) 3. Andryuchechkin, B.V., Cherkez, V.V., Pavlova, T.V., Zhidomirov, G.M., Eltsov, K.N.: Structural transformations of Cu (110) surface induced by adsorption of molecular chlorine. Surf. Sci. 608, 135 (2012) 4. Wan, L.-J., Itaya, K.: In situ scanning tunneling microscopy of Cu(110): atomic structures of halide adlayers and anodic dissolution. J. Electroanal. Chem. 473, 10 (1989) 5. Li, W.H., Wang, Y., Ye, J.H., Li, S.F.Y.: In Situ STM Study of Chloride Adsorption on Cu(110) Electrode in Hydrochloric Acid Aqueous Solution. J. Phys. Chem. B 105, 1829 (2001) 6. Goletti, C., Bussetti, B., Violante, A., Bonanni, B., Di Giovannantonio, M., Serrano, G., Breuer, S., Gentz, K., Wandelt, K.: Cu(110) Surface in Hydrochloric Acid Solution: Potential Dependent Chloride Adsorption and Surface Restructuring. J. Phys. Chem. C 119, 1782 (2015) 7. Barati, G., Solokha, V., Wandelt, K., Hingerl, K., Cobet, C.: Chloride-induced morphology transformations of the Cu (110) surface in dilute HCl. Langmuir. 30, 14486 (2014) 8. Carley, A.F., Davies, P.R., Harikumar, K.R., Jones, R.V.A.: A low energy pathway to CuCl2 at Cu(110) surfaces. Phys. Chem. Chem. Phys. 11, 10899 (2009) 9. Stickney, J.L., Ehlerz, C.B., Gregory, B.W.: Adsorption of gaseous and aqueous hydrochloric acid on the low-index planes of copper. Langmuir. 4, 1368 (1988) 10. Barritt, E.E., Smith, C.I., Marin, D.S., Gentz, K., Wandelt, K., Weightman, P.: Optical response of the Cu(110)/ electrolyte interface. J. Phys. Conf. Ser. 286, 012028 (2011)

Chapter 190

Hydrohalic acids interaction with copper surfaces: CuI compound formation M. Nowicki and K. Wandelt

Chapters 182[https://doi.org/10.1007/978-3-662-53908-8_182], 183[https://doi.org/10.1007/978-3-66253908-8_183], 184[https://doi.org/10.1007/978-3-662-53908-8_184], 185[https://doi.org/10.1007/978-3662-53908-8_185], 186[https://doi.org/10.1007/978-3-662-53908-8_186], 187[https://doi.org/10.1007/ 978-3-662-53908-8_187], 188[https://doi.org/10.1007/978-3-662-53908-8_188] and 189[https://doi.org/ 10.1007/978-3-662-53908-8_189] described the mere adsorption of chloride, bromide, and iodide anions on the copper electrode surfaces in the potential regime above the hydrogen evolution and below the copper dissolution reaction. Already in this potential range, the adsorption is accompanied by some restructuring of the first copper layer, namely, in the form of the “electrochemical annealing,” leading to low-energy and rather defect-free terraces and step edges in the case of Cu(100) and Cu(111) or in the form of a faceting of the Cu(110) surface in the presence of chloride and bromide anions. Next we will address the influence of the halide anions on the copper dissolution process at more positive potentials. Only in the case of iodide, this leads to the formation of new stable surface phases. Figure 190.1 shows cyclic voltammograms of Cu(111) in both the blank and the 0.1 mM KI containing 5 mM H2SO4 electrolyte [1]. The potential window is limited by two processes: (i) the copper dissolution reaction (CDR) at the anodic limit and (ii) the hydrogen evolution reaction (HER) with an exponential increase of the cathodic current. The pair of additional peaks P at
30 mV and P0 at
200 mV in the blank H2SO4 solution represents the adsorption and desorption of SO42
anions, respectively, which will be discussed in great detail in Chaps. 193[https://doi.org/10.1007/978-3-662-53908-8_193]–197[https://doi. org/10.1007/978-3-662-53908-8_197]. The dashed curve in Fig. 190.1 represents the CV of Cu(111) in the iodide-containing electrolyte and shows a number of distinct new current peaks. Firstly, the couple of adsorption/desorption peaks of sulfate anions on Cu(111) is fully suppressed. This is due to the fact that iodide anions adsorb stronger on Cu(111), so that all adsorbed sulfate anions are displaced by iodide. However, no adsorption/desorption peaks of iodide on copper are observed (compare Fig. 187.1[https://doi. org/10.1007/978-3-662-53908-8_187]). Instead a large and broad anodic peak system close to the onset of the copper dissolution reaction (denoted P1–2) is centered at +214 mV. The corresponding reduction peaks are P0 at +100 mV, P’3 at +40 mV, and P’2 at
110 mV. The correlation of the corresponding peak pairs P1/P’1 and P2/P’2 is possible by measuring a series of cyclo-voltammograms with constant cathodic but increasing anodic limit as shown in Fig. 190.2 [1]. The most striking deviation from the CV in the pure supporting electrolyte is the anodic peak system P1–2 centered at about E ¼ +214 mV which arises from the formation of CuI compound (see below). A very similar voltammetric behavior was also reported by Broekmann et al. for Cu(100) exposed to the same electrolyte [2], by Irish et al. for polycrystalline copper in an iodide-containing electrolyte at pH ¼ 9.2 [3], and by Inukai et al. for Cu(111) exposed to an iodideM. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_190

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Current density [μA/mm2]

containing solution with diluted perchloric acid serving as supporting electrolyte [4]. The crystal orientation and the nature of the supporting electrolyte have obviously no significant effect on the electrochemical current characteristics with respect to the copper iodide interaction. P1-2 2 P 0 P' –2

P'3 P'2 –400

–200

P'1

Cu re-deposition Cure-deposition

0 200 E [mV] vs RHE

400

Fig. 190.1 Cyclic voltammogram of a Cu(111) surface in pure 5 mM H2SO4 (black curve) and in 5 mM H2SO4 + 1 mM KI solution (grey curve). Scan rate dE/dt ¼ 10 mV/s. The different peaks P and the arrows 1–3 are explained in the text (From Ref. [1])

Fig. 190.2 CuI compound formation on a Cu(111) electrode surface in 5 mM H2SO4 + 1 mM KI solution upon gradual shifting of the anodic limit to more positive potentials, which enables a correlation of anodic and cathodic peaks P (see text) (From Ref. [1])

It is actually both the low solubility product of CuI bulk with Ks ¼ 1.2  10–11.3 mol2 L
2 and the fact that cupric ions are not stable in aqueous iodide-containing electrolytes which govern the voltammetric behavior of copper at high potentials. The pronounced anodic current waves are explained in terms of massive CuI formation involving electro-oxidation of copper to cuprous Cu+ species and the formation of bulk (CuI)n. After passing the peak system P1–2, the anodic current does not drop to zero in Fig. 190.1 indicating that the reactive copper dissolution may be slowed down by the presence of the CuI film but not fully suppressed. Obviously the grown CuI film is not efficient in passivating the copper electrode against

190

Hydrohalic acids interaction with copper surfaces: CuI compound formation

3

further anodic dissolution; only the copper dissolution is shifted by about 60 mV to higher potentials in the presence of CuI compared to the pure supporting H2SO4 electrolyte. According to measurements on both Cu(111) and Cu(100), the three further cathodic current peaks denoted P’1 (E ¼ +95 mV), P’2 (E ¼
102 mV), and P’3 (E ¼ +40 mV) evolving in the reverse potential scan have been assigned to the electroreduction and dissolution of various solid CuI phases. While the origin of the current wave P’3 in Fig. 190.1 is unclear [2], the two other peaks have been rationalized in terms of two CuI phases, which differ in their structural relationship to the copper substrate surface. An initial 2D CuI phase with the closest structural relationship to the underlying copper surface reveals the smallest potential hysteresis for its formation and dissolution (P1/P’1), while a significantly larger hysteresis was found for the growth and dissolution of 3D CuI clusters (P2/P’2), which feature only a loose structural relationship to the metallic electrode surface [2]. This interpretation is based on in situ STM measurements described in the following. Exchanging the blank H2SO4 electrolyte for the iodide-containing one at a fixed potential leads to the spontaneous formation of a well-ordered iodide layer. Similar to bromide and chloride on Cu(111), the iodide anion layer exhibits a pronounced electro-compression behavior as shown and discussed in Chap. 187[https://doi.org/10.1007/978-3-662-53908-8_187]. Applying higher potentials up to +100 mV gives rise to a uniaxial compression of this adlayer and the appearance of a striped long-range superstructure superimposed to the atomic-scale corrugation. Sweeping the electrode potential then to values E > 120 mV results in even more drastic structural changes of the electrode surface as shown in Fig. 190.3. Figure 190.3a shows six terraces (T1–T6) of a Cu(111) surface covered with the saturated and uniaxially compressed iodide layer at E ¼ +122 mV like in Fig. 187.2[https://doi.org/10.1007/978-3-662-539088_187]. At +130 mV (Fig. 190.3b), it becomes evident that the surface undergoes already a reaction. Copper steps recede with time according to an inverse step flow mechanism. Note that copper dissolution in the pure supporting electrolyte starts only at about E ¼ +280 mV; see, e.g., Fig. 190.1. The white dashed lines in each image indicate the position of the respective step in the preceding image. From these results, it becomes obvious that iodide facilitates and accelerates the copper oxidation. However this local copper dissolution in the iodide-containing electrolyte does not lead to a soluble product, which diffuses into the bulk solution like in the case of chloride and bromide. Instead a rapid nucleation and growth of a 2D CuI film happens. From one scan line to the next, this 2D CuI film appears in the STM image of Fig. 190.3c; copper terraces already covered by the 2D CuI film are labeled as T10 and T20 , whereas terraces still covered by the iodide adsorption layer are denoted as T1–T6. From Fig. 190.3, it becomes evident that the dissolution processes at steps and the nucleation of the 2D CuI film are causally correlated with each other and the experimental results can be explained on the basis of the following scenario: depending on the applied potential, an equilibrium concentration of mobile cuprous species, namely, CuI or [CuI2]
monomers, is discussed to exists on the surface [3, 5] as intermediate products of the copper oxidation reaction. Since the exact chemical nature of this mobile species, however, is not known, we simply denote it CuI in the following.

Fig. 190.3 Series of in situ STM images of a Cu(111) surface in 5 mM H2SO4 + 1 mM KI solution showing copper dissolution at steps (a, b) and the sudden growth of a two-dimensional CuI film (c). T1–T6 denote terraces with adsorbed iodide (see Fig. 187. 2c[https://doi.org/10.1007/978-3-662-53908-8_187]), while T10 and T20 denote terraces covered with a 2D CuI compound film; note the sudden change from T2 to T20 in panel (c). M marks a stationary defect. The white dashed lines indicate the position of the step edges in the preceding image. All images 109 nm  109 nm, IT ¼ 1.3 nA, UB ¼ 166 mV; (a) E ¼ +122 mV, (b) and (c) E ¼ +130 mV (Ag/AgCl). Recording time per image 16.8 s with no delay between the images (From Ref. [1])

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M. Nowicki and K. Wandelt

Before reaching the potential range where the 2D film is formed, these diffusing cuprous species are in equilibrium with step edges which are the sources for these species, and their concentration on terraces increases with increasing potential until a critical threshold, i.e., the solubility product, is exceeded which gives rise to the surface-confined nucleation and growth of the 2D CuI film. The growing 2D CuI film acts as a sink for the mobile CuI species [2]. From Fig. 190.3c, it becomes evident that the growing 2D CuI film reveals a high defect density (black pits in the film) shortly after its initial formation. However, post-growth ripening processes lead to a significant improvement of the atomic ordering and a decrease of the pit density with time. The apparent step height of the 2D CuI film is determined to be dCuI ¼ 0.35  0.015 nm. This value is in agreement with the iodide interlayer spacing along the (111) direction in crystalline CuI with dCuI(111) ¼ 0.35 nm. Figure 190.4a displays the fcc (face-centered cubic) unit cell of crystalline CuI (zinc blende type) with a lattice constant of aCuI ¼ 0.6063 nm. In this zinc blende-type structure, iodide and cuprous ions are tetrahedrally coordinated by the respective counter-ions. Figure 190.4b represents a cut through the crystalline structure of the bulk CuI phase parallel to the (111) plane including one central layer of cuprous ions that is “sandwiched” by two iodide layers. The same stacking sequence is assumed for the 2D CuI film on Cu(111) with the lower iodide layer being the preexisting iodide adsorbate layer in direct contact to the metallic copper substrate [1]. According to this interpretation, the 2D CuI film forms a CuI bilayer on top of the preexisting iodide adsorbate layer resulting in a I-CuI triple layer. In this simple picture, the a priori specifically adsorbed iodide does not chemically “react” with the mobile cuprous CuI species but serves as a chemically inert structural template for the CuI bilayer formation on top. All dynamics (growth, ripening, decay) as observed in the STM images solely affects the CuI bilayer on top of the iodide adsorption layer. This hypothesis will be substantiated in the next chapter by means of high-resolution photoemission experiments. Strong evidence supporting the structural relationship of the 2D film with the (111) plane of bulk CuI comes from an analysis of the in-plane structure. As shown in Fig. 190.5, the 2D film is characterized by a pseudohexagonal Moire´ pattern. Following the reasoning above, this Moire´-type modulation arises from a mismatch of the grown CuI bilayer with the underlying iodide adsorption layer and not from a mismatch between the complete I-CuI triple layer and the Cu(111) surface lattice. The same explanation was also given by Andryushechkin et al. for 2D CuI films grown on Cu(100) and Cu(111) under UHV conditions by dissociative iodine adsorption [6].

