Structure and Electronic Properties of Ultrathin In Films on Si(111) 9811968713, 9789811968716

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Springer Theses Recognizing Outstanding Ph.D. Research

Shigemi Terakawa

Structure and Electronic Properties of Ultrathin In Films on Si(111)

Springer Theses Recognizing Outstanding Ph.D. Research

Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

Theses may be nominated for publication in this series by heads of department at internationally leading universities or institutes and should fulfill all of the following criteria • They must be written in good English. • The topic should fall within the confines of Chemistry, Physics, Earth Sciences, Engineering and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder (a maximum 30% of the thesis should be a verbatim reproduction from the author’s previous publications). • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the significance of its content. • The theses should have a clearly defined structure including an introduction accessible to new PhD students and scientists not expert in the relevant field. Indexed by zbMATH.

Shigemi Terakawa

Structure and Electronic Properties of Ultrathin In Films on Si(111) Doctoral Thesis accepted by Kyoto University, Kyoto, Japan

Author Dr. Shigemi Terakawa Max Planck Institute of Microstructure Physics Halle (Saale), Germany

Supervisor Prof. Tetsuya Aruga Kyoto University Kyoto, Japan

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-981-19-6871-6 ISBN 978-981-19-6872-3 (eBook) https://doi.org/10.1007/978-981-19-6872-3 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 This work is subject to copyright. All rights are solely and exclusively licensed 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, expressed 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. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Supervisor’s Foreword

Dr. Shigemi Terakawa received a degree of Doctor of Science from Kyoto University, Japan in March 2022, for his doctoral thesis entitled “Structure and electronic properties of ultrathin In films on Si(111)”. Adsorption of metal atoms on atomically flat surfaces of semiconductors has long been a subject of intense studies to establish, for instance, ultrathin conducting films and to study their intriguing properties inherent to low-dimensional systems. In particular, the adsorption of transition metal atoms on semiconductor surfaces was intensively studied for decades. However, this often resulted in the formation of insulating metal silicide films. Dr. Terakawa’s doctoral thesis is on his establishing a single-atomic-layer phase of In on the Si(111) surface and the characterization of its atomic and electronic structure, and his discovery of a novel ordered In-Mg surface alloy with intriguing electronic structure. The bilayer indium film on Si(111) has been intensively studied because of its two-dimensional nearly free-electron band structure. As to the thinnest limit singlelayer indium film, there has been a serious controversy even on its identification. Dr. Terakawa conducted scanning tunneling microscopy (STM), angle-resolved photoelectron spectroscopy (ARPES), and low-energy electron diffraction (LEED) and eventually established the atomic and electronic structure of the monatomic In film on Si(111). He further discovered in this system the first metal–insulator phase transition in a single-layer metal film by means of ARPES and precision surface conductivity measurement. He further explored the two-dimensional alloying behavior of indium with magnesium on the Si(111) surface, and succeeded in forming threeatomic-layer-thick ordered In-Mg alloy films on Si(111) surface. He showed by combining ARPES and theoretical calculations based on density-functional theory that this three-atomic layer surface alloy is quite unique: the dangling bonds of the Si substrate are terminated by Mg atoms in the bottom-most layer and, as a result, the outer two In layers behave like a “free-standing” two-dimensional metal.

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Supervisor’s Foreword

Dr. Terakawa, by establishing scientific facts and views as briefed above on these ultrathin metal films, made a significant contribution to the science of surfaces and ultrathin films. I believe that his achievements will inspire the further development in this field. Kyoto, Japan August 2022

Prof. Tetsuya Aruga

Abstract

Ultrathin metal films on atomically flat semiconductor substrates are intriguing to investigate physical properties of two-dimensional (2D) metals. Indium-adsorbed Si(111) surfaces are one of the most explored metal/semiconductor systems. However, a single-layer metal, the thinnest 2D metal, is not established and the influence of the metal–semiconductor interface on the properties of the metal layers is not yet understood. The first theme of this thesis is a single-layer phase of indium on the Si(111) surface. The double-layer phase of indium has been extensively studied because of its 2D free-electron-like electronic structure and superconducting transition. However, a single-layer phase was not established, although it has been suggested from microscopic observations using scanning tunneling microscopy (STM) and theoretical calculations. I succeeded in growing the single-layer phase with high crystallinity and revealed the atomic structure and electronic properties using low-energy electron diffraction (LEED), STM, and angle-resolved photoelectron spectroscopy (ARPES). It has a uniaxially incommensurate monolayer structure and metallic band structure, which indicates that this phase is a single-layer metal of indium on Si(111). Moreover, the single-layer metal was found to exhibit a metal–insulator transition upon cooling. The second theme is a surface alloy composed of indium and magnesium on the Si(111) surface. I found a novel triple-layer surface alloy formed by magnesium deposition onto the double-layer phase of indium. ARPES experiments and theoretical calculations revealed the intriguing properties of the triple-layer metal. The deposited magnesium is intercalated between the indium layers and silicon substrate to form a crystalline buffer layer, which decouples the top two metal layers from silicon dangling bonds. As a result, the top two layers behave like a nearly freestanding double-layer metal.

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Parts of this thesis have been published in the following journal articles: • Shigemi Terakawa, Shinichiro Hatta, Hiroshi Okuyama, and Tetsuya Aruga, “Identification of single-layer metallic structure of indium on Si(111)”, Journal of Physics: Condensed Matter 30 365002 (2018). • Shigemi Terakawa, Shinichiro Hatta, Hiroshi Okuyama, and Tetsuya Aruga, “Structure and phase transition of a uniaxially incommensurate In monolayer on Si(111)”, Physical Review B 100, 115428 (2019). • Shigemi Terakawa, Shinichiro Hatta, Hiroshi Okuyama, and Tetsuya Aruga, “Ultrathin (In, Mg) films on Si(111): A nearly freestanding double-layer metal”, Physical Review B 105, 125402 (2022).

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Acknowledgements

I would like to express my sincere appreciation to my supervisor Professor Tetsuya Aruga (Kyoto University, Japan) for his thoughtful guidance and constructive discussions. I also thank Associate Professor Hiroshi Okuyama (Kyoto University, Japan) for his insightful suggestions, particularly in STM experiments. I am particularly grateful to Assistant Professor Shinichiro Hatta (Kyoto University, Japan) for his kind support and advice. He also gave me much guidance about experimental techniques and data analyses. I thank Professor Kazutoshi Takahashi and Assistant Professor Masaki Imamura (Saga University, Japan) for their support and cooperation for the experiments in SAGA Light Source. Mr. Masashi Ohashi and Mr. Kenta Kuroishi (Kyoto University, Japan) helped me with conducting STM experiments. I am grateful to Dr. Hiroyuki Koshida (Tokyo University, Japan) and members of Surface Chemistry Laboratory of Kyoto University for our fruitful discussions. I also thank the Japan Society for the Promotion of Science for the financial support. Finally, I would especially like to thank my parents for their constant support and encouragement during my Ph.D. studies.

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Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Ultrathin Metal Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Thin Indium Films on Si(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 In/Si(111) Surface Superstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Bonding Between Metal Layers and Substrates . . . . . . . . . . . . . . . . . . 9 1.5 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Low-Energy Electron Diffraction (LEED) . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Kinematic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Dynamical Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Scanning Tunneling Microscopy (STM) . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Theory and Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Angle-Resolved Photoelectron Spectroscopy (ARPES) . . . . . . . . . . . 2.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Four-Point-Probe (4PP) Conductivity Measurements . . . . . . . . . . . . . 2.4.1 Theory and Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Chamber 1 (ARPES, LEED) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Chamber 2 (ARPES, LEED) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Chamber 3 (STM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.4 Chamber 4 (4PP Conductivity Measurements, LEED) . . . . . . 2.5.5 Chamber 5 (LEED) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.6 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15 15 15 18 19 19 20 21 21 23 25 25 25 26 27 27 28 28 28 29

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3 Structure and Electronic Properties of In Single-Layer Metal on Si(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1 Introduction . . . . . . . . . . . . . . . . √ . . . . . .√ . . .. . . . . . . . . . . . . . . . . . . . . . . 31 7 × 3 -Hex 3.2 Preparation of the In/Si(111) √ √  and 7 × 3 -Striped Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 √ √  3.3 The Atomic Structure of the In/Si(111) “ 7 × 3 ”-Hex Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 LEED and STM Observations . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Structure Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 First-Principles Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Electronic Structure and Phase Transition of the Indium Monolayer on Si(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Electronic Structure of the In/Si(111) Hex Phase . . . . . . . . . . 3.4.2 Phase Transition of the In/Si(111) Hex Phase . . . . . . . . . . . . . 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Structure and Electronic Properties of Ultrathin (In, Mg) Films on Si(111) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Structure Change by Mg Deposition onto the In/Si(111) √ √  7 × 3 -Rect Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 LEED and STM Observations . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Structure Determination by First-Principles Calculation .... √ √  4.3 The Electronic Structure of the (In, Mg)/Si(111) 3× 3 Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 ARPES Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Band Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35 35 39 41 44 44 47 50 50 53 53 54 54 55 59 59 62 68 69

5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Chapter 1

Introduction

1.1 Ultrathin Metal Films When the thickness of bulk metals reduces and approaches the Fermi wavelength of electrons (several tens of Å), the electrons are confined in the metal films and energy quantization known as quantum-well states occurs [1–3]. Thinner films of mono-atomic and a few atomic layer thickness can be considered two-dimensional (2D) metals since the electrons are almost completely confined in 2D planes. Such ultrathin films cannot stand alone and they are formed on surfaces of crystals such as semiconductors. They are called surface superstructures with structures unique to surfaces and have long been investigated in the field of surface science [4, 5]. In recent years, have also attracted great attention as 2D materials as the 2D materials research progresses including graphene [6], and many efforts have been made to discover new materials and elucidate their physical properties [7]. Innovation in surface analysis techniques such as angle-resolved photoelectron spectroscopy (ARPES) with 2D detectors and in situ conductivity measurements under ultrahigh vacuum (UHV) [8, 9] have greatly contributed to the understanding of their electronic properties. Previous studies have found a lot of 2D metals on semiconductor substrates with attractive physical properties such as metal-insulator transition, Rashba spin splitting, and 2D superconductivity [10–17]. Indium-adsorbed Si(111) surfaces, hereafter In/Si(111), are one of the most explored metal adsorbed semiconductor surfaces, and the atomic structures and electronic properties of various phases with different indium coverages are well established [18–20]. A single-layer metallic phase was suggested from first-principles calculations [21, 22], but it is not yet experimentally established despite extensive research on In/Si(111). Furthermore, although the interface between 2D metals and substrates should strongly affect the atomic structures and electronic properties of metal layers, the influence of the interface on the properties of the indium layers has not been studied by modifying the interface structure. In order to elucidate the properties of ultrathin indium films on Si(111), research combining the investigation of

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. Terakawa, Structure and Electronic Properties of Ultrathin In Films on Si(111), Springer Theses, https://doi.org/10.1007/978-981-19-6872-3_1

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1 Introduction

electronic properties by photoelectron spectroscopy and conductivity measurements, and determination of atomic structure is necessary. In this thesis, I report the experimental and theoretical studies of the ultrathin indium films on Si(111) to establish a single-layer metallic phase of indium, and to reveal the effects of the interface between indium layers and silicon substrates on the properties of the indium layers. The rest of this chapter summarizes previous studies of In/Si(111). Chapter 2 explains experimental techniques used in the thesis. In Chap. 3, I report the formation of the single-layer indium film, and investigate its atomic structure and electronic properties. In Chap. 4, I report the formation of a triple-layer film with a nearly freestanding nature by magnesium deposition onto the double-layer indium film, and reveal the atomic structure and electronic properties. In Chap. 5, I give conclusions of my research.

1.2 Thin Indium Films on Si(111) Indium is a p-block metal in group 13. Indium is one of the raw materials of indium tin oxide (ITO) widely used as transparent conductive electrodes in flat panel displays and solar cells. Indium is also used as solder and high-vacuum seals since it has a low melting point (430 K) and is very soft with high ductility [23, 24]. Since the p-block metals are located between the transition metals and nonmetals, they have some covalent character, which results in crystalline structure distorted from high-symmetry structures such as face-centered cubic (fcc) and body-centered cubic (bcc) lattices. Indium crystallizes in body-centered tetragonal (bct) structure with a = b = 3.253 Å and c = 4.943 Å (Fig. 1.1) [25]. This structure can be regarded as a distorted fcc lattice. The c/a ratio (1.520) is 7.4% larger than that for the fcc lattice. This distortion lowers the symmetry and 12 nearest neighbor atoms in the fcc lattice are subgrouped into 4 nearest neighbors at 3.25 Å located in the same (001) plane and 8 next nearest neighbors at 3.38 Å located in the adjacent (001) planes. This unique bct structure of indium gathered attention, and the electron-concentration-

Fig. 1.1 Atomic structure of bulk indium. The blue balls represent indium atoms, and the red lines show the bct unit cell

1.2 Thin Indium Films on Si(111)

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Fig. 1.2 a LEED patterns for a 10-layer-thick indium film grown on Si(111) at 50 K [37]. b Distances between the LEED spots indicated by the dashed line in a as a function of indium coverage [37]

induced and pressure-induced structural changes were widely investigated [26–35]. The crystal structure of indium under high pressure is still under investigation. The tetragonal structure transforms into orthorhombic structure at around 50 GPa, and it transforms again into tetragonal structure at around 150 GPa [36]. The transformation to the closest packed fcc structure is predicted above 800 GPa [33], but it is not yet experimentally observed. The atomic structure of metal films grown on semiconductor substrates can be different from that of bulk metals due to bonding at the interfaces. The indium film grown on the Si(111) substrate has fcc(111) structure at lower thickness and changes to bct(101) structure with increasing thickness [37, 39]. Figure 1.2 shows the lowenergy electron diffraction (LEED) pattern for the indium film grown on Si(111) at 50 K. The spot distances for a six-layer film are the same in all directions with six-fold rotational symmetry, indicating that the film has the fcc(111) structure. The bonding at the interface realizes the fcc structure, which is predicted only under ultrahigh pressure in bulk. For higher thickness films, two of the distances are shorter than the other. This pattern shows that the structure of the films changes from ideal hexagonal fcc structure to distorted hexagonal bct structure. The temperature dependence of the growth mode of the indium films has also been well studied. The films grow in a quasilayer-by-layer mode below 150 K, and preferred thicknesses with a trilayer period appear by annealing above 200 K [38, 40]. Figure 1.3a shows the X-ray reflectivity from a 10-layer indium film grown at 135 K and from that after annealing at 210 and 240 K. The corresponding thickness distributions are shown in Fig. 1.3b. The film grown at 135 K has a narrow thickness distribution with a width of 2–3 layers centered at 10 layers. The data at 210 and 240 K show peak thicknesses of 10, 13, and 16 layers, indicating that the films of these thicknesses are preferably grown by annealing. This result is explained by the “electronic growth”, where the quantumwell states in thin metal films play a significant role in stabilizing the films and determining the favorite thicknesses [41].

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1 Introduction

Fig. 1.3 a Log plot of the X-ray reflectivity (red circles) taken from a 10-layer-thick indium film (√ √ ) 3 × 3 surface at 135 K, and from the same film after annealing at grown on the In/Si(111) 210 and 240 K. The black curves are fitting curves [38]. b The corresponding thickness distributions [38]

1.3 In/Si(111) Surface Superstructures The structure and electronic properties of the thin indium films on Si(111) have been investigated in terms of quantum-well states as described in Sect. 1.2. However, the atomic structure of the interfaces between the indium films and silicon substrates is not yet decided and precise control of thickness at atomic scale is still challenging. On the other hand, Si(111) surfaces covered with indium less than two-atomic-layer thick have long been studied as surface superstructures in the field of surface science, and their atomic and electronic structure are well established. The indium films in Sect. 1.2 are prepared by deposition of indium onto substrates below room temperature (RT), where the films grow in a quasi-layer-by-layer mode. In contrast at and above RT, 2D superstructures are formed only at one-layer and two-layer thickness, and threedimensional (3D) islands are formed above two-layer thickness. This growth mode is called Stranski–Krastanov growth mode [42, 43]. There are many phases of In/Si(111) depending on indium coverage and temperature [18–20]. Figure 1.4 shows the phase diagram displaying the phases observed tunneling)microscopy (STM) as a function of indium coverage. at RT by scanning (√ √ 7 × 3 -rect phases are of particular interest because of their The (4 × 1) and metallic electronic structure and relevant physical properties.

