Scanning Probe Microscopy (2 vol. set): Electrical and Electromechanical Phenomena at the Nanoscale [v. 1&2, 1 ed.] 0387286675, 0387286683, 9780387286679, 9780387286686, 2172441058, 3019753597

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SCANNING PROBE MICROSCOPY

SCANNING PROBE MICROSCOPY ELECTRICAL AND ELECTROMECHANICAL PHENOMENA AT THE NANOSCALE Volume II

Sergei Kalinin Alexei Gruverman Editors

Alexei Gruverman Dept. Materials Science and Engineering North Carolina State University Raleigh, NC, 27695 USA alexei [email protected]

Sergei Kalinin Oak Ridge National Laboratory Oak Ridge, TN, 37831 USA sergei2.kalininweb.com

Library of Congress Control Number: 2006926451 ISBN-10: 0-387-28667-5 ISBN-13: 978-0387-28667-9

e-ISBN-10: 0-387-28668-3 e-ISBN-13: 978-0387-28668-6

Printed on acid-free paper.
C

2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com

Contents

List of Contributors ..................................................................

ix

About the Editors .....................................................................

xix

VOLUME II Part III. Electrical SPM Characterization of Materials and Devices

559

III.1. Scanning Voltage Microscopy: Investigating the Inner Workings of Optoelectronic Devices ................................................... 561 Scott B. Kuntze, Dayan Ban, Edward H. Sargent, St. John Dixon-Warren, J. Kenton White, and Karin Hinzer III.2. Electrical Scanning Probe Microscopy of Biomolecules on Surfaces and at Interfaces .............................................. Ida Lee and Elias Greenbaum

601

III.3. Electromechanical Behavior in Biological Systems at the Nanoscale ............................................................... A. Gruverman, B. J. Rodriguez, and S. V. Kalinin

615

III.4. Scanning Capacitance Microscopy: Applications in Failure Analysis, Active Device Imaging, and Radiation Effects............ 634 C. Y. Nakakura, P. Tangyunyong, and M. L. Anderson III.5. Kelvin Probe Force Microscopy of Semiconductors ................. Y. Rosenwaks, S. Saraf, O. Tal, A. Schwarzman, Th. Glatzel, and M.Ch. Lux-Steiner

663

v

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Contents

III.6. Nanoscale Characterization of Electronic and Electrical Properties of III-Nitrides by Scanning Probe Microscopy ......... B. J. Rodriguez, A. Gruverman, and R. J. Nemanich III.7. Electron Flow Through Molecular Structures ........................ Sidney R. Cohen III.8. Electrical Characterization of Perovskite Nanostructures by SPM .......................................................................... K. Szot, B. Reichenberg, F. Peter, R. Waser, and S. Tiedke

690

715

746

III.9. SPM Measurements of Electric Properties of Organic Molecules 776 Takao Ishida, Wataru Mizutani, Yasuhisa Naitoh, and Hiroshi Tokumoto III.10. High-Sensitivity Electric Force Microscopy of Organic Electronic Materials and Devices ....................................... 788 William R. Silveira, Erik M. Muller, Tse Nga Ng, David H. Dunlap, and John A. Marohn Part IV. Electrical Nanofabrication

831

IV.1. Electrical SPM-Based Nanofabrication Techniques................ 833 Nicola Naujoks, Patrick Mesquida, and Andreas Stemmer IV.2. Fundamental Science and Lithographic Applications of Scanning Probe Oxidation............................................. 858 J. A. Dagata IV.3. UHV-STM Nanofabrication on Silicon ................................ Peter M. Albrecht, Laura B. Ruppalt, and Joseph W. Lyding

880

IV.4. Ferroelectric Lithography................................................. 906 Dongbo Li and Dawn A. Bonnell IV.5. Patterned Self-Assembled Monolayers via Scanning Probe Lithography.......................................................... 929 James A. Williams, Matthew S. Lewis, and Christopher B. Gorman IV.6. Resistive Probe Storage: Read/Write Mechanism .................. Seungbum Hong and Noyeol Park

943

Contents

vii

Introduction: Scanning Probe Microscopy Techniques for Electrical and Electromechanical Characterization ....................................... S. V. Kalinin and A. Gruverman

1

Part I. SPM Techniques for Electrical Characterization

9

VOLUME I

I.1. Scanning Tunneling Potentiometry: The Power of STM applied to Electrical Transport......................................................... A. P. Baddorf

11

I.2. Probing Semiconductor Technology and Devices with Scanning Spreading Resistance Microscopy .......................................... P. Eyben, W. Vandervorst, D. Alvarez, M. Xu, and M. Fouchier

31

I.3. Scanning Capacitance Microscopy for Electrical Characterization of Semiconductors and Dielectrics .................. J. J. Kopanski

88

I.4. Principles of Kelvin Probe Force Microscopy............................ 113 Th. Glatzel, M.Ch. Lux-Steiner, E. Strassburg, A. Boag, and Y. Rosenwaks I.5. Frequency-Dependent Transport Imaging by Scanning Probe Microscopy ............................................................... Ryan O’Hayre, Minhwan Lee, Fritz B. Prinz, and Sergei V. Kalinin

132

I.6. Review of Ferroelectric Domain Imaging by Piezoresponse Force Microscopy .............................................................. A. L. Kholkin, S. V. Kalinin, A. Roelofs, and A. Gruverman

173

I.7. Principles of Near-Field Microwave Microscopy ...................... Steven M. Anlage, Vladimir V. Talanov, and Andrew R. Schwartz I.8. Electromagnetic Singularities and Resonances in Near-Field Optical Probes .................................................................. Alexandre Bouhelier and Renaud Bachelot

215

254

I.9. Electrochemical SPM: Fundamentals and Applications............. 280 T. J. Smith and K. J. Stevenson I.10. Near-Field High-Frequency Probing ..................................... C. A. Paulson and D. W. van der Weide

315

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Contents

Part II. Electrical and Electromechanical Imaging at the Limits of Resolution II.1. Scanning Probe Microscopy on Low-Dimensional Electron Systems in III-V Semiconductors .......................................... Markus Morgenstern

347

349

II.2. Spin-Polarized Scanning Tunneling Microscopy....................... 372 Wulf Wulfhekel, Uta Schlickum, and J¨urgen Kirschner II.3. Scanning Probe Measurements of Electron Transport in Molecules 395 Kevin F. Kelly and Paul S. Weiss II.4. Scanning Probe Microscopy of Individual Carbon Nanotube Quantum Devices .............................................................. C. Staii, M. Radosavljevic, and A. T. Johnson

423

II.5. Conductance AFM Measurements of Transport Through Nanotubes and Nanotube Networks....................................... 440 M. Stadermann and S. Washburn II.6. Theory of Scanning Probe Microscopy................................... 455 Vincent Meunier and Philippe Lambin II.7. Multi-Probe Scanning Tunneling Microscopy .......................... Shuji Hasegawa

480

II.8. Dynamic Force Microscopy and Spectroscopy in Vacuum......... 506 Udo D. Schwarz and Hendrik H¨olscher II.9. Scanning Tunneling Microscopy and Spectroscopy of Manganites 534 Christoph Renner and Henrik M. Rønnow Index .....................................................................................

974

List of Contributors

Peter M. Albrecht Beckman Institute 405 N. Mathews Urbana, IL 61801 Phone: 217-244-1058 Fax: 217-244-1995 E-mail: [email protected] David Alvarez Infineon Technologies 05452 Essex Junction, VT, USA Phone: 1-802-769-4904 E-mail: david.alvarez@infineon.com Dr. Meredith L. Anderson Sandia National Laboratories P.O. Box 5800, MS1077 Albuquerque, NM 87185-1077 E-mail: [email protected] Prof. Steven M. Anlage Center for Superconductivity Research Department of Physics University of Maryland College Park, MD 20742-4111, USA Phone: +001 301 405 7321 Fax: +001 301 405 3779 E-mail: [email protected] http://www.csr.umd.edu

Dr. Arthur P. Baddorf Oak Ridge National Laboratory 1 Bethel Valley Road, Bldg. 3025 Oak Ridge, TN 37831-6030 Phone: (865) 574-5241 Fax: (865) 574-4143 E-mail: [email protected] http://nanotransport.ornl.gov Prof. R. Bachelot Laboratoire de Nanotechnologie et d’Instrumentation Optique Institut Charles Delaunay CNRS-FRE 2848 Universit´e de Technologie de Troyes F-10010 Troyes, France E-mail: [email protected] Dayan Ban University of Waterloo Department of Electrical and Computer Engineering 200 University Ave. West Waterloo, Ontario A. Boag Faculty of Engineering TEL-AVIV UNIVERSITY Tel-Aviv 69978, ISRAEL

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List of Contributors

Prof. Dawn A. Bonnell Department of Materials Science and Engineering The University of Pennsylvania 3231 Walnut Street, Philadelphia PA 19104 Phone: 215 898 6231 Fax: 215 573 2128 E-mail: [email protected] Dr. Alexandre Bouhelier Laboratoire de Physique de l’Universit´e de Bourgogne UMR 5027 Facult´e des Sciences Mirande—9 Avenue Alain Savary B.P. 47 870—F-21078 DIJON Cedex—FRANCE E-mail: [email protected] Dr. Sidney R. Cohen Director, Surface Analysis Laboratory Chemical Research Support Weizmann Institute of Science Rehovot 76100 ISRAEL Phone: 972 8 934 2703 Fax: 972 8 934 4137 E-mail: [email protected] http://www.weizmann.ac.il/Chemical Research Support/surflab/

Prof. David Dunlap Dept. of Physics and Astronomy Univ. of New Mexico Albuquerque, NM 87131 Phone: (505) 277-2120 Fax: (505) 277-1520 E-mail: [email protected] Dr. P. Eyben Kapeldreef 75, B-3001 Leuven, Belgium Phone: 32 16 281 305 E-mail: [email protected] Dr. Marc Fouchier Veeco instruments S.A.S. Z .I. de la Gaudr´ee—11 rue Marie Poussepin BP 43—91412 Dourdan—France Phone: +33 (0)6 24 60 19 23 E-mail: [email protected] Dr. Thilo Glatzel Institute of Physics, University of Basel Klingelbergstr. 82 CH-4056 Basel Phone: +41(0)61 267-3730 Fax: +41(0)61 267-3795 E-mail: [email protected] http://www.physik.unibas.ch