a

Iodide b

Cuprous Ion Iodide layer d2 = 0.2625 nm Cu/I-bilayer

Cuprous Ions Iodide layer

d1 = 0.0875 nm

I-Template

Fig. 190.4 (a) Face-centered cubic unit cell of crystalline CuI (zinc blende type), (b) I-Cu-I triple layer in bulk CuI parallel to the (111) plane (From Ref. [1])

190

Hydrohalic acids interaction with copper surfaces: CuI compound formation

5

Fig. 190.5 In situ STM images of the 2D CuI film on Cu(111) in 5 mM H2SO4 + 1 mM KI solution. (a) Moire´-type pseudohexagonal long-range height modulation of the 2D CuI film, 27 nm  27 nm, IT ¼ 4.5 nA, UB ¼ 372 mV, E ¼ +125 mV (Ag/AgCl); (b) high-resolution image of the CuI film, enabling correlation between the atomic-scale structure and the Moire´ superstructure, 12 nm  12 nm, IT ¼ 4.5 nA, UB ¼ 372 mV, E ¼ +125 mV; (c) even higher-resolution image of the CuI film showing clearly dislocations in the CuI film (follow white dashed lines), 5.2 nm  5.2 nm, IT ¼ 4.5 nA, UB ¼ 371 mV, E ¼ +125 mV (From Ref. [1])

The corrugation amplitude of the Moire´ pattern amounts to 0.05  0.0 nm, which is about one order of magnitude larger than the corrugation amplitude of the wavy long-range height modulation of the uniaxially incommensurate iodide adsorbate layer in Fig. 187.2c[https://doi.org/10.1007/978-3-66253908-8_187]. Distances between Moire´ maxima in Fig. 190.5a vary between 4.3 and 5.8 nm. This broad distribution of distances points to a not perfect long-range order within this CuI bilayer. Note, however, that the CuI bilayer undergoes a ripening process after its initial growth leading to a significant improvement of the lateral order and the STM images in Fig. 190.5b represent the CuI bilayer already in an advanced stage of ripening. On the atomic scale, the CuI bilayer reveals an almost hexagonal arrangement of STM dots (Fig. 190.5c), which are assigned to the terminating iodide of the CuI bilayer. Similar to the CuI bilayer found on Cu(100) under UHV and electrochemical conditions, the iodide nearest neighbor distance on Cu(111) is 0.41  0.03 nm very similar to the interatomic spacing of iodide and cuprous ions of 0.4287 nm within the (111) plane of bulk CuI. The observed slight compressing of the CuI bilayer with respect to an ideal (111) plane of bulk CuI may originate from the “template” effect of the preexisting iodide adsorption layer underneath [1]. A similar effect was reported for an epitaxial pseudohexagonal CuBr(111) film on a square c(2  2)-Br template structure in UHV [7]. This 2D CuI film is stable only within a narrow potential window ranging from about +100 mV to +125 mV. At further increased electrode potential, the copper dissolution continues as evidenced by the persistently high current in the CV (Fig. 190.1) but now in the presence of the covering 2D CuI film, which obviously does not act as an effective passivation layer. This further copper dissolution leads to the nucleation and growth of 3D CuI clusters of enormous height (Fig. 190.6). These STM observations, of course, do not reveal whether the 3D CuI clusters nucleate directly on top of the 2D CuI film or in solution followed by their precipitation onto the 2D CuI film. But their rather irregular appearance and distribution seems to support the latter process. In any case, a disruption of the 2D CuI film upon further CuI growth on top can be excluded, because the atomically flat areas visible between the clusters correspond still to the 2D CuI film. Hence, the 2D CuI film grown on the preexisting iodide adsorbate can be regarded as a thermodynamically stable “wetting layer” [1].

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Fig. 190.6 (a) 3D CuI clusters, 293 nm  293 nm, IT ¼ 0.1 nA, UB ¼ 433 mV. The image was registered at E ¼ +120 mV after the potential had shortly been raised beyond peak P1–2 in Fig. 190.1 (arrow 3) (From Ref. [1])

Symbols and abbreviations Short form

Full form

CDR STM HER RHE 2D UHV

copper dissolution reaction scanning tunneling microscopy hydrogen evolution reaction reference hydrogen electrode two-dimensional ultrahigh vacuum

References 1. Hai, N.T.M., Huemann, S., Hunger, R., Jaegermann, W., Wandelt, K., Broekmann, P.: Combined Scanning Tunneling Microscopy and Synchrotron X-Ray Photoemission Spectroscopy Results on the Oxidative CuI Film Formation on Cu (111). J. Phys. Chem. C111, 14768 (2007) 2. Broekmann, P., Anastasescu, M., Spaenig, A., Lisowski, W., Wandelt, K.: Atomic structures and dynamics of a Cu(100) electrode in dilute hydrobromic acid: An in situ STM study. J. Electroanal. Chem. 500, 241 (2001) 3. Irish, D.E., Stolberg, L., Shoesmith, D.W., Lisowski, W., Wandelt, K.: Surface enhanced Raman spectroscopy and electrochemistry at the copper/iodide, water interface. Surf. Sci. 158, 238 (1985) 4. Inukai, J., Osawa, Y., Itaya, K.: Adlayer Structures of Chlorine, Bromine, and Iodine on Cu(111) Electrode in Solution: In-Situ STM and ex-Situ LEED Studies. J. Phys. Chem. B 102, 10034 (1998) 5. Bertocci, U.: Application of electrochemical theory to the behaviour of copper in cupric and cuprous solutions. Eletrochim. Acta. 11, 1261 (1966) 6. Adryushechkin, B.V., Eltsov, K.N., Shevlyuga, V.M.: CuI growth on copper surfaces under molecular iodine action: influence of the surface anisotropy in the iodine monolayer. Surf. Sci. 566 – 568, 203 (2004) 7. Nakamura, C.Y., Altman, E.T.: Visualization of etching mechanisms of vicinal Cu surface using scanning tunneling microscopy. J. Vac. Sci. Technol. A 16, 1566 (1998)

Chapter 191

Hydrohalic acids interaction with copper surfaces: XPS of Cu(111) – iodide interaction M. Nowicki and K. Wandelt

Very strong evidence for the above-made distinction between the preexisting iodide adlayer, the thermodynamically stable CuI bilayer on top, and the ultimate formation of 3D CuI clusters comes from ex situ XPS measurements using synchrotron light [2]. The copper sample was emersed from the electrochemical environment at three particular potentials (see arrows 1–3 in Fig. 190.1[https://doi.org/10.1007/978-3-66253908-8_190]) being characteristic for the presence of (1) the iodide adsorbate (Eemersion ¼  100 mV), (2) the 2D CuI film (Eemersion ¼ + 125 mV), and (3) the 3D CuI clusters (Eemersion ¼ + 175 mV). Note that in the latter case prior to emersion, the anodic peak system P1–2 had been exceeded in anodic direction in order to produce the 3D CuI clusters before the sample was removed from the electrolyte at +175 mV. Excitation of the photoelectron spectra was done with different photoenergies in order to vary the escape depth of the photoelectrons and thereby the information depth [1]. Wide survey spectra (Fig. 191.1a) show only very small amounts of oxygen-containing species (O1s  529–535 eV) on the surface mainly originating from residual water traces. The complete absence of any sulfur-related emission (S2p  164.5–170.5 eV) clearly indicates that the surfaces can be transferred without an undesired drying of the remnant electrolyte. Small amounts of carbon are detectable in all spectra (C1s  283–286 eV) as an unavoidable contamination in this kind of transfer experiments.

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_191

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Fig. 191.1 (a) X-ray photoelectron survey spectra monitored with synchrotron radiation of Ephoton ¼ 720 eV after the sample was emersed from the 5 mM H2SO4 + 1 mM KI solution at (1) E ¼ 100 mV (I adsorbate), (2) E ¼ +125 mV (2d CuI film), and (3) E ¼ +175 mV (3D CuI clusters). (b) The enlarged I4d5/2, 3/2 spectra taken with a more surface sensitive photon energy of Ephoton ¼ 245 eV clearly distinguish between adsorbed (1) and incorporated iodine in the 2D film or 3D clusters (2, 3) (From Ref. [1])

As a general trend, one realizes in Fig. 191.1a a damping of the copper-related emission (Cu3p, Cu3s, CuVB) and in turn an increase of the iodide-related emissions (I4d, I MNN, I3d) by going from the spectrum of the I adsorbate to the 3D clusters. A detailed analysis of the Cu3p, I4d-photoemission, and I M4N4,5N4,5-Auger signals yields the following picture: a shift of the Cu3p3/2 spin-orbit component (not shown) by 0.25 eV to higher binding energy (EB) from 75.03 eV to 75.28 eV is consistent with an oxidation of copper, and the latter value agrees with that found for bulk Cu2O [3]. The I4d emission shown on an expanded energy scale in Fig. 191.1b clearly differentiates between the adsorbed iodide (in contact with the copper substrate) and an iodine species in the 2D/3D overgrowth. The I4d emission of the adsorbed layer (1) indicates just one single iodine component with a spin-orbit splitting of 1.70 eV and the 4d5/2 maximum at EB ¼ 49.27 eV, both values are in excellent agreement with results obtained after dissociative iodine adsorption in UHV [4]. More complex is the I4d emission of the 2D CuI film (2), which is actually the superposition of two components as evidenced from the fitting procedure in spectrum (2) of Fig. 191.1b. Component I can be associated with the adsorbed iodide species in direct contact with the metallic copper surface. The component II contributing to the I4d5/2 emission of the 2D film (spectrum 2) is ascribed to the terminating iodide species of the I-CuI triple layer with the I4d5/2 peak maximum at EB ¼ 49.90 eV. The shift toward higher binding energy amounts to ΔE ¼ 0.50 eV with respect to component I [1]. Interestingly, the I4d5/2 core-level binding energy of the iodide species in the terminating layer of the 2D film is almost identical to the one found for the iodide species in the 3D CuI clusters with EB ¼ 49.89 eV (spectrum 3). Interesting is also that the I4d emission originating from the 3D CuI clusters can be fitted with the same two components as the spectrum of the 2D film. This points to an inhomogeneous and rough surface morphology with cluster-free patches exposing still only the 2D film, consistent with the STM observations in Fig. 190.6[https://doi.org/10.1007/978-3-662-53908-8_190]. For completion, it shall be mentioned that also an analysis of the I M4N4,5N4,5 Auger spectra of the three different species, adsorbed iodide, 2D film and 3D clusters, yields the same picture, namely, a clear distinction between adsorbed I on the metal electrode and an iodide species bound within either the 2D CuI film or the 3D CuI clusters. A similar surface compound formation with Cl and Br on copper is (at the applied concentrations) not found due to the higher solubility of the relevant compounds.

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Hydrohalic acids interaction with copper surfaces: XPS of Cu(111) – iodide interaction

3

Symbols and abbreviations Short form

Full form

STM 2D XPS UHV

scanning tunneling microscopy two-dimensional X-ray photoelectron spectroscopy ultrahigh vacuum

References 1. 2. 3. 4.