1.3 In/Si(111) Surface Superstructures

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Fig. 1.4 Phase diagram of In/Si(111) at RT

(√ √ ) The 7 × 3 -rect phase has double-layer structure with indium coverage of 2.4 ML, where 1 ML is defined as the atom density of an unreconstructed Si(111) atoms surface (7.83 × 1014 cm−2 ). Each layer has a quasi-rectangular array of indium (√ √ ) similar to the (001) plane of bulk bct indium (Fig. 1.5a) [21, 44, 49]. The 7× 3 rect phase has 2D nearly-free-electron band structure with circular Fermi surface (FS) (Fig. 1.5b) [45] and exhibits a superconducting transition at ∼3 K, which is almost the same as that of bulk indium (Fig. 1.5d) [15, 16, 46, 50]. Recent high-resolution ARPES measurements have reported spin splittings of the FS (Fig. 1.5c) [46, 51]. The (4 × 1) phase (1.0 ML) has a quasi-one-dimensional (1D) structure with zigzag arrangement of indium atoms (Fig. 1.6a) [47, 52] and exhibits a metalinsulator transition at ∼120 K [11, 12, 48, 53]. The band maps measured by ARPES in Fig. 1.6b show that the m2 and m3 bands are crossing the Fermi level (E F ) at 130 K, and that band gaps are open at 80 K [48]. In addition, a sharp conductivity drop associated with the transition is observed in surface conductivity measurements (Fig. 1.6c) [12]. Recent first-principles calculation has suggested a single-layer metallic phase of (√ √ ) 7 × 3 periodicity [22]. Figure 1.7 shows the structure model. In/Si(111) with The unit cell contains seven indium atoms, and two of them (dark blue) are weakly bonded to silicon and protruding compared to the other five (light blue). The singlelayer metallic phase is not yet experimentally established. There are two candidates for the single-layer( metallic phase with indium coverage between the (4 × 1) phase √ √ ) 7 × 3 -rect phase (2.4 ML) in the phase diagram (Fig. 1.4). (1.0 ML) and the (√ √ ) 7 × 3 -hex and The two phases were found using STM, and they are called (√ √ ) 7 × 3 -striped phases. (√ √ ) 7 × 3 -hex phase is formed by RT deposition of indium on the The (√ √ ) 3 × 3 phase (1/3 ML) and observed in the coverage between In/Si(111) (√ √ ) 7 × 3 -rect phases (Fig. 1.8a) [20]. Note that the indium covthe (2 × 2) and

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(√ √ ) 7 × 3 -rect phase [44]. The blue and orange (√ √ ) circles represent indium and silicon atoms, respectively. b ARPES FS map of the 7 × 3 -rect (√ √ ) phase [45]. The green, blue, and red lines indicate the surface Brillouin zones of 7× 3 , (1 × 1) and (1 × 1) for the square lattice of indium, respectively. c High-resolution FS map [46]. are indicated by the arrows. d Temperature dependence of zero bias resistance The spin (√splittings √ ) 7 × 3 -rect phase [15]. The red lines and blue lines are data measured using the probe for the configurations I and II, respectively. The inset shows resistances for a wider temperature range. Tc indicates the superconducting transition temperature Fig. 1.5 a Structure model of the In/Si(111)

1.3 In/Si(111) Surface Superstructures

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Fig. 1.6 a Structure model of the In/Si(111) (4 × 1) phase [47]. The black and gray circles represent indium and silicon atoms, respectively. b ARPES band maps of the (4 × 1) phase at 130 and 80 K [48]. c Temperature dependence of the conductivity σ of the (4 × 1) phase [12]

(√ √ ) Fig. 1.7 Structure model of the single-layer phase of In/Si(111) with 7 × 3 periodicity (1.4 ML) [22]. The dark blue and light blue circles show indium atoms, and the yellow circles show silicon atoms. The dark blue indium atoms protrude more than the light blue ones

erages shown in Fig. 1.8a were underestimated compared to those (√ of√the)currently established structural models of (2 × 2) (1.0 ML) [55, 56] and 7 × 3 -rect (2.4 (√ √ ) 7 × 3 -hex phase was found to undergo a transition to ML). Interestingly, the (√ √ ) 7 × 7 phase at 265–225 K [20, 57]. Figure 1.8b shows the STM image of a (√ (√ √ ) √ ) 7 × 3 -hex and 7 × 7 phases, and the linear the surface with coexisting

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1 Introduction

(a)

0.33 ML

0.93 ML

0.63 ML (b)

1.08 ML (c)

Fig. (√ 1.8√a )STM images of structural transformation for RT deposition of indium on the In/Si(111) 3 × 3 surface [20]. The indium coverages are shown in the bottom left corner. Note that these values were underestimated compared to the indium coverages of the currently established structural models. Scale of the images: (top left) 500 × 250 Å2 , (bottom left and top right) 700 × 350 Å2 , (bottom 600 × 300 Å2 , (insets) 70 × 50 Å2 . b STM image of the surface obtained by cooling (√ right) √ ) 7 × 3 -hex phase (160 × 160 Å2 ) [20]. The linear structure in the top left part and the the (√ (√ √ ) √ ) honeycomb structure in the bottom right part correspond to the 7 × 3 -hex and 7× 7 (√ √ ) 7 × 3 -striped and (4 × 1) phases at phases, respectively. c STM image of the coexisting darker linear structure and brighter linear structure correspond to the (4 × 1) and RT [54]. The ( √ √ ) 7 × 3 -striped phases, respectively

structure in the top left part and the honeycomb structure in the bottom right part (√ (√ √ ) √ ) correspond to the 7 × 3 -hex and 7 × 7 phases, respectively. (√ √ ) 7 × 3 -striped phase is formed by annealing the indium-deposited The Si(111) surface and always observed as a minor domain coexisting with the (4 × 1) phase (1.0 ML) (Fig. 1.8c) [18, The darker and brighter linear structures (√19, 54]. √ ) correspond to the (4 × 1) and 7 × 3 -striped phases, respectively.

1.4 Bonding Between Metal Layers and Substrates

9

Because it is difficult to prepare high-quality samples of the two phases with macro-scale (mm order) sizes, they have been investigated mostly by microscopic observations, and thus their physical properties are not well understood. In addition, the sensitivity of STM images tip )and image acquisition conditions makes it (√ to √ 7 × 3 phases [54, 58]. difficult to identify the two

1.4 Bonding Between Metal Layers and Substrates In general, ultrathin metal films on silicon substrates have structures unique to surface superstructures and different from those of the bulk metals because of the bonding with the dangling (bonds of the silicon substrates [59–62]. The rectangular structure √ √ ) 7 × 3 -rect phase similar to bulk indium is an exceptional of the In/Si(111) case. Moreover, its rectangular structure is in contrast to the hexagonal structure of indium films on Si(111) thicker than 2 ML. These facts suggest that the bonding between the indium layer and silicon substrate(plays an important role in stabilizing √ √ ) 7 × 3 -rect phase. The bonding the rectangular double-layer structure of the (√ √ ) 7 × 3 -rect phase, which results in also affects the electronic structure of the deformation from 2D free-electron band structure [21, 44, 45]. In order to decouple metal layers from the dangling bonds of silicon substrates, proper interface structures (buffer layers) have to be inserted between the metal layers and substrates. Buffer layers are also necessary in the case of the graphene on the SiC(0001) substrate [63–66]. Although the epitaxial monolayer graphene (Fig. 1.9a, left) consists of two carbon layers, the layer covalently bonded to the substrate called “zero-layer” graphene does not show π bands, which are characteristic of graphene. Therefore, the band structure (Fig. 1.9b, left) shows a linear dispersion of the π bands peculiar to the monolayer graphene. After hydrogen intercalation (Fig. 1.9a, right),

Fig. 1.9 Side view models for (left) the epitaxial monolayer graphene on SiC(0001) and (right) the monolayer graphene decoupled from the substrate after hydrogen intercalation [63]. b Dispersion of the π bands measured with ARPES for each of a [63]

10

1 Introduction

(√ (√ √ ) √ ) Fig. 1.10 Structure model for a (Tl, Pb)/Si(111) 3 × 3 [17], b (Tl, Sn)/Si(111) 3× 3 (√ √ ) 3 × 3 [77]. a The blue circles are Tl atoms; the orange circles [76], and c (Tl, Mg)/Si(111) are Pb atoms; and the yellow, gray, and white circles are Si atoms. b The purple circles are Tl atoms; the orange circles are Sn atoms; and the yellow, gray, and white circles are Si atoms. c The gray and green circles are Tl atoms; the orange circles are Mg atoms; and the blue circles are Si atoms

“zero-layer” graphene is decoupled from the substrate and quasi-freestanding bilayer graphene appears, yielding the double π bands (Fig. 1.9b, right). Such interface engineering is one of the most important topics in the research of the quantum-well states of thin metal films, and the influence of the interface on the growth mode and electronic properties of metal films has been well investigated [3, 67–75]. In these studies, the interface structure has been changed by using substrates terminated by different metal atoms. However, it is still difficult to obtain highly crystalline thin films with thickness particularly less than five layers. In this study, I focus on surface alloys on Si(111) as a method to modify the interface structure between the metal films and substrates. The surface alloys on Si(111) have recently been investigated to explore novel physical properties which are not observed in ultrathin metal films consisting of single elements. New intriguing materials have been found by combination of different heavy metals with large spin– orbit interaction, e.g., single-layer metal exhibiting both Rashba spin splitting and superconductivity [17, 78–81]. These surface alloys are formed by deposition of one of the elements onto the ultrathin films of the other elements kept at around RT. In this deposition process, the structure of the pristine ultrathin films breaks, and new structure of surface alloys is formed by mixture of the two elements and large change of atom positions including breaking of the bonds between the metal atoms and substrates. There are some kinds of structures of the surface alloys depending on the constituent elements. Figure 1.10a, b, and c illustrates the structure models of surface alloys obtained by deposition of Pb, Sn, and Mg on a single-layer Tl film on Si(111) (coexisting single-layer and double-layer Tl films in (c)), respectively. In the case of Pb, Tl and Pb atoms are located at almost the same height and form a singlelayer structure [17]. In the case of Sn and Mg, Sn and Mg atoms are intercalated between the Tl layer and Si substrate and form double-layer structures [76, 77]. In the (Tl, Mg) surface alloy, metallic bands are composed mostly of the orbitals of the

References

11

top Tl layer and the bottom (Tl, Mg) layer scarcely contributes to the metallic bands [77]. Although the spin splitting of the metallic bands was mainly discussed in the previous study, I consider that the preparation method of this (Tl, Mg) surface alloy can be utilized to modify the interface structure of ultrathin indium films on Si(111) substrates.

1.5 Outline of the Thesis In this thesis, I report experimental and theoretical studies on the following two themes: 1. Establishment of the preparation method for the indium single-layer phase on Si(111) and investigation of its atomic structure and electronic properties. I( report the) preparation of high-quality samples of the In/Si(111) (√ methods √ √ √ ) 7 × 3 -hex and 7 × 3 -striped phases and the relationship between the two phases revealed by a diffraction method, which directly reflects the atomic structure. The atomic structure and electronic properties of the phases are investigated by ARPES, LEED and STM, and compared with theoretical results by first-principles calculations. Moreover, temperature-dependent change of the electronic properties is studied using ARPES and four-point-probe conductivity measurements. 2. Investigation of the atomic structure and electronic properties of a magnesiumdeposited ultrathin indium film on Si(111). I report the formation of a new ultrathin metal film on Si(111) by deposition of magnesium onto the double-layer indium film. The atomic structure is investigated using LEED, STM and first-principles calculations. The electronic band structure is studied by ARPES, and the charge density distributions are calculated to reveal the effects of the magnesium deposition on the atomic structure and electronic properties of the ultrathin indium films.

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12

1 Introduction

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50. Zhang T, Cheng P, Li Wj, Sun Yj, Wang G, Zhu Xg, He K, Wang L, Ma X, Chen X, Wang Y, Liu Y, Lin Hg, Jia Jf, Xue QK (2010) Nat. Phys. 6:104 51. Kobayashi T, Nakata Y, Yaji K, Shishidou T, Agterberg D, Yoshizawa S, Komori F, Shin S, Weinert M, Uchihashi T, Sakamoto K (2020) Phys. Rev. Lett. 125:176401 52. Mizuno S, Mizuno YO, Tochihara H (2003) Phys. Rev. B 67:195410 53. Yeom HW, Takeda S, Rotenberg E, Matsuda I, Horikoshi K, Schaefer J, Lee CM, Kevan SD, Ohta T, Nagao T, Hasegawa S (1999) Phys. Rev. Lett. 82:4898 54. Shin D, Woo J, Jeon Y, Shim H, Lee G (2015) J. Korean Phys. Soc. 67:1192 55. Chou JP, Wei CM, Wang YL, Gruznev DV, Bondarenko LV, Matetskiy AV, Tupchaya AY, Zotov AV, Saranin AA (2014) Phys. Rev. B 89:155310 56. Kwon SG, Kang MH (2014) Phys. Rev. B 89:165304 57. Mihalyuk AN, Alekseev AA, Hsing CR, Wei CM, Gruznev DV, Bondarenko LV, Matetskiy AV, Tupchaya AY, Zotov AV, Saranin AA (2016) Surf. Sci. 649:14 58. Suzuki T, Lawrence J, Walker M, Morbec JM, Blowey P, Yagyu K, Kratzer P, Costantini G (2017) Phys. Rev. B 96:035412 59. Hupalo M, Chan TL, Wang CZ, Ho KM, Tringides MC (2002) Phys. Rev. B 66:161410(R) 60. Stepanovsky S, Yakes M, Yeh V, Hupalo M, Tringides MC (2006) Surf. Sci. 600:1417 61. Kuzumaki T, Shirasawa T, Mizuno S, Ueno N, Tochihara H, Sakamoto K (2010) Surf. Sci. 604:1044 62. Lee SS, Song HJ, Kim ND, Chung JW, Kong K, Ahn D, Yi H, Yu BD, Tochihara H (2002) Phys. Rev. B 66:233312 63. Riedl C, Coletti C, Iwasaki T, Zakharov AA, Starke U (2009) Phys. Rev. Lett. 103:246804 64. Ohta T, Bostwick A, McChesney JL, Seyller T, Horn K, Rotenberg E (2007) Phys. Rev. Lett. 98:206802 65. Razado-Colambo I, Avila J, Vignaud D, Godey S, Wallart X, Woodruff DP, Asensio MC (2018) Sci. Rep. 8:10190 66. Briggs N, Gebeyehu ZM, Vera A, Zhao T, Wang K, De La Fuente Duran A, Bersch B, Bowen T, Knappenberger KL, Robinson JA (2019) Nanoscale 11:15440 67. Schmidt T, Bauer E (2000) Phys. Rev. B 62:15815 68. Ricci DA, Miller T, Chiang TC (2004) Phys. Rev. Lett. 93:136801 69. Tang Z, Teng J, Jiang Y, Jia J, Guo J, Wu K (2007) J. Appl. Phys. 102:053504 70. Slomski B, Meier F, Osterwalder J, Dil JH (2011) Phys. Rev. B 83:035409 71. Starfelt S, Zhang HM, Johansson LS (2018) Phys. Rev. B 97:195430 72. Starfelt S, Johansson LS, Zhang HM (2019) Surf. Sci. 682:25 73. Starfelt S, Johansson LS, Zhang HM (2020) Surf. Sci. 692:121531 74. Starfelt S, Lavén R, Johansson LS, Zhang HM (2020) Surf. Sci. 701:121697 75. Sugawara K, Seo I, Yamazaki S, Nakatsuji K, Gohda Y, Hirayama H (2021) Surf. Sci. 704:121745 76. Gruznev DV, Bondarenko LV, Matetskiy AV, Tupchaya AY, Alekseev AA, Hsing CR, Wei CM, Eremeev SV, Zotov AV, Saranin AA (2015) Phys. Rev. B 91:035421 77. Tupchaya AY, Bondarenko LV, Vekovshinin YE, Yakovlev AA, Mihalyuk AN, Gruznev DV, Hsing CR, Wei CM, Zotov AV, Saranin AA (2020) Phys. Rev. B 101:235444 78. Osiecki JR, Sohail HM, Eriksson PE, Uhrberg RI (2012) Phys. Rev. Lett. 109:057601 79. Gruznev DV, Bondarenko LV, Matetskiy AV, Yakovlev AA, Tupchaya AY, Eremeev SV, Chulkov EV, Chou JP, Wei CM, Lai MY, Wang YL, Zotov AV, Saranin AA (2014) Sci. Rep. 4:4742 80. Matetskiy AV, Kibirev IA, Mihalyuk AN, Eremeev SV, Gruznev DV, Bondarenko LV, Tupchaya AY, Zotov AV, Saranin AA (2017) Phys. Rev. B 96:085409 81. Gruznev DV, Zotov AV, Saranin AA (2017) Jpn. J. Appl. Phys. 56:08LA01

Chapter 2

Experimental Methods

2.1 Low-Energy Electron Diffraction (LEED) Low-energy electron diffraction (LEED) is an experimental technique to study the surface structures of solids. Low-energy (10–500 eV) electrons are incident on the surface and diffraction patterns of the electrons scattered by atoms near the surface are observed. Because the inelastic mean free path of low-energy electrons in solids is less than ∼10 Å, LEED has high surface sensitivity and has been used to determine various surface structures. LEED patterns are analyzed based on two different theories: kinematic theory and dynamical theory. In the kinematic theory, surface unit cells and symmetries can be decided. In the dynamical theory, the atom positions (x, y, and z) in the unit cells, in other words, the atomic structures near the surfaces can be determined. Furthermore, analyses of spot shapes can give information about the crystallinity and domain sizes of surface structures.

2.1.1 Kinematic Theory Incident electrons on a surface are assumed to be elastically scattered only once by surface atoms and emitted into vacuum. We first consider the electron scattered by a single atom. According to the plane wave approximation, the wave function is represented as (2.1) φ 0 = φ0 ei k0 ·r , where k0 is the wave vector of the incident electron. The wave function of the electron scattered by an atom j is represented as φ = (φ0 ei k0 ·r /R) f j (k0 , k) ei (k−k0 )·R j ,

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. Terakawa, Structure and Electronic Properties of Ultrathin In Films on Si(111), Springer Theses, https://doi.org/10.1007/978-981-19-6872-3_2

(2.2)

15

16

2 Experimental Methods

where R is the coordinates of the observation point, R j is the coordinates of the scattering atom, and k is the wave vector of the scattered electron. φ0 ei k0 ·r /R, f j (k0 , k) and ei (k−k0 )·R j represent spherical wave function, atomic scattering factor for the atom j and phase shift, respectively. When considering the scattering from entire surface atoms, the wave function φ is represented as φ∝

{

f j (k0 , k) ei (k−k0 )·R j .