Dr. John A. Dagata Precision Engineering Division National Institute of Standards & Technology 100 Bureau Drive MS 8212 Gaithersburg MD 20899-8212 USA Phone: 301-975-3597 Fax: 301-869-0822 E-mail: [email protected]

Prof. Christopher Gorman Department of Chemistry North Carolina State University 314 Dabney Hall Raleigh, NC 27695-8204 Phone: 919-515-4252 Fax: 919-515-8920 E-mail: Chris [email protected]

Dr. St. J. Dixon-Warren Chipworks 3685 Richmond Road, Suite 500 Ottawa, Ontario, Canada

Dr. Elias Greenbaum Chemical Sciences Division Oak Ridge National Laboratory Oak Ridge, TN 37831 USA

List of Contributors

Phone: 865-574-6835 Fax: 865-574-1275 E-Mail: [email protected] Prof. Alexei Gruverman Department of Materials Science and Engineering North Carolina State University Raleigh, NC 27695, USA Phone: +1 (919) 5133319 Fax: +1 (919) 5157724 E-mail: Alexei [email protected] Prof. S. Hasegawa Department of Physics School of Science University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, JAPAN Phone/Fax +81-3-5841-4167 E-mail: [email protected] Dr. K. Hinzer Bookham 10 Brewer Hunt Way Ottawa, Ontario Dr. Hendrik H¨olscher Center for NanoTechnology (CeNTech) University of Muenster Gievenbecker Weg 11 48149 Muenster, Germany Phone: +49 (0) 251 83-63832 Fax: +49 (0) 251 83 -63873 E-mail: [email protected] http://www.uni-muenster.de/nanoforce Dr. Seungbum Hong Semiconductor Device and Material Lab Samsung Advanced Institute of Technology P.O. Box 111, Suwon 440-600, Korea E-mail: [email protected]

xi

Dr. Takao Ishida Nanotechnology Research Institute (NRI), National Institute of Advanced Industrial Science and Technology (AIST) 1-1-1 Higashi, Tsukuba, Ibaraki 305-8562, Japan Phone: +81-29-861-7203, Fax: +81-29-861-2786 E-mail: [email protected] Prof. A.T. Charlie Johnson, Jr Department of Physics and Astronomy University of Pennsylvania, 209 S. 33rd St., Philadelphia PA 19104-6396 Phone: (215) 898-9325 Fax: (215) 898-2010 Email: [email protected] Dr. Sergei V. Kalinin Materials Sciences and Technology Division and Center for Nanophase Materials Sciences Oak Ridge National Laboratory 1 Bethel Valley Rd Bldg. 3025, MS6030 Oak Ridge, TN 37831 Phone: (865) 241-0236 Fax: (865) 574-4143 E-mail: [email protected] Prof. Kevin F. Kelly ECE Dept., MS-366 Rice University PO Box 1892 Houston, TX 77005-1892 Phone: 713-348-3565 Fax: 713-348-5686 E-mail: [email protected] Dr. Andrei Kholkin Department of Ceramics and Glass Engineering &

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List of Contributors

Center for Research in Ceramic and Composite Materials (CICECO), University of Aveiro 3810-193 Aveiro, Portugal Phone: +351 234370235 Fax: +351 234425300 E-mail: [email protected] Prof. Jurgen ¨ Kirschner Max-Planck Institut f¨ur Mikrostrukturphysik Weinberg 2 06120 Halle Germany Phone: +49-345-5582656 Fax: +49-345-5511223 E-mail: [email protected] J.J. Kopanski National Institute of Standards and Technology Semiconductor Electronics Division 100 Bureau Dr., stop 8120 Gaithersburg, MD 20899-8120 E-mail: [email protected] Prof. Philippe Lambin FUNDP Rue de Bruxelles 61 B-5000 Namur, Belgium S. B. Kuntze University of Toronto Department of Electrical and Computer Engineering 10 King’s College Rd. Toronto, Ontario Dr. Ida Lee Oak Ridge National Laboratory 1 Bethel Valley Road PO Box 2008 Building 4500N, MS 6194, Room A8 Oak Ridge, TN 37831

Phone: 865-241-6695 or 865-574-6183 Fax: 865-574-1275 E-Mail: [email protected] Minhwan Lee Stanford University Department of Mechanical Engineering 440 Escondido Mall Building 530, Room 226 Stanford, CA. 94305 Phone: 650-723-6488 Fax: 650-723-5034 M. Lewis Department of Chemistry North Carolina State University 314 Dabney Hall Raleigh, NC 27695-8204 Dongbo Li Department of Materials Science and Engineering The University of Pennsylvania 3231 Walnut Street, Philadelphia, PA 19104 Phone: 215 898 3446 Fax: 215 573 2128 E-mail: [email protected] Prof. Dr. Martha Ch. Lux-Steiner Department of Heterogeneous Material Systems (SE2) Hahn-Meitner-Institut Berlin Glienicker Str. 100 D-14109 Berlin Fon: +49 30 8062-2462 Fax: +49 30 8062-3199 Email: [email protected] Prof. Joseph W. Lyding Beckman Institute 405 N. Mathews Urbana, IL 61801 Phone: 217-333-8370 Fax: 217-244-1995 E-mail: [email protected]

List of Contributors

Prof. John A. Marohn Dept. of Chemistry and Chemical Biology 150 Baker Laboratory Cornell University Ithaca, NY 14853-1301 Phone: 607-255-2004 Fax: 607-255-4137 E-mail: [email protected] Dr. Patrick Mesquida Division of Engineering King’s College London Strand, London WC2R 2LS Phone: +44 (0)20 7848 2241 Fax: +44 (0)20 7848 2932 E-mail: [email protected] Dr. Vincent Meunier Computer Science and Mathematics Division & Center of Nanophase Materials Sciences Oak Ridge National Laboratory 1 Bethel Valley Rd. Oak Ridge, TN 37831 E-mail: [email protected] Dr. Wataru Mizutani Nanotechnology Research Institute (NRI) National Institute of Advanced Industrial Science and Technology (AIST) 1-1-1 Higashi, Tsukuba, Ibaraki 305-8562, Japan Phone: +81-29-861-2434 Fax: +81-29-861-2786 E-mail: [email protected] Dr. Markus Morgenstern II. Inst. of Physics B RWTH Aachen University D-52056 Aachen, Germany Phone: (++)49-241-80-27075/6

xiii

Fax: (++)49-241-80-22306 E-mail: [email protected] E.M. Muller Dept. of Chemistry and Chemical Biology 150 Baker Laboratory Cornell University Ithaca, NY 14853-1301 Dr. Yasuhisa Naitoh Nanotechnology Research Institute (NRI) National Institute of Advanced Industrial Science and Technology (AIST) 1-1-1 Higashi, Tsukuba, Ibaraki 305-8562, Japan Phone: +81-29-861-7892 Fax: +81-29-861-2786 E-mail: [email protected] Dr. Craig Y. Nakakura Sandia National Laboratories P.O. Box 5800, MS1077 Albuquerque, NM 87185-1077 E-mail: [email protected] Dr. Nicola Naujoks Nanotechnology Group ETH Zurich Tannenstrasse 3 CH-8092 Zurich, Switzerland Phone: +41 44 632 69 89 Fax: +41 44 632 12 78 E-mail: [email protected] http://www.nanotechnology.ethz.ch Prof. Robert J. Nemanich Department of Physics North Carolina State University Raleigh, NC 27695-8202 Phone: (919) 515-3225 Fax: (919) 515-7331

xiv

List of Contributors

E-mail: Robert [email protected] www.ssl.physics.ncsu.edu

Phone: 650-723-6488 Fax: 650-723-5034

T.N. Ng Dept. of Chemistry and Chemical Biology 150 Baker Laboratory Cornell University Ithaca, NY 14853-1301

Dr. Marko Radosavljevic Components Research Intel Corporation, RA3-252 5200 NE Elam Young Parkway Hillsboro, OR 97124 Phone: 503-613-4732 E-mail: [email protected]

Prof. Ryan O’Hayre Colorado School of Mines Department of Metallurgical and Materials Engineering 1500 Illinois St. Golden, CO. 80401 Phone: 303-273-3770 Fax: 303-273-3795 Dr. Charles Paulson Department of Electrical Engineering 1415 Engineering Dr. Madison, WI 53706 E-mail: [email protected] Mr. Noyeol Park Vice President Storage System Division Semiconductor Business Samsung Electronics Suwon, Korea Dr. Frank Peter Research Center Juelich 52425 Juelich, Germany Phone: +492461616479 E-mail: [email protected] Prof. Fritz Prinz Stanford University Department of Mechanical Engineering 440 Escondido Mall Building 530, Room 226 Stanford, CA. 94305

Dr. Bernd Reichenberg aixACCT Systems GmbH Dennewartstrasse 25-27 52068 Aachen, Germany E-mail: [email protected] Dr. Christoph Renner London Centre for Nanotechnology and Department of Physics and Astronomy University College London Gordon Street 17-19 London WC1E 6BT, UK Phone: +44 (0)20 7679 3496 Fax: +44 (0)20 7679 1360 E-mail: [email protected] http://www.cmmp.ucl.ac.uk/∼cr/ Dr. Andreas Roelofs Seagate Technology 1251 Waterfront Place Pittsburgh, PA 15222, USA Phone: +1 (412) 918 7028 Fax (412) 918 7222 E-mail: [email protected] Dr. Brian J. Rodriguez Materials Science and Technology Division Oak Ridge National Laboratory 1 Bethel Valley Rd Bldg. 3137, MS6057