Hai, N.T.M., Huemann, S., Hunger, R., Jaegermann, W., Wandelt, K., Broekmann, P.: J. Phys. Chem. C 111, 14768 (2007) Mayer, T., Lebedev, M.V., Hunger, R., Jaegermann, W.: Appl. Surf. Sci. 252, 31 (2005) Cook, M.G., McIntyre, N.S.: Anal. Chem. 47, 2208 (1975) DiCenzo, S.B., Wertheim, G.K., Buchanan, D.N.E.: Phys. Rev. B 24, 6143 (1981)

Chapter 192

Copper surfaces in perchloric acid M. Nowicki and K. Wandelt

The interaction of perchlorate anions (ClO4
) with (noble) metal surfaces is considered to be very weak, i.e., nonspecific. While the behavior of copper electrodes in alkaline or neutral perchlorate-containing solutions has been studied intensively [1–3], less is known about the interfacial chemistry of copper in acidic perchloratecontaining solutions, and this is only from “classical” electrochemical measurements. The cyclic voltammogram of Cu(111) in HClO4
or NaClO4/HClO4 solutions of pH ¼ 1.5–3.5 showed a clearly irreversible behavior with an anodic and a well-separated cathodic peak, which were assigned to the formation of an oxidic surface species [4]. This interpretation was supported by in situ SHG (Second Harmonic Generation) measurements, which revealed a signal very similar to that found after oxygen adsorption in UHV [5, 6]. Also Brisard et al. [7] considered the in situ formation of an oxygen species even though their CV showed a deviating behavior, which was speculated to result from chloride contamination. By contrast, Wan et al. [8] did not find any peaks in the Cu(111) CV in 10
1 M HClO4 in contradiction to all other publications. In situ AFM measurements on Cu(111) in 10
1 M HClO4 solution by Cruickshank et al. [9, 10] showed a (√2√2)R45 superstructure which by analogy to measurements in UHV was interpreted in terms of a Cu2O layer. These authors excluded the influence of chloride contamination because no Cl-induced superstructure formation (see Chap. 185[https://doi.org/10.1007/978-3-662-53908-8_185]) was observed on Cu(111) under the same experimental conditions. In view of these conflicting results, the exact knowledge of the chemical composition of the ClO4
exposed surface is obviously important. However, none of these early investigations was done with a Cu(111) or Cu(100) surface which was prepared and well characterized under UHV conditions; all samples were “electrochemically prepared” prior to their investigation in ClO4
-containing solution. Likewise none of these early interpretations relied on methods sensitive and specific to the chemical nature of the supposed surface species. Duisberg [11, 12] presented the first results obtained from a Cu(111) electrode surface which was prepared and characterized before and after transfer between UHV and an electrochemical cell without contact to air using a “transfer system” as mentioned in Sect. 179.14[https://doi.org/10.1007/978-3-662-53908-8_179]. Figure 192.1 shows the cyclic voltammogram of a Cu(111) electrode prepared and characterized in UHV and transferred into a 10
2 M HClO4 solution. It shows a pair of peaks at +180 mV (RHE) and a broad rather structureless double-layer regime before the onset of the hydrogen evolution at negative potentials. The minimal shift of 4 mV between the two peaks identifies the underlying processes, namely, adsorption (Arev) and desorption (Drev) of ClO4
as being reversible, in agreement with the notion of ClO4
being a weak adsorbate.

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_192

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Arev

Current density [µA/cm2]

10 0

Drev

-10

-20 -30

-40

HER -300

-200

-100

0

100

Potential vs. RHE [mV]

200

300

Fig. 192.1 Cyclic voltammogram of a UHV-prepared Cu(111) sample immersed at E ¼ +200 mV into 10 mM HClO4 solution. The “reversible” pair of peaks Arev and Drev is assigned to adsorption/desorption of ClO4
anions (HER ¼ hydrogen evolution reaction) (From Refs. [11, 12])

This CV, however, is not stable. Repeated cycling between +200 mV and
400 mV changes the CV very fast within the first 10 cycles (dE/dt ¼ 10 mV/s) and then still changes continuously for hours (5 h). Figure 192.2a shows a superposition of the first (“reversible CV”) and the 110th cycle, the latter corresponding nearly to the final “stationary CV”. Figure 192.2b displays a superposition of the 90th, nearly stationary CV, and the first CV of an “electrochemically prepared” sample. These latter two CVs basically agree in all dominant features, which are formed with the UHV-prepared sample only after 100 cycles or hours of continuous cycling. This leads to the compelling conclusion that all earlier measurements with the “electrochemically prepared” samples are not representative for a virgin Cu(111) surface but for an electrochemically drastically modified Cu(111) sample. Only the “reversible,” i.e., the first CV of the UHV-prepared, and thus truly clean and well-ordered Cu(111) surface can be regarded as the characteristic “fingerprint” of a virgin Cu(111) electrode surface [12].

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a 20

Current density [µA/cm2]

A

-160 mV

10

Arev

0

Drev

-10 60 mV

-20 -30 -40

K

-50

1. CV 110. CV

-60 -70 -400

-300

-200

-100

0

100

200

Potential vs. RHE [mV]

Current density [µA/cm2]

b

20

CV UHV preparation, 90. cycle

10 0 -10 -20 -30 -40

CV el.chem. preparation, 1. cycle

-50 -400

-300

-200

-100

0

100

Potential vs. RHE [mV]

200

300

Fig. 192.2 (a) Comparison of the 1st and 110th cyclic voltammogram of Cu(111) in 10 mM HClO4 solution. Potential sweep rate 10 mV/s. The dashed trace is identical to the CV shown in Fig. 192.1. (b) Comparison of the 90th CV of a UHV-prepared Cu(111) surface with the 1st CV of an electrochemically prepared Cu(111) surface in 10 mM HClO4. Potential sweep rate 10 mV/s (From Refs. 11, 12)

An identification of the chemical modification leading from the “reversible” to the “stationary” CV is obviously not possible by “classical electrochemical” measurements. A first hint to the chemical transformation of the Cu(111) surface during cycling in HClO4 comes from the earlier SHG and AFM measurements [5, 6, 9, 10] which pointed to an oxygenation of the surface. This could be verified by ex situ XPS studies using a “transfer system.” A UHV-prepared Cu(111) surface was cycled in HClO4 solution until the “stationary” CV was reached, transferred back into the UHV analysis chamber, and then analyzed by means of the MgKα – excited XPS Cu2p, O1s, and Cl2p spectra. Immediately after transfer, the XPS spectra indicate the presence of Cu0, Cu2+, Cl
, ClO4
, and H2O on the surface. Like in the case of chloride adsorption (see Fig. 185.5[https://doi.org/10.1007/978-3-662-53908-8_185]), LEIS spectra show a very (moderately) fast removal of perchlorate (chloride) from the surface but a persistence of an oxidic species. Immediately after transfer, this oxidic species is identified as Cu(OH)2, which in UHV during the XPS and LEIS measurements converts into stable Cu2O (see Fig. 192.3) [12].

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M. Nowicki and K. Wandelt

Intensity

Cu2p3/2

XPS

935.47 eV

Intensity

925

930

945

940

935

O1s

524

528

532

536

540

Intensity

Cl2p

194

198

202

206

210

Binding energy (eV)

Fig. 192.3 XPS spectra (MgKα) of the Cu2p3/2-, O1s-, and Cl2p-levels registered after 0 (∙ ∙ ∙ ∙ ∙ ∙), 13 (____), 104 (_ _ _ _), and 182 (- - - -) minutes of He+ (1000 eV) bombardment. Note the immediate disappearance of the O1s (532 eV) and Cl2p (208 eV) component of H2O and HClO4, respectively, which causes an immediate increase of the Cu2p3/2 signal. The further decrease of adsorbed oxygen (530 eV) and chloride (199 eV) is comparably slow (From Refs. [11, 12])

Symbols and abbreviations Short form

Full form

AFM SHG HER RHE XPS UHV LEIS

atomic force microscopy second harmonic generation hydrogen evolution reaction reference hydrogen electrode X-ray photoelectron spectroscopy ultrahigh vacuum low-energy ion spectroscopy

References 1. 2. 3. 4. 5. 6. 7. 8.

Ikemiya, N., Kubo, T., Hara, S.: Surf. Sci. 323, 81 (1995) Chu, Y.S., Roninson, I.K., Gewirth, A.A.: J. Chem. Phys. 110, 5952 (1999) Schwarz, D.T., Muller, R.H.: Surf. Sci. 248, 349 (1991) Vilche, J.R., Jüttner, K.: Electrochim. Acta. 32, 1567 (1987) Bradley, R.A., Friedrich, K.A., Wong, E.K.L., Richmond, G.L.: J. Electroanal. Chem. 309, 319 (1991) Wong, E.K.L., Friedrich, K.A., Robinson, J.M., Bradley, R.A., Richmond, G.L.: J. Vac. Sci. Technol. A 10, 2985 (1992) Brisard, G.M., Zenati, E., Gasteiger, H.A., Markovic, N.M., Ross, P.N.: Langmuir. 11, 2221 (1995) Wan, L.-J., Itaya, K.: Langmuir. 13, 7173 (1997)

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9. Cruichshank, B.J., Sneddon, D.D., Gewirth, A.A.: Surf. Sci. Lett. 281, L308 (1993) 10. LaGraff, J.R., Gewirth, A.A.: Surf. Sci. Lett. 326, L641 (1995) 11. Duisberg, M., Wahl, P., Wandelt, K.: An ex situ study of Pb underpotential deposition on Cu(111), In: Vanysek, P., Alodan, M., Lipkowski, J., Magnussen, O.M. (eds.) Electrochemical Science and Technology of Copper: Proceedings, vol. PV2000-30. Electrochemical Society, Pennington (2002). ISBN:1-56677-297-4 12. Duisberg, M.: Anioneneinfluss auf die elektrochemische Metallabscheidung: Blei auf Kupfer(111). Ph.D. Thesis, University of Bonn (2001)

Chapter 193

Copper surfaces in sulfuric acid: sulfate adsorption on Cu(100) and Cu(111) M. Nowicki and K. Wandelt

In contrast to the hydrohalic and perchloric acids, sulfuric acid is a di-protonic acid and can, thus, donate up to two protons: H2 SO4 þ H2 O⇄HSO4  þ H3 Oþ HSO4  þ H2 O⇄SO4 2 þ H3 Oþ In the range 1  pH  3, both types of anions, bisulfate (HSO4) and sulfate (SO42), coexist in solution. Since their relative concentrations near an electrified interface may – and most likely will – not be the same as in the bulk solution, we will for the sake of simplicity in the following speak only about sulfate (SO42) anions, which, compared to the monovalent halide and perchlorate anions, are doubly charged. Moreover, unlike the atomic halide ions, sulfate is a molecular ion of tetrahedral structure (Fig. 193.1a) with internal degrees of freedom, e.g., vibrations. The more complex structure, on the one hand, leads to the question of the real adsorption geometry but, on the other hand, also gives the option to tackle this problem with spectroscopy as an additional analytical tool.

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_193

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Fig. 193.1 Cyclic voltammogram of Cu(100) and Cu(111) in 5 mM H2SO4 solution. Interestingly, even though the CV of Cu (100) does not show a distinct SO42- adsorption peak (a) ex situ XPS spectra of this surface after emersion at positive potentials show a clear SO42 (and SO32, see text) related spin-orbit split S2p signal (c). Vice versa, a clear IR line at 1220 cm1 can be measured (d) after (red) and before (blue) the SO42 adsorption peak in the CV (b) peak of the Cu(111) electrode (red and blue arrow)

Figure 193.1a, b shows typical cyclovoltammograms registered with Cu(100) and Cu(111) in 5 mM H2SO4 solution with scan rates of 10 mV/s [2–5]. Besides the hydrogen evolution reaction and copper dissolution/redeposition currents at their cathodic and anodic limits, respectively, both CVs look surprisingly different. While there is hardly any further current modulation in the CV from the Cu(100) surface, there are very pronounced current peaks in the CV of the Cu(111) sample (similar to chloride adsorption on both surfaces). These extra peaks are generally related to the sulfate adsorption (positive scan) and sulfate desorption (negative scan), which in turn seems to suggest that there is no sulfate adsorption on Cu(100). In order to increase the surprise even further, IR spectra (Fig. 193.1d) measured in situ from the Cu(111) surface at potentials below and above the sulfate adsorption peak (arrows in the CV in Fig. 193.1b) are almost identical, suggesting that sulfate is on the Cu(111) surface below and above the alleged “adsorption peak” [6]. Final verification that SO42 is adsorbed comes from ex situ XPS: S2p (and O1s) spectra at the respective BE and of the correct intensity ratio do prove that sulfate is adsorbed on both copper surfaces – in particular also on the Cu(100) electrode. In particular, Fig. 193.1c shows the spin-orbit split S2p spectrum of adsorbed sulfate (SO42) anions (the second S2p doublet originates from sulfite (SO32) anions, a consequence of “dry reduction” of SO4 by the photoemitted electrons [7]). This example underlines the

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Copper surfaces in sulfuric acid: sulfate adsorption on Cu(100) and Cu(111)