(2.3)

j

The sum of f j in the unit cell is called structure factor F. F is dependent on atomic scattering factor f j and atom positions in the unit cell. The lattice vectors can be expressed as R j = n 1 a1 + n 2 a2 (1 ≤ n 1 ≤ M1 , 1 ≤ n 2 ≤ M2 ), where a1 and a2 are the unit vectors of the surface 2D lattice, and M1 and M2 are the numbers of the lattice points along each direction. Substitution of this into Eq. 2.3 gives the following equation: M1 M2 { { ein 1 a1 ·(k−k0 ) ein 2 a2 ·(k−k0 ) . (2.4) φ∝F n 1 =1

n 2 =1

The scattering intensity I is proportional to the square of φ. I ∝ |F|2 |G|2 , G =

M1 { n 1 =1

ein 1 a1 ·(k−k0 )

M2 {

ein 2 a2 ·(k−k0 ) .

(2.5)

n 2 =1

|G|2 is expanded to |G|2 =

sin2 [{M1 a1 · (k − k0 )}/2] sin2 [{M2 a2 · (k − k0 )}/2] . sin2 [{a2 · (k − k0 )}/2] sin2 [{a1 · (k − k0 )}/2]

(2.6)

The condition for constructive interference is given by the Laue condition, (1/2)a1 · (k − k0 ) = h 1 π, (1/2)a2 · (k − k0 ) = h 2 π (h 1 , h 2 : integers).

(2.7)

In other words, when (k − k0 ) matches the integral multiple of the reciprocal lattice vectors, high scattering intensity is observed. Ewald sphere construction can visually explain the LEED pattern. In the case of 3D diffraction, the scattering intensity along the surface normal direction is strong at discrete points satisfying the Laue condition. In contrast, the reciprocal lattices for a 2D lattice are considered as rods normal to the surface. Equation 2.7 is satisfied when the components of the scattered vector in the direction parallel to the surface agree with those of a 2D reciprocal lattice vector (k'll − kll = g ll ). Elastically scattered vectors k' can be obtained by the following steps as shown in Fig. 2.1a: (1) The wave vector k of the incident beam is positioned with its end at the origin (0 0) of the 2D reciprocal lattice.

2.1 Low-Energy Electron Diffraction (LEED)

17

Fig. 2.1 a Ewald sphere construction for the case of single elastic diffraction only from surface atoms, which corresponds to an ideal 2D lattice. b Ewald sphere construction for the case of single elastic diffraction from topmost and underlying several-layer atoms, which corresponds to a quasi2D lattice

(2) The sphere with radius |k' | = |k| (the Ewald sphere) is drawn with its center at the beginning of the incident vector k. (3) The wave vector of the scattered beam k' is defined as the vector with its beginning at the center of the Ewald sphere and its end at the intersection point between a reciprocal lattice rod and the sphere. We have discussed the Laue function G, but the structure factor F is also a factor to decide scattering intensity. For atoms j = 1 to s in a unit cell, F=

s {

f j ei (k−k0 )·r j ,

(2.8)

j=1

where r j and f j are the positions and atomic scattering factor of the atom j, respectively. Considering the equation r j = x j a1 + y j a2 , the structure factor for the reciprocal lattice points (h 1 , h 2 ) is expressed as Fh 1 ,h 2 =

s {

f j e2πi (h 1 x j +h 2 y j ) .

(2.9)

j=1

The scattering intensity is the multiplication of F and G, and hence the spots for F = 0 disappear even though they fulfill the Laue condition. These spots are called missing spots.

18

2 Experimental Methods

2.1.2 Dynamical Theory The kinematic theory is accurate when electrons are scattered by an ideal 2D lattice. However on real surfaces, incident electrons penetrate solids and are multiply scattered. As a result, the intensity of the reciprocal lattice rods is no longer constant and varies depending on the atom positions in the topmost atoms and underlying several-layer atoms. This means that the measurement and analysis of the intensity distribution of reciprocal lattice rods can determine the surface atomic structure. In order to obtain the intensity distribution of a reciprocal lattice rod, the spot intensity is measured while changing the energy of the incident electron. Dependent on the energy, the radius of the Ewald sphere changes and the intersection point between the sphere and the rod moves, which results in the intensity change of the diffraction spot. This is schematically drawn in Fig. 2.1b. The obtained data of the spot intensities as a function of the incident electron energy are known as LEED I -V curves. The LEED I -V curves directly reflect the surface atomic structure. We can confirm whether two phases with the same 2D unit cell have identical atomic structure or not by I -V analyses. We can also decide the surface atomic structure by comparing the experimental I -V curves and those dynamically calculated for structure models. For quantitative comparison of two sets of I -V curves, a reliability factor (R-factor) is used. A commonly used R-factor is the Pendry R-factor (RP ) [1]. RP is suggested to treat all peaks with equal weight since the intensity of the spots in higher energy is much weaker than that in lower energy due to thermal and atomic scattering effects but all peaks have equally valuable geometrical information [2]. RP is based on the logarithmic derivative of the I -V curves, L = I ' /I, ) ( Y = L/ 1 + Voi2 L 2 ,

(2.10) (2.11)

where I and I ' are an I -V curve and its energy derivative. Voi is the imaginary part of the inner potential and empirically set to about −4 eV. RP is calculated as {(

(Y1,g − Y2,g )2 dE

g

RP = { (

2 2 (Y1,g + Y2,g )dE

,

(2.12)

g

where g describes the reciprocal lattice points, and 1 and 2 are labels. In general, R ≤ 0.2 indicates a good agreement and R ≥ 0.4 indicates a poor agreement. In this work, RP is used to quantitatively compare two sets of experimental I -V curves measured for two surfaces prepared by different methods. Voi is set to −4 eV.

2.2 Scanning Tunneling Microscopy (STM)

19

G4 G3 G2 G1

Viewport

Electron gun Sample

-Vp

Fluorescent screen +2.7 kV UHV chamber

-Vp+V

Fig. 2.2 Schematic of a LEED apparatus

2.1.3 Apparatus Figure 2.2 shows a schematic of a LEED apparatus used in this work. It consists of an electron gun (filament), four mesh grids (G1 –G4 ), and fluorescent screen. The grids G1 and G4 are equipotential to the grounded sample. The grids G2 and G3 screen out inelastically scattered electrons and secondary electrons. A voltage of +2.7 kV is applied to the fluorescent screen, and scattered electrons are accelerated and hit the screen to emit photons. Because the screen is transparent, the diffraction pattern is observed through the viewport on the side of the electron gun using a camera. In order to avoid the influence of magnetic fields such as terrestrial magnetism, the chamber has magnetic shielding.

2.2 Scanning Tunneling Microscopy (STM) Scanning Tunneling microscopy (STM) [3] is microscopy using the tunneling effect of electrons. STM can image surfaces at atomic resolution, which is less than 0.1 Å for the surface normal (z) direction and less than 1 Å for the surface parallel (x, y) directions.

20

2 Experimental Methods

monitor

feedback loop z

tube scanner

x, y

scan control

tip

current detection

sample

Vs

Fig. 2.3 Schematic of an STM apparatus

2.2.1 Theory and Apparatus Figure 2.3 shows a schematic of an STM apparatus. It consists of a tube scanner with a tip, a tunnel current detector, and a feedback circuit. The tube scanner has piezoelectric elements attached to the electrodes for x, y, and z axes, which enable atomic-scale 3D positioning of the tip. When the metal tip is brought close to a conductive surface with a distance where the electron clouds of the tip and the surface overlap (∼10 Å) and a bias voltage (VS ) is applied between the tip and the sample, a tunnel current (a few nA) flows. The tip is scanned on the surface in the surface parallel (x, y) directions, while the tunneling current is kept at a predetermined level by changing the height (z) of the tip. The realspace image can be obtained from the applied voltage on the z piezoelement to keep the tunneling current constant. Because the relationship between the displacement of the piezoelectric elements and the applied voltages is dependent on temperature, the displacement is calibrated by obtaining atomic-scale STM images of well-defined surface structures. When the bias voltage V is applied to the sample, the tunneling current I is expressed as follows by the model using Wentzel–Kramers–Brillouin (WKB) approximation [4–6]. (

eV

I ∝

ρS (E)ρT (E − eV )T (z, eV , E)dE,

(2.13)

0

where ρT(S) and T are the density of states in the tip (sample) and the tunneling transition probability, respectively. T is given by ) √ / 2z 2m φS + φT eV −E , + T (z, eV , E) ~ exp − h 2 2 )

(2.14)

2.3 Angle-Resolved Photoelectron Spectroscopy (ARPES)

21

where φT(S) is the work function of the tip (sample), m is the mass of a free electron, and z is the distance between the tip and sample. Equations 2.13 and 2.14 indicate that the tunneling current I is proportional to exponential of the tip-sample distance z. This is why STM has high sensitivity along the surface normal (z) direction. Note that I also depends on the density of states in the sample (ρS ), showing that the STM images do not reflect only heights (atomic structures) but also electronic properties of the sample surface.

2.3 Angle-Resolved Photoelectron Spectroscopy (ARPES) Photoelectron spectroscopy (PES) is an experimental technique to measure the kinetic energies of photoelectrons emitted by photons from solid, liquids, or gases. Angle-resolved photoelectron spectroscopy (ARPES) is a technique measuring the kinetic energies and emission angle distributions of the photoelectrons and is widely used to investigate electronic band structure of solids. Ultraviolet light is often used as incident light in ARPES. The obtained spectra sensitively reflect the electronic properties near the surface of solids because the energies of the photoelectrons are 10–100 eV and the inelastic mean free path for the electrons is ∼10 Å.

2.3.1 Theory The basic theory for ARPES is the photoelectric effect found by Hertz in 1887. When an electron in a solid with binding energy E B is excited by incident light with energy hν and emitted to vacuum as a photoelectron with kinetic energy E kin , the following energy conservation law is derived using work function φ. hν = E kin + φ + E B .

(2.15)

This is schematically drawn in Fig. 2.4a. The work function φ is defined as φ = E vac − E F using the vacuum level E vac and the Fermi level E F . E kin is defined with reference to E vac . E B is defined with respect to E F and an absolute value. Since the values of hν and φ are known, the binding energy E B of the electron in the solid can be determined by measuring the kinetic energy E kin of the emitted electron. Enormous calculation is necessary to extract detailed information about the electronic structure from photoemission spectra in a quantum-mechanically exact manner [7]. In order to facilitate the analyses of photoemission spectra, a three-step model is often used [8–10]. In this model, photoemission process is separated into three

22

2 Experimental Methods

Fig. 2.4 Schematics of a energy conservation and b momentum conservation when a photoelectron is emitted from a solid to vacuum

separate processes: (1) excitation of an electron from an initial state in the occupied state to a final state in the unoccupied state, (2) transport of the electron to the surface, (3) transmission through the surface into vacuum. The three steps are described in detail below. (1) Excitation of electron When an electron is excited from an initial state to a final state in the solid by a weak perturbation H of the light field, the transition probability Pi f is expressed from Fermi’s golden rule as Pi f =

2π ||2 δ(E f − E i − hω). h

(2.16)

The perturbation H is expressed as H=

e e e ( A · p + p · A) = ( A · p) − ih∇ · A ~ ( A · p), 2m m m

(2.17)

where A and p are the vector potential of the light filed and the momentum operator, respectively. The last approximation is based on the assumption that the A is constant (∇ · A = 0) because the wavelength of ultraviolet light is more than a hundred times larger than the inter-atomic distance. Therefore, the transition probability of the electron by the light field is given by Pi f ∝

2π ||2 δ(E f − E i − hω). h

(2.18)

2.3 Angle-Resolved Photoelectron Spectroscopy (ARPES)

23

(2) Transport of photoelectron to the surface The photoexcited electron is transported to the surface of the solid. During the transport, electrons may undergo inelastic scattering from, for example, other electrons, phonons, and defects and lose the information of the energy and momentum of the initial state. The excitation occurs not only near the surface but also inside the solid because the penetration depth of the ultraviolet light is several hundred Å. However, only the electrons near the surface can reach the surface without being inelastically scattered because the energy of the excited electron is several tens of eV and the inelastic mean free path is about 3–10 Å. The inelastically scattered electrons are observed as backgrounds in the photoelectron spectra. (3) Escape of photoelectron into vacuum The photoelectron escapes from the surface into vacuum and loses the energy equal to the work function. The parallel momentum components of the photoelectron are conserved during this step since the translational symmetry parallel to the surface is not broken. This is schematically illustrated in Fig. 2.4b. For the wave vector kex in the vacuum, the wave vectors ki and k f of the initial and final states in the solid, respectively, and the surface reciprocal lattice vector G s , the momentum conservation parallel to the surface is expressed as follows: kex ll = k f ll = kill + G s .

(2.19)

The kinetic energy E kin of the electron is E kin =

h2 (k ex )2 h2 {( ex )2 ( ex )2 } = kll + k⊥ . 2m 2m

(2.20)

When the electron is emitted with an emission angle θ with respect to the surface normal, the wave number parallel to the surface in vacuum is / kllex

=

2m E kin sin θ. h2

(2.21)

Therefore, the parallel component of the momentum of the electron in the solid (kill ) is obtained using Eq. 2.19. In addition, the binding energy E B is calculated from the energy conservation Eq. 2.15. Finally, we achieve the relationship between the binding energy and the momentum of the electron in the solid, that is, the dispersion relation.

2.3.2 Apparatus ARPES measurements are carried out using a hemispherical electron energy analyzer. Figure 2.5 schematically illustrates the analyzer. The main components are

24

2 Experimental Methods

Fig. 2.5 Schematic of the hemispherical electron energy analyzer

electron lenses, hemispheres and an electron detector. Electrons emitted from the sample are focused onto the entrance slit of the analyzer by the electrostatic lenses. The electrons are decelerated or accelerated through the lenses and enter the analyzer so that the energy distribution of the electrons is centered around certain pass energy. This is because the resolution of the analyzer is dependent on the kinetic energy of the electrons entering the analyzer. The energy analyzer consists of two concentric hemispheres with a constant voltage difference applied between them. Electrons are distributed on the exit slit dependent on their kinetic energies by the radial electrostatic field between the hemispheres. Only the electrons with a certain energy window around the pass energy can reach the exit slit, and those with too high or too low energies collide with the hemispheres. After the electrons go through the hemispherical analyzer, they are counted by a 2D detector. The detector is composed of a microchannel plate (MCP) with a phosphor screen and a CCD camera. The electrons entering the MCP produce a cascade of secondary electrons and they hit the phosphor screen. Finally, the 2D image with energy and momentum information is captured by the CCD camera.

2.5 Experiments Fig. 2.6 Schematic of the 4PP conductivity measurement

25

d = 800 μm

Sample V

Ta probes

2.4 Four-Point-Probe (4PP) Conductivity Measurements 2.4.1 Theory and Apparatus Conductivity measurements are carried out using a home-built four-point probe (4PP) system. Figure 2.6 schematically illustrates the system. The L-shaped probes are attached in situ to the sample surface, and temperature and current (I )-voltage (V ) characteristics are measured. During the sample preparation, the probes do not interrupt depositions and LEED observations on the surface because they can be rotated by 180◦ degrees. The probes are pressed by springs onto the sample surface after they are cleaned by argon sputtering in a UHV chamber. The 4PP apparatus enables us to observe temperature dependence of conductivity over a wide temperature range of 10–350 K [11, 12]. The conductivity measurements of ultrathin metal films on semiconductor substrates are possible by using high-resistivity (low-doped) substrates. Sheet resistivity ρ2D of the sample is obtained by multiplying resistance R4PP (the slope of I -V ) and a geometrical correction factor Fp calculated from the layout of the contact points and the sample size [13]. ρ2D = Fp R4PP .

(2.22)

Sheet conductivity σ is σ = 1/ρ2D . We use [S/▢] as the unit of σ , where ▢ is not a unit but a mark to explicitly indicate that it is the sheet conductivity.

2.5 Experiments In this work, experiments were carried out in five different UHV chambers. Chambers 1, 3, 4, and 5 are placed at the surface chemistry laboratory of Kyoto University and chamber 2 is at the SAGA Light Source. All the chambers have direct-current heating sample stages and evaporators so that sample preparations and analyses of physical properties can be done in UHV. Each chamber is explained in detail below.