List of Contributors

Oak Ridge, TN 37831 Phone: (865) 574-0791 Fax: (865) 576-8135 E-mail: [email protected] Dr. Henrik M. Rønnow Laboratory for Neutron Scattering ETH-Z¨urich & Paul Scherrer Institute 5232 Villigen Switzerland Phone: +41 56 310 4668 Fax: +41 56 310 2939 E-mail: [email protected] Prof. Yossi Rosenwaks Faculty of Engineering Elec. Lab. Building, room 231 TEL-AVIV UNIVERSITY Tel-Aviv 69978, ISRAEL Phone: +972-3-6406248 Fax: +972-3-6423508 E-mail: [email protected] http://www.eng.tau.ac.il/∼yossir/ rosenwaks.html Laura B. Ruppalt Beckman Institute 405 N. Mathews Urbana, IL 61801 Phone: 217-244-5665 Fax: 217-244-1995 E-mail: [email protected] S. Saraf Faculty of Engineering TEL-AVIV UNIVERSITY Chemical Department Tel-Aviv 69978, ISRAEL E-mail: mailto:[email protected] Prof. E.H. Sargent University of Toronto Department of Electrical and Computer Engineering

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10 King’s College Rd. Toronto, Ontario Dr. Uta Schlickum Institut de Physique des Nanostructures EPFL/SB/IPN, PHB-Ecublens, Station 3 CH-1015 Lausanne Switzerland Phone: +41 (0)21 69 34 742 Fax: +41 (0)21 69 33 604 E-mail: uta.schlickum@epfl.ch Dr. Andrew R. Schwartz Neocera Inc. 10000 Virginia Manor Road Beltsville, MD 20705, USA Phonr: +001 301 210 1010 Fax: +001 301 210 1042 E-mail: [email protected] http://www.neocera.com Prof. Udo D. Schwarz Department of Mechanical Engineering Yale University P.O. Box 208284 New Haven, CT 06520-8284 USA Phone: +1-203-432-7525 Fax: +1-203-432-6775 E-mail: [email protected] http://www.eng.yale.edu/nanomechanics A. Schwarzman Faculty of Engineering TEL-AVIV UNIVERSITY Tel-Aviv 69978, ISRAEL W.R. Silveira Dept. of Chemistry and Chemical Biology 150 Baker Laboratory Cornell University Ithaca, NY 14853-1301

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List of Contributors

Timothy J. Smith Department of Chemistry and Biochemistry University of Texas at Austin 1 University Station/MC A5300 Austin, TX 78712 E-mail: [email protected] Dr. Michael Stadermann L-234 Chemistry & Material Science Lawrence Livermore National Laboratory 7000 East Ave Livermore, Ca 94550 Dr. Cristian Staii Department of Chemistry Princeton University Princeton, NJ 08544 Phone: 609 258-3962 E-mail: [email protected] Prof. Andreas Stemmer Nanotechnology Group ETH Zurich Tannenstrasse 3 CH-8092 Zurich SWITZERLAND Phone: +41 44 632 4572 Fax: +41 44 632 1278 E-mail: [email protected] Prof. Keith Stevenson Department of Chemistry and Biochemistry University of Texas at Austin 1 University Station/MC A5300 Austin, TX 78712 Phone: (512)232-9160 E-mail: [email protected] E. Strassburg Faculty of Engineering

TEL-AVIV UNIVERSITY Tel-Aviv 69978, ISRAEL Prof. Kristof Szot Institute of Physics, University of Silesia 40-007 Katowice, Poland and Research Center Juelich 52425 Juelich, Germany Phone: +492461616479 email: [email protected] O. Tal Faculty of Engineering TEL-AVIV UNIVERSITY Tel-Aviv 69978, ISRAEL Dr. Vladimir V. Talanov Neocera Inc. 10000 Virginia Manor Road Beltsville, MD 20705, USA Phone: +001 301 210 1010 Fax: +001 301 201 1042 E-mail: [email protected] http://www.neocera.com Dr. Paiboon Tangyunyong Sandia National Laboratories P.O. Box 5800, MS1081 Albuquerque, NM 87185-1081 E-mail: [email protected] Dr. Stephan Tiedke aixACCT Systems GmbH Dennewartstrasse 25-27 52068 Aachen, Germany Phone: +492419631410 E-mail: [email protected] Prof. Hiroshi Tokumoto Nanotechnology Research Center Research Institute for Electronic Science Hokkaido University

List of Contributors

Kita-ku N21 W10, Sapporo 001-002, Japan Phone:+81-11-706-9354 Fax:+81-11-706-9355 E-mail: [email protected] Prof. W. Vandervorst Kapeldreef 75, B-3001 Leuven, Belgium tel 32 16 281 286 E-mail: [email protected] Prof. Rainer Waser Research Center Juelich 52425 Juelich, Germany Phone: +492461615811 E-mail: [email protected] Prof. Sean Washburn Dept Physics and Astronomy Univ North Carolina at Chapel Hill Chapel Hill, NC 27599-3255 Prof. Daniel van der Weide Department of Electrical & Computer Engineering University of Wisconsin 1415 Engineering Dr Madison WI 53711, USA Phone: 608-265-6561 Fax: 815-371-3407 E-mail: [email protected] http://vdw.ece.wisc.edu Prof. Paul S. Weiss Department of Chemistry and Physics

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104 Davey Laboratory The Pennsylvania State University University Park, PA 16802-6300, USA Phone: +1 (814) 865-3693 Fax: +1 (814) 863-5516 E-mail: [email protected] http://www.nano.psu.edu/ J.K. White Bookham 10 Brewer Hunt Way Ottawa, Ontario J. Williams Department of Chemistry North Carolina State University 314 Dabney Hall Raleigh, NC 27695-8204 Prof. Wulf Wulfhekel Physikalisches Institut Universit¨at Karlsruhe Wolfgang Gaede Strasse 1 76131 Karlsruhe Germany Phone: +49-721-6083440 Fax: +49-721-6086103 E-mail: [email protected] Dr. M. Xu Kapeldreef 75, B-3001 Leuven, Belgium Phone: 32 16 288 024 E-mail: [email protected]

About the Editors

Sergei Kalinin is currently a research staff member at the Oak Ridge National Laboratory, Materials Sciences and Technology Division and Center for Nanophase Materials Science. He completed his Ph.D. in Materials Science at the University of Pennsylvania in 2002 (with Prof. Dawn Bonnell). His previous undergraduate and graduate work in Materials Science was conducted at Moscow State University, Moscow, Russia. The focus of his current research interests is interplay between electromechanical, transport, and mechanical phenomena in inorganic and biological systems using local probes. He serves as a member of American Vacuum Society NSTD board and member of editorial board for Journal of Nanoelectronics and Optoelectronics. As a student, he earned multiple research awards including American Vacuum Society Graduate Student Award and several Materials Research Society Graduate Student Awards. He was recognized with the Ross Coffin Purdy Award of American Ceramics Society (2003) for the development of Scanning Impedance Microscopy for characterization of frequency-dependent transport on the nanoscale. He is also a recipient of Wigner Fellowship of Oak Ridge National Laboratory (2002) and an Oak Ridge National Laboratory Early Career Accomplishment Award for Science and Technology (2005). He has authored more than 70 scientific papers, six book chapters and five patents on various aspects of SPM.

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About the Editors

Alexei Gruverman is currently a Research Associate Professor in the Department of Material Science and Engineering, North Carolina State University. He received his PhD degree in Solid State Physics from the Ural State University in Russia. After graduation, he worked as a postdoctoral researcher at the Joint Research Center for Atom Technology (JRCAT), Japan, where he initiated a project on scanning probe microscopy studies of ferroelectrics. He then joined Sony Corporation to work on the problems related to characterization and reliability of ferroelectric memory devices by SPM. In 2000, he joined the faculty at North Carolina State University. He has published over 80 articles in refereed journals, several book chapters and edited one book. His current research interests are in the field of ferroelectric nanostructures and thin films, nanoscale phenomena in ferroic materials, mechanical properties of biomaterials and non-volatile information storage technologies. He is a recipient of the Ikeda Award (2004) for contribution to SPM studies of ferroelectrics.

Introduction Scanning Probe Microscopy Techniques for Electrical and Electromechanical Characterization S.V. KALININ AND A. GRUVERMAN

Progress in modern science is impossible without reliable tools for characterization of structural, physical, and chemical properties of materials and devices at the micro-, nano-, and atomic scale levels. While structural information can be obtained by such established techniques as scanning and transmission electron microscopy, high-resolution examination of local electronic structure, electric potential and chemical functionality is a much more daunting problem. Local electronic properties became accessible after the development of Scanning Tunneling Microscopy by G. Binnig and H. Rohrer in 1981 at IBM Zurich 25 years ago—an invention that earned its authors the Nobel Prize in Physics five years later [1]. Based on the quantum mechanical tunneling between an atomically sharp metallic tip and conductive surface, scanning tunneling microscopy (STM) has become the first instrument to generate real-space images of surfaces with atomic resolution and has triggered development of new classes of STM-related techniques. In 1986, Binnig, Quate, and Gerber demonstrated atomic force microscope (AFM) based on the mechanical detection of the Van der Waals forces between the tip and the surface using a pliable cantilever [2]. It was almost immediately realized that AFM could be extended to map forces of various types, such as magnetic and electrostatic forces, as well as for probing chemical interactions. This dual capability of probing currents and forces at the nanometer and atomic level has led to a rapid growth of a variety of scanning probe microscopy (SPM) techniques over the last two decades. Techniques such as AFM, magnetic force microscopy (MFM), electrostatic force microscopy (EFM), scanning capacitance microscopy (SCM), near-field scanning optical microscopy (NSOM), and others have emerged to provide capability to access local electrical, magnetic, chemical, mechanical, optical, and thermal properties of materials on the nanometer scale. It has been demonstrated that the SPM approach allows not only imaging, but also control and modification of the local structure and material functionality at the nano- and atomic level. As a consequence, the last two decades have witnessed an explosive growth in application of SPM techniques in a wide spectrum of fields of science, ranging from condensed matter physics, chemistry and materials science to medicine and biology. It will not be an exaggeration to say that the rapid development of nanoscience and nanotechnology in the last two decades was strongly 1