3

great caution that needs to be exercised in the interpretation of CV traces. Neither the presence nor the absence of current peaks in a cyclic voltammogram is definitive proof or disproof for the presence or absence of an adsorbate, let alone the chemical nature. Obviously, sulfate adsorption on the Cu(100) surface is not accompanied by a conspicuous charge transfer, while this is the case on Cu(111). This strongly suggests a different interaction and bonding of these anions with both surfaces, which certainly most convincingly manifests itself in the influence of the adsorbate on the surface structure as discussed in the following. Consistent with the featureless CV of the Cu(100) surface, no sulfate-induced structural changes can be detected with in situ STM throughout the entire double-layer regime of this surface. This together with the XPS evidence that SO42 is adsorbed indicates a very weak, nonlocalized interaction. Mobile, nonspecifically adsorbed SO42 anions escape the detection with STM. Quite on the contrary, dramatic – and appealing – structural changes are observed upon sulfate adsorption on the Cu(111) surface which helps to understand several peculiarities of the related current peaks in the CV of this surface and which is (i) a huge hysteresis between the adsorption and desorption potentials (Fig. 193.1b), which suggests a strong kinetic hindrance of at least one of the processes, (ii) the desorption signal clearly exhibits two peaks, and (iii) the total desorption current (peak area) is much larger than the total adsorption current. Thus, the CV trace, reflecting a surprising complexity of the adsorption/desorption behavior, in principle contains a lot of information. However, further spectroscopic and microscopic methods are indispensable to assign and explain the various features. We start with the surprising difference in the adsorption and desorption peak intensities, even after subtraction of a Butler-Volmer fit of the hydrogen evolution current on the bare Cu surface similar to Fig. 185.1[https://doi.org/10.1007/978-3-662-53908-8_185]. This is due to an additional hydrogen evolution current from the sulfate-covered Cu surface: The presence of the adsorbed layer of negatively charged sulfate anions (i) increases the concentration of H3O+ ions near the electrode surface, and (ii) reduces the overpotential necessary for the hydrogen reduction reaction. As a consequence of this so-called Frumkineffect [1], the first steep flank of the desorption peak originates from hydrogen evolution on the sulfatecovered Cu surface. Inasmuch as the potential decreases sulfate anions continuously desorb, the Frumkineffect subsides and the hydrogen evolution decreases which causes the first (larger) peak in the cathodic current signal. The following enhanced sulfate desorption itself then produces the second peak until at last the hydrogen evolution current from the sulfate-free Cu surface prevails at the cathodic limit. If the potential is cycled only in the range between 150 and 300 mV the exponential increase of the cathodic current between 250 and 300 mV is clearly detected, but no adsorption feature between 100 and 150 mV in the reverse anodic scan is noted, because the surface remained sulfate covered. Only if the cathodic scan is extended below 350 mV both the true sulfate desorption peak and the sulfate re-adsorption signal show up. The most direct chemical proof for the presence (above +150 mV) and absence (below 400 mV) of sulfate on the surface comes from ex situ XPS and in situ Fourier transform infrared spectroscopy (FTIR) measurements like in Fig. 193.1c and d [6, 7]. Symbols and abbreviations Short form

Full form

BE FTIR RHE XPS STM

binding energy Fourier transform infrared spectrometer reference hydrogen electrode X-ray photoelectron spectroscopy scanning tunneling microscopy

References 1. 2. 3. 4.

Frumkin, A.: Z. Phys. Chem. A 164, 121 (1993) Vogt, M.R., Lachenwitzer, A., Magnussen, O.M., Behm, R.J.: Surf. Sci. 399, 49 (1998) Broekmann, P., Wilms, M., Spaenig, A., Wandelt, K.: Prog. Surf. Sci. 67, 59 (2001) Wilms, M., Broekmann, P., Kruft, M., Park, Z., Stuhlmann, C., Wandelt, K.: Surf. Sci. 402–404, 83 (1998)

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5. Broekmann, P., Wilms, M., Kruft, M., Stuhlmann, C., Wandelt, K.: J. Electroanal. Chem. 467, 307 (1999) 6. Broekmann, P., Wilms, M., Arenz, M., Spaenig, A., Wandelt, K.: Atomic structure of Cu(111) surfaces in dilute sulfuric acid solution. In: Wandelt, K., Thurgate, S. (eds.) Solid-Liquid Interfaces, Macroscopic Phenomena – Microscopic Understanding Topics in Applied Physics, vol. 85, p. 141. Springer, Heidelberg (2003. ISBN:3-540-42583-7) 7. Huemann, S.: Elektrochemische Präparation ultradünner Cadmiumsulfid- und Cadmiumiodid-Filme auf niedrigindizierten Kupfer-Einkristall-Elektroden. Ph.D. Thesis, University of Bonn (2007)

Chapter 194

Copper surfaces in sulfuric acid: sulfate structure on Cu(111) M. Nowicki and K. Wandelt

The presence or absence of a surface-bound sulfate layer can also be visualized by in situ EC-STM. Figure 194.1b displays a potentiodynamic STM measurement recorded from top (left) to the bottom (right) while the potential is simultaneously scanned from point a in the CV (Fig. 194.1a) via b and c back to point d (equal to a). Each horizontal scan line from left to right represents the STM profile for a given (very narrow range of) potential change along a distance of 39 nm. The data in Fig. 194.1, thus, represent a superposition of spatial and temporal changes of the surface structure [2]. In the range between the points a and b, a well-ordered hexagonal structure covers the four visible terraces I–IV. At point b, i.e., the onset of sulfate desorption, this structure disappears rather suddenly and does not reappear until near point c. Considering the size of the image, 39
39 nm, in Fig. 194.1c it is obvious that the periodicity of the resolved structure in the upper and lower part is roughly 3 nm, thus certainly not atomic.

Fig. 194.1 Correlation of (a) the cyclic voltammogram and (b) a potentiodynamic in situ STM image (39 nm
39 nm) of a Cu(111) surface in 5 mM H2SO4 solution. The STM image was registered (from top to bottom) while the electrode potential was scanned from a via b and c back to d ¼ a. The characteristic large-scale pattern seen from a to b disappears once the SO4 desorption peak (Des.) is approached, and reappears only once the “adsorption” peak (Ads.) at c is reached (I–IV denote terraces)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_194

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High-resolution STM images recorded at a constant sample potential either from the sulfate-free (below 850 mV vs Hg/Hg2SO4) or the sulfate-covered surface (above 500 mV), but different bias potentials provide deeper insight into the structure of this 3 nm superstructure. A large-scale potentiostatic image of the SO42-induced surface structure is displayed in Fig. 194.2a. Line scans (Fig. 194.2b) along the three main axes show indeed periodicities in the nanometer range, namely, 2.7  0.2 nm and 3.45  0.2 nm [4]. Surprisingly, despite the strict hexagonal structure of the Cu (111) substrate, this long-range superstructure is not strictly hexagonal, but stretched in one direction.1 An immediate consequence of this anisotropy is the occurrence of different domains rotated by 120 with respect to each other as demonstrated by Fig. 194.3, with some disorder along the domain boundaries.

Fig. 194.2 In situ STM image of the sulfate adsorption induced long-range periodicity (Moire´) of a Cu(111) electrode surface in 5 mM H2SO4 solution, 64 nm
64 nm, IT ¼ 1 nA, UB ¼ 195 mV, E ¼ 440 mV (Hg/Hg2SO4); (b) line scans along the white lines in panel (a); (c) pair-distance distribution of the Moire´-pattern in panel (a); (d) distribution of angles between triples of nearest Moire´ units (From Ref. [2])

1

This is not an artifact due to possible drift during the STM registration; the figure is explicitly drift corrected.

194

Copper surfaces in sulfuric acid: sulfate structure on Cu(111)

3

Fig. 194.3 In situ STM image showing the three possible rotational domains (I, II, III) of the sulfate-induced structure on Cu(111) in 5 mM H2SO4 solution, 18 nm
18 nm, IT ¼ 1 nA, UB ¼ 100 mV, E ¼ 440 mV (Hg/Hg2SO4) (From Ref. [4])

A zoom into one such domain reveals a structure as depicted in Fig. 194.4. On this scale (7.6
7.6 nm) the individual adsorbed particles become visible. The rows of bright dots correspond to the sulfate anions with an intermolecular separation along the rows of 0.47 nm. The distance between sulfate anions in adjacent rows is 0.71 nm. The zigzag rows of smaller but clear dots visible in this high-resolution image between the chains of sulfate anions are assigned to coadsorbed water molecules or most likely hydronium ions [3, 4, 5], which may be regarded as a two-dimensional hydration of the adsorbed anions. These hydronium ions compensate the negative charge of the sulfate ions and probably are held via hydrogenbridge bonds between them, contributing to the stability of this sulfate-water coadsorption layer. Indeed, with increasing pH of the solution this coadsorption structure breaks down.

Fig. 194.4 In situ STM image of the highly ordered SO42 layer on Cu(111) after slow adsorption, 7.5 nm
7.6 nm, IT ¼ 1 nA, UB ¼ 120 mV, E ¼ 56 mV (RHE). Between the SO42 anions (big spots), forming a (√3
√7)-unit cell, zig-zag rows of water molecules (weak spots) are visible (see text) (From Ref. [4])

Based on the real space structure visible in Fig. 194.4 and the distances and angles read thereof, it is possible to devise a unit cell of the sulfate adlayer as shown in Fig. 194.5. This structure is very similar to those observed for sulfate layers on other fcc(111) transition metal surfaces like Au, Pt, Pd, Ir, and Rh in dilute sulfuric acid solution [6–13] and has – shortly but not quite correctly – been denoted as (√3
√7) R19.1 structure (Fig. 194.5a). The vectors of the unit cell of the sulfate layer are rotated by 30 and are √3and √7-times longer compared to those of the respective metal substrate surface. It is, however, interesting to note that in the case of Cu, these unit vectors do not exactly correspond to √3-times (4.43 Ǻ) and √7times (6.77 Ǻ) of the Cu-Cu interatomic distance at the bare Cu(111) surface (Fig. 194.5b). Consequently,

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unlike on all other fcc(111) surfaces the STM image of the sulfate layer does not reflect a fully commensurate structure with a (111) plane of the Cu substrate, which is consistent with the slightly distorted hexagonal symmetry (Fig. 194.2a, b) and with the observation of the long-range superstructure displayed in Figs. 194.1, 194.2, and 194.3 and also visible in Fig. 194.4 (dark regions). This long-range Moire´-type superstructure does not exist on any of the other fcc(111) surfaces. The origin of this new superstructure can be found by applying the “spectroscopic” STM mode, which helped already to determine the exact adsorption site of chloride anions on Cu(111) in Chap. 185.

Fig. 194.5 (a) Hard-sphere model of the SO42 + H2O co-adsorption structure found on various (111) surfaces of fcc-metals. (b) Structure parameters of the unit-cell of the SO42 + H2O co-adsorption layer on Cu(111) as determined from in situ images like the one shown in Fig. 194.4

Figure 194.6a, b shows experimental in situ STM images taken from the sulfate-covered surface with different tunneling conditions [1]. Besides the long-range superstructure (dark regions), the images show (a) the more coarse net of bigger bright dots from the overlayer and (b) a finer net of smaller bright dots arising from the Cu substrate. Since both images have been measured sequentially with some possible drift in between, it is not possible to superimpose them directly in order to fix the adsorption site of the sulfate anions. What is possible, however, is to measure the respective unit cells in panels a (a, b) and b (a0 , b0 ) and compare their sizes, which leads to the surprising result that a ¼ √3 a0 and b ¼ √7 b0 (Fig. 194.6b), i.e., the sulfate structure is commensurate with the copper layer underneath.

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Copper surfaces in sulfuric acid: sulfate structure on Cu(111)

5

Fig. 194.6 Dependence of the sulfate-induced structure on Cu(111) on the tunneling conditions: (a) 5.9 nm
5.9 nm, IT ¼ 10 nA, UB ¼ 2 mV, E ¼ +100 mV; (b) 5.9 nm
5.9 nm, IT ¼ 2 nA, UB ¼ 2 mV, E ¼ +100 mV (RHE). While measurement (a) emphasizes the (√3
√7)-SO4 overlayer, measurement (b) shows the Cu(111) surface underneath the adsorbate layer. The unit cell of the sulfate structure (a) is commensurate with the expanded Cu(111) surface layer underneath (b) (From Ref. [4])

The obvious contradiction between the existence of the long-range superstructure as a consequence of incommensuracy, on the one hand, and the commensuracy resulting from the comparison of panels a and b in Fig. 194.6, on the other hand, can be solved by comparing the lattices of the bare Cu(111) surface (at very negative potentials) in Fig. and the Cu layer underneath the adsorbed sulfate layer (Fig. 194.6b), which discloses that the Cu-Cu interatomic distance underneath the sulfate layer is expanded by 4%. Assuming that only the first (top-most) Cu layer is affected by this expansion, it is this first copper layer which is now incommensurate with the second (bulk-like) Cu(111) plane while the (√3
√7)R19.1 sulfate lattice is commensurate with the first expanded Cu layer [1]. The SO42-Cu interaction is so strong that the sulfate anions force the Cu atoms underneath into a more favorable distance, similar to an interatomic distance like in the Rh(111) or Ir(111) surface plane where the adsorbed sulfate layer is commensurate without expansion of the substrate surface. Symbols and abbreviations Short form

Full form

RHE XPS STM

reference hydrogen electrode X-ray photoelectron spectroscopy scanning tunneling microscopy

References 1. 2. 3. 4.