26

2 Experimental Methods

Fig. 2.7 Schematic of chamber 1

2.5.1 Chamber 1 (ARPES, LEED) LEED and ARPES experiments were carried out in chamber 1. Figure 2.7 shows the schematic illustration of the chamber. It is composed of preparation and analysis chambers and equipped with turbomolecular pumps, an ion pump, and a titanium sublimation pump. The base pressure after bakeout is lower than 1 × 10−10 Torr. In the preparation chamber, samples are prepared by cleaning of silicon substrates, depositions of indium and magnesium, and heating of substrates, and LEED patterns are observed. The analysis chamber has μ-metal shields to avoid the influence of magnetic fields. The sample is placed at a six-axis cryogenic manipulator with threeaxis positioning (X, Y, and Z) and three-axis rotation (O (polar), φ (azimuth), and γ (tilt)). ARPES and LEED I -V experiments are conducted with precise control of the positions and angles of the samples as well as temperatures in a range from 30 K to RT. ARPES experiments The chamber is equipped with a He discharge lamp (Scienta Omicron VUV5000). The monochromatized He Iα radiation (hν = 21.2 eV) is used to excite valence electrons. Scienta Omicron R3000 electron energy analyzer was used. The analyzer simultaneously detect electrons emitted in an angle range of ±8◦ . Spectra in a wider

2.5 Experiments

27

angle range are obtained by rotating the polar angle (O). In addition, constant energy maps are generated from 2D emission angle distributions of photoelectrons by rotating the tilt angle. Note that the energy in the experimental spectra is displayed with reference to the Fermi level E F , that is, binding energy. The Fermi level was determined by fitting the photoelectron spectra measured for polycrystalline tantalum foils, which are equipotential to the sample. LEED experiments Each of the preparation and analysis chambers has OCI LEED. For the LEED I -V measurements, LEED patterns are recorded in increments of 1 eV by a CMOS camera (The Imaging Source). The I -V curves were normalized by the primary beam currents and averaged over the symmetry equivalent beams.

2.5.2 Chamber 2 (ARPES, LEED) ARPES experiments with a synchrotron light source were carried out in chamber 2. LEED (Scienta Omicron) was used to check the quality of the samples. The chamber is composed of preparation and analysis chambers, equipped with turbomolecular pumps, cryopumps, an ion pump, and a titanium sublimation pump. The base pressure after bakeout is ∼ 2 × 10−10 Torr. ARPES experiments The ARPES measurements were carried out using monochromatized synchrotron radiation and an MBS A-1 electron energy analyzer. 90-eV light was used as the excitation √ √ light because the intensity of the photoelectron spectra of the In/Si(111) ( 7 × 3)-rect phase, whose band structure is well established, was strongest in 90 eV compared to other energies between 89 and 116 eV. The Fermi level was determined by fitting the photoelectron spectra measured for a gold sample, which is equipotential to the sample. All experiments were conducted at RT.

2.5.3 Chamber 3 (STM) STM measurements were performed using Unisoku USM-1200. The chamber is composed of preparation and analysis chambers, equipped with a turbomolecular pump, an ion pump, and a titanium sublimation pump. The base pressure after bakeout is lower than 1 × 10−10 Torr. STM experiments STM images were obtained in the constant-current mode. In Chap. 3, STM experiments were performed at RT with a tungsten tip electrochemically etched in 2 mol/L NaOH solution. In Chap. 4, STM experiments were performed at 78 K with a UNISOKU PtIr tip.

28

2 Experimental Methods

2.5.4 Chamber 4 (4PP Conductivity Measurements, LEED) 4PP conductivity measurements and LEED observations were carried out in chamber 4. It is equipped with a turbomolecular pump, an ion pump, and a titanium sublimation pump. The base pressure after bakeout is lower than 1 × 10−10 Torr. A sample is placed at a helium-cooled manipulator with a thermal radiation shield and the conductivity can be measured below 10 K. Tantalum probes cleaned in situ by argon sputtering were used. OCI LEED was used to examine the quality of the samples.

2.5.5 Chamber 5 (LEED) The chamber is equipped with OCI LEED and used to optimize the preparation recipes of samples before the experiments in chambers 1–4. It is pumped with a turbomolecular pump and a titanium sublimation pump. The base pressure after bakeout is lower than 1 × 10−10 Torr. A sample is placed at a liquid-nitrogen-cooled manipulator. Sample preparation methods were investigated by LEED observations of samples prepared by deposition of indium and magnesium on substrates at different temperatures from RT to liquid-nitrogen temperature, and annealing.

2.5.6 Samples In this section, samples used in each chamber are described. The temperature of sample surfaces during cleaning and annealing was measured with a pyrometer. The emissivity of the pyrometer was set to 0.67. Substrates For the ARPES and LEED experiments in chambers 1, 2, and 5, highly doped ntype Si(111) substrates (ρ3D < 0.02 Ω cm) were used. The substrates were cut from 0.5-mm-thick wafers into strips of 3 mm × 12 mm, 4 mm × 21 mm, and 3 mm × 16 mm for chambers 1, 2, and 5, respectively. For the STM experiments in chamber 3, highly doped n-type Si(111) substrates (ρ3D < 0.005 Ω cm) were used. For the conductivity measurements in chamber 4, low-doped n-type Si(111) substrates (ρ3D ∼ 1000 Ω cm) were used to reduce bulk contribution to conduction, and cut into strips of 3 mm × 16 mm. All substrates were degassed at ∼800 K by directcurrent heating for more than 10 hours in the UHV chambers. After degassing, the substrates were cleaned by heating at 1320 K (1500 K only for the STM experiments to obtain large terraces). The procedures resulted in the observation of sharp LEED patterns and STM images of the Si(111) (7 × 7) dimer–adatom–stacking-fault (DAS) structure [14, 15].

References

29

Evaporators Indium was evaporated from a home-built evaporator using an alumina crucible. Solid indium (purity 99.99%) in the crucible was heated and melted by applying a direct current to a tungsten wire wrapped around the crucible, and the evaporated indium gas was deposited on the substrates. The crucible was sufficiently degassed and the pressure during the evaporation was lower than 5 × 10−10 Torr. The deposition rate was calibrated according to the formation of the In/Si(111) (4 × 1) phase (1.0 ML) by adsorption of indium onto Si(111) (7 × 7) at RT followed by annealing at 570 K. Magnesium was evaporated from a home-built evaporator using a tantalum crucible. Solid magnesium (purity 99.98%) was cleaned with aqueous nitric acid and acetone before putting it in the crucible. The magnesium in the crucible was heated and sublimated by applying a direct current to a tungsten wire in insulating tubes around the crucible, and the evaporated magnesium gas was deposited on the substrates. The temperature of the crucible was PID controlled and the target temperature was reached within 3 minutes and stabilized. The pressure during the evaporation was lower than 3 × 10−10 Torr. The deposition rate was measured by a quartz microbalance.

References 1. Pendry JB (1980) J. Phys. C: Solid State Phys. 13:937 2. Van Hove MA, Weinberg WH, Chan CM (1986) Low-Energy Electron Diffraction Experiment, Theory and Surface Structure Determination. Springer Series in Surface Sciences. Springer, Berlin 3. Binnig G, Rohrer H (1987) Rev. Mod. Phys. 59:615 4. Tersoff J, Hamann DR (1983) Phys. Rev. Lett. 50:1998 5. Tersoff J, Hamann DR (1985) Phys. Rev. B 31:805 6. Lang ND (1986) Phys. Rev. B 34:5947(R) 7. Feibelman PJ, Eastman DE (1974) Phys. Rev. B 10:4932 8. Berglund CN, Spicer WE (1964) Phys. Rev. 136:A1030 9. Krolikowski WF, Spicer WE (1969) Phys. Rev. 185:882 10. Hüfner S (2003) Photoelectron Spectroscopy, Principles and Applications. Advanced Texts in Physics. Springer, Berlin 11. Hatta S, Noma T, Okuyama H, Aruga T (2014) Phys. Rev. B 90:245407 12. Hatta S, Noma T, Okuyama H, Aruga T (2017) Phys. Rev. B 95:195409 13. Yamashita M, Agu M (1984) Jpn. J. Appl. Phys. 23:1499 14. Takayanagi K, Tanishiro Y, Takahashi S, Takahashi M (1985) Surf. Sci. 164:367 15. Hamers RJ, Tromp RM, Demuth JE (1986) Phys. Rev. Lett. 56:1972

Chapter 3

Structure and Electronic Properties of In Single-Layer Metal on Si(111)

3.1 Introduction The indium single-layer metal on Si(111) suggested by first-principles calcula(√ was √ ) (√ √ ) tions [1, 2] as described in Chap. 1. The 7 × 3 -hex [3] and 7 × 3 -striped [4, 5] phases were independently reported as a phase with ∼1 ML coverage from the STM experiments. However, their relationship and physical properties are still poorly understood because the preparation methods for the two phases are not yet established. (√ √ ) 7× 3 In this thesis, I have focused on the following four topics about the (√ √ ) 7 × 3 -striped phases. hex and (1) To establish the preparation methods(of the high-quality samples with macro(√ √ ) √ ) √ 7 × 3 -hex and 7 × 3 -striped scale (mm order) dimensions of the phases. (2) To reveal the relationship between the hex and striped phases using LEED I -V analyses. (3) To reveal the atomic structure of the hex and striped phases, and verify whether they have single-layer structure. (4) To reveal the electronic structure and its temperature evolution of the hex and striped phases.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. Terakawa, Structure and Electronic Properties of Ultrathin In Films on Si(111), Springer Theses, https://doi.org/10.1007/978-981-19-6872-3_3

31

32

3 Structure and Electronic Properties of In Single-Layer Metal on Si(111)

(√ √ ) 7 × 3 -Hex 3.2 Preparation of the In/Si(111) (√ √ ) and 7 × 3 -Striped Phases (√ √ ) 7 × 3 -hex phase, which was formed by indium (√ (√ √ ) √ ) 3 × 3 surface [3]. The pristine 3× 3 deposition at RT on the In/Si(111) surface (Fig. 3.1a) was reported to include some point defects such as vacancy of and substrate surface indium atoms [5], and substitution of surface( indium atoms √ √ ) 3 × 3 surface (1/3 ML) silicon atoms [6]. In order to reduce these defects, the was prepared by deposition of excess(indium followed by annealing at a temperature √ ) √ as low as possible. The high-quality 3 × 3 surface was successfully obtained by 3-ML indium deposition and annealing at 810–820 K. Figure 3.1a–d the evolution of the LEED patterns during indium depo(√presents √ ) 3 × 3 surface at RT. As indium coverage increases, the LEED sition onto the (√ √ ) 3 × 3 (1/3 ML, Fig. 3.1a) → (2 × 2) (1.0 ML, pattern changes as follows: (√ √ ) 7 × 3 (1.4 ML, Fig. 3.1c). At around 2 ML, the spot intensity Fig. 3.1b) → (√ √ ) 7 × 3 periodicity persists (2.8 distribution is greatly changed although the ML,(Fig. 3.1d).)This behavior is schematically explained in Fig. 3.1e and f, where √ √ the 7 × 3 spots with high intensity are colored. The different spot intensity distribution at the same electron energy indicates that the two LEED patterns cor(√ √ ) respond to two phases which have different atomic structures with the 7× 3 periodicity. Because the sequential change of the superstructures in Fig. 3.1a–d agrees observed LEED well with the previous STM observation (Fig. 1.8a) (√[3], the (√ patterns √ ) √ ) 7 × 3 -hex and 7× 3 at 1.4 ML and above 2 ML correspond to the rect phases,)respectively. It should be noted that the coverage range when only the ( √ √ 7 × 3 -hex spots appear is very small (∼0.1 ML). Above (below) this cover(√ √ ) 7 × 3 -rect ((2 × 2)) phase was coexisting. Precise control of age range, the (√ √ ) 7 × 3 -hex the deposited indium amount is required to selectively prepare the phase. (√ √ ) Next I present the results of the 7 × 3 -striped phase. Figure 3.2a shows the LEED pattern of the surface obtained by the deposition of 1.2-ML indium on Si(111) (7 × 7) surface at RT followed by annealing at 640 K. The yellow spots lines indicate triple-domain (4 × 1) and fundamental (1 × 1) spots. The (√ (√other √ ) √ ) 7 × 3 -striped phase. In the previous studies, the 7× 3 come from the striped phase was observed as a minor domain coexisting with the (4 × 1) phase (√ √ ) 7 × 3 -striped and (4 × 1) (Fig. 1.8c) [4, 5]. In this study, the surface where the First, I present the results of the

3.2 Preparation of the In/Si(111)

(a)

(√ (√ √ ) √ ) 7 × 3 -Hex and 7 × 3 -Striped Phases

(b)

(0 1)

(0 1)

(1 0)

70 eV

(c)

(1 0)

70 eV

(d)

(0 1)

(0 1)

(1 0)

85 eV

(e)

33

(1 0)

85 eV

(f)

(0 1) (1 0)

(0 1) (1 0)

(√ (√ √ ) √ ) 3 × 3 , b (2 × 2), c 7 × 3 -hex, and d Fig. 3.1 LEED patterns at RT of In/Si(111) a (√ √ ) 7 × 3 -rect. The primary electron energy is presented in the bottom left corners. Schematic (√ (√ √ ) √ ) LEED patterns of the e 7 × 3 -hex and f 7 × 3 -rect phases. Observable superstructure (√ √ ) spots are shown by filled circles. Red, green, and blue circles identify three domains of 7× 3 rotated by 120◦

34

3 Structure and Electronic Properties of In Single-Layer Metal on Si(111)

(a)

(b)

(0 1)

(0 1)

(1 0)

(1 0)

70 eV (√ √ ) Fig. 3.2 a LEED pattern of the surface with coexisting In/Si(111) 7 × 3 -striped and (4 × 1) phases at RT. The spots of and fundamental (1 × 1) are designated by the yellow (√ lines.√The ) (√(4 × 1) √ ) 7 × 3 -striped phase. b Schematic LEED pattern of the 7× 3 other spots are from the striped phase. Only the dominant domain is drawn

phases are coexisting with nearly equal areas was successfully prepared by precise control of indium coverage and annealing temperature. This is shown by the com(√ √ ) 7 × 3 -striped and (4 × 1) phases parable intensities of the LEED spots of the and the STM images (see Fig. 3.5a). (√ (√ √ ) √ ) 7 × 3 -hex and 7× 3 We compare the domain distributions in the striped phases. While the three domains rotated by 120◦ are coexisting with almost the (√ √ ) same intensities for the 7 × 3 -hex phase (Fig. 3.1c and e), the domain distribu(√ √ ) 7 × 3 -striped phase (Fig. 3.2a) is not even and there is one dominant tion of the domain (shown in Fig. 3.2b. The difference in sample preparation: indium deposi(√ RT √ ) √ ) √ tion for 7 × 3 -hex, and direct-current annealing for 7 × 3 -striped, may affect this distribution difference. (√ √ ) 7 × 3 -hex Figure 3.3 shows a comparison of the LEED I -V curves for the (√ √ ) 7 × 3 -striped phases. The agreement of the I -V curves is excellent for all and (√ (√ √ ) √ ) 7 × 3 -hex and 7× 3 the spots and RP is 0.16. This indicates that the striped phases, which were recognized as different phases due to the different preparation have the same atomic structure. Hereafter, we refer to this phase as (√methods, √ ) 7 × 3 -hex phase irrespective of the preparation methods. the

3.3 The Atomic Structure of the In/Si(111) “

(√ √ ) 7 × 3 ”-Hex Phase

(-6/5 -1/5)

35

(0 2)

(6/5 1/5) (2 0) (-4/5 6/5) (1 1)

(4/5 -6/5) (-1/5 4/5)

(0 1) (1/5 -4/5) (1/5 1/5)

Fig. 3.3 Comparison of LEED I -V curves of the (solid) phases

(1 0)

(√ (√ √ ) √ ) 7 × 3 -hex (dotted) and 7 × 3 -striped

3.3 The Structure of the In/Si(111) (√Atomic √ ) “ 7 × 3 ”-Hex Phase 3.3.1 LEED and STM Observations (√ √ ) In order to investigate the atomic structure of the 7 × 3 -hex phase, the LEED patterns are further Figure 3.4a shows the LEED pattern of the surface (√ analyzed. √ ) 7 × 3 -hex and (4 × 1) phases at RT prepared by annealing. with coexisting Figure 3.4b presents the LEED pattern by cooling the surface to ( 130 K. Upon (√ obtained √ ) √ √ ) cooling, the LEED pattern of the 7 × 3 -hex phase changes to the 7× 7 pattern, while the (1 × ( 1) and (4 ×)1) spots indicated by the blue lines (√do not√change. ) √ √ 7 × 7 phase was also reported in the 7 × 3 -hex The transition into the (√ √ ) 3 × 3 surface (Fig. 1.8b) [3, phase prepared by RT indium deposition on the 7, 8]. However, the transition was rather diffuse and weak LEED spots of the hex phase were observed even at 100 K because of the insufficient ordering of the sample [7, 8]. In this work, the surface prepared by annealing shows clear transition and no LEED spots of the hex phase are observed at 130 K. Consequently, this sample is