2

Introduction

stimulated by the availability of SPM techniques, and in turn constantly stimulates development of novel SPM probes. In parallel with the development of ambient SPM techniques, a significant progress was achieved in the development of high-resolution ultrahigh vacuum (UHV) SPM systems. Compared to ambient systems, UHV operation imposes major difficulties in the sample preparation and microscope operation. However, it provides a potential for true atomic resolution imaging both in STM and AFM modes. STM sensitivity to local electronic properties provided physicists with the tool to probe electronic phenomena such as edge states in quantum Hall systems, phase separation and charge ordering in strongly correlated oxides, and transport in mesoscopic conductors. In the context of surface science and catalysis, the capability to probe chemical and photochemical processes on the atomic level have emerged. Many ambient electrostatic and electromechanical probes can be implemented in UHV conditions as well. As such, UHV SPM paves the way to the investigation of fundamental electrical and mechanical properties of materials at the atomic level. One of the primary challenges in the SPM applications to local electrostatic and electromechanical phenomena is quantitative analysis of the acquired signal. Indeed, a typical SPM image, were it a surface potential map, electromechnical activity map, capacitance distribution or a gate potential image, provides a quantitative measure of local surface properties. However, image formation mechanisms in most SPM techniques are extremely complex due to the geometry of tipsurface system and multitude of contributing interactions. For example, noticeable progress in understanding such well-established topographic imaging techniques as non-contact AFM or intermittent contact AFM was achieved only in the last few years. The problem of quantitative interpretation of the local property map is even more difficult; further progress requires thorough understanding of the image formation mechanisms through combination of first-principles methods to describe atomistic processes at tip-surface junction, continuum mechanics, and electrostatics to describe long-range interactions and cantilever dynamics. However, once achieved, this transforms SPM from a mere imaging tool into a quantitative probe of local physical phenomena on the nanoscale, realizing an age-old dream of precise measurements of physical and chemical properties on nanometer, molecular, and ultimately atomic levels. Tremendous growth in SPM instrumentation, theory, and applications have resulted in a large number of monographs, books, and reviews addressing general aspects of SPM [3–12], including STM studies of atomic structure and electronic phenomena [13–16], electrochemical SPM [17], theoretical aspects of AFM [18] and STM [19], nanofabrication [20], application of SPM in biology and bioengineering [21–24]. However, there is a long-due need to bring together a permanently growing knowledge base on the practical and theoretical aspects of advanced electrical and electromechanical SPM techniques. The goal of this book is to provide a comprehensive reference on the nanoscale characterization of electrical and mechanical properties of functional materials by SPM techniques and to make readers aware of tremendous developments in the field in the last decade. This

Introduction

3

book provides a link between well-established ambient SPM techniques and UHV SPM, materials and device applications, and theoretical basis for interpretation of SPM data. While a number of SPM techniques have been used in a variety of scientific fields ranging from semiconductors to ferroelectrics to optics, in this book various aspects of these techniques will be presented on an interdisciplinary basis. By bringing together critical reviews written by the leading researchers from the different scientific disciplines relevant information will be conveyed that will allow readers to learn more about the fundamental and technological advances and future trends in the different fields of nanoscience. The book comprises 35 chapters divided into four parts. Part I introduces the reader to the technical and instrumental features of SPM techniques for electrical, electromechanical, transport, near-field optical and microwave characterization. Part II deals with the SPM imaging at the resolution limit in molecular systems, complex oxides, and low-dimensional structures, as well as theoretical underpinnings of SPM. Part III illustrates application of SPM to electrical and electromechanical characterization of a broad spectrum of materials ranging from semiconductors to polymers to biosystems. Finally, Part IV discusses SPM-based devices and nanofabrication methods. Chapter I.01 by A. P. Baddorf reviews technical aspects of Scanning Tunneling Potentiometry (STP), an extension of STM to transport measurements. The chapter discusses applications of STP to probe mesoscopic transport in low-dimensional systems, defect-induced scattering, and transport tin phase-separated strongly correlated oxides. Further prospects of transport imaging with nanometer and atomic resolution are discussed. Chapter I.02 by P. Eyben et al., discusses implementation, probe choice, calibration, and theoretical aspects of Scanning Spreading Resistance Microscopy, the technique that has emerged as one of the primary tools for dopant profiling and device characterization and failure analysis on the nanoscale. Chapter I.03 by J. Kopanski discusses principles of SCM and its application to electrical characterization of semiconductors and dielectric films, integrated circuit failure analysis, quantitative dopant profiling, and optical pumping for carrier mobility measurements. Chapter I.04 by T. Glatzel et al., discusses Kelvin Probe Force Microscopy (KPFM), introduces principles of amplitude and frequency detection in KPFM and relevant theory. The chapter describes in detail resolution theory and probe function determination in KPFM, paving the way for quantitative measurements of electrostatic surface potentials, photovoltaic phenomena, and work function distributions. Chapter I.05 by O’Hayre et al introduces two SPM techniques for probing frequency-dependent transport at the nanoscale. Nanoimpedance microscopy is a current-based technique combining conventional impedance spectroscopy with AFM. Scanning Impedance Microscopy (SIM) is a force-based technique in which AFM probe detects amplitude and phase of local voltage oscillations induced by lateral periodic bias applied through macroscopic electrodes. These methods are similar to conventional 4-probe resistance measurements, in which AFM tip is used as a moving electrode, providing advantage of high spatial resolution. Piezoresponse Force Microscopy (PFM) and its application for imaging, spectroscopy, and manipulation of ferroelectric domains are

4

Introduction

reviewed in Chapter I.06 by Kholkin et al. The chapter briefly discusses principles and image formation mechanism in PFM, as well as its application to imaging of polar nanodomains in ferroelectric relaxors, high-density data storage, and ferroelectric capacitor characterization. Near-Field Microwave Microscopy is described in Chapter I.07 by Anlage et al. The authors review the basic concepts of nearfield interactions between a source and sample, present a historical overview and discuss quantitative approaches to interpretation of near-field microwave images. Chapter I.08 by A. Bouchelier and R. Bachelot discusses implementation and application of apertureless Near Field Optical Microscopy and related techniques. The tip enhancement of electromagnetic field allows imaging and spectroscopy of optical phenomena on the length scales well below optical wavelength. Application of SPM techniques to the study of electrochemical interfaces is discussed in Chapter I.09 by T. Smith and K. Stevenson. These techniques include Electrochemical Scanning Tunneling Microscopy (EC-STM), Electrochemical Atomic Force Microscopy (EC-AFM), and hybrid techniques such as Scanning Electrochemical Microscopy - Atomic Force Microscopy (SECM-AFM) and Local Electrochemical Impedance Spectroscopy - Atomic Force Microscopy (LEIS-AFM). Application of electrochemical SPM in the emerging areas of energy storage and conversion, corrosion, catalysis, and electrochemical deposition processes are described. Recent theoretical and instrumental developments in high-frequency near field probes are reviewed in Chapter I.10 by C. Paulsen and D. Van der Weide, providing a unified description of a broad range of optical, infrared, and microwave probes. The chapter also provides a theoretical framework for the interpretation of near-field experiments, as well as extensive literature survey and discussion of future potential of these techniques. Part II of the book combines a number of reviews on experimental and theoretical aspects of fundamental electrical and electromechanical phenomena on the nanoand atomic scales and describes the recent instrumental and theoretical advances in high-resolution imaging of electrical, transport, and electromechanical properties on surfaces, low-dimensional systems, nanotubes and nanowires, and molecules. In Chapter II.01, M. Morgenstern describes applications of STM and AFM for probing transport phenomena in 2D electron systems in high-mobility III-V semiconductors. Imaging nanomagnetic and spin structure of materials with nanometer and atomic resolution by Spin–polarized STM (SpSTM) is described in chapter II.02 by W. Wulfhekel et al. Probe fabrication, one of the key components for successful SpSTM experiment, is discussed in detail. The principles and advantages of constant-current, spectroscopic, and differential magnetic modes of SpSTM are discussed. The applications for imaging ferromagnetic and antiferromagnetic surfaces of bulk materials and thin-film systems are illustrated. Approaches for fabrication and probing of molecular electronic devices are described in Chapter II.03 by K. Kelly and P. S. Weiss. Self-assembled monolayers are utilized to isolate molecules with various electronic properties to determine the fundamental transport mechanisms, and the relationships between molecular structure, environment, connection, coupling, and electrical functionality. STM of individual conjugated molecules inserted in alkanethiol SAM illustrates a rich gamut of electronic

Introduction

5

behavior, including reversible conductance switching. SPM imaging and control of charge transport in individual carbon nanotubes and carbon nanotube networks are discussed in Chapters II.04 and II.05. In Chapter II.04, C. Staii et al., discuss the application of Scanning Gate Microscopy (SGM), EFM, SIM, and thermal SPM to probe electronic structure of individual defects in carbon nanotube circuits. Applications of high-frequency SGM and SIM and memory effects in nanotube circuits are presented. In Chapter II.05, M. Stadermann and S. Washburn describe the application of conductive SPM to networks of carbon nanotubes to map current paths and differentiate semiconducting and metallic nanotubes, as well as to probe conductance decay at nanotube junctions. In Chapter II.06, V. Meunier and P. Lambin apply a density functional theory to model STM images of carbon nanotubes and grain boundaries in graphene. The transport properties of single-wall nanotubes and tip-tube interactions in SGM and EFM are modeled using non-equilibrium Green’s function theory. In Chapter II.07, S. Hasegawa discusses instrumentation and application of multiple-probe STM for surface transport studies. Precise positioning of conductive tips allows probing conductance through step edges and orientation dependence of conductance. Ultimately, this technique is being developed as a probe of a surface transport Green’s function. Principles and application of Dynamic Force Microscopy (DFM), also referred to as Non-Contact Atomic Force Microscopy, are described in Chapter II.08 by U. Schwarz and H. H¨olscher. Application of DFM for atomic-resolution imaging of conductors, semiconductors, and insulators are described. DFM probing of surface electrostatic properties including charge distributions around charged monoatomic vacancies and individual doping atoms in semiconductors are illustrated. Application of high-resolution STM to probe atomic and electronic structure and electronic inhomogeneities in manganites are described in Chapter II.09 by C. Renner and H. Ronnow. These studies illustrate the impact high-resolution probes can have on understanding the fundamental physical phenomena in strongly-correlated complex oxides including manganites, cuprates, and relaxors. Part III includes a series of reviews on application of ambient SPM techniques for characterization of transport, electromechanical, optical, and electrical phenomena in materials, heterostructures, and devices. A number of topics, such as transport in semiconductor optoelectronic and electronic structures, imaging and quantification of electroactive grain boundaries, dislocations and interfaces, electromechanical imaging of biological systems, and photovoltaic phenomena in photosynthetic molecules are covered. In Chapter III.01, S. Kuntze et al., describe application of Scanning Voltage Microscopy (SVM) and Scanning Differential Resistance Microscopy (SDRM) for in-situ imaging of operational electronic devices. Examples include direct observation of the current blocking breakdown in a buried heterostructure laser, effect of current spreading inside actively biased ridge waveguide lasers, origin of anomalously high series resistance encountered in ridge lasers and electron over-barrier leakage. Instrumentation and imaging mechanisms in SVM and SDRM are discussed and sources of artifacts (such as circuit time constants and photocurrent) are analyzed. Chapter III.02 by I. Lee and E. Greenbaum describes application of KPFM and EFM to probe photovoltaic activity in