5. 6. 7. 8. 9. 10. 11. 12. 13.

Broekmann, P., Wilms, M., Spaenig, A., Wandelt, K.: Prog. Surf. Sci. 67, 59 (2001) Wilms, M., Broekmann, P., Kruft, M., Park, Z., Stuhlmann, C., Wandelt, K.: Surf. Sci. 402–404, 83 (1998) Broekmann, P., Wilms, M., Kruft, M., Stuhlmann, C., Wandelt, K.: J. Electroanal. Chem. 467, 307 (1999) Broekmann, P., Wilms, M., Arenz, M., Spaenig, A., Wandelt, K.: Atomic structure of Cu(111) surfaces in dilute sulfuric acid solution. In: Wandelt, K., Thurgate, S. (eds.) Solid-Liquid Interfaces, Macroscopic Phenomena – Microscopic Understanding Topics in Applied Physics, vol. 85, p. 141. Springer, Heidelberg (2003. ISBN:3-540-42583-7) Wilms, M., Broekmann, P., Stuhlmann, C., Wandelt, K.: Surf. Sci. 416, 121 (1998) Edens, G.-J., Gao, X., Weaver, M.: J. Electroanal. Chem. 375, 357 (1994) Magnussen, O.M., Ocko, B.M., Hotlaos, J., Behm, R.J.: Faraday Discuss Chem. Soc. 94, 329 (1992) Funtikov, A.M., Linke, U., Stimming, U., Vogel, R.: Surf. Sci. 324, L343 (1995) Funtikov, A.M., Stimming, U., Vogel, R.: J. Electroanal. Chem. 428, 147 (1997) Wan, L.-J., Yau, S.L., Itaya, K.: J. Phys. Chem. 99, 9507 (1995) Wan, L.-J., Hara, M., Inukai, J., Itaya, K.: J. Phys. Chem. 103, 6978 (1999) Wan, L.-J., Suzuki, T., Sashikata, K., Okada, J., Inukai, J., Itaya, K.: J. Electroanal. Chem. 484, 189 (2000) Kim, Y.-G., Soriaga, J.B., Vigh, G., Soriaga, M.P.: J. Colloid Interface Sci. 227, 505 (2000)

Chapter 195

Copper surfaces in sulfuric acid: sulfate adsorption configuration M. Nowicki and K. Wandelt

As emphasized earlier the more complex structure of the sulfate anion as compared to the simple spherical shape of the halides makes several different adsorption configurations thinkable. On the Cu(111) surface the SO42
tetrahedra could in principle be bound via one oxygen atom on top of one Cu atom, between two Cu atoms (bridge) or in the center between three Cu atoms (hollow), while the other three oxygen atoms point into the solution. The SO42
tetrahedra could also be bound via two oxygen atoms to two Cu atoms or via three oxygen atoms to three Cu atoms, to name only high symmetry configurations. It would appear that infrared spectroscopy (IR) is the method of choice to distinguish between these adsorption configurations of different symmetry. For instance, if the Td symmetry of the free anion is reduced to either C3v or C2v symmetry upon adsorption, three (νs(SO), νs(SO3), and δs(SO4)) or four (2 νs(SO2), 2 δs(SO2)) bands should be expected. Indeed, many IR studies have been devoted to this problem; however, without definitive results [2, 3–6], the main reason being that on various fcc(111) surfaces only one strong band (plus a weak signal or shoulder) is detected. This does not allow to clearly discriminate between the possible configurations. Also the comparison of this band’s energy position to spectra of sulfato-complexes of known bond configuration of the sulfate anions to the metal center did not lead to a conclusive picture. Instead, new information about the exact adsorption site and the geometry of the adsorption complex could be gained from high-resolution in situ STM measurements. Figure 195.1a shows a potentiostatic STM image of the sulfate-covered Cu(111) surface with high atomic resolution monitored at a sample potential of
120 mV. The tunneling parameters (Ub ¼
130 mV, It ¼ 40 mV) were chosen such that features of the adsorbate as well as of the substrate are visible in the same image. Here it is already interesting to note that each corner of the SO4
unit cell is made up by two bright spots. Using the same Fourier filtering procedure as presented in Fig. 185.3[https://doi.org/10.1007/978-3-662-53908-8_185], both contributions are separated, back transformed into real space, and shown in Fig. 195.1c, d for the adsorbate and the substrate structure, respectively. Since these two lattices are inferred from the same STM image, their superposition suggests a twofold bridging coordination for the sulfate anions, i.e., a C2v symmetry, in clear contrast to all earlier IR results [1, 7]. The sulfate anions are suggested to be bound via two oxygen atoms to two Cu atoms. This result is actually supported by similar STM observation for adsorbed sulfate on Au(111) [8].

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_195

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Fig. 195.1 Fourier-analysis of an in situ STM image of the (√3  √7)-SO4 adlayer on Cu(111) which contains contributions of both the adlayer and the Cu substrate. (a) Measured image, 2.8 nm  2.8 nm, IT ¼ 40 nA, UB ¼
130 mV, E ¼
120 mV (RHE); (b) powerspectrum of the image in panel (a); (c) low-frequency and (d) high-frequency contribution to the image in panel (b). Since the partial images (c) of the SO42
– lattice (large unit cell), and (d) of the Cu substrate underneath (small unit cell) stem from the same measurement, their superposition yields the absolute adsorption site of the SO42
anions on the Cu(111) surface (see text) (From Ref. [1])

The superposition of two lattices of slightly different lattice constants leads to the formation of a third “superlattice” called Moire´. Its periodicity and orientation depends on both the lattice mismatch and a possible angle of rotation between both sublattices. In the present case (i) the measured lattice size of the first expanded Cu layer (Fig. 194.6[https://doi.org/10.1007/978-3-662-53908-8_194]) and its commensuracy with the measured SO42
overlayer, (ii) the lattice size of the Moire´ superstructure (Fig. 194.2[https://doi.org/10.1007/978-3-662-53908-8_194]), and (iii) an angle of rotation of ~6 between the sulfate lattice and the Moire´ lattice are consistent with an unreconstructed second copper (111) plane. The mismatch between the expanded first Cu layer and the bulk-like second Cu layer is the reason for the occurrence of the Moire´-type superstructure. In addition, either one of the two copper layers or both must be slightly distorted to give the non-ideally hexagonal symmetry of the superstructure. Symbols and abbreviations Short form

Full form

RHE IR fcc STM

reference hydrogen electrode infrared face-centered cubic scanning tunneling microscopy

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3

References 1. Broekmann, P., Wilms, M., Arenz, M., Spaenig, A., Wandelt, K.: Atomic structure of Cu(111) surfaces in dilute sulfuric acid solution. In: Wandelt, K., Thurgate, S. (eds.) Solid-Liquid Interfaces, Macroscopic Phenomena – Microscopic Understanding Topics in Applied Physics, vol. 85, p. 141. Springer, Heidelberg (2003. ISBN:3-540-42583-7) 2. Edens, G.-J., Gao, X., Weaver, M.: J. Electroanal. Chem. 375, 357 (1994) 3. Ataka, K., Osawa, M.: Langmuir. 14, 951 (1998) 4. Iwasita, T., Nart, F.C.: Surf. Sci. Rep. 99, 322 (1998) 5. Iwasita, T., Nart, F.C., Rodes, A., Pastor, E., Weber, M.: Electrochim. Acta. 40, 53 (1995) 6. Nakamoto, K.: Infrared and Raman Spectra of Inorganic and Coordination Compounds, 4 edn. Wiley, New York (1986) 7. Lennartz, M., Broekmann, P., Arenz, M., Stuhlmann, C., Wandelt, K.: Surf. Sci. 442, 215 (1999) 8. Wandlowski, T.: Private communication

Chapter 196

Copper surfaces in sulfuric acid: sulfate-induced surface morphology M. Nowicki and K. Wandelt

Obviously the sulfate-induced expansion of the lattice constant of the first Cu layer by 4% implies an increase of the area occupied by a given number of Cu atoms by 8% or, vice versa, a displacement of 8% of Cu atoms out of a given area. This displacement of copper atoms is, indeed, observed. Figure 196.1 shows two large-area STM images (a) before sulfate adsorption at negative and (b) after formation of the Moire´ superstructure at positive potentials [1]. The gross surface morphology, as judged by the step structure, is very similar in both images, but there are many new small islands in panel b. High-resolution images of this spotty surface in Fig. 196.2 show that the islands are not only also covered by the Moire´ structure but that the size and shape of the islands are “quantized” in units of the Moire´ structure. The same Moire´ structure on the islands as on the surrounding terraces as well as the measured island height prove that these are mono-atomically high Cu islands with unreconstructed Cu(111) immediately underneath. Their relative total area is consistent with the displacement of 8% of copper atoms out of the surface as a consequence of the surface expansion [1, 2].

Fig. 196.1 Morphological changes induced by sulfate adsorption on Cu(111) in 5 mM H2SO4 solution (a) before sulfate adsorption, 340
340 nm, IT ¼ 1 nA, UB ¼ 20 mV, E ¼ 266 mV; (b) after sulfate adsorption, 340
340 nm, IT ¼ 1 nA, UB ¼ 20 mV, E ¼ +155 mV (RHE). Note the same gross step structure in both panels besides the many small new islands in panel (b) (From Ref. [2])

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_196

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Fig. 196.2 Enlarged in situ STM image of islands formed in Fig. 196.1. (a) 31
31 nm, IT ¼ 1 nA, UB ¼ 70 mV, note the Moire´ structure on both the islands and the surrounding terrace; (b) 21
21 nm, IT ¼ 1 nA, UB ¼ 70 mV. In both images the electrode potential E ¼ 140 mV (RHE) was reached in positive sweep direction. Note that size and shape of the islands are “quantized” in units of the Moire´ structure. The arrow in (b) points to a patch of disordered SO42 adsorbate (see text) (From Ref. [2])

The “quantization” of the size (and shape) of the islands suggests that one Moire´ unit is a particularly stable building block of this superstructure. This is also suggested by the step structure of the Moire´-covered Cu surface: kinks along the steps are always due to the end of a row of Moire´-units. Moreover, in Fig. 196.2b there is a diffuse region between the two visible islands (arrow). This region is also sulfate-covered (see Chap. 193[https://doi.org/10.1007/978-3-662-53908-8_193]) but not Moire´ structured. The reason is the following: One Moire´ unit is built from a given number of sulfate anions and copper atoms underneath. The diffuse region in Fig. 196.2b is too small to deliver enough displaced Cu atoms to form one complete Moire´ unit. Symbols and abbreviations Short form

Full form

RHE STM

reference hydrogen electrode scanning tunneling microscopy

References 1. Broekmann, P., Wilms, M., Spaenig, A., Wandelt, K.: Prog. Surf. Sci. 67, 59 (2001) 2. Broekmann, P., Wilms, M., Arenz, M., Spaenig, A., Wandelt, K.: Atomic structure of Cu(111) surfaces in dilute sulfuric acid solution. In: Wandelt, K., Thurgate, S. (eds.) Solid-Liquid Interfaces, Macroscopic Phenomena – Microscopic Understanding Topics in Applied Physics, vol. 85, p. 141. Springer, Heidelberg (2003. ISBN:3-540-42583-7)

Chapter 197

Copper surfaces in sulfuric acid: sulfate adsorption/ desorption kinetics M. Nowicki and K. Wandelt

The large separation between the peaks of sulfate adsorption and sulfate desorption in Figs. 193.1[https:// doi.org/10.1007/978-3-662-53908-8_193] and 194.1[https://doi.org/10.1007/978-3-662-53908-8_194] was already taken as an indication of a strong kinetic hindrance of one or both of these processes. This, in turn, allows one to control the rate of Moire´ formation by choosing an appropriate constant adsorption potential [1, 2]. In Fig. 197.1 a series of six STM images shows the slow Moire´ formation process. Starting from a negative potential where no sulfate is present on the surface the potential was stepped to the constant potential of
70 mV (Hg/Hg2SO4), and the same surface area was imaged with a delay time of 2 min between successive images. In the first image (Fig. 197.1a), two flat terraces of Cu(111) with a monatomic step are shown, but no Moire´ structure can be seen yet. In panel (b) at the upper right and lower left corner (arrows), small areas of the Moire´ emerge, which grow from the step edge onto the upper terrace, manifested by the height profile in Fig. 197.2 taken along the white line in Fig. 197.1b. These Moire´ patches appear darker (lower) than the surrounding terrace due to their different electronic properties. Note also that the Moire´ structure formed in these initial patches is identical to the one that finally covers the whole surface (Fig. 197.1f), despite the expected repulsive interaction between the SO42
anions, which should prevent this early aggregation. This behavior contradicts the well-known phenomenon of continuous electro-compression of a complete and commensurate anion monolayer with increasingly positive electrode potential as was, for instance, described for adsorbed iodide on Cu(100) in Chap. 183[https://doi. org/10.1007/978-3-662-53908-8_183]. The unusual behavior of sulfate on Cu(111), instead, points to the particular stability of the Moire´ structure and the screening effect of the coadsorbed water molecules between the sulfate anions (see Chap. 194[https://doi.org/10.1007/978-3-662-53908-8_194]). The following panels (c–f) in Fig. 197.1 show the steady growth of this structure from the step edge onto the upper terrace. Starting in panel (c) the Moire´ structure is also growing in from the next step to the right (not shown in the image). Furthermore at the end of the STM series, the nucleation and growth of an additional Moire´ covered island can be observed in the upper left corner in panels e and f (arrows), a consequence of the displacement of copper atoms out of the first copper layer which accompanies the reconstruction/expansion of this layer (see Chap. 194[https://doi.org/10.1007/978-3-662-53908-8_194]).