36

3 Structure and Electronic Properties of In Single-Layer Metal on Si(111)

appropriate for studying the phase transition although it is coexisting with the (4 × 1) phase. Figure 3.4c and d shows close-up of the patterns of Fig. 3.4a and b. (√ images (√LEED √ ) √ ) The reciprocal lattice points of 7 × 3 and 7 × 7 determined with respect red and (blue circles, to the positions of the (1 × 1) and (4 × 1) spots are shown (√ by √ ) √ √ ) respectively. The reciprocal and real lattices of the 7 × 3 and 7× 7 (√ √ ) 7× 7 are depicted in Fig. 3.4e and f, respectively. There are two domains of which are symmetric with respect to)the mirror planes of Si(111) in contrast to one (√ √ dominant domain of the 7 × 3 -hex phase. (√ √ ) 7 × 3 lattice point The LEED spot of the hex phase deviates from the (see the right red circle in Fig. 3.4c), while (good agreement between the spots and √ √ ) the reciprocal lattice points is seen for the 7 × 7 phase (see the blue circles in Fig. 3.4d). The hex spots appear as the satellite spots around each (1 × 1) spot with the constant distance in the [110] direction. As indicated by the double-headed arrow 3.4c and e, the distance for the hex phase is 0.70 Å−1 , while that (√in Fig. √ ) for 7 × 3 is 0.65 Å−1 . The deviation of the spot position in the hex phase (√ √ ) 7 × 3 periodicity indicates that the hex phase does not have commensurate but incommensurate structure with respect to the Si(111) substrate. The LEED pattern of the hex phase is interpreted to result from the double scattering by the Si(111) substrate and the incommensurate indium overlayer. The separation between the lattice lines to [112] was measured to be 8.92 ± 0.10 Å, which is 93% of that (√ parallel √ ) for the 7 × 3 lattice (9.60 Å, Fig. 3.4f). On the other hand, the other group of lattice lines was unable to be examined due to the absence of the spots corresponding to (−2/5 3/5) of electron energy (Fig. 3.4c and e). Hereafter, we remove (√ irrespective √ ) the term “ 7 × 3 ” from the name of this phase and call it the hex phase. Figure 3.5a shows a large-scale STM image of the surface with coexisting hex and (4 × 1) phases at RT. The brighter areas on a terrace correspond to the hex phase, and the darker ones correspond to the (4 × 1) phase. Both the phases have large domain sizes of more than several hundred Å with nearly equal distribution on a terrace. Figure 3.5b shows a close-up image of a region including the phase boundary. Both phases are observed as chain structures, and the chains along [112] with narrower spacing in the bottom right part correspond to the hex phase. The distance between the chains was determined to be 8.8 ± 0.5 Å with reference to that of the (4 × 1) phase [9, 10]. This value is consistent with that obtained from the above LEED analysis. Figure 3.5c shows an atomically resolved STM image of the hex phase. Detailed structures of the chains and boundaries between the domains rotated by 120◦ are clearly seen. A closer look shows that the chains are classified into two kinds of structure: the “zigzag” type and the “linear” type, as indicated by the letters Z and L in Fig. 3.5c. The two types of chains are enlarged in Fig. 3.5d. They appear in an

3.3 The Atomic Structure of the In/Si(111) “

(√ √ ) 7 × 3 ”-Hex Phase

(a) RT

37

(b) 130 K Ep=70 eV

(1 0)

(0 1)

(1 0)

(c) RT

(0 1)

(d) 130 K

0.70 Å-1

(e)

(f)

7× 3

(1/2 0) (0 1/2) (1/7 2/7)

7×

7

(1/5 1/5)

9.60 Å

0.65 Å-1 [110]

(-2/5 3/5) (-2/7 3/7) (0 0)

[112]

(√ √ ) 7 × 3 -hex and (4 × 1) phases at Fig. 3.4 LEED patterns of the surfaces with coexisting a (√ √ ) 7 × 7 and (4 × 1) phases at 130 K. The blue transparent lines indicate the (1 × 1) RT and b and (4 × 1) spots. c and d Enlarged images of the region indicated by the dashed rectangles in a solid blue circles represent the reciprocal lattice and b, respectively.(The dotted)black,(solid red, and √ √ √ √ ) 7 × 3 , and 7 × 7 , respectively. The spot indicated by the arrow in points of (4 × 1), to the major domain. e rotated(by 120◦ compared c is the hex spot belonging to the( minor domain √ ) √ √ ) √ 7 × 3 (red) and 7 × 7 (blue), and the corresponding and f The reciprocal lattices of real-space unit cells. The (4 × 1) reciprocal lattice points (black) are also depicted in e

38

3 Structure and Electronic Properties of In Single-Layer Metal on Si(111)

Fig. 3.5 a Large-scale STM image (2400 × 1300 Å2 ) of the surface covered with the hex and (4 × 1) phases, acquired at sample bias VS = −2.0 V and tunneling current I = 0.1 nA. b STM image of the adjacent hex and (4 × 1) phases (220 × 400 Å2 , VS = 1.5 V, I = 0.1 nA). c Highresolution STM image of the hex phase (140 × 140 Å2 , VS = 0.3 V, I = 0.1 nA). d Enlarged images of the (left) zigzag and (right) linear atomic chains of the hex phase, clipped from the dotted and solid rectangles in c. The letters Z and L on the left and bottom sides of c indicate the types of chains. The area enclosed by the dashed box corresponds to the structure model shown in Fig. 3.6b. All the STM images were taken at RT

3.3 The Atomic Structure of the In/Si(111) “

(√ √ ) 7 × 3 ”-Hex Phase

39

irregular order with a nearly equal frequency. On the other hand, their periodicities along the chains defined and coincide with each other. The period was (√are well √ ) 3 × 3 times as long as the lattice constant of Si(111) (1 × 1), evaluated to be (√ √ ) 7 × 3 lattice. which is the same as that of the commensurate The above analyses of the LEED patterns and STM images revealed uniaxially incommensurate structure of the indium overlayer of the hex phase. The overlayer is commensurate with respect to the substrate lattice along the [112] direction, parallel to the chains, and incommensurate along the [110] direction, perpendicular to the chains.

3.3.2 Structure Model We consider the atomic structure of the hex phase based on the zigzag and linear chain structures observed by STM. Figure 3.6a illustrates the structure model of the hex phase by Park and Kang (see also Fig. 1.7) [2]. This model was proposed as the (√ √ ) 7 × 3 periodicity. The unit most stable structure of indium monolayer with cell contains seven indium atoms and its coverage is 7/5 = 1.4 ML. Five of the atoms indicated by the light blue circles are near the T1 sites of the Si(111) substrate and the other two indicated by the dark blue circles are near the H3 sites. The atoms near the H3 sites are weakly bonded to silicon and located at higher positions than the atoms near the T1 sites, resulting in the zigzag chain structure. This chain structure is quite similar to the STM image of the zigzag chain (Fig. 3.5d), which indicates that the structure model is partly appropriate. However, the feature of the linear chain does not appear in this model, and we incorporate the experimentally established incommensurability into the model. We first focus on the dashed line on(the left side) of Fig. 3.6a. These lines indicate √ √ 7 × 3 unit cell along the [110] direction the positions of the indium atoms in the and they are uniformly distributed. Accordingly, the structure of the indium overlayer can be regarded as consisting of indium rows running along [112] with the interrow distance λIn = 9.60/7 = 1.37 Å. The difference in the periodicity of the indium rows λIn and that of the H3 sites (half of the surface lattice constant of Si(111) (1 × 1), the dotted lines on the right side of Fig. 3.6a) induces the two protruding indium rows near the H3 sites in the unit cell to form the zigzag chain structure. Next we assume a contraction of the indium overlayer along the [110] direction. This causes the shift of the position of each indium row with respect to the substrate along [110], which leads to the modulation of the period of protruding indium rows near the H3 sites, which is the period of the chain structure. We use a model of superposition of two 1D waves with different wave vectors ki = 2π/λi (i = In, H3 ) (to evaluate) the degree of contraction. The superposed wave has wave vectors k± = kIn ± k H3 /2, and k− representing an envelop curve corresponds to the period of the chain structure. Using the value obtained from the LEED analysis (λ− = 2π/k− =

40

3 Structure and Electronic Properties of In Single-Layer Metal on Si(111)

(b)

(a)

(c)

λ H3

λIn [110] [112]

Si (T1)

Si (T4)

L Z L L Z L Z L L Z L Z Z L Z L Z Z L Z

In

(√ √ ) Fig. 3.6 a Schematic of the most stable monolayer structure with the 7 × 3 periodicity (1.4 (√ √ ) ML) by Park and Kang [2]. The red parallelogram indicates the 7 × 3 unit cell. b and c The model of the incommensurate hex phase. The dark blue indium atoms are close to the H3 sites and protrude more than the light blue ones. The rectangle in c marks the region enlarged in b. The letters Z and L on the right side indicate the types of atomic chains

This value is 2.1%±0.3% smaller than 8.92 ± 0.10 Å), λIn = 1.34 Å( is obtained. √ √ ) the interrow distance of the 7 × 3 model. Considering this contraction, the experimentally observed structure of the hex phase is reproduced. Figure 3.6b and c shows a structure model of the incommensurate hex phase constructed as follows: (a) An indium row on the dashed line in Fig. 3.6b is placed at the T1 sites. (b) Other indium rows are arranged with an equal distance of 1.34 Å along [110]. (c) The atom positions are adjusted ( along [112])so that the positions are consistent √ √ with the local geometry in the 7 × 3 model. According to the model, indium atoms are located away from the T4 sites. This feature can be seen in Fig. 3.6a and b, where yellow-colored silicon T4 atoms stand out. (d) The indium atoms near the H3 sites are made higher than surrounding other indium atoms.

3.3 The Atomic Structure of the In/Si(111) “

(√ √ ) 7 × 3 ”-Hex Phase

41

As a result, zigzag and linear chain structures appear. The zigzag chain is composed of paired rows of indium atoms slightly shifted from the H3 sites, whereas the linear chain is composed of a single row of indium atoms on the H3 site. The arrangement of the two types of chains is sensitive to the degree of contraction. I found that the model at the contraction of 2.4% shows good agreement with the STM image. The arrangement of the chains L-Z-L-L-· · · of the STM image (Fig. 3.5c) perfectly matches that of the model (Fig. 3.6c). In this model, we separate the zigzag and linear chains according to the distance of the indium rows from the H3 sites, but the separation criteria have some arbitrariness. In the experimental STM image (Fig. 3.5c), chain structures intermediate between the zigzag and linear chains are also observed, indicating that the heights of the indium atoms are flexibly varied depending on the adsorption sites. This feature corresponds to the STM image of Fig. 3.5b, where atomic chains are uniformly observed irrespective of zigzag and linear chains. The sizes of the domains with uniformly distributed chain structures are several hundred Å and are comparable to terrace widths. This structural feature causes the sharp LEED spots located at the position corresponding to the chain period. The elongation and splitting of spots are not observed, although they are known for well-investigated surface incommensurate structures such as Pb/Si(111) [11, 12].

3.3.3 First-Principles Calculation The stability of the uniaxially incommensurate structure of the hex phase is investigated by first-principles total-energy calculation. The calculation was performed by applying the augmented plane waves plus local orbitals method implemented in the ( √ ) WIEN2K simulation package [13]. A long-period commensurate 7 × 3 model ( √ ) was used as a model of the incommensurate structure. The 7 × 3 model has 20 indium rows and 14 top silicon atoms in the unit cell, and its coverage is 20/14 = 1.43 ML. This corresponds to 2% contraction. The In/Si(111) structures were modeled by a periodic slab consisting of three silicon bilayers, an indium monolayer, and a vacuum region. Hydrogen atoms were used to saturate the silicon dangling bonds at the bottom layer of the slab. The bottom-most silicon atoms were kept fixed at the bulk positions with an optimized silicon lattice constant of 5.477 Å. The remaining atoms were fully relaxed until the residual force atom was smaller than 1 (√on each √ ) 7 × 3 unit cell and 2 × 6 × 1 mRy/bohr. k-point meshes of 3 × 6 × 1 for the ( √ ) for the 7 × 3 unit cell were used. The optimized structure is shown in Fig. 3.7. The Z-L-Z chain sequence observed in the image is reproduced. The total energies of the contracted model and the (√ STM √ ) 7 × 3 model are compared. The mass balance associated with the contraction ( (√ √ ) √ ) 7 × 3 structure to the 7 × 3 structure is represented as of the

42

3 Structure and Electronic Properties of In Single-Layer Metal on Si(111)

[112] [110]

[111] [110] ( √ ) Fig. 3.7 Top and side view of the optimized structure of the 7 × 3 model. The blue, white, orange, and pink circles represent indium, silicon (T1 ), silicon (T4 ), and hydrogen atoms, respectively. The(other silicon atoms are omitted and only the atomic bonds (are drawn. The solid rectangle √ ) √ √ ) 7 × 3 lattice contracted shows the 7 × 3 unit cell. The dotted parallelogram indicates the by 2% along the [110] direction

2 14 In(ref) + In7 (Si6 H)5 −→ In20 (Si6 H)14 , (3.1) 5 5 (√ ( √ ) √ ) where In7 (Si6 H)5 and In20 (Si6 H)14 indicate 7 × 3 and 7 × 3 slab models, In(ref) indicates an indium(atom which is incorporated into the (√ respectively. √ ) √ ) 7 × 3 structure to form the contracted 7 × 3 structure. (√ √ ) 7 × 3 unit cell △E c The energy change associated with the contraction per is given as )] ( 5 [ △E c = E √ − 0.4E In + 2.8E √7×√3 . (3.2) 14 7× 3

3.3 The Atomic Structure of the In/Si(111) “

(√ √ ) 7 × 3 ”-Hex Phase

43

( √ ) E 7×√3 and E √7×√3 denote the total energies of the optimized 7 × 3 and (√ √ ) 7 × 3 structures, respectively. E In is the energy per atom of indium which (√ √ ) 7 × 3 structure. is to be incorporated into the In order to examine the relative stability of the contracted and uncontracted structures, the reference state of indium, In(ref), should be specified. Indium atoms in the (4 × 1) phase coexisting with the hex phase are not appropriate because the (4 × 1) structure is highly stable and the transfer of indium atoms from the (4 × 1) phase to the hex phase is implausible. Another candidate is an indium atom in bulk indium islands, which could be formed during the initial indium deposition on the clean Si(111) surface. However, the wide-area STM image of the surface after annealing (Fig. 3.5a) does not show indium islands remaining on the surface. This suggests that indium islands are not in equilibrium with the hex phase at least at a later stage of the formation of the ordered structures. A plausible candidate of In(ref) is an isolated indium adatom, which should exist throughout the formation process of the surface covered with the hex and (4 × 1) phases. In this case, the stability of the contracted structure depends on the energetics (√ √ ) of the incorporation of indium adatoms into the 7 × 3 structure. In order to determine and E In , the energies of an indium adatom on adsorption sites (√ In(ref) √ ) of the 7 × 3 structure were calculated by fully relaxing the positions of the indium adatom as well as the atoms of the indium overlayer and silicon substrate. The most stable adsorption site is a threefold hollow site over indium atoms in the trough between protruding indium rows (trough site) shown in Fig. 3.8. The energy even lower than that in per atom of indium adsorbed on the trough site is( found to be √ √ ) the bulk indium because of the relaxation of the 7 × 3 indium overlayer. Note that the indium adatom is never incorporated into the indium layer because it results in a too dense (1.6 ML) indium overlayer. I chose as In(ref) this indium adatom on (√ √ ) 7 × 3 structure. the trough site of the uncontracted After the optimization of both the slab (models, the) contraction energy △E c was √ √ obtained from Eq. 3.2 to be −18 meV per 7 × 3 unit cell. The result suggests (√ √ ) 7 × 3 structure with that the contracted structure is more stable and that the indium adatoms is not energetically stable and will be transformed into the contracted structure by accepting indium adatoms into the monolayer. This is consistent with the experimental observation of the contracted overlayer structure.