6

Introduction

Photosystem I (PSI) reaction centers, DNAs, protein microarrays on surfaces, and PSI at the air–liquid interfaces, providing insights into fundamental mechanisms of photosynthesis. In Chapter III.03, A. Gruverman et al., describe application of Piezoresponse Force Microscopy (PFM) to probe the structure of biomaterials with nanometer scale spatial resolution, utilizing ubiquitous presence of piezoelectricity in biopolymers. Examples of bioelectromechanical imaging include human tooth, femur canine cartilage, deer antler, and butterfly Vanessa Virginiensis wing scales. A potential of PFM to study the internal structure and orientation of the protein microfibrils is illustrated. Application of SCM for failure analysis of semiconductor devices, carrier dynamics in FET channel during device operation, and visualization of radiation effects are described in Chapter III.04 by C. Nakakura et al. Extensive practical experimental details and a broad range of examples render this chapter extremely useful for SCM practitioners. Application of KPFM for local studies of surface band bending, defects, and grain boundaries in semiconductors are presented in Chapter III.05 by Rosenwaks et al. This chapter also reviews recent KPFM studies of local electronic phenomena in quantum wells and organic light-emitting devices, and develops KPFM framework for spectroscopic studies of surface states. Chapter III.06 by B. Rodriguez et al., summarizes recent applications of SPM to nanoscale studies of the electric properties of III-nitride thin films, bulk crystals and heterostructures. The chapter illustrates the complementary application of techniques such as KPFM, conductive AFM, and PFM to probe charge defects and inversion boundaries in these materials. Measurement of surface polarity and the screening mechanism of III-nitrides using SPM and Photoelectron emission Microscopy are discussed. In Chapter III.07, S. Cohen gives a broad perspective on electron flow in molecular systems. This research is motivated by advent of molecular electronics, drive to understand a charge transfer in biological systems, and functionality and performance bottlenecks in devices such as organic light emitting diodes and dye-sensitized solar cells. SPM measurements of electron flow through DNA and STM measurements of isolated molecules on a semiconductor surface are discussed in detail. The principles and instrumentation for local conductance imaging of perovskite thin films are discussed in Chapter III.08 by C. Szot et al. Imaging of conductive paths in insulating oxides provides real-space information on electrical activity of defects and dislocations. The role of surface adsorbates on electrical and PFM imaging is discussed. In Chapter III.09, T. Ishida et al., describe methods for evaluating the electric properties of conjugated molecules embedded in alkanethiol SAMs, including electrical conduction and barrier height measurements of SAMs and single molecules using STM and conductive AFM. Finally, in Chapter III.10, W. Silveira et al., review application of high-sensitivity EFM to probe charge transport and local electronic properties in organic electronic devices. Instrumentation and contrast formation in EFM are also described in detail. Part IV of the book is devoted to the SPM-based devices and nanofabrication methods. In Chapter IV.01, N. Naujoks et al., describe application of charge lithography for fabrication of nanostructures. In this method, charged patterns deposited by an AFM tip are used to attract oppositely charged nanoparticles, resulting in

Introduction

7

a stable deposited pattern. Nano-oxidation of semiconductor and metal surfaces is described in Chapter IV.02 by J. Dagata. The author introduces the method, describes relevant technical and theoretical details, and discusses the potential and limitations of this nanofabrication technique. Nanofabrication on the atomic level is introduced in Chapter IV.03 by P. Albrecht et al. Development of the atomic-resolution hydrogen resist technique and its application to the templated self-assembly of molecular systems on silicon are described. A mechanism of tipinduced desorption is determined through isotope studies. An integration of carbon nanotubes with silicon and the III-V compound semiconductors is explored. Ferroelectric lithography is described in Chapter IV.04 by D. Li and D. Bonnell. Several methods, including contact electrode, SPM, and e-beam are used to pattern domains on ferroelectric surfaces in the absence of a top electrode. The domain specific reactivity in metal photodeposition process and domain patterning are combined into a fabrication process that is demonstrated for several classes of magnetic and optoelectronic nanostructures. Chapter IV.05 by M. Lewis et al. introduces several methods of nanopatterning in SAM systems. Additive, subtractive, and exchange approaches for SAM lithography are described. Finally, in Chapter IV.06, S. Hong and N. Park describe application of resistive SPM probes for data storage in ferroelectric medium, potentially opening the pathway for Tbit density storage. Overall, the book is intended to present a unified outlook on all aspects of modern electrical and electromechanical probes and combine practical and theoretical aspects of these techniques and applications ranging from fundamental physical studies to device characterization and failure analysis to nanofabrication. We hope that this book will develop new educational advances by helping students and postdoctoral scientists significantly improve their knowledge on the new applications of SPM and on the nanoscale properties of a number of functional materials, such as electroactive polymers, biomolecules, piezoelectrics, and so on. It is our expectation that with SPM becoming a must-know technique in many scientific disciplines, this book will become a valuable source of information for interdisciplinary research that can be used as a reference handbook.

References 1. G. Binnig, H. Rohrer, Ch. Gerber, E. Weibel, Phys. Rev. Lett. 49, 57 (1982); Phys. Rev. Lett. 50, 120 (1983). 2. G. Binnig, C. F. Quate, Ch. Gerber, Phys. Rev. Lett. 56, 930 (1986). 3. D. A. Bonnell (Ed.), Scanning Probe Microscopy and Spectroscopy: Theory, Techniques and Applications. 2nd Edn, Wiley VCH, New York, 2000. 4. R. Wiesendanger (Ed.), Scanning Probe Microscopy and Spectroscopy-Methods and Applications, Cambridge University Press, Cambridge UK, 1994. 5. G. Friedbacher, H. Fuchs, Classification of Scanning Probe Microscopies—(Technical Report), Pure and Appl. Chem. 71, 1337 (1999). 6. L. Bottomley, “Scanning Probe Microscopy,” Anal. Chem., 70, 425R-475R (1998). 7. E. Meyer, Atomic Force Microscopy: Fundamentals to Most Advanced Applications, Springer-Verlag New York, November 2003.

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8. A. De Stefanis, A. A. G. Tomlinson, Scanning Probe Microscopies: From Surfaces Structure to Nano-Scale Engineering, Trans Tech Publications, April 2001. 9. E. Meyer, H. J. Hug, R. Bennewitz, Scanning Probe Microscopy: The Lab on a Tip, Springer 2003. 10. B. Bhushan, H. Fuchs (Eds.), Applied Scanning Probe Methods II: Scanning Probe Microscopy Techniques, Applied Scanning Probe Methods III: Characterization, Applied Scanning Probe Methods IV: Industrial Applications, Springer, 2006. 11. R. J. Colton, A. Engel, J. E. Frommer et al. (Eds.), Procedures in Scanning Probe Microscopies, John Wiley, 1998. 12. M. T. Bray, S. H. Cohen, M. L. Lightbody (Eds.), Atomic Force Microscopy/Scanning Tunneling Microscopy, Springer, 1995. 13. R. Wiesendanger, H. J. Guntherodt (Eds.), Scanning Tunneling Microscopy III: Theory of STM and Related Scanning Probe Methods (Springer Series in Surface Sciences), Springer, 1997. 14. C. Bai, Scanning Tunneling Microscopy and Its Application (Springer Series in Surface Sciences), Springer, 2000. 15. W. Hofer, A. Foster, A. Shluger, “Theories of Scanning Probe Microscopes at the Atomic Scale,” Rev. Mod. Phys. 75, 1287 (2003). 16. S. Morita, R. Wiesendanger, E. Meyer (Eds.), Noncontact Atomic Force Microscopy, Springer Verlag, 2002. 17. A. J. Bard, M. V. Mirkin, Scanning Electrochemical Microscopy (Monographs in Electroanalytical Chemistry and Electrochemistry Series), CRC Press, 2001. 18. R. Garcia, R. Perez, “Dynamic Atomic Force Microscopy Methods,” Surf. Sci. Rep., 47, 197–301 (2002). 19. A. Foster, W. Hofer, Scanning Probe Microscopy: Atomic Scale Engineering by Forces and Currents (NanoScience and Technology), Springer, 2006. 20. H. T. Soh, K. W. Guarini, C. F. Quate, Scanning Probe Lithography (Microsystems, Volume 7), Kluwer Academic Publishers, 2001. 21. B. P. Jena, J. K. H. Horber (Eds), Atomic Force Microscopy in Cell Biology (Methods in Cell Biology, Volume 68), Academic Press, 2002. 22. V. J. Morris, A. P. Gunning, A. R. Kirby, Atomic Force Microscopy for Biologists, World Scientific publishing, 1999. 23. P. C. Braga, D. Ricci (Eds.), Atomic Force Microscopy: Biomedical Methods and Applications (Methods in Molecular Biology), Humana Press, 2003. 24. Vladimir Tsukruk (Ed.), Advances in Scanning Probe Microscopy (Macromolecular Symposia 167), John Wiley & Sons, 2001.