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_197

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Fig. 197.1 (a) – (f) Sequence of in situ STM images showing the growth of the SO42
-induced Moire´ superstructure across terraces starting from upper step edges. All images: 101 nm  101 nm, IT ¼ 1 nA, UB ¼ 169 mV, E ¼
70 mV (RHE). The time interval between successive images is 2 min. (a) Sulfate-free surface at negative potentials. Arrows in (b) point to incipient Moire´ growth which continues at E ¼
70 mV (RHE) in (c) – (f). Arrows in (e) and (f) indicate Moire´-covered islands (From Ref. [1])

z-corrugation [nm]

197

Copper surfaces in sulfuric acid: sulfate adsorption/desorption kinetics

3

SO4,ad

0.2

0.07 nm 0.1

2.0 nm

Moiré

0.13 nm 0.0

SO4,ad 0

20

40

60

distance [nm]

80

100

Fig. 197.2 Height profile measured along the white line in Fig. 197.1b (From Ref. [1])

These STM images indicate the presence of the adsorbed sulfate only through the appearance of the Moire´ and the (√3√7)R19.1 -SO42
structure and do not directly indicate the existence of a preceding mobile precursor state of adsorbed sulfate anions. At most, the rather (and increasingly) fuzzy appearance of the large Moire´-free terraces in panels (b) and (c) in Fig. 197.1 may hint to the existence of such a mobile adsorption phase. But as indicated in Chap. 193[https://doi.org/10.1007/978-3-662-53908-8_193] and Fig. 193.1, the presence of such a disordered phase of adsorbed sulfate comes from a series of FTIR spectra, which were deliberately recorded within the potential regime before the onset of the Moire´ formation process. The IR spectra shown in Fig. 197.3a were recorded after a sudden potential step from
350 mV (RHE), where definitely no sulfate is present on the surface, to a potential of
200 mV (RHE). At this fixed potential, spectra were recorded continuously for about 15 min with a total recording time of 60 s per spectrum [4]. Even though below
200 mV no formation of the Moire´ structure is imaged in STM yet, the formation of a small symmetric S-O stretching band at about 1210 cm
1 can already be observed in the infrared spectra [3, 5]. The integrated intensity of this band, i.e., the surface coverage, grows continuously up to about 6 min adsorption time and then saturates (Fig. 197.3b).

Fig. 197.3 (a) Series of infrared difference spectra recorded after potential steps from E ¼
350 mV to E ¼
200 mV (RHE) as a function of time; the background spectrum was registered at E ¼
350 mV (see CV in Fig. 193.1[https://doi.org/10.1007/ 978-3-662-53908-8_193]); (b) integrated absorption band intensity from panel (a) plotted against adsorption time (From Ref. [1])

Series of IR spectra covering the whole adsorption/desorption regime were registered by changing the electrode potential in steps of 50 mV from
400 to +100 mV and back to
400 mV, with an accumulation time of 4 min per spectrum and the background spectrum (of the sulfate-free surface) taken at
350 mV. In Fig. 197.4 the relative integrated intensity is plotted as a function of the applied potential and manifests a

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M. Nowicki and K. Wandelt

clear hysteresis in the intensity (coverage) change in the anodic direction (adsorption) versus cathodic direction (desorption). In the anodic run, the sulfate adsorption starts at a potential just above
250 mV, and the coverage increases continuously (with decreasing slope) over the whole range toward positive potentials. Conversely, in the cathodic run, the desorption process sets in at potentials lower than
200 mV, and sulfate is still present on the surface between
200 mV and
300 mV.

Fig. 197.4 Integrated intensity of the infrared band shown in Fig. 197.3b as a function of electrode potential. The potential of beginning Moire´ formation is indicated by the arrow. Note the pronounced hysteresis between SO42- adsorption and Moire´ formation on the one hand and Moire´ decay and SO42- desorption on the other hand (From Ref. [1])

These results prove that the sulfate adsorption starts at potentials considerably more negative than does the Moire´ formation at
70 mV, but the adsorbed sulfate molecules are still very mobile on the surface and can therefore not be imaged by STM (except by the unspecific diffuseness in images like Fig. 197.1b, c mentioned above). Conversely, from the cathodic run of the IR series shown in Fig. 197.4, it is apparent that the desorption process is not kinetically hindered; the complete desorption occurs in a narrow potential window. This finding is in full agreement with the decay of the Moire´ structure and the sulfate desorption behavior as observed in STM. The persistence of small Moire´ patches until the very end of the desorption process again points to the extraordinary stability of this structure. Hence, a comparison of the STM and FTIR data shows that, unlike the adsorption process, the sulfate molecules desorb directly from the surface after lifting the Moire´ reconstruction. It is the Moire´ formation which is a kinetically hindered slow process due to the massive mass transport and reordering in the copper surface, whereas the desorption occurs in a relatively narrow potential window. Very similar findings from a combination of in situ STM and RAS measurements were described in Chap. 189[https://doi.org/10.1007/978-3-662-53908-8_189] for the reactive restructuring of a Cu(110) surface in hydrochloric acid. Due to the strong kinetic hindrance of the Moire´ formation the adsorption rate and, hence, the value of the electrode potential at which the adsorption takes place has a significant influence on the final order of the sulfate overlayer. This can be verified by STM images taken immediately after a sudden potential change (potential step) [1, 4] as shown in Fig. 197.5. Only parts of the surface are covered with an ordered Moire´ structure, whereas the rest of the surface is covered with a disordered sulfate adlayer. Nonetheless, an IR spectrum obtained from this surface and compared to that of a complete and well-ordered Moire´ structure (obtained after slow potential change and, hence, slow sulfate adsorption) shows (i) the same band position which suggests the same local electric field at the sites of individual sulfate molecules and, hence, essentially the same adsorbate density as well as (ii) the same integrated intensities of both spectra. It is only the ordering of the sulfate adlayer, i.e., the Moire´ formation, which depends on the adsorption rate but not the mere sulfate coverage itself. This is very plausible in the light of the expansion of the first Cu layer and the concomitant transport of copper atoms involved in the severe restructuring of the surface.

197

Copper surfaces in sulfuric acid: sulfate adsorption/desorption kinetics

5

Fig. 197.5 In situ STM image of a less ordered sulfate structure measured after a potential step from E ¼
350 mV (RHE) (see CV in Fig. 193.1[https://doi.org/ 10.1007/978-3-662-53908-8_193]) to E ¼ +100 mV (RHE). 76 nm  76 nm, IT ¼ 1 nA, UB ¼
100 mV, measured at E ¼ +200 mV. However, according to Fig. 193.1[https://doi.org/10.1007/978-3-662-539088_193], the actual SO42- coverage as measured by the IR intensity is nearly independent of the degree of structural order (From Ref. [1])

Symbols and abbreviations Short form

Full form

RHE STM IR FTIR

reference hydrogen electrode scanning tunneling microscopy infrared Fourier transform infrared spectrometer

References 1. Broekmann, P., Wilms, M., Arenz, M., Spaenig, A., Wandelt, K.: Atomic structure of Cu(111) surfaces in dilute sulfuric acid solution. In: Wandelt, K., Thurgate, S. (eds.) Solid-Liquid Interfaces, Macroscopic Phenomena – Microscopic Understanding Topics in Applied Physics, vol. 85, p. 141. Springer, Heidelberg (2003. ISBN:3-540-42583-7) 2. Wilms, M., Broekmann, P., Stuhlmann, C., Wandelt, K.: Surf. Sci. 416, 121 (1998) 3. Lennartz, M., Broekmann, P., Arenz, M., Stuhlmann, C., Wandelt, K.: Surf. Sci. 442, 215 (1999) 4. Arenz, M., Broekmann, P., Lennartz, M., Vogler, E., Wandelt, K.: Phys. Status Solidi A 187, 63 (2001) 5. Shingaya, Y., Ito, M.: J. Electroanal. Chem. 467, 299 (1999)

Chapter 198

Hydrohalic acid anion interaction with silver surfaces: Ag(100) – chloride M. Nowicki and K. Wandelt

The onset of chloride adsorption on Ag(100) in 0.02 M KCl + 0.03 M KClO4 solution is characterized by an initial broad CV peak (from about
1.1 to about
1.0 V (SCE ¼ saturated calomel electrode)) corresponding to a lattice gas phase. A sharp peak at
0.63 V (SCE) indicates the onset of an ongoing transformation of the lattice gas into an ordered c(2  2) structure. Like in UHV the anions reside in fourfold hollow sites. The c(2  2) phase is stable until at potentials E >
0.20 V (SCE) complex AgClx surface compounds are formed. Long-range interactions are dominated by electrostatic dipole-dipole interactions between the electrosorbedCl anions (Cl is the most electronegative among the three halides Cl, Br, I.) [1–4]. Symbols and abbreviations Short form

Full form

UHV SCE

ultrahigh vacuum saturated calomel electrode

References 1. 2. 3. 4.

Abou Hamad, I., Wandlowski, T., Brown, G., Rikvold, P.A.: J. Electroanal. Chem. 554/555, 211 (2003) Abou Hamad, I., Mitchell, S.J., Wandlowski, T., Rikvold, P.A., Brown, G.: Electrochim. Acta.50, 5518 (2005) Bowker, M., Waugh, K.C., Wolfindale, B., Lamble, G., King, D.A.: Surf. Sci. 179, 254 (1987) Fu, H., Jia, L., Wang, W., Fan, K.: Surf. Sci. 584, 187 (2005)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_198

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Chapter 199

Hydrohalic acid anion interaction with silver surfaces: Ag(100) – bromide M. Nowicki and K. Wandelt

A sharp CV peak at 0.75 V (Ag/AgCl) corresponding to a disorder-order phase transition is, like with Ag (100)-Cl, also preceded by a broad peak. In the ordered c(2  2) phase, the bromide anions reside in fourfold hollow sites and cause a buckling of the second Ag layer. The concentration dependence of the lateral interactions, as revealed by Monte-Carlo simulations, indicates a change in charge state with coverage (and, thus, potential) of the adsorbed bromide [1–9], similar to Br/Cu(100), see Chap. 184 [https://doi.org/10.1007/978-3-662-53908-8_184].