44

3 Structure and Electronic Properties of In Single-Layer Metal on Si(111)

Fig. 3.8 Most stable structure of an indium adatom adsorbed ) (√ on √the 7× 3 In/Si(111) monolayer. The green circles represent the adsorbed indium adatoms. The colors of the other atoms are the same as those in Fig. 3.7. The solid parallelogram (√ √ ) 7× 3 represents the unit cell

[112] [110]

In adatom

[111] [110]

3.4 Electronic Structure and Phase Transition of the Indium Monolayer on Si(111) 3.4.1 Electronic Structure of the In/Si(111) Hex Phase I performed ARPES experiments to investigate the electronic structure of the In/Si(111) hex phase. Figure 3.9a shows ARPES constant energy contours measured at the Fermi level (E F ) of the triple-domain hex phase prepared by RT indium deposition. The contours are composed of a circle surrounding the first (1 × 1) surface Brillouin zone (SBZ) and six arcs inside it. The arcs are attributed to circles centered at neighboring (1 × 1) T points. Figure 3.9b and c shows ARPES band maps along T-K -M and T-M, respectively. A strong band feature near the T point below 0.2 eV is identified as the silicon valence bands. The two bands labeled S and S ' are indium-derived surface-state bands in the bandgap of bulk silicon. They are sym-

3.4 Electronic Structure and Phase Transition of the Indium Monolayer on Si(111)

45

Fig. 3.9 ARPES data of the triple-domain In/Si(111) hex phase. a Fermi surface map measured at RT using hν = 21.2 eV. The energy window was 50 meV and the spectra were symmetrized according to the mirror and threefold rotational of Si(111). The solid white and dashed (√ symmetries √ ) 7 × 3 SBZ for one of the three coexisting domains, red lines denote the (1 × 1) SBZ and the (√ √ ) respectively. The arrows indicate the Fermi contours of the unintentionally coexisting 7× 3 rect phase. Band maps along b T-K -M and c T-M at RT using hν = 90 eV. S and S ' represent the indium-derived surface-state bands

metrical with respect to M and disperse toward E F . The S band crosses E F at 1.29 Å−1 along T-K and at 1.33 Å−1 along T-M, which indicates that the hex phase is a single-layer metal with metallic band structure. The S and S ' bands correspond to the circular Fermi surface. The ARPES band structure shows only the periodicity of the (1 × 1) SBZ reflecthas to ing the incommensurate structure of the hex phase. However, periodic ( structure √ ) be assumed for comparison with calculational band structure. The 7 × 3 model in Fig. 3.7 has a small SBZ, which makes it difficult to interpret the band structure. Therefore, we compare the experimental band structure with that calculated for the (√ √ ) 7 × 3 model (Fig. 1.7) [2], which is the smallest structure model with the characteristics of the hex phase. It is meaningful to compare the experimental Fermi surface of the incommensurate hex phase and the theoretical Fermi surface calculated (√ √ ) 7 × 3 model in the extended zone scheme. for the commensurate (√ √ ) 7 × 3 SBZs. Figure 3.10b shows The dashed lines in Fig. 3.9a represent the (√ √ ) 7 × 3 SBZ considering the Fermi surface of the hex phase reconstructed into a

46

3 Structure and Electronic Properties of In Single-Layer Metal on Si(111)

(√ √ ) Fig. 3.10 a Calculated Fermi surface of the In/Si(111) 7 × 3 single-layer model (1.4 ML, Fig. 1.7) [2]. Schematic drawings( of the experimental Fermi surface of the b In/Si(111) hex phase √ √ ) (this work) and c the In/Si(111) 7 × 3 -rect phase [14]

the coexistence of the three rotated hex domains. The arc-shaped Fermi surface over the adjacent SBZs( is consistent with the observed circular Fermi surface. Taking the √ √ ) 7 × 3 SBZ into consideration, the Fermi contours symmetsymmetry in the by dotted lines. Figure 3.10a presents the Fermi rical with respect to T-Y are (√drawn √ ) surface calculated for the 7 × 3 single-layer model (1.4 ML) [2]. It consists of three parts labeled 1, 2, and 3. The small hexagons around T (the Fermi contours 1) are formed from the silicon valence band top. In our measurements, the silicon valence band top lies ∼0.2 eV below E F , and hence the corresponding Fermi surface is not observed. The Fermi contours 2 and 3 are formed from indium-derived surface bands and they agree with the experimental Fermi contours. Although the experimental Fermi contours have a slightly larger value of Fermi wavevector (kF ), the difference between the experimental Fermi contour and theoretical Fermi contour 3 is smaller than 0.05 Å−1 . Fermi surface is also observed for the double-layer In/Si(111) (√Circular √ ) 7 × 3 -rect phase (Fig. 1.5b) [14]. The radius of the circular Fermi surface of the rect phase is kFx = 1.41 Å−1 and kFy = 1.40 Å−1 , which are larger than that of the hex phase by 0.1 Å−1 . The difference in kF is resolved in the Fermi surface map of Fig. 3.9a. The unintentionally formed rect phase shows the Fermi contours, as indicated by the black arrows, outside the circular Fermi surface of the hex phase. Then, we discuss the difference in Fermi surface topology between the hex and rect phases. The large Fermi circle of the rect phase is constructed from the Fermi surface of domain (Fig. 3.10c). The Fermi circle is separated into many arcs in the (√a single √ ) 7 × 3 SBZ. On the other hand, the circular Fermi surface of the hex phase is constructed not from the Fermi surface of a single domain (Fig. 3.10b) but from the

3.4 Electronic Structure and Phase Transition of the Indium Monolayer on Si(111)

47

overlap of the Fermi surfaces of the three rotated domains. The Fermi surface of the single-domain hex phase has a 2D anisotropic character, which reflects the chain-like structure of the hex phase. The different Fermi surface topology of the hex and rect phases suggests that the 2D free-electron-like electronic structure is suppressed for the indium single layer due to the bonding between the indium layer and silicon substrate.

3.4.2 Phase Transition of the In/Si(111) Hex Phase (√ √ ) As already shown in Fig. 3.4, the In/Si(111) hex phase changes to the 7× 7 phase at low temperature. Figure 3.11a shows the LEED pattern change during coolRT to 200 K. The (1/2 ing of the surface with coexisting hex and (4 × 1) phases (√ from √ ) 7 × 7 spots are seen below 0) and (0 1/2) spots are due to the (4 × 1) phase. The 240 K on both sides of the hex spot. When the temperature reaches 200 K, the hex (√ √ ) 7× 7 spot completely disappears. At intermediate temperatures, the hex and spots are simultaneously observed. Temperature-dependent change of the spot widths and positions is negligible for all the spots. Figure 3.11b shows the intensities of the the spot intensity spots as a function of temperature. With decreasing temperature, (√ √ ) 7 × 7 phase increases of the hex phase decreases at 250–210 K and that of the concomitantly, while that of the (4 × 1) phase increases monotonically according to the Debye–Waller effect. Figure 3.12 shows the temperature dependence of the sheet conductivity σ of the surface with coexisting hex and (4 × 1) phases during cooling from RT to 67 K and subsequent heating to RT. The rate of temperature increase and decrease was ±2.4 K/min. Upon cooling from RT, σ shows a sharp drop at T1↓ = 250 K. Since the temperature range of the rapid decrease in σ agrees with that of the LEED (√ pattern √ ) 7× 7 . change, this decrease corresponds to the structural change from hex to After the gradual decrease, σ shows a drop again at T2↓ = 118 K. The second drop is attributed to the metal–insulator transition from (4 × 1) to (8 × 2) [15, 16]. Upon heating, σ increases with temperature, and the transition temperatures for the hex and (4 × 1) phases are shifted to higher temperature (T2↑ = 128 and T(1↑ = 291 K). √ ) √ Therefore, both the transitions show hysteresis with 41 K width for hex– 7 × 7 and 10 K width for (4 × 1)–(8 × 2), which indicates that both the transitions are of first order. The hysteresis behavior of the (4 × 1) phase shows little difference from the previous studies for the surface fully covered with the (4 × 1) phase (Fig. 1.6c) [16]. The temperature range for the transition of the hex phase is consistent with that reported in the previous STM study for the hex phase without coexisting (4 × 1) phase [3]. It is therefore suggested that the two transitions do not affect each other. The σ -T curves in Fig. 3.12 exhibit nonmetallic temperature dependence in the entire temperature range, while the hex and (4 × 1) phases have metallic band struc-

48

3 Structure and Electronic Properties of In Single-Layer Metal on Si(111)

Fig. 3.11 a Close-up views of the LEED patterns measured during cooling for the surface with The solid red circle, blue squares, and dotted green coexisting hex and (4 × 1) phases ( (E p = 56 eV). √ ) √ 7 × 7 , and (4 × 1) phases, respectively. b The intensities circles show the spots of the hex, of the superstructure spots of the three phases as a function of temperature upon cooling

tures. Similar behavior was also observed in the (4 × 1) phase and was interpreted as hopping conduction between the metallic domains separated by the boundaries between the (4 × 1) domains rotated by 120◦ , acting as line defects [16]. On the surface with coexisting hex and (4 × 1) phases, the (4 × 1) phase grows across a terrace. Accordingly, the domain boundaries of the (4 × 1) domains should play an important role in the conduction mechanism. Note that the boundaries between the three rotated hex domains, and between the hex and (4 × 1) phases are atomically smooth as observed by STM (Fig. 3.5c and b) and that they do not significantly affect electron transport. the change of the band structure at the transition from hex to (√We discuss √ ) 7 × 7 . Figure 3.13 shows ARPES Fermi surface maps of the coexisting surface measured at RT and 130 K. Fermi contours of both the hex and (4 × 1) phases are observed at RT (Fig. 3.13a). The arc-shaped contours of the hex phase are indiphase [17, cated by the dashed curves. The other contours come from the (4 × 1) (√ √ ) 7× 7 18]. Figure 3.13b shows the Fermi surface of the surface with coexisting and (4 × 1) phases measured at 130 K. The Fermi arcs of the hex phase completely disappear. In the whole (1 × 1) SBZ, no Fermi contours except for those of the triple-domain (4 × 1) phase [17, 18] were found. The sharp conductivity drop and disappearance of the Fermi surface indicate that the transition of the hex phase to the ( √ ) √ 7 × 7 phase is an electronic metal–insulator transition. (√ √ ) 7 × 7 phase, a structure model is proposed from first-principles For the calculation [2]. The structure has a similar feature to the hex phase with chains

3.4 Electronic Structure and Phase Transition of the Indium Monolayer on Si(111)

100

49

T1↑

90

T1↓

80

σ (μS/□)

70 60

T T2↓ 2↑

50 40 30

cooling heating

20 10 0 50

100

150

200 T (K)

250

300

Fig. 3.12 Temperature dependence of the sheet conductivity σ of the surface with coexisting hex and (4 × 1) phases. The blue and red curves show the data measured during cooling and heating, respectively

Fig. Fermi ) surface maps of the surfaces with coexisting a hex and (4 × 1) phases at RT and (√3.13 √ 7 × 7 and (4 × 1) phases at 130 K. The maps were obtained with an energy window of b 50 meV. The solid lines represent the (1 × 1) SBZs. The dashed curves in a indicate the observed Fermi surface of the hex phase. The dotted curves represent the replica of the Fermi surfaces of the triple-domain (4 × 1) phase [17, 18]

50

3 Structure and Electronic Properties of In Single-Layer Metal on Si(111)

composed of protruding indium atoms, and its coverage is 10/7 ML. This coverage agrees with that of the incommensurate hex phase (1.43 ML). However, metallic band structure was predicted and it does not agree with our ARPES result. The observed hysteresis behavior of the σ -T curves suggests that the transition is associated with an energy barrier due to large structural transformation. Moreover, a two-step increase was observed on the heating σ -T curve, which should be involved the transition (√ with √ ) 7 × 7 phase is a process. The determination of the atomic structure of the future task.

3.5 Summary I have established the single-layer indium metal(on Si(111))and revealed (√its atomic √ √ √ ) structure and electronic structure. Although the 7 × 3 -hex and 7× 3 striped phases were recognized as different phases dependent on their preparation methods, the two phases were found to have an identical atomic structure from LEED I -V analysis. From the results of the LEED and STM experiments, the hex phase incommensurate structure with the indium monowas found to have a uniaxially (√ √ ) 7 × 3 by 2.1%±0.3% in the [110] direction. ARPES layer contracted from measurements have revealed the metallic band structure of the hex phase. The Fermi surface has an anisotropic shape reflecting the undulating sheet-like structure of the hex phase consisting of atomic of protruding indium atoms. Upon cooling, (√ chains √ ) 7 × 7 phase with the disappearance of the Fermi the hex phase changes to the surface and the conductivity drop with a large thermal hysteresis, which indicates a first-order metal–insulator transition.

References 1. Uchida K, Oshiyama A (2013) Phys. Rev. B 87:165433 2. Park JW, Kang MH (2016) Phys. Rev. Lett. 117:116102 3. Saranin AA, Zotov AV, Kishida M, Murata Y, Honda S, Katayama M, Oura K, Gruznev DV, Visikovskiy A, Tochihara H (2006) Phys. Rev. B 74:035436 4. Park S-i, Nogami J, Quate CF (1988) J. Microsc. 152:727 5. Kraft J, Ramsey MG, Netzer FP (1997) Phys. Rev. B 55:5384 6. Cho SW, Nakamura K, Koh H, Choi WH, Whang CN, Yeom HW (2003) Phys. Rev. B 67:035414 7. Mihalyuk AN, Alekseev AA, Hsing CR, Wei CM, Gruznev DV, Bondarenko LV, Matetskiy AV, Tupchaya AY, Zotov AV, Saranin AA (2016) Surf. Sci. 649:14 8. Shirasawa T, Yoshizawa S, Takahashi T, Uchihashi T (2019) Phys. Rev. B 99:100502(R) 9. Bunk O, Falkenberg G, Zeysing JH, Lottermoser L, Johnson RL, Nielsen M, Berg-Rasmussen F, Baker J, Feidenhans’l R (1999) Phys. Rev. B 59:12228 10. Mizuno S, Mizuno YO, Tochihara H (2003) Phys. Rev. B 67:195410 11. Seehofer L, Falkenberg G, Daboul D, Johnson RL (1995) Phys. Rev. B 51:13503

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12. Stepanovsky S, Yakes M, Yeh V, Hupalo M, Tringides MC (2006) Surf. Sci. 600:1417 13. Blaha P, Schwarz K, Madsen GKH, Kvasnicka D, Luitz J, Laskowski R, Tran F, Marks LD (2018) WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties. Techn. Universität Wien, Austria 14. Rotenberg E, Koh H, Rossnagel K, Yeom HW, Schäfer J, Krenzer B, Rocha MP, Kevan SD (2003) Phys. Rev. Lett. 91:246404 15. Tanikawa T, Matsuda I, Kanagawa T, Hasegawa S (2004) Phys. Rev. Lett. 93:016801 16. Hatta S, Noma T, Okuyama H, Aruga T (2017) Phys. Rev. B 95:195409 17. Yeom HW, Takeda S, Rotenberg E, Matsuda I, Horikoshi K, Schaefer J, Lee CM, Kevan SD, Ohta T, Nagao T, Hasegawa S (1999) Phys. Rev. Lett. 82:4898 18. Ahn JR, Byun JH, Koh H, Rotenberg E, Kevan SD, Yeom HW (2004) Phys. Rev. Lett. 93:106401

Chapter 4

Structure and Electronic Properties of Ultrathin (In, Mg) Films on Si(111)

4.1 Introduction I have revealed the atomic structure and electronic properties of the indium singlelayer metal on Si(111), the In/Si(111) hex phase, in Chap. 3. The single-layer hex (√ √ ) 7× 3 phase has anisotropic electronic structure, whereas the double-layer rect phase has 2D isotropic nearly free-electron band structure. This difference suggests that the electronic properties of the indium monolayer are strongly affected by the bonding with the silicon dangling bonds. Moreover, even in the double-layer ( √ ) √ 7 × 3 -rect phase, the bonding with the silicon danglind bonds affects the electronic structure, which results in deformation from 2D free-electron band structure [1–3]. In order to obtain nearly freestanding ultrathin indium films with little effect from silicon substrates, buffer layers have to be inserted between the indium layers and silicon substrates. In this work, I adopted a method of deposition of other metal atoms on ultrathin indium films on Si(111) to prepare a buffer layer as proposed in Chap. 1. I investigated the effects of the deposition on the structure and electronic(properties)of ultrathin √ √ 7 × 3 -rect phase indium films. As a pristine indium film, I used the In/Si(111) because it has the commensurate structure, which is useful for first-principles calculations. As a deposition atom, I chose magnesium. When deposited directly on the Si(111) (7 × 7) surface, magnesium is so strongly bonded to silicon that it forms magnesium silicide even at RT [4, 5]. I expected that this high reactivity of magnesium results in breaking of bonds between indium and silicon and formation of new interface structure. In this research, I have focused on the following three topics: (1) To reveal the atomic structure(of the ultrathin films obtained by magnesium √ √ ) 7 × 3 -rect phase. deposition onto the In/Si(111)

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. Terakawa, Structure and Electronic Properties of Ultrathin In Films on Si(111), Springer Theses, https://doi.org/10.1007/978-981-19-6872-3_4

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4 Structure and Electronic Properties of Ultrathin (In, Mg) Films on Si(111)

(2) To reveal the electronic structure of the ultrathin (In, Mg) films. (3) To reveal the freestanding nature of the ultrathin films by comparing the electronic properties before and after magnesium deposition.