I SPM Techniques for Electrical Characterization

I.1 Scanning Tunneling Potentiometry: The Power of STM applied to Electrical Transport A. P. BADDORF

The introduction of scanning tunneling microscopy (STM) followed by scanning tunneling spectroscopy (STS) opened experimental access to the geometric and electronic structure of materials on an atomic scale and essentially ushered in the modern field of nanoscience. The goal of scanning tunneling potentiometry (STP) is to adapt the scanning tunneling probe to measure electrical transport on the same length scale. The approach is to establish a current laterally in the sample, then to map the voltage locally by determining the tip bias that produces no tunneling at each point. The technique is similar to the macroscopic four-probe method commonly adopted for measuring electrical transport, with the inner two probes replaced by a scanning tunneling tip. This chapter describes principles, reviews approaches, and illustrates capabilities of STP.

1 Introduction The link between the nanoscale and the human scale, be it quantum computing, nanomechanics, or nanotube devices, is almost always by electrical current. In today’s world, where electronic devices proliferate, the fundamental and practical importance of understanding electronic transport in nanoscale devices is immense. Milestones in condensed matter physics which have the greatest potential to impact the world are often associated with discovery of novel electronic transport phenomena, frequently encountered in materials of nanometer length scales and reduced dimensionality. Examples abound, not the least of which date back to the birth of the transistor, or more recently high Tc superconductivity, giant magnetoresistance, and superconducting quantum interference devices (SQUID). Tools that can measure electrical conductivity at these small length scales are needed to understand the mechanisms of transport and to take full advantage of our modern electronics oriented world. The invention of scanning tunneling microscopy (STM) by Gerd Binnig and Heinrich Rohrer [1] in 1981 at IBM Zurich (1986 Nobel Prize) opened the way to exploration of electronic states and transport with atomic resolution. In STM, a voltage is applied between a conducting tip and surface, and the current between the 11

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two is measured. (Conducting here simply means sufficient electron mobility that the current limitation comes from the tunneling gap. With very low currents, STM imaging can be performed on quite high resistance materials.) As the tip is brought closer to the surface, tunneling of the electrons through the gap produces a current before the two physically touch. Because this is a quantum mechanical process through a barrier where the electrons cannot stay, the current is exponentially dependent on the gap distance. This strong dependence on tip distance makes the current quite suitable for feedback, i.e., to maintain a constant tip-surface separation electronically. By scanning the tip, usually by deflection of piezoelectric materials, and monitoring the tunneling current, a topographical map of the surface is obtained [2]. In reality a STM image is much more complex and rich with information. Scanning with a constant current is not actually a map of the atomic topography, but more correctly a map of the electronic overlap between tip and substrate, which determines the tunneling current. For an ideal tip this provides a map of the electronic states of the substrate, often, but not always, related to the geometric structure. Exceptions led to early mistakes in structural models, for example, the “definitive” identification of p(2 × 1)O/Cu(110) as a buckled row structure [3]— later shown to be an added row [4]—or the interpretation of STM images of (2 × 3)N/Cu(110) as a missing row [5]—later shown to be a compressed, buckled row [6]. An imperfect tip can further complicate interpretation by introducing multiple tunneling sources (a double tip) or directional tunneling from p, d, or f electronic orbitals. Imaging of electronic states is not ideal for those interested predominantly in atomic arrangement, but it is ideal if you want to know where the electrons are and what they are doing, for example, in order to study chemical bonding or conductivity. Even conventional STM can provide extraordinary information on the local electronic levels at a surface, particularly through measurements of current versus tip-surface voltage (I-V) at individual tunneling sites. I-V measurements are closely related to local transport properties when the dependence is determined at voltages near the Fermi energy, E f . Electrical conductivity requires electron density at E f and available states just above E f to allow movement of charge. Insulators or poor conductors will show a gap, equivalent to an I-V curve with near zero slope at E f . It is not surprising that soon after the invention of the STM, other IBM Zurich researchers modified the technique to measure spatial distributions of electric potential. Paul Muralt, then a postdoctoral scientist, and Dieter W. Pohl published the first description of this modification in 1986 and named the new technique “scanning tunneling potentiometry,” or STP [7]. The addition to conventional STM that is central to STP is a voltage bias along the surface of the sample. A schematic of the STP setup is shown in Figure 1. As the tip is scanned along the surface the tunneling current becomes highly sensitive to the local tip-surface voltage difference; since the tip voltage is known, a map to the surface voltage can be obtained. Of course, variations in tunneling current due to surface topography must

I.1. Scanning Tunneling Potentiometry

13

FIGURE 1. Schematic illustration of the STP technique, which combines a lateral voltage across the sample with an STM for imaging of the local surface topography and potential.

be distinguished from those due to the lateral voltage drop. Approaches to make this distinction will be discussed below.

2 STP Technique 2.1 Sample Conditions For conventional detection electronics and tunneling equipment, voltages must be limited to the order of tens of volts to avoid arcing and to protect sensitive amplifiers. Across a typical 1-cm sample, 10 V corresponds to 1 mV/µm or 1 µV/nm. With a typical G
tunneling resistance, a uniform conductor would require equipment with a sensitivity of 1 pA/µm or 1 fA/nm. A femtoamp precision is too demanding for common STP circuitry, but a pA is certainly achievable. One solution that can provide a greater lateral resolution is to study smaller samples, for example, to lithographically create electrodes to apply the lateral voltage across a few tens of microns. Another solution is to study materials that are not uniform, so that much larger voltage drops and corresponding tunneling current contrasts are observed at boundaries or defects of interest. However, sensitivity to small current changes can still be a limiting factor in STP spatial resolution. For good conductors, even 10 V/cm is too large to maintain. A 1-cm-long copper sample with 1-mm-diameter cross section will draw a little over a 1,000 A with application of 10 V, and sample heating could be a problem! This illustration reveals the need for relatively high resistance samples in STP to maintain a sufficient voltage drop across the sample. To minimize current and sample heating, sample resistances should be well over 100
. At the same time, STP’s foundation on tunneling current requires a non-insulating sample, with resistivity well beneath a typical tunneling resistance of a G
. Appropriate samples include semiconductors, poor metals, thin films, and nanometer structures. By reducing the dimensions of the conductor, quite high current densities become possible. For example in

14

A. P. Baddorf FIGURE 2. Illustration of a possible source of artifacts in STP due to the finite size of the tip. Reprinted with permission from A. D. Kent et al. [9]. Copyright 1990, AVS The Science & Technology Society.

Tip

Surface Potential V

Topographic Image z

Potentiometric Image V x

˚ on InP-based multilayers, studying Bi films with thicknesses between 20 and 30 A Briner et al. [8] reported current densities up to 8 × 106 A/cm2 , avoiding sample heating since the total current was under 0.5 A. One additional sample requirement should be noted. As with topographical STM measurements, the sample should be flat in comparison to the tip radius. Otherwise, the tip tunneling will abruptly jump from one area on the surface to another during scanning. This effect is well known in topographical studies and leads to a loss of detail or resolution in the image. In potentiometric measurements, the opposite occurs. Instead of loss of detail, new, unwanted features are added to the image, specifically abrupt discontinuities in the electrical potential. The mechanism for this is shown in Figure 2, with the top panel illustrating a geometry where the tunneling location will jump and the middle and bottom panels showing the results in topographic and potentiometric scans. Such discontinuous voltage jumps were observed in early STP studies of evaporated Au films [9] and were the focus of a publication by Pelz [10] in the same year.

2.2 Distinguishing Topography and Voltage A key to scanning tunneling potentiometry is discrimination between the surface topography and the lateral voltage applied along the surface of the sample. The only parameter measured by STM is the current through the tip, which is a function of both the sample-tip separation and the voltage difference. A simple measurement of tip current cannot distinguish between changes in the sample distance (topography) and voltage (potentiometry). An abrupt change in the tunneling current in a scan could imply either the presence of a physical step or a voltage step, for example,

I.1. Scanning Tunneling Potentiometry

15

at a grain boundary. In principle, topography and voltage can be distinguished by analyzing the dependence of the tunneling current on the tip-surface separation; in a simple model, tunneling current has a contribution exponential in the tipsurface separation but only proportional to the voltage difference. In practice this approach is too time consuming and complicated, and the accuracy is dependent on the electronic density of states in the tip and surface. Three approaches have succeeded in separating signals from topography and potentiometry. The first, used in the original experiments by Muralt et al. [7,11], observes tunneling current at two frequencies which can be distinguished using lock-in technology. For simplicity, one of these tunneling currents is taken at zero frequency, i.e., dc. With this approach the topography and potentiometry signals are measured simultaneously. The second approach, introduced by Feenstra and coworkers [12], uses an interrupted feedback, first measuring the surface topography, and then retracing that topography with the feedback off to determine the potentiometry. The third approach has found limited application, but proof-ofprinciple has been demonstrated by M¨oller et al. that tunneling noise can be used as feedback for surface topography, leaving tip voltage to determine potentiometry. The following sections will discuss these three approaches in more detail. 2.2.1 Simultaneous ac and dc Feedback A rather elegant solution to distinguish topography and potentiometry while measuring only a single parameter, tunneling current, was introduced by Muralt and Pohl in 1986 and improved later by several groups. The idea is to separate tunneling current due to topography from potentiometry by using ac current to control the tip-surface separation and dc current to identify the voltage drop across the sample. The two can be separated electronically in the feedback loop using a lock-in amplifier. A schematic of the apparatus used at the Indian Institute of Science [13– 15] for simultaneous ac and dc feedback is shown in Figure 3. An ac bias, Vac , is applied to the entire sample (actually both contacts) while a dc bias, Vdc , is applied across the sample surface. Both voltages produce tunneling current through the tip; however, the lock-in amplifier on the right isolates the ac signal to provide height feedback to the STM Z piezo and topographical information. The tunneling signal is simultaneously fed to an integrator, where the ac component is averaged away, leaving the dc signal, which represents the tunneling due to the local potential due to the lateral dc bias. The integrator serves two other functions. The first is to feed back a dc voltage to the sample that nulls the dc tunneling current. The voltage is applied to both ends of the sample (through both adding operational amplifiers in Figure 3) so the dc voltage across the sample remains Vdc . The second function of the integrator is to report the voltage required to null the dc tunneling current; this is the local potentiometry voltage below the tip. This approach, where the tunneling current is nulled by adjusting the potential, is reminiscent of an impedance bridge and provides high sensitivity to small variations. Simultaneous ac and dc feedback has clear advantages of simplicity and of a constant tunneling resistance. In practice, however, the two signals cannot be