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

Jovic, V.D.: Chem. Biochem. Eng. Q. 23, 11 (2009) Wandlowski, T., Wang, J.X., Ocko, B.M.: J. Electroanal. Chem. 500, 418 (2001) Abou Hamad, I., Wandlowski, T., Brown, G., Rikvold, P.A.: J. Electroanal. Chem. 554/555, 211 (2003) Gutta, P., Hoffmann, R.: J. Phys. Chem. A 107, 8184 (2003) Abou Hamad, I.: Ph. D. Thesis, University of Bonn (2006) Hanewinkel, C., Otto, A., Wandlowski, T.: Surf. Sci. 429, 255 (1999) Wang, S., Rikvold, P.A.: Phys. Rev. B 65, 155406 (2002) Abou Hamad, I., Mitchell, S.J., Wandlowski, T., Rikvold, P.A., Brown, G.: Electrochim. Acta. 50, 5518 (2005) Ocko, B.M., Wang, J.X., Wandlowski, T.: Phys. Rev. Lett. 79, 1511 (1997)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_199

1

Chapter 200

Hydrohalic acid anion interaction with silver surfaces: Ag(100) – iodide M. Nowicki and K. Wandelt

The system has extensively been studied in UHV [2] and solution. In 0.1 HClO4 + 1 mM KI, cyclic voltammetry and in situ STM yield only an ordered c(2  2) phase on Ag(100), with the iodide particles in fourfold hollow sites. With increasing iodide coverage at positive potentials, a 2D silver iodide compound is formed which in STM images appears as a (2√2  12√2)R45 superstructure superimposed on the quasihexagonal atomic structure. Etching rates, i.e., silver dissolution of the iodide covered Ag(100) surface, were found to depend on the step direction, suggesting an influence of the adlayer structure near the steps on the dissolution process (see also Cu(100)-Br) [1–3]. Symbols and abbreviations Short form

Full form

STM UHV

scanning tunneling microscopy ultrahigh vacuum

References 1. Teshima, T., Ogaki, K., Itaya, K.: J. Phys. Chem. B 101, 2053 (1997) 2. Andryshechkin, B.V., Zhidomirov, G.M., Eltsov, K.N., Hladchanka, Y.V., Korlyukov, A.A.: Phys. Rev. B 80, 125409 (2009) 3. Kleinherbers, K.K., Janssen, E., Goldmann, A., Saalfeld, H.: Surf. Sci. 215, 394 (1989)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_200

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Chapter 201

Hydrohalic acid anion interaction with silver surfaces: Ag(111) – chloride M. Nowicki and K. Wandelt

Cl-Ag(111) interaction was studied by in situ STM, LEED, AES, and DFT. In 5  10 4 M KCl + 0.1 KPF6 Cl is described to form a (1.38  1.38) structure before a sharp CV peak at 0.0 V (SCE) as seen with in situ STM [in UHV (√3  √3)R30 ] [1–12]. Symbols and abbreviations Short form

Full form

LEED STM UHV AES SCE DFT

low-energy electron diffraction scanning tunneling microscopy ultrahigh vacuum Auger electron spectroscopy saturated calomel electrode density functional theory

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Foresti, M.I., Innocenti, M., Forni, F., Guidelli, R.: Langmuir. 14, 7008 (1998) Foresti, M.L., Innocenti, M., Logio, F., Becucci, L., Guidelli, R.: J. Electroanal. Chem. 649, 89 (2010) Yamada, T., Ogaki, K., Okubo, S., Itaye, K.: Surf. Sci. 369, 321 (1996) Andryshechkin, B.V., Eltsov, K.N., Shevlyuga, V.M., Yurov, V.Y.: Surf. Sci. 407, L633 (1998) Rovida, G., Pratesi, F., Maglietta, M., Ferroni, E.: Jpn. J. Appl. Phys. 2 (Suppl 2), 117 (1974) Goddard, P.J., Lambert, R.M.: Surf. Sci. 67, 180 (1977) Bowker, M., Waugh, K.C.: Surf. Sci. 134, 639 (1983) Kleinherbers, K.K., Goldmann, A.: Fresenius Zeitschrift – ZeitschriftfürAnalytischeChemie. 329, 285 (1987) Aloisi, G., Funtikov, A.M., Will, T.: J. Electroanal. Chem. 370, 297 (1994) Gava, P., Kodalj, A., de Gironcoli, S., Baroni, S.: Phys. Rev. B 78, 165419 (2008) Foresti, M.L., Innocenti, M., Forni, F., Guidelli, R.: Langmuir. 14, 7008 (1998) Foresti, M.L., Innocenti, M., Logio, F., Becucci, L., Guidelli, R.: J. Electroanal. Chem. 649, 89 (2010)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_201

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Chapter 202

Hydrohalic acid anion interaction with silver surfaces: Ag(111) – bromide M. Nowicki and K. Wandelt

Using in situ STM and CV, bromide is found to form a (√3  √3)R30 structure before and a (√7  √7) R19.1 structure after a sharp CV peak at 0.0 V (SCE) in 5  10 4 M KBr + 0.1 M KPF6 solution [1–3]. Symbols and abbreviations Short form

Full form

SCE STM

saturated calomel electrode scanning tunneling microscopy

References 1. 2. 3.

Foresti, M.I., Innocenti, M., Forni, F., Guidelli, R.: Langmuir. 14, 7008 (1998) Foresti, M.L., Innocenti, M., Logio, F., Becucci, L., Guidelli, R.: J. Electroanal. Chem. 649, 89 (2010) Yamada, T., Ogaki, K., Okubo, S., Itaya, K.: Surf. Sci. 369, 321 (1996)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_202

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Chapter 203

Hydrohalic acid anion interaction with silver surfaces: Ag(111) – iodide M. Nowicki and K. Wandelt

CV and STM reveal that on Ag(111), iodide forms a (√3  √3)R30 before and a (8  8) structure after a sharp CV peak at ~ 0.2 V (SCE) in 5  10 4 KI + 0.15 M NaOH solution, the latter being most likely a higher-commensurate compound overlayer. Note that the Br and Cl- CV peaks appear at more positive potentials (0.0 V (SCE)) than that of iodide ( 0.2 V), like on Cu(111), see Fig. 181.1[https://doi.org/10.1007/978-3-662-53908-8_181]. Cyclic voltammetry indicates iodide adsorption/desorption in the range 0.8 V to 0.6 V (Ag/AgCl) and a phase transition at 0.05 V, i.e., formation of bulk AgI, in 0.1 mM HI + 0.1 mM KI, buffered with KF-KOH at pH 10. Also a continuous structural compression of the I-lattice from the (√3  √3R–30 ) via a (√3qRβ  √3) R30 to the (√3  √3)R30 followed by an abrupt phase transition into a rotated hexagonal (√3r  √3r)R (30 + α) structure with increasing potential has been described on the basis of in situ STM and ex situ LEED studies. The latter phase is attributed to a Moire´ superstructure [1–3]. Symbols and abbreviations Short form

Full form

STM SCE LEED

scanning tunneling microscopy saturated calomel electrode low-energy electron diffraction

References 1. 2. 3.

Foresti, M.I., Innocenti, M., Forni, F., Guidelli, R.: Langmuir. 14, 7008 (1998) Foresti, M.L., Innocenti, M., Logio, F., Becucci, L., Guidelli, R.: J. Electroanal. Chem. 649, 89 (2010) Yamada, T., Ogaki, K., Okubo, S., Itaye, K.: Surf. Sci. 369, 321 (1996)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_203

1

Chapter 204

Hydrohalic acid anion interaction with silver surfaces: Ag(110) – chloride, bromide, and iodide M. Nowicki and K. Wandelt

UHV-based AES, XPS, LEED, and thermal desorption spectroscopy (TDS) measurements are described in [1, 4]. Only one TDS peak is found for all three halides and shows very similar adsorption/desorption characteristics. LEED reveals a p(2
1) ! c(4
2) phase transition. While the most stable adsorption sites of chlorine on Ag(100) and Ag(111) are the hollow sites, the most stable site of all three halides on Ag(110) is the short-bridge site as concluded from DFT calculations [1–5]. Symbols and abbreviations Short form

Full form

LEED XPS UHV AES TDS

low-energy electron diffraction X-ray photoelectron spectroscopy ultrahigh vacuum Auger electron spectroscopy thermal desorption spectroscopy

References 1. 2. 3. 4. 5.

Hinzert, H., Kleinherbers, K.K., Janssen, E., Goldmann, A.: Appl. Phys. A Mater. Sci. Process. 49, 313 (1989) Wang, Y., Sun, Q., Fan, K., Deng, J.: Chem. Phys. Lett. 334, 411 (2001) Fui, H., Jia, L., Wang, W., Fan, K.: Surf. Sci. 584, 187 (2005) Bange, K., Strehler, B., Sass, J.K.: J. Electroanal. Chem. Interfacial Chem. 229, 87 (1987) Tang, H.-R., Wang, W.-N., Li, Z.-H., Dai, W.-L., Fan, K.-N., Dang, J.-F.: Surf. Sci. 450, 133 (2000)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_204

1

Chapter 205

Silver surfaces in perchloric acid: Ag(110) – perchlorate M. Nowicki and K. Wandelt

Co-adsorption experiments of ClO4 and water in UHV were carried out with high-resolution electron energy loss spectroscopy (HREELS), LEED, TDS, and work function measurements [3] in order to simulate the Ag(110)-electrolyte interface. ClO4 adsorbed on the bare Ag(110) surface yields HREELS losses at 640, 915, 1020, and 1220 cm 1 characteristic of tridentate adsorption (through three oxygen atoms). Co-adsorption of H2O at 170 K and low ClO4 coverages yields a lift-off of the adsorbed ClO4 species and a hydration of the ions as suggested by HREELS losses at 610, 880, and 1090 cm 1, resembling the vibrational spectrum of fully (tetrahedrally) hydrated ClO4 in solution. Co-adsorption of H2O at high ClO4 coverages does not lead to lift-off and hydration, i.e., the hydration energy does not exceed the ClO4 adsorption energy [1, 2]. Symbols and abbreviations Short form

Full form

LEED HREELs UHV TDS

low-energy electron diffraction high-resolution electron energy loss spectroscopy ultrahigh vacuum thermal desorption spectroscopy

References 1. 2. 3.

Krasnopoler, A., Stuve, E.M.: J. Vac. Sci. Technol. A. 13, 1681 (1995) Stuve, E.M., Krasnopoler, A., Sauer, D.E.: Surf. Sci. 335, 177 (1995) Pirug, G., Bonzel, H.P.: Surf. Sci. 405, 87 (1998)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_205

1

Chapter 206

Silver surfaces in sulfuric acid: Ag(100) – sulfate M. Nowicki and K. Wandelt

Frumkin adsorption isotherms of sulfate adsorption were determined by means of radiometry from HClO4 solution on the three low-index planes Ag(100), Ag(111), and Ag(110). It was found that the adsorption strength decreases in the order Ag(111) > Ag(110) > Ag(100) and showed an intermediate behavior on a polycrystalline silver electrode. The stronger interaction with Ag(111) can be explained by the match between the tetrahedral symmetry of the anion and the trigonal symmetry of the substrate [see however Cu (111), Chap. 195[https://doi.org/10.1007/978-3-662-53908-8_195]]. With STM an incommensurate (1.3
3) structure was observed, corresponding to a coverage of 0.25 ML. Since this structure is only stable in acidic solution (pH ¼ 1), it is likely that this structure is stabilized by H3O+ ions (like on Cu(111), Chap. 194[https://doi.org/10.1007/978-3-662-53908-8_194]). The structure, however, is not stable at potentials slightly above 0.2 V (SCE). The presence of sulfate does not affect the oxidation potential of silver electrodes but facilitates the hydrogen evolution reaction. The sequence of adsorption in a neutral solution is quite different to that in acidic solution and follows the sequence of the potential of zero charge (Epzc): 0.48 V, 0,65 V, and 0.77 V (RHE) for Ag(111), Ag (100), and Ag(110), respectively [1–4]. Symbols and abbreviations Short form

Full form

STM ML SCE RHE

scanning tunneling microscopy monolayer saturated calomel electrode reference hydrogen electrode

References 1. 2. 3. 4.

Smolinski, S., Zelenay, P., Sobkowski, J.: J. Electroanal. Chem. 442, 41 (1998) Sobkowski, J., Smolinski, S., Zelenay, P.: Colloids Surf. A: Physico Chem. Eng. Asp. 134, 39 (1998) Stevenson, K.J., Gao I, X., Hatchett, D.W., White, H.S.: J. Electroanal. Chem. 447, 43 (1998) Schweizer, M., Kolb, D.M.: Surf. Sci. 544, 93 (2003)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_206

1

Chapter 207

Silver surfaces in sulfuric acid: Ag(111) – sulfate M. Nowicki and K. Wandelt

In 0.05 M H2SO4 solution, CV shows a characteristic “butterfly”-shaped peak between 0.7 and 0.4 V (Ag/AgCl), and STM reveals a c(3  3√3) structure for the adlayer. Adsorption of sulfate from alkaline solution is inhibited due to the strong specific adsorption of OH-. In situ IR measurements demonstrate specific SO42 adsorption, but the potential dependence of the sulfate coverage indicates significant repulsion between the adsorbed sulfate anions. It appears that on the (111) surface of sp-metals, like Ag and Au, the adsorbed species is SO42 (sulfate), while on the d-metal Pt, the predominant species is HSO4 (bisulfate) [1, 2]. Symbols and abbreviations Short form

Full form

STM IR

scanning tunneling microscopy infrared

References 1. 2.