4.2 Structure Change by Mg Deposition onto the In/Si(111) (√ √ ) 7 × 3 -Rect Phase 4.2.1 LEED and STM Observations (√ √ ) Deposition of magnesium onto the In/Si(111) 7 × 3 -rect phase (Fig. 4.1a) at 300 K leads(to the formation of three new superstructures. At 0.25-ML(magnesium √ √ ) √ √ ) 3× 3 coverage, a 2 3 × 2 3 pattern shows up (Fig. 4.1b). Above 0.3 ML, and (4 × 4) spots simultaneously and become intense with increasing mag( √ appear √ ) nesium coverage, while the 2 3 × 2 3 spots become weak. At 1.0 ML, only (√ √ ) 3 × 3 and (4 × 4) spots are observed (Fig. 4.1c). At lower growth temthe peratures, the intensity (√of the√(4)× 4) spots, one of which is circled in Fig. 4.1c, is 3 × 3 pattern is observed at 210 K (Fig. 4.1f), while the weaker and only the ( √ √ ) 2 3 × 2 3 pattern does not change (Fig. 4.1e). After the magnesium deposition, no change in the LEED patterns was observed down to 30 K except for monotonic increase of the spot intensity according to the Debye–Waller effect. Note that the (√ √ ) 3 × 3 spots, and that the (4 × 4) spots are always observed together with the surface covered only with the (4 × 4) phase is not obtained. Figure 4.2a) shows STM image of the surface with coexisting (√a large-scale ( √ √ √ ) 3 × 3 phases. The darker area on a terrace from the top2 3 × 2 3 and ( √ √ ) right corner is the 2 3 × 2 3 phase. The close-up view in Fig. 4.2b shows that the structure defective. The characteristic triangular depressions arranged ( √is rather (√ are √ ) √ ) with 2 3 × 2 3 periodicity, but their shapes are irregular. The 3 × 3 phase ( √ √ ) looks brighter than the 2 3 × 2 3 phase on a terrace (Fig. 4.2a). Dark lines along the directions are noticeable. Figure 4.2c and d shows high-resolution images of an area including the dark line. A well-ordered hexagonal array of bright(protrusions √ √ ) 3× 3 is visible. On both sides of the line, the protrusions belong to the same grid as displayed in Fig. 4.2d. In contrast, dark depressions are present in the opposite sides in the lower-right half of the cells: left sides in the upper-left domain (√and right √ ) 3 × 3 domains are antiphase domain. This indicates that the upper and lower domains, and the dark lines along are domain boundaries between the antiphase

4.2 Structure Change by Mg Deposition onto the In/Si(111)

(b)

(a) (0 1)

(√ √ ) 7 × 3 -Rect Phase

55

(c) (0 1)

(1 0)

(0 1) (1 0)

(1 0)

300 K (d)

(e) (0 1)

(f) (0 1)

(0 1) (1 0)

(1 0)

(1 0)

210 K (√ √ ) Fig. 4.1 LEED pattern changes by magnesium deposition on the In/Si(111) 7 × 3 -rect (√ √ ) phase at a, b, c 300 K, and d, e, f 210 K. a, d The 7 × 3 -rect phase, b, e 0.25-ML magnesium electron( energy is 85) eV. The deposition, and c, f 1.0-ML magnesium deposition. The (√primary √ ) √ √ 7 × 3 , b, e 2 3 × 2 3 , and c, f parallelograms represent the reciprocal unit cells of a, d (√ √ ) 3 × 3 (dotted) and (4 × 4) (solid). One of the (4 × 4) spots is indicated by the red circle in c

(√ √ ) domains. Hereafter, we focus on the 3 × 3 phase because it is revealed that (√ √ ) 3 × 3 phase has high crystallinity from the LEED and STM observations. the

4.2.2 Structure Determination by First-Principles Calculation (√ √ ) 3 × 3 phase, I In order to reveal the atomic structure of the (In, Mg)/Si(111) performed a first-principles total-energy calculation. The calculation was performed using projector-augmented-wave (PAW) [6, 7] method implemented in the Vienna ab initio simulation package (VASP) [8, 9]. The generalized gradient approximation [10] was employed as the exchange(GGA) of Perdew, Burke, and Ernzerhof (PBE) (√ √ ) correlation functional. The (In, Mg)/Si(111) 3 × 3 surface was modeled by a periodic slab consisting of three Si bilayers, an (In, Mg) bilayer or trilayer and a vacuum region of ∼15 Å. H atoms were used to saturate the silicon dangling bonds

56

(a)

4 Structure and Electronic Properties of Ultrathin (In, Mg) Films on Si(111)

[110]

(b)

[112] 2√3×2√3

√3×√3 √3×√3 20 nm

(c)

2 nm

(d)

2 nm

1 nm

( √ √ ) Fig. 4.2 a Large-scale STM image of the surface covered with the (In, Mg)/Si(111) 2 3 × 2 3 ( √ (√ √ ) √ ) 3 × 3 phases. High-resolution STM images of b the 2 3 × 2 3 phase and c and (√ ( √ √ ) √ ) 3 × 3 phase. The parallelogram in b represents the 2 3 × 2 3 unit cell. (d) Close-up (√ (√ √ ) √ ) views of the 3 × 3 phase. The 3 × 3 lattices are drawn by the solid lines. The images were obtained at a sample bias VS = 1.0 V, tunneling current I = 0.5 nA, b VS = 0.1 V, I = 1.0 nA, and c, d VS = 0.5 V, I = 1.0 nA. All the images were measured at 78 K

at the bottom layer of the slab. The bottom-most silicon atoms were kept fixed at the bulk positions with an optimized silicon lattice constant of 5.468 Å. The remaining atoms were relaxed until the residual force on each atom was smaller than 0.01 eV/Å. The T-centered 6 × 6 × 1 Monkhorst-Pack [11] k-point mesh was used to sample the SBZs for structure searching. For stable configurations, atom positions were further optimized using increased k-point mesh of 9 × 9 × 1 and a substrate thickness of six Si bilayers, and the electronic band structure was calculated.

4.2 Structure Change by Mg Deposition onto the In/Si(111)

(√ √ ) 7 × 3 -Rect Phase

57

To investigate the relative stability of models with different indium and magnesium coverages, formation energies defined as follows were compared after relaxing the initial structures. E f = E InMg/SiH − n E In − m E Mg − 3E SiH ,

(4.1)

(√ √ ) 3 × 3 and where E InMg/SiH and E SiH denote total energies of (In, Mg)/Si(111) Si(111) (1 × 1) slabs, respectively. E In and E Mg are the energies of bulk indium and n and m are the numbers of the indium and bulk magnesium per atom, (√ respectively. √ ) 3 × 3 unit cell. magnesium atoms per Structure determination was performed according to the following steps. First, all possible configurations of double-layer structures with threefold rotational symmetry examined. Structures whose axis is set at the T1 , T4 , and H3 sites of Si(111) (√ were √ ) with each layer composed of four In/Mg atoms per 3 × 3 unit cell were found to show lower E f values. Then, structures with stacking of two or three layers with four metal atoms per layer per unit cell were tested. The number of indium and magnesium atoms were, respectively, set as six to(eight and ) one to six, considering √ √ 7 × 3 -rect phase is 2.4 ML that the initial indium coverage of the In/Si(111) and that the deposited magnesium amount is around 1 ML. It is found that stable structures have a bottom layer configuration of(Fig. 4.3b in √ √ ) 3× 3 common. It contains three magnesium atoms and an indium atom per unit cell. In the unit cell, one of the silicon dangling bonds at T1a is terminated by the indium atom, while the other two at T1b and T1c are saturated by the magnesium atoms forming a kagome lattice. Stable structures were further explored by fully relaxing the positions of the top and middle layers relative to the bottom layer of Fig. 4.3b. Figure 4.3a and b illustrates the most stable structure. It consists of three atomic layers, which have nearly closepacked structure stacked in an The contrasting ABA stacked structure (√ABC sequence. √ ) 3 × 3 unit cell. The top, middle, and bottom layers is less stable by 49 meV per have In4 , In3 Mg1 , and In1 Mg3 compositions per unit cell, respectively. Each of the layers is flat with height difference less than 0.14 Å except for the bottom indium atom located 0.25 Å higher than the bottom magnesium atoms. The mean interlayer spacing is 2.68 Å (top-middle), 2.49 Å (middle-bottom), and 2.29 Å (bottom-top silicon layer). The structure exhibits structural from rectangular arrangement (√ transformation √ ) 7 × 3 -rect phase to hexagonal arrangement of indium atoms in the In/Si(111) by magnesium deposition. The average inter-atomic distance between the top indium atoms is 3.33 Å, which agrees with the nearest neighbor distance of the previously reported hexagonal indium films and islands [12–14]. The atom density is only 0.5% higher than that of the (101) plane, the closest packed plane, of bulk bct indium [15]. Figure 4.3c shows an empty-state simulated STM image. The image was generated from the local density of states 0–0.5 eV above the theoretical Fermi level [16]. The calculated STM image with bright protrusions and dark depressions closely

58

4 Structure and Electronic Properties of Ultrathin (In, Mg) Films on Si(111)

[112]

(a)

[111]

[110] top

middle bottom

In

[110]

Si

Mg (b) bottom layer + Si (T1, T4)

T1a top layer + Si (T1, T4)

middle layer + Si (T1, T4)

T1b T1c In1 (c)

Fig. 4.3 a (left) and (right) top views of the optimized structure of the triple-layer (In, (√ Side √ ) 3 × 3 phase. b The top views of the top, middle, and bottom layers presented Mg)/Si(111) Si (T4 ) atoms. c Simulated empty-state STM image. The solid lines in a–c show with(Si (T1 ) and √ ) √ 3 × 3 cells. The dashed line in a represents the location of the cross sections shown in the Fig. 4.7c and d

4.3 The Electronic Structure of the (In, Mg)/Si(111)

(√ √ ) 3 × 3 Phase

59

resembles the experimental STM image with a sample bias of 0.5 V (Fig. 4.3d). Although the top indium atoms are located at nearly the same height, only the atom on the T1c site (In1 in Fig. 4.3b) appears as a bright protrusion. The other top indium atoms are not clearly resolved and the dark depression is seen on the T1a site, where the bottom indium atom resides. The two domains observed in the STM image (Fig. 4.2d) can be interpreted as structures whose lateral positions of the middle and bottom layers are reversed but those of the top layers are identical. Note that the second most stable structure in the total-energy calculation is an In7 Mg5 triple-layer structure. The atomic structure is the same as that of the In8 Mg4 structure (Fig. 4.3) except that the In1 atom is replaced by a magnesium atom. The formation energy is calculated to be 11 meV higher than that of the In8 Mg4 model. The In7 Mg5 structure is considered to coexist with the In8 Mg4 structure as point defects and appear as randomly distributed dark protrusions, one of which is indicated by the arrow in the STM image (Fig. 4.2c). The number of the dark protrusions is ∼7% of the total protrusions. It is suggested that the In7 Mg5 structure is related to the coverage compensation of indium atoms as discussed later.

4.3 The Structure of the (In, Mg)/Si(111) (√ Electronic √ ) 3 × 3 Phase 4.3.1 ARPES Experiments (√ √ ) Figure 4.4a shows the ARPES Fermi surface map of the (In, Mg)/Si(111) 3× 3 phase. It has circular contours surrounding the (1 × 1) SBZs in common with (√ Fermi √ ) 7 × 3 -rect phase (Fig. 1.5b). While the Fermi surface of the the In/Si(111) (√ √ ) 7 × 3 -rect phase is composed of a single circle (Fig. 4.5b), that of In/Si(111) (√ √ ) the 3 × 3 phase is composed of two concentric circles centered at T points of (√ √ ) 3 × 3 SBZs with distortion from ideal circles near the SBZ boundaries. the The solid black and dashed red circles in the lower-right part of Fig. 4.4a depict circles with k = 1.29 Å−1 and k = 1.46 Å−1 , respectively. We call the smaller one the “inner” circle and the larger one the “outer” circle. The relationship between the observed Fermi contours and the two circles is schematically drawn in Fig. 4.5a. The black curves represent the contours related to the inner circle, and the orange curves to the outer circle. The inner circles form a hexagram centered at T and (circles at K). √ √ The outer circles form a larger hexagram with corners going outside the 3× 3 SBZ, arcs which are surrounding K and bent near the zone boundaries, and ellipses at M.

4 Structure and Electronic Properties of Ultrathin (In, Mg) Films on Si(111)

Fig. 4.4 a Fermi surface map (In, Mg)/Si(111) (√ of the √ ) 3 × 3 phase. The energy window was 20 meV and the spectra were symmetrized according to the mirror and threefold rotational symmetries of Si(111). The dotted white and solid orange are the (√ lines √ ) 3× 3 (1 × 1) and SBZs, respectively. The solid black and dashed red circles in the lower-right part T display circles( centered at √ √ ) 3× 3 points of the SBZs with radii of k = 1.29 Å−1 and k = 1.46 Å−1 , respectively. Band maps along b T-M and c T-K (√ -M-K √ )of the 3 × 3 SBZs. The (In, Mg)-induced metallic surface states are denoted as U1 -U6 . The thick arrows in a and c indicate the bands of the coexisting double-layer ( √ √ ) 3 × 3 phase

(a)

Γ0

M1 K1

Γ1 M3

M2

K2

[112]

60

(b)

[110]

U1

U2

Γ0

M1

U3

Γ1

M2

(c) U6

U4 U3

U5

U1

Γ0

K1

M3

K2

4.3 The Electronic Structure of the (In, Mg)/Si(111)

(√ √ ) 3 × 3 Phase

61

Fig. 4.5 Schematic drawings of the (experimental Fermi surface of a the (In, Mg)/Si(111) ( √ ) √ √ ) √ 3 × 3 phase and b the In/Si(111) 7 × 3 -rect phase [1]. The black and orange curves in respectively. The dotted red curves a represent the contours ascribed to the inner and(outer circles, √ √ ) in b describe circles centered at T points of the 7 × 3 SBZs with a radius of k = 1.41 Å−1 along [110] and k = 1.40 Å−1 along [112]

Figure 4.4b and c shows band maps along T-M and T-K -M-K of the

(√

3×

√ ) 3

SBZs. The bands dispersing downward from T 0 at 0.75–0.95 eV and 2.0 eV are silicon valence bands. The lower band is the silicon bulk valence band. The upper bands are sub-bands due to the quantum confinement in the narrow space-charge layer with upward band bending [17]. We discuss surface-state bands near E F . Along T-M (Fig. 4.4b), three metallic bands labeled U1 , U2 and U3 are clearly observed. The U1 band has a “W” shape with the bottom at ∼0.4 eV. The U2 band has a “V” shape with the bottom at ∼1.7 eV extending toward the M points above 0.8 eV. The U1 and U2 bands cross E F at 1.29 and 1.46 Å−1 , respectively, on the T 1 -M 2 line. The U3 band exhibits a steep dispersion above 2.6 eV and almost degenerates with the U2 band near E F . A blurred feature is also observed at M 1 although the dispersion is not clear. The U1 and U2 bands correspond to the inner Fermi circle indicated by the black curves and the U3 band to the outer Fermi circle indicated by the orange curves in Fig. 4.5a. Along T-K -M-K (Fig. 4.4c), the inner Fermi circle appears as the electron pockets U6 and the U1 band. The U1 band is only weakly observed in the far right of Fig. 4.4c. The outer Fermi circle appears as the U3 and U4 bands on the T-K line, and the U4 band crosses E F at 1.44 Å−1 . The U4 and U5 bands show complicated band dispersions along K -M-K , where the Fermi contours deviate from the circles. The U4 band has energy minima of 0.5 eV near K and 0.7 eV at M and touches E F at midpoints between M and K . The U5 band dispersing downward from M at E F shows a minimum at between M and K , and extends in the energy range of 0.6–0.9 eV toward T.

4 Structure and Electronic Properties of Ultrathin (In, Mg) Films on Si(111)

[112]

[111]

62

[110] top bottom

In

Si

[110]

(√ √ ) 7 × 3 -rect Fig. 4.6 (left) Side and (right) top views of the atomic structure of the In/Si(111) (√ √ ) phase. The solid parallelogram represents the 7 × 3 unit cell. The dashed line represents the location of the cross sections shown in Fig. 4.7e and f

4.3.2 Band Calculation In order to gain insight into the origin of the inner and outer Fermi circles, I calculated the electronic band structure charge density distributions at E F for the triple(√ and √ ) layer (In, Mg)/Si(111) 3 × 3 phase (Fig. 4.3a) and made a comparison with (√ √ ) 7 × 3 -rect phase. Figure 4.6 shows the those of the double-layer In/Si(111) (√ √ ) 7 × 3 -rect phase, which was obtained by atomic structure of the In/Si(111) optimizing the atom positions of the slab (a vacuum region of ∼15 Å, an In bilayer, six Si bilayers, and a H monolayer) constructed from the atomic structure determined by LEED and surface X-ray diffraction [18]. 4.7a shows the calculated band structure of the triple-layer (In, Mg)/Si(111) (√Figure √ ) 3 × 3 phase. The sizes of circles and squares are proportional to the contributions of In 5sp and Mg 3s, respectively. The color scale of the circles represents the relative contribution of In 5spx p y and 5 pz , where the z-axis is normal to the surface. There is good agreement between the theoretical and experimental band structure. The experimentally identified U1 -U6 bands are reproduced except that the downward dispersion toward M of the U4 band lies at lower binding energy than that in the experiment. Some of the calculated bands are hardly detectable in the experimental band structure due to the matrix element effects. For example, the U1 , U2 and U3 bands highlighted by the thick yellow curves along T-M are clearly detected in the ARPES band map, but the bands between U2 and U3 , and outside U3 with smaller slopes are only faintly seen.

4.3 The Electronic Structure of the (In, Mg)/Si(111)

(√ √ ) 3 × 3 Phase

63

(√ √ ) Fig. 4.7 Calculated band structure of a the triple-layer (In, Mg)/Si(111) 3 × 3 phase and b (√ √ ) the double-layer In/Si(111) 7 × 3 phase. The sizes of the circles and squares are proportional to the contribution of In 5sp and Mg 3s, respectively. The relative contribution of In 5spx p y and 5 pz is shown by the color scale. The thick yellow curves highlight the U1 , U2 and U3 bands clearly ( ) detected in ARPES band map along T-M (Fig. 4.4b). Charge density distributions in the 110 plane ( (the ) dashed line in Fig. 4.3a) of the c U3 and d U1 states at E F . Charge density distributions in the 110 plane (the dashed line in Fig. 4.6) of the e V1 and f V2 states at E F . g In-plane averaged charge density distributions along z, the [111] direction

Note that the band marked by the red arrows in Fig. 4.4a and c is observed between the U4 and U6 bands and crosses E F at 1.38 Å−1 along T-K . This band does not appear in the calculated band structure in Fig. 4.7a. The band to a double-layer (√ is ascribed ( √ √ ) √ ) 3 × 3 phase. The most stable double-layer 3 × 3 model was found to be the In5 Mg3 structure (Fig. 4.8a) with stacking of the top In4 and bottom In1 Mg3 layers of the triple-layer model in Fig. 4.3. The structure is quite similar to the double(√ √ ) layer structure of the (Tl, Mg)/Si(111) 3 × 3 phase (Fig. 1.10c) [19], where both of indium and thallium are group 13 metals.