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FIGURE 3. Schematic of STP using simultaneous ac and dc feedback as implemented at the Indian Institute of Science. Reprinted with permission from G. Ramaswamy et al. [15]. Copyright 1998 Springer-Verlag.

entirely separated, which may limit the voltage sensitivity. Kirtley and Washburn [16] and also Pelz and Koch [17] have pointed out that when scanning, the tunneling resistance undergoes large, broadband fluctuations because of finite gain and instability of the feedback electronics. These fluctuations will appear as broadband current noise in the tunneling and, although generated by the ac topography signal, will mix into the low-frequency signal interpreted as surface potential. Ramaswamy et al. [15] found that current noise was a practical limitation in their voltage measurements. However, with “somewhat critical adjustments of different time constants” in the lock-in and integrator circuits, which had to be different by a factor of 5–7, they were able to resolve chemical potential to 100 µeV, finally achieving the limit of their 16-bit analog-to-digital converter. 2.2.2 Interrupted Feedback The interrupted-feedback approach to separating topographic and potential signals in STP has its origins in the “sample and hold” technique of Feenstra and

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coworkers [12]. The “sample and hold” method was developed to measure I-V curves accurately in scanning tunneling spectroscopy. First topology, or tip height for a single point, is determined in the usual way, with the feedback loop to the z piezo active. The feedback loop is then interrupted and the tip (or sample) bias used for topographic scanning switched off. With the tip held at a fixed position, I-V characteristics are quickly measured before drift becomes significant. Adaptation of the “sample and hold” method to potentiometry is straightforward and was adopted by Kirtley et al. in 1988 [16]. Again the main distinction in STP is a voltage applied laterally along the sample surface. To cycle the voltage between the sample and tip, the tunneling bias is applied as a square-wave. In the portion of the cycle when the sample-tip voltage is high, the feedback to the z piezo is active and the surface topography determined. When the square-wave voltage is zero, the feedback loop is interrupted and the tip position fixed. The remaining tunneling current is dependent on the local potential of the surface due to the laterally applied voltage and can be used to create a potential map. As described, the local potential of the surface should be small compared to the square-wave voltage so it contributes little to the topographic image. This is readily accomplished by using a bridge, so that the potential across the surface remains arbitrarily large, but the local potential under the tip is close to zero, but still dependent on lateral position. The inset in Figure 4 illustrates this bridge, with Vs the lateral voltage for potentiometry and the tip bias voltage Vb referenced to a fraction of Vs so that the local voltage under the tip is close to zero.

FIGURE 4. (A) Scanning electron microscope image showing the STM tip on a 20-µm patterned line. (B) Typical I-V curve showing the interpolation of the local potential Vloc value. The inset shows the circuitry used to reduce the voltage under the tip to near zero. Reprinted with permission from B. Grevin et al. [19]. Copyright 2000 by the American Physical Society.

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The interrupted feedback technique was further refined in the middle of the 1990’s by the IBM group of Feenstra [8,18]. This advance was made practical by faster data acquisition and computers. These groups realized that more precise measurements of the local voltage could be obtained by measuring complete I-V curves rather than simply measuring the residual tunneling current when the feedback is interrupted. Panel B of Figure 4 shows a typical I-V curve for potentiometry. The curve does not pass through the origin, since the local voltage under the tip is not zero. The x-intercept, where the measured tunneling current is zero, corresponds to the local voltage. In Figure 4 this point is labeled Vloc . Noise in the data requires a fit to the data to extract the voltage value and is a major source of error. Grevin et al. [19] averaged 50 spectra to find the zero current value. The width of the I-V scan and nature of the fit varies widely in different applications, ranging from ±5 mV with a linear fit in the work of Kent on YBa2 Cu3 O7−x superconductors [9] to ±650 mV and a third-order polynomial fit in a study of Bi films by Briner et al. [8]. In 2002, Feenstra’s group extended this approach to include semiconductor surfaces, which have a gap near zero voltage, by searching for a constant, but nonzero current value [20]. The interrupted feedback technique has two distinct advantages over the earlier simultaneous ac and dc feedback. First, there are no requirements for a lock-in amplifier or integrator and no need to balance frequencies and filters carefully. Second, voltage measurements can be more precise due to a better signal-to-noise ratio. The dominant noise-limiting measurement is in the tunneling resistance, which increases with the tunneling voltage. The interrupted-feedback approach allows topography to be determined at a relatively high voltage, with greater noise, while the potential is measured at low voltage and low noise. Because of this, Kirtley et al. [16] claim they achieved signal-to-noise ratios that were ten times better than the earlier work with simultaneous dc and ac feedback. Interrupted feedback is not without its faults. One notable problem inherent to the procedure is that the topography is not measured at a constant tunneling resistance and error will be introduced by inconsistencies in the tip height. Although the tunneling current and sample bias are held constant to determine the topography, local variations in the surface potential change the tunneling resistance and therefore the tip-sample separation. For low-resolution experiments distortions will not be significant, since the tunneling resistance depends exponentially on the tip-sample separation. However, the goal of atomic height resolution over an area with a significant voltage drop may not be achievable due to a distortion of several angstroms caused by variations in the tunneling resistance [16]. 2.2.3 Scanning Noise Potentiometry In 1991, M¨oller et al. [21] introduced a variation of scanning tunneling microscopy that they titled scanning noise potentiometry. The basis of this technique is that a voltage is not needed between the tip and sample to produce a tunneling current. Even at zero bias, thermal fluctuations, known as Johnson noise, produce measurable current between the tip and sample, although there is no net current. The key

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is that the tunneling resistance for these fluctuations is exponentially related to the tip-surface distance and can be used to provide feedback for topographical mapping. As the tip is scanned across the surface, any dc current observed represents a local voltage on the surface. A feedback loop consisting of an integrator and a voltage divider can be introduced to maintain the dc tunneling current at zero; the tip voltage required to null the current provides a value for the local surface voltage. M¨oller et al. [21] estimated the accuracy of the local potential measurements on polycrystalline silver to be about 1 µV. The foundation of scanning noise microscopy was explored more thoroughly by Koslowski and Baur in 1995 [22]. On a practical side, their publication lists several critical adjustments to the feedback circuit (lock-in amplifier settings) to avoid artifacts in the potential map. Their research also discovered that the thermal noise current does not follow the Nyquist formula, which predicts that the square of the noise current is inversely proportional to the tunneling junction resistance [23]. This leaves unresolved the exact nature of the noise in the technique. It may be worth noting that neither of these publications actually applied this technique to potentiometry of a laterally applied voltage and instead measured only variations in chemical potential of unbiased samples. However, the approach has been shown to map local potentials and its extension to STP is simply a matter of applying a lateral voltage. In a real sense, scanning noise microscopy is not very different from simultaneous ac and dc feedback. With noise microscopy, the ac signal is simply measured without a tip-sample bias and is consequently not periodic. The very low voltages involved do make it more susceptible to stray capacitances, for example, between the microscope leads and the sample, leading to cross-talk between topography and potential. As with the simultaneous ac and dc feedback approach, a lock-in technique can help suppress the interference caused by stray capacitance [22].

3 Applications of Scanning Tunneling Potentiometry Scanning tunneling potentiometry has been applied to a surprisingly diverse set of phenomena. The technique is continuously evolving, so that many publications begin with descriptions of improvements in the approach. Yet the authors have also been innovative in the application of STP to a wide variety of materials and physical responses. This section will review and categorize some of these applications.

3.1 Grain Boundaries A natural and most common application of STP has been to measure electrical transport across grain boundaries. The original work introducing STP by Muralt and Pohl was a study of granular Au on a SiO2 substrate and falls into this category [7]. Early work on Au60 Pd40 alloy films by Kirtley et al. [16] is shown in Figure 5. The potentiometric images on the right share many, but not all, of the features of the topography shown on the left. This is interpreted as a fairly constant voltage

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FIGURE 5. Topographic (top) and potentiometric (bottom) images of grain boundaries in a Au60 Pd40 film under fields of 85, −85, and 2 V/cm. Potentiometric images have a full vertical scale of 450µV. Images are 24 × 25 nm2 . Reprinted figure with permission from J.R. Kirtley et al. [16]. Copyright 1988 by the American Physical Society.

within grains and abrupt voltage drops at grain boundaries. This pattern, with small voltage contrast within grains and large contrast at boundaries, has been observed in a wide variety of materials. A typical profile of the voltage drop at a grain boundary is shown in Figure 6, reproduced from a study of Au grains by Schneider et al. [24]. The dashed-dotted line represents the average voltage drop generated in the region by the macroscopic field. A much more abrupt voltage change of 25 µV is observed over a 2-nm distance at a grain boundary. As a cautionary reminder of complications mentioned above in the discussion of sample conditions, voltage drops observed in any region where the topography changes may be exaggerated due to tip effects. One great feature of STP is that it provides a complete two-dimensional map of the local voltages. From the slope at each point a map of the electric field in the surface can be computed. Ramaswamy et al. have made such a map for the region around a grain boundary in a polycrystalline Pt film that is reproduced in Figure 7 [15]. Corresponding topography images are interpreted to show that the region where the electric field is large is a grain boundary and that the electric field lines are perpendicular to the boundary. From this map and knowledge of the mean free path of the electrons, the authors have determined the reflection coefficient of electrons at a surface grain boundary to range between 0.5 and 0.7. This value is lower than an average from bulk resistivity data, which the authors attribute either to significant scattering apart from grain boundaries or the reduced dimensionality of the surface.

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FIGURE 6. Data cross section through a grain boundary of a polycrystalline Au film. The dashed-dotted line represents the average voltage drop from the macroscopic field. At the boundary there is a 250-mV drop within the 2-nm experimental resolution. Reprinted with permission from M. A. Schneider et al. [24]. Copyright 1996, American Institute of Physics.