Schweizer, M., Kolb, D.M.: Surf. Sci. 544, 93 (2003) Marinkovic, N.S., Marinkovic, J.S., Adzic, R.R.: J. Electroanal. Chem. 467, 291 (1999)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_207

1

Chapter 208

Silver surfaces in sulfuric acid: Ag(110) – sulfate M. Nowicki and K. Wandelt

In 0.1 M H2SO4, no ordered adlayer was found in combined STM and CV measurement [1]. Symbols and abbreviations Short form

Full form

STM

scanning tunneling microscopy

References 1.

Schweizer, M., Kolb, D.M.: Surf. Sci. 544, 93 (2003)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_208

1

Chapter 209

Hydrohalic-acid anion interaction with gold surfaces: Au(100) – chloride M. Nowicki and K. Wandelt

In 0.1 M H2SO4 + 1 mM HCl, Cl displaces SO4. At +0.12 V (SCE), the adsorption of a disordered Cl layer begins and lifts the Au(100) reconstruction. At +0.71 V (SCE), a phase transitions into an ordered c(√2  p) R45 (22  p  2.3) structure, a uniaxially incommensurate, quasi-hexagonal structure. Dissolution of Au starts from steps via the formation of AuCl, AuCl2, AuCl3, and AuCl4 complexes. The detachment of an Au atom from a step edge proceeds with an activation energy of 0.7 eV. In agreement with the displacement of SO4 by Cl, gold islands on the surface decay fast in the presence of Cl ions in sulfuric acid solution, a process also known as “electrochemical annealing” [1–8] (see also Sect. 179.13[https://doi.org/10.1007/978-3-662-53908-8_179]). Symbols and abbreviations Short form

Full form

SCE

saturated calomel electrode

References 1. Migani, A., Sousa, C., Illas, F.: Surf. Sci. 574, 297 (2005) 2. Kubo, K., Hirai, N., Hara, S.: Appl. Surf. Sci. 237, 301 (2004) 3. Aldous, L., Silvester, D.S., Villagran, C., Pitner, W.R., Compton, R.G., Lagubas, M.-C., Hardacre, C.: New J. Chem. 30, 1576 (2006) 4. Mesgar, M.: Ph.D. Thesis, University of Ulm (1996) 5. Cuesta, A., Kolb, D.M.: Surf. Sci. 465, 310 (2000) 6. Mesgar, M., Kaghazchi, P., Jacob, T., Pichardo-Pedrero, E., Giesen, M., Ibach, H., Luque, N.B., Schmickler, W.: ChemPhysChem. 14, 233 (2013) 7. Iwai, H., Okadat, M., Fukutani, K., Murata, Y.: J. Phys. Condens. Matter. 7, 5163 (1995) 8. Al-Shakran, M., Beltramo, G., Giesen, M.: Phys. Chem. Chem. Phys. 16, 12143 (2014)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_209

1

Chapter 210

Hydrohalic-acid anion interaction with gold surfaces: Au(100) – bromide M. Nowicki and K. Wandelt

In 0.1 M H2SO4 + 1 mMKBr solution, bromide adsorption begins at 0.12 V (SCE) and results in the formation of a disordered Brad layer which lifts the Au(100) reconstruction accompanied by island formation. At +0.1 V (SCE), a phase transition and the formation of a c(√2  2√2)R45 structure are observed, and starting at 0.48 V (SCE), i.e., with increasing coverage, a further commensurateincommensurate transition into a c(√2p)R45 phase (with p  2√2), i.e., a uniaxial, continuous compression phase, occurs whose coverage increases from 0.5 to 0.65 ML with increasing potential. While bromide resides in the hollow sites on Ag(100), it prefers the twofold bridge sites on Au(100) as concluded from DFT calculations. No ordered Brad structures are observed in alkaline solution, which is explained in terms of competitive adsorption of Br and OH [1–9]. Symbols and abbreviations Short form

Full form

DFT SCE ML

density functional theory saturated calomel electrode monolayer

References 1. 2. 3. 4. 5.

6. 7. 8. 9.

Ocko, B.M., Magnussen, O.M., Wang, J.X., Wandlowski, T.: Phys. Rev. B. 53, R7654 (2003) Ocko, B.M., Wang, J.X., Wandlowski, T.: Phys. Rev. Lett. 79, 1512 (1997) Ocko, B.M., Magnussen, O.M., Wang, J.X., Adzic, R.R., Wandlowski, T.: Phys. B Condens. Matter.221, 238 (1996) Wang, S., Rikvold, P.A.: Phys. Rev. B 65, 155406 (2002) Lucas, C.A., Markovic, N.M.: In-situ X-ray diffraction studies of the electrode/solution interface. In: Alkire, R.C., Kolb, D. M., Lipkowski, J., Ross, P.N. (eds.) Advances in Electrochemical Science and Engineering, vol. 9. Wiley-VCH, Weinheim (2006). ISBN:3-527-31317-6 Blizanac, B.B., Lucas, C.A., Gallagher, M., Arenz, M., Ross, P.N., Markovic, N.M.: J. Phys. Chem. B 108, 5304 (2004) Vivek, J.P., Burgess, J.J.: Langmuir. 28, 5040 (2012) Cueast, A., Kolb, D.M.: Surf. Sci. 465, 310 (2000) Wandlowski, T., Wang, J.X., Magnussen, O.M., Ocko, B.M.: J. Chem. Phys. 100, 10277 (1996)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_210

1

Chapter 211

Hydrohalic-acid anion interaction with gold surfaces: Au(100) – iodide M. Nowicki and K. Wandelt

STM and LEED studies in UHV yield a c(p√2  2√2)R45 structure at coverages slightly higher than 0.4 ML which compresses uniaxially with increasing coverage. For θI> 0.5 ML, the structure transforms into a rotated hexagonal structure [1]. Symbols and abbreviations Short form

Full form

STM LEED UHV ML

scanning tunneling microscopy low-energy electron diffraction ultrahigh vacuum monolayer

References 1.

Valenzuela-Benavides, J., Herrera-Zaldivar, M.: Surf. Sci. 592, 150 (2005)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_211

1

Chapter 212

Hydrohalic-acid anion interaction with gold surfaces: Au(111) – chloride M. Nowicki and K. Wandelt

In 0.1 M KClO4 + 10 3 M HClO4 + 10 3 M KCl solution at 0.2 V (SCE), adsorption of Cl starts with the formation of a disordered layer, which at +0.75 v (SCE) undergoes a disorder-order phase transition [12]. Magnussen et al. [16] describe the ordered incommensurate structure as a compressible structure which eventually could also be explained by a (√3  √3)R30 structure. The Au-Cl bond becomes more covalent (less ionic) with increasing Cl coverage as concluded from DFT calculations. At Cl coverages >0.33 ML, the formation of a complex superlattice of a Au-Cl surface compound is reported [1–18]. Symbols and abbreviations Short form

Full form

DFT SCE ML

density functional theory saturated calomel electrode monolayer

References 1.

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Lucas, C.A., Markovic, N.M.: In-situ X-ray diffraction studies of the electrode/solution interface. In: Alkire, R.C., Kolb, D.M., Lipkowski, J., Ross, P.N. (eds.) Advances in Electrochemical Science and Engineering, vol. 9. Wiley-VCH, Weinheim (2006). ISBN:3-527-31317-6 Blizanac, B.B., Lucas, C.A., Gallagher, M., Arenz, M., Ross, P.N., Markovic, N.M.: J. Phys. Chem. B 108, 5304 (2004) Vivek, J.P., Burgess, J.J.: Langmuir. 28, 5040 (2012) Cueast, A., Kolb, D.M.: Surf. Sci. 465, 310 (2000) Wandlowski, T., Wang, J.X., Magnussen, O.M., Ocko, B.M.: J. Chem. Phys. 100, 10277 (1996) Valenzuela-Benavides, J., Herrera-Zaldivar, M.: Surf. Sci. 592, 150 (2005) Baker, T.A., Friend, C.M., Kaxiras, E.: J. Chem. Phys. 130, 084701 (2009) Gao, W., Baker, T.A., Zhou, L., Pinnaduwage, D.S., Kaxiras, E., Friend, C.M.: J. Am. Chem. Soc. 130, 3560 (2008) Baker, T.A., Friend, C.M., Kaxiras, E.: J. Am. Chem. Soc. 130, 3720 (2008) Spencer, N.D., Lambert, R.M.: Surf. Sci. 107, 237 (1981) Kastanas, G.N., Koel, B.E.: Appl. Surf. Sci. 64, 235 (1993) Baker, T.A.: Ph.D. Thesis, Harvard University, Cambridge (2009) Zeltkov, V.V., Cherkez, V.V., Andryshechkin, B.V., Zhidomirov, G.M., Kierren, B., Fagit-Revurat, Y., Malterre, D., Eltsov, K.N.: Phys. Rev. B 89, 195425 (2014)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_212

1

2

M. Nowicki and K. Wandelt

14. Cherkev, V.V., Zheltov, V.V., Didiot, C., Kierren, B., Fagot-Revurat, Y., Malterre, D., Andryshechkin, B.V., Zhidomirov, G.M., Eltsov, K.N.: Phys. Rev. B 93, 045432 (2016) 15. Zheleva, Z.V., Dhanak, V.R., Held, G.: Phys. Chem. Chem. Phys. 12, 10754 (2010) 16. Magnussen, O.M., Ocko, B.M., Adzic, R.R., Wang, J.X.: Phys. Rev. B 51, 5510 (1995) 17. Ye, S., Ishibashi, C., Uosaki, K.: Langmuir. 15, 807 (1999) 18. Shi, Z., Wu, S., Lipkowski, J.: J. Electroanal. Chem. 384, 171 (1995)

Chapter 213

Hydrohalic-acid anion interaction with gold surfaces: Au(111) – bromide M. Nowicki and K. Wandelt

In 0.1 M HClO4 + 1 mMNaBr solution, adsorption of bromide begins at 0.12 V (Ag/AgCl) and lifts the Au(111) reconstruction. At 0.42 V, formation of an ordered (√3  √3)R30 -Br structure, according to surface X-ray scattering (SXS) and STM, turns into a hexagonal close-packed structure whose Br-Br spacing shrinks with increasing potential from 4.24 Å at the critical ordering potential to 4.03 Å at 300 mV more positive potential, and the structure rotates upon changes of the substrate potential (and coverage) by ~20 ; in fact the resultant structure may also be explained by a (2√7  2√7)R19.1 structure [1–3]. Symbols and abbreviations Short form

Full form

SXS STM

surface X-ray scattering scanning tunneling microscopy

References 1. 2. 3.

Magnussen, O.M., Ocko, B.M., Wang, J.X., Adzic, R.R.: J. Phys. Chem. 100, 5500 (1996) Magnussen, O.M., Ocko, B.M., Adzic, R.R., Wang, J.X.: Phys. Rev. B 51, 5510 (1995) Tao, N.J., Lindsay, S.M.: J. Phys. Chem. 96, 5213 (1992)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_213

1

Chapter 214

Hydrohalic acid anion interaction with gold surfaces: Au(111) – iodide M. Nowicki and K. Wandelt

Iodine adsorption from a dilute solution in methanol leads to a (√3  √3)R30 structure at Pt(311)>Pt(110)>Pt(100), probably due to the abundance of threefold hollow sites on the respective surface [1–3].

References 1. 2. 3.

Atard, G.A., Brew, A., Hunter, K., Sharman, J., Wright, E.: Phys. Chem. Chem. Phys. 16, 13689 (2014) Markovic, N.M., Ross, P.N.: Surf. Sci. Rep. 45, 117 (2002) Sawatari, Y., Inukai, J., Ito, M.: J. Electron Spectrosc. Relat. Phenom. 64(65), 515 (1993)

M. Nowicki (*) Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland e-mail: [email protected] K. Wandelt Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Institute of Physical and Theoretical Chemistry, University of Bonn, Bonn, Germany e-mail: [email protected] © Springer-Verlag GmbH Germany 2018 G. Chiarotti, P. Chiaradia (eds.), Physics of Solid Surfaces, Subvolume B, https://doi.org/10.1007/978-3-662-53908-8_230

1

Chapter 231

Platinum surfaces in sulfuric acid: general remarks M. Nowicki and K. Wandelt

Infrared and CV measurements indicate strong adsorption on Pt above 0.15 V (RHE) and a decrease of the oxygen reduction reaction (ORR) by the adsorbed SO42 /HSO4 anions; the sequence is Pt(111)