64

4 Structure and Electronic Properties of Ultrathin (In, Mg) Films on Si(111)

Figure 4.8b (√shows√ the ) band structure calculated for the double-layer (In, Mg)/Si(111) 3 × 3 structure. It has a metallic band at the position between the U4 and U6 bands of the triple-layer structure as indicated by the red arrow. The position relationship of the three bands agrees with that of the experimentally observed bands. (√ √ ) 3 × 3 phase is much less stable by > 250 meV per unit The double-layer (√ √ ) 3 × 3 phase, but it should be formed for the coverage cell than the triple-layer (√ √ ) compensation. The triple-layer (In, Mg)/Si(111) 3 × 3 phase has an In8 Mg4 composition with total coverage of 2.67 ML (In) and 1.33 ML (Mg). The indium coverage is slightly higher than the initial coverage of 2.4 ML for the In/Si(111) (√ √ ) 7 × 3 -rect phase before magnesium deposition. Therefore, indium atoms are insufficient to cover the whole surface by the triple-layer structure even if the tripleexisting as point defects is considered. As a result, the doublelayer In 7 Mg5 structure (√ √ ) layer 3 × 3 structure should coexist to compensate the loss of the indium (√ √ ) coverage. In the STM experiments, the double-layer 3 × 3 phase is observed as a minor domain surrounded by the triple-layer phase with a domain size of 400– 600 Å, which results in the weak but sharp band in ARPES. (√observed √ ) 3 × 3 phase are predominantly The surface-state bands of the triple-layer composed of In 5s and 5 p orbitals. A small contribution of the Mg 3s orbital is found mainly in the unoccupied bands near T, indicating that the magnesium atoms are almost completely ionized. Highly dispersive bands including U1 , U2 , and U3 bands have In 5spx p y character. On the other hand, flat bands, for instance, at ∼1.0 eV below E F along K -M-K , have In 5 pz character. The different contributions of the indium atoms in the top layer can explain the simulated STM image in Fig. 4.3c with only the In1 atom (Fig. 4.3b) brightly visible at the positive sample bias. The 5 pz orbital of the top In1 atom mainly contributes to the flat bands at 0–1.0 eV above E F , while those of the other top indium atoms contribute to the bands below E F . Therefore, only the In1 has a large contribution to the unoccupied states and it is brightly seen in the empty-state STM image. ) ( Figure 4.7c and d shows the charge density distributions in the 110 plane of the U3 and U1 states at E F along T-K . As expected from their In 5spx p y character, both the U3 and U1 states have wave functions widely distributed in the in-plane direction. However, they show striking difference along the out-of-plane direction. The U3 state is spread over the three metal layers with a broad peak centered at the middle layer in the in-plane averaged charge density plot in Fig. 4.7g. On the other hand, the U1 state has two peaks: one is localized in the top layer and the other is located in the middle and bottom layers. The two different vertical charge distributions indicate that the U3 and U1 states are, respectively, states with zero and one nodal planes parallel to the surface, or, in other words, bonding and antibonding states between the top In layer and the middle-bottom (In, Mg) layers. The bonding character is also found in the U2 and U4 bands along T-K , which correspond to the outer Fermi circle, and

4.3 The Electronic Structure of the (In, Mg)/Si(111)

(√ √ ) 3 × 3 Phase

65

Fig. 4.8 a (left) and (right) top views of the optimized structure (of the double-layer (In, (√ Side √ ) √ √ ) 3 × 3 phase. The solid parallelogram represents the 3 × 3 unit cell. b Mg)/Si(111) Calculated band structure of the double-layer model in a. The sizes of circles and squares and the color scale are defined in the same way as in Fig. 4.7

the antibonding character is in the U6 band at K , which corresponds to the inner Fermi circle. Therefore, the outer and inner Fermi circles are due to the bonding and antibonding states between the top and middle-bottom layers, respectively. The outer circle comes from the bonding states with higher binding energy and the inner circle from the antibonding states with lower binding energy. now compare the electronic states of the triple-layer Mg)/Si(111) (√ (In, (√Let us √ ) √ ) 3 × 3 phase with those of the double-layer In/Si(111) 7 × 3 -rect phase. (√ √ ) 7 × 3 -rect phase has 2D nearly free-electron band structure, The In/Si(111) (√ √ ) 7 × 3 SBZ and most of the Fermi surface is parts of a circle folded into the except for butterfly features [1], as indicated in Fig. 4.5b. The arcs extending along T-Y is ascribed to the V1 band in the calculated band structure along T-X in Fig. 4.7b.

66

4 Structure and Electronic Properties of Ultrathin (In, Mg) Films on Si(111)

The V1 band is of In 5spx p y character. The charge density distribution is shown in Fig. 4.7e. The V1 state has a wave function widely distributed both in the in-plane and out-of-plane directions, and the in-plane averaged distribution in Fig. 4.7g shows a single peak. This clearly indicates that the V1 band is a bonding state (√ between √ ) the top and bottom indium layers. Most of the metallic bands of the 7× 3 phase show bonding character and they compose the circular Fermi surface. The antibonding states have little contribution to metallic bands because of mixing with silicon dangling-bond states. An exception is seen in the butterfly parts of the Fermi surface. The V2 band in Fig. 4.7b forms the butterfly wing near X . As shown in Fig. 4.7f and g, the V2 state has an antibonding character with a nodal plane between the two indium layers. The V2 state does not mix with silicon dangling-bond states and remains metallic. This is because it has nodal planes perpendicular to the surface and the positions of the top silicon atoms coincide with one of the nodal planes. We now discuss the electronic properties of a freestanding double-layer indium film without a substrate. Figure 4.9a illustrates the atomic structure, which corresponds to the two (001) planes of bulk bct indium. The dark and light blue circles represent indium atoms in the top and bottom layers, respectively. The two layers are identical to each other and form square lattices. Calculated Fermi surface is shown in Fig. 4.9b. The Fermi contours are mainly composed of In 5 p orbitals. The small circles (orange curves) centered at the T points of the (1 × 1) SBZs are of 5 pz character. They do not appear at E F in the double-layer In/Si(111) phase because of mixing with silicon. The two large circles highlighted by the thick green and pink curves are of 5 px p y character. Figure 4.9c presents charge density distributions of the R1 and R2 states at E F along T 0 –T 1 . The R1 state corresponding to the outer Fermi circle has a bonding character with a large charge distribution between the two indium layers. On the other hand, the R2 state corresponding to the inner Fermi circle has a large charge distribution outside the two layers and shows an antibonding character with a nodal plane between them. These characteristic electronic properties of the freestanding double-layer indium film closely resemble those of the triple-layer (In, Mg)/Si(111) ( √ √ ) 3 × 3 phase. It should be noted here that a freestanding double-layer film with a hexagonal lattice has almost the same electronic properties and that the difference in lattices, square or hexagonal, does not influence the discussion. of the electronic properties of (In, Mg)/Si(111) (√the triple-layer (√Comparison √ ) √ ) 3 × 3 phase, the double-layer In/Si(111) 7 × 3 -rect phase, and the freeindium film has revealed that the electronic properties of the standing double-layer (√ √ ) 3 × 3 phase are close to those of the freestanding double-layer indium film. The bottom In1 Mg3 layer serves as a buffer layer to decouple the metallic bands from the silicon dangling-bond and)realize a nearly freestanding double-layer metal (√states√ 3 × 3 phase. in the (In, Mg)/Si(111) bonding and antibonding states with zero and one nodal planes in the ) (√The √ 3 × 3 phase are different from the well-known quantum-well states with one

4.3 The Electronic Structure of the (In, Mg)/Si(111)

(√ √ ) 3 × 3 Phase

67

Fig. 4.9 a Structure and b calculated Fermi surface of the freestanding double-layer indium film. The red square in a represents the (1 × 1) unit cell. The black thin lines in b show the (1 × 1) SBZs of the square lattice. The black and orange curves in b indicate the Fermi contours composed of In 5 p x p y and In 5 p z orbitals, respectively. The thick green and pink circles highlight the two circular Fermi contours centered at T 0 . c Charge density distributions of the R1 and R2 states at E F along T 0 –T 1

68

4 Structure and Electronic Properties of Ultrathin (In, Mg) Films on Si(111)

and two antinodes in thin metal films with thickness typically larger than five layers. The antinodes of the quantum-well states arise from envelope functions due to the out-of-plane confinement of bulk Bloch waves and the wave functions are oscillating with a period of(approximately lattice constants [20, 21]. Instead, the √ √ ) 3 × 3 phase can be regarded as atomically ultraelectronic properties of the thin quantum-well states, which have been less explored because of the difficulty in preparing well-ordered metal films with a few layer thickness. Previous studies tried to make ultrathin metal films after preparing buffer layers by termination of silicon dangling bonds with other metal atoms [22–25]. I propose a new method to create a buffer layer by magnesium deposition onto ultrathin metal films on Si(111), where the deposited magnesium atoms are intercalated between the metal film and silicon substrate to form a buffer layer. In this work, I have established the triple-layer metal film exhibiting electronic properties of nearly freestanding double-layer film on the buffer layer. Double-layer film with a single layer on the buffer layer could be obtained by using the single-layer In/Si(111) hex phase established in Chap. 3 (√ √ ) 7 × 3 -rect phase as a pristine strucinstead of the double-layer In/Si(111) (√ √ ) 3 × 3 phase ture. I have already reported the coexistence of the double-layer (√ √ ) 3 × 3 phase in this work. as a minor domain surrounded by the triple-layer Films of thickness more than two layers may also be formed by indium deposition onto the triple-layer films considering the little difference in in-plane atom density between the films on Si(111) and bulk indium. This demonstrates the possibility of (In, Mg)/Si(111) becoming a beneficial model for exploring the evolution of metallic electronic properties from 2D to 3D.

4.4 Summary I have revealed the atomic structure and electronic properties of a new triple-layer metal obtained by magnesium deposition onto the double-layer In/Si(111) (√ film √ ) 7 × 3 -rect phase. The deposited magnesium atoms are intercalated between (√ √ ) 3 × 3 phase consisting of three the indium layers and silicon substrate to form a (√ √ ) 3× 3 hexagonal close-packed metal layers stacked in the ABC sequence. The phase has free-electron-like metallic electronic structure. The Fermi surface is composed of two circles centered at T points with different radii. The two Fermi circles are associated with bonding and antibonding states with zero and one nodal planes between the top and middle layers.(The bottom layer consisting of three magne√ √ ) 3 × 3 unit cell serves as a buffer layer to sium atoms and an indium atom per decouple the metallic bands from silicon dangling-bond states and realize a nearly freestanding double-layer metal.

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Chapter 5

Conclusions

Single-layer In film I successfully prepared macro-scale order) samples of the two phases known as (√ (√ (mm √ ) √ ) the “ 7 × 3 ”-hex and “ 7 × 3 ”-striped phases. Although the two phases were regarded as different phases depending on their preparation methods, the LEED I -V analysis found that they are identical to each other. We call this phase the In/Si(111) hex phase hereafter. Detailed analyses of LEED( spots and)STM images revealed that the hex phase √ √ 7 × 3 structure but uniaxially incommensurate does not have commensurate monolayer structure. The indium overlayer is contracted by 2.1%±0.3% in the [110] (√ √ ) direction as compared with that of the commensurate 1.4-ML 7 × 3 structure. The contraction induces an irregular arrangement of the zigzag and linear types of atomic chains composed of protruding indium atoms located near the H3 sites of Si(111). First-principles calculation revealed that(the contracted monolayer structure √ √ ) 7 × 3 structure. is energetically favorable than the uncontracted Metallic band structure of the hex phase was observed by ARPES experiments. The Fermi surface has an anisotropic arc-shaped character, which(is in contrast to √ √ ) 7 × 3 -rect the isotropic circular Fermi surface of the double-layer In/Si(111) phase. The anisotropic nature of the hex phase reflects the atomic structure of the hex phase consisting of atomic chains. (√ √ ) 7 × 7 phase at 250–210 K upon cooling. The hex phase changes to the ARPES and conductivity measurements demonstrated that the transition induces the disappearance of the metallic surface states and a sharp drop in sheet (√ conductivity, √ ) 7 × 7 is an respectively. These results indicate that the transition of hex to electronic metal–insulator transition.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. Terakawa, Structure and Electronic Properties of Ultrathin In Films on Si(111), Springer Theses, https://doi.org/10.1007/978-981-19-6872-3_5

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5 Conclusions

Triple-layer (In, Mg) film

(√ √ ) I found that the magnesium deposition onto the double-layer In/Si(111) 7× 3 (√ √ ) 3 × 3 periodicity from LEED and rect phase induces a new structure with the (√ √ ) 3× 3 STM observations. First-principles calculation revealed that the (In, Mg) phase consists of three hexagonal close-packed metal layers stacked in the ABC sequence. The top, middle, and bottom layers have, respectively, In4 , In3 Mg1 , and In1 Mg3 compositions, which indicates that the deposited magnesium atoms are intercalated between the indium layers and silicon substrate. (√ √ ) 3 × 3 phase Metallic bands were found in the triple-layer (In, Mg)/Si(111) by ARPES experiments. The Fermi is composed of two circles with different (√ surface √ ) radii centered at T points of the 3 × 3 SBZs, whereas that of the double-layer (√ √ ) 7 × 3 -rect phase consists of a single circle. In/Si(111) The band structure calculated for the triple-layer structure reproduces the experimentally observed band structure. The calculations of the charge density distributions found that the two Fermi circles come from bonding and antibonding states between the top and middle layers. The larger Fermi circle corresponds to the bonding state with higher binding energy, and the smaller one to the antibonding states with lower binding energy. The bottom layer has only a small contribution to the metallic bands and acts as a buffer layer to decouple the metallic bands from the silicon danglingbond states and realize a nearly freestanding double-layer metal.

(√ √ ) 7 × 3 -rect phase, b the single(√ √ ) layer In/Si(111) hex phase, and c the triple-layer (In, Mg)/Si(111) 3 × 3 phase. The paral(√ (√ √ ) √ ) lelograms in a and c represent the unit cells of 7 × 3 and 3 × 3 , respectively

Fig. 5.1 Atomic structure of a the double-layer In/Si(111)

5 Conclusions

Summary

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(√ √ ) Figure 5.1 shows the atomic structure of the double-layer In/Si(111) 7× 3 rect phase, the single-layer In/Si(111) hex phase, and the triple-layer (In, Mg)/Si(111) ( √ √ ) 3 × 3 phase. The arrangement of indium atoms in the ultrathin indium films on Si(111) is greatly transformed: bulk-like square arrangement in the double-layer film, undulating sheet structure composed of quasi-hexagonal arrangement with protruding atoms in the single-layer film, and hexagonal close-packed arrangement in the Mg-intercalated films. The electronic properties are also largely altered depending on their atomic structures. This demonstrates that the structure and electronic properties of ultrathin films consisting of indium, which is a p-block metal both with metallic and covalent characters, are flexibly changed depending on the thickness and interface structure. Further exploration of physical properties of ultrathin indium films, such as the mechanism of the metal–insulator transition of the singlelayer phase and the possibility of superconducting transition of the triple-layer (√ hex √ ) 3 × 3 phase, is highly desirable.

Curriculum Vitae

Shigemi Terakawa Max Planck Institute of Microstructure Physics Nano-Systems from ions, spins and electrons Weinberg 2, 06120 Halle (Saale), Germany e-mail: [email protected]

Education • Doctor of Science (April 2019–March 2022). Department of Chemistry, Graduate School of Science, Kyoto University. Supervisor: Prof. Tetsuya Aruga. • Master of Science (April 2017–March 2019). Department of Chemistry, Graduate School of Science, Kyoto University. Supervisor: Prof. Tetsuya Aruga. • Bachelor of Science (April 2013–March 2017). Division of Chemistry, Faculty of Science, Kyoto University. Professional Experience • Postdoctoral Researcher (April 2022–Present). Max Planck Institute of Microstructure Physics. • Research Fellow (DC2) (April 2020–March 2022). The Japan Society for the Promotion of Science (JSPS).

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. Terakawa, Structure and Electronic Properties of Ultrathin In Films on Si(111), Springer Theses, https://doi.org/10.1007/978-981-19-6872-3

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Honors and Awards • Student Presentation Award, the Physical Society of Japan (March 2022). • Student Presentation Award, Annual Meeting of The Japan Society of Vacuum and Surface Science 2019 (October 2019). • Student Award, ACSIN-14/ICSPM26 (October 2018). Research interests My research fields are surface science and 2D materials. I have investigated the structure and electronic properties of atomically thin metal films on semiconductor surfaces using various experimental techniques (ARPES, LEED, and STM) and DFT calculation. A characteristic feature of my research is to explore intriguing and new physical properties by preparing unique 2D materials on solid surfaces under ultrahigh vacuum conditions. I am now particularly interested in novel electronic properties observed in heterostructures of 2D magnetic materials and topological materials. Publications (1) Shigemi Terakawa, Shinichiro Hatta, Hiroshi Okuyama, and Tetsuya Aruga, “Ultrathin (In, Mg) films on Si(111): A nearly freestanding double-layer metal”, Physical Review B 105, 125402 (2022). (2) Shigemi Terakawa, Shinichiro Hatta, Hiroshi Okuyama, Tetsuya Aruga, “Uniaxially Incommensurate Structure and Metal-insulator Transition of Metallic Indium Monolayer on Si(111)”, Vacuum and Surface Science 63, 425 (2020). (3) Shigemi Terakawa, Shinichiro Hatta, Hiroshi Okuyama, and Tetsuya Aruga, “Structure and phase transition of a uniaxially incommensurate In monolayer on Si(111)”, Physical Review B 100, 115428 (2019). (4) Shigemi Terakawa, Shinichiro Hatta, Hiroshi Okuyama, and Tetsuya Aruga, “Identification of single-layer metallic structure of indium on Si(111)”, Journal of Physics: Condensed Matter 30, 365002 (2018).