STP has been applied to grain boundaries in carbon resistors [25] and films of carbon [26] and AuPd [17]. Scanning noise potentiometry has been used to examine grain boundaries in silver [21]. More recently, renewed interest in the colossal magnetoresistance (CMR) in manganites has led to a several STP studies of perovskite Lax Ca1−x MnO3 [14,27,28] and Lax Sr1−x MnO3 [19,29] films. An

FIGURE 7. A map of the electric field evaluated in a region around a grain boundary. Direction and size of the arrows represents that of the field. Reprinted with permission from G. Ramaswamy et al. [15]. Copyright 1998 Springer-Verlag.

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Potential image

Topography image

FIGURE 8. (A) The 64 × 80-nm2 STM topograph of a 3-nm-thick Bi film with a 2.4-nm-deep void. (B) The reduced STP potential after subtraction of a linear back-ground. Contours indicate STP potential before background subtraction. (C) A cross-sectional cut along the arrows in B (solid line) and computed curve for purely diffusive transport (dashed line). Reprinted with permission from Feenstra et al. [37]. Copyright 1998, Elsevier.

15 Potential (mV)

10 5 0 −5

−10 −15 −300 −200 −100

0

100 200 300 400

example of STP images from a CMR film, La0.76 Ca0.33 MnO3 , is shown in Figure 8. By examining this material Paranjape et al. [27] found that annealing increased grain sizes, but also boosted grain boundary resistance, resulting in larger CMR values.

3.2 Phase Separation Much of the controversy surrounding the nature of CMR in manganites has concerned the size and role of phase separation. From a theoretical standpoint, Dagotto et al. [30] have argued that phase separation is fundamental to CMR behavior. This viewpoint was given strong experimental support from STM experiments on La0.7 Ca0.3 MnO3 by F¨ath et al. [31]. Phase separation is a natural question to

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address with STP, which combines both spatial resolution and electronic transport. In 2002, the University of Geneva group examined epitaxial films of a similar CMR material, La0.7 Sr0.3 MnO3 grown in situ on SrTiO3 [32]. Unlike previous workers, they found no evidence of phase separation on the same mesoscopic scale of 100 nm. This does not rule out separation on a much smaller length scale, but from STP data the authors were able to argue that mesoscopic phase separation was not shared by all CMR materials.

3.3 Superconductivity In addition to the manganites, complex oxides include the high-temperature superconducting cuprates; and, surprisingly, these too have been the subject of STP studies. High-temperature superconductivity holds such high scientific and technological interest that almost every technique has been applied. The surprise is that a technique for measuring local potential drops has been successfully applied to a material that by definition should have none. The first STP studies on cuprites, published by Kent et al. [33], were on YBa2 Cu3 O7−x and Y1−x Prx Ba2 Cu3 O7 compounds above the critical temperature where the materials remained resistive. Results showed a connection between a distribution of insulating inhomogeneities that were responsible for the high normal-state resistivities observed in these films. To explore the nature of the superconducting state, in a later paper Kent et al. [9] added a 9.5-nm Au film on top of a 400-nm-thick YBa2 Cu3 O7−x film grown epitaxially on a SrTiO3 substrate. The Au film remained resistive below the superconducting transition, allowing application of STP. At 77 K, below the superconducting transition, a potentiometric plot without structure was observed. However, in the center of the transition, at a temperature of 85 K, a step in the potential was observed in one region of the film. This was correlated with a topographical feature and interpreted as a normal region in the YBa2 Cu3 O7−x film. Their approach demonstrated the ability of STP to study normal-superconducting phase transitions.

3.4 Electromigration Resistivity to an electrical current slows the electron flow, but also creates an electrostatic field and a drag on the scatterers that can lead to atomic migration. Electromigration is of great interest to the semiconductor industry, which would prefer their devices to remain as they were made. The electromigration kinetics of gold on a carbon film were explored using STM and STP by Besold et al. in 1994 [34]. The geometry of STP experiments allows quite high current densities; in this experiment a current density of 104 A/cm2 was applied to a 1–2-nm Au film for over 200 hours. The Au atoms migrated differently in two time regimes. After the first 60 hours, the Au coalesced to form more stable (111) facets. The key result, however, was that the initial movement of the Au was toward the cathode. This meant the electrostatic force was greater than that of the momentum drag of

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the electrons. In this sense the kinetics of Au migration was opposite that of Al, another common electrode material for semiconductor connections.

3.5 Defects The nature of electrical resistivity on an atomic scale, where the physical interactions are controlled by quantum mechanics, can be studied in real space by STP images at defects. In a classic paper in 1957, Landauer described the influence of scattering centers in metallic films in a novel way which still has great relevance to our views of transport today [35]. At a scattering center for ballistic transport, Landauer predicted a pile-up of charge that leads to the formation of a dipole in the electrochemical potential. Dipoles from scattering centers then contribute to the electrical field driving the current. The size of the dipoles depends on the macroscopic field. However, the magnitude of the dipoles will differ from a conventional application of Ohm’s law due to the quantum mechanical nature of the interactions. A quantum mechanical analysis of defect scattering indicates that the charge density in the pile-up contains an oscillatory perturbation due to interference. This perturbation has the same origin as the Friedel oscillations screening a charged impurity in a free-electron gas [36]. This residual resistivity dipole at a defect was the focus of research by Briner, Feenstra, Chin, and Woodall [8,18,37]. Their central data was taken with STP and is shown in Figure 8. The top panel in the figure shows a STM topograph of a void in a Bi film grown on an InP-based multilayer. The central image shows the local potential measured with STP for a current applied from left to right, with an overlay of contours with equal potential. Clearly, the black-and-white contrast represents a residual resistivity dipole structure due to pile-up of electrons. Figure 8(c) shows a cross-sectional cut of the potential through the center of the dipole and a curve computed for diffusive transport. The observed dipole is significantly larger than that expected for diffusive transport, confirming the existence of a residual resistivity dipole associated with Landauer’s theory. No oscillations were observed in the electron-density profile of the dipole; however, the experiments were done at room temperature, where thermal noise is probably large compared to the size of the interference effects. A nice comparison of the electric field maps in the vicinity of defects and grain boundaries was published by Ramaswamy and Raychaudhuri in 1999 [13]. They mapped local transport field variations in a polycrystalline Pt film evaporated on glass using STP. Figure 9 shows the field maps determined for (a) a grain boundary, (b) a triple point, and (c) a void in the film. They discovered very poor electronic screening near these defects, leading to large local fields. The fields were smallest at the grain boundary, then increased at the triple point and were greatest at the void.

3.6 Thermoelectric Voltage Dissimilar metals connected in a temperature gradient generate a thermoelectric voltage. A common application is measurement of the temperature relative to

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FIGURE 9. Local transport fields for (a) a grain boundary, (b) a triple point, and (c) a void in a Pt film. Reprinted with permission from Geetha Ramaswamy and A. K. Raychaudhuri [13]. Copyright 1999, American Institute of Physics.

ambient with a thermocouple. In a related manner, it has been known since 1940 that a voltage will be generated across a tunneling junction even with similar metals at different temperatures [38]. This voltage can be several µV/K and is sufficient to measure with potentiometry. The idea of mapping the thermoelectric voltage with a scanning probe was first presented by Xu et al. in 1994 [39]. Experimental realization of the approach took six more years. Hoffman et al. [40] then used a 40-mW laser diode to heat a STM tip about 5 K and measured the thermoelectric voltage generated across the surface separating the signal from topography with simultaneous feedback. For Au films on mica, they were able to resolve individual Au atoms and steps by thermoelectric voltage. With the laser off they saw no signal. Adjacent to steps, the influence of Friedel oscillations was observed as a standing wave. From a detailed analysis of the oscillations the authors concluded that the thermoelectric signal was complementary to conventional d I /d V measurements in its sensitivity to the local density of states. They next added Ag to the Au and were able to distinguish the two elements by thermoelectric signal. Finally, a thermoelectric signal was demonstrated on a Si(111)-(7x7) surface.

3.7 Photoexcitation Light shining on a surface can excite charge carriers through the photoelectric effect. For a semiconducting material, the charge is not immediately dissipated since there are no states available at the Fermi energy. Instead, the induced charge produces a local photovoltage. Cahill and Hamers used STP to map this photovoltage on Si(001)-(2x1) illuminated with a 10-mW He-Ne laser [41]. By modulating the laser with an electro-optic crystal and crossed polarizer, they were able to detect photovoltages under the tunneling tip using a lock-in amplifier. Results revealed that the observed voltage depended both on the intensity of the laser light and on the tunneling current in the STP. Both combine to produce band bending at the semiconductor surface. Cahill and Hamers used this information to map the local band bending across the surface, noting increases of nearly 50% near atomic scale defects.

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3.8 Schotkky Barriers Band bending also plays a prominent role in the nature of metal-semiconductor interfaces. A Schotkky barrier forms as the Fermi energy of the metal aligns with the energy of the majority carrier band edge of the semiconductor. This rectifying barrier for electrical conduction is an essential component in the successful design and operation of any semiconductor device. Interest in the height and shape of the local Schotkky barrier motivated Tanimoto and Arai to apply STP to the junction between an InGaAs film epitaxially grown on InP(100) and non-alloyed Pt/Au contacts [42]. The I-V characteristics of the interfaces showed linear ohmic behavior; however STP showed quite different voltage drops at the cathode and anode. With 2 V across the device, the voltage drop at the cathode was 0.34 V over 30 nm, while at the anode the voltage drop was only 0.01 V over the same region. Furthermore, the voltage drop at the anode was proportional to the total device voltage, but that at the cathode increased rapidly when the device voltage was above 4 V. These characteristics were attributed to the Schotkky barrier characteristics of the metal-semiconductor interface. Near the cathode and anode, potential drops reflected the carrier accumulation and/or depletion due to the carrier velocity dependence on the electric field.

3.9 p-n Junctions One of the most basic interfaces in semiconductor electronics is the p-n junction. Several groups have examined these p-n junctions using STP. Some of the first STP experiments were performed on the interfaces between AlGaAs sandwiched between n- and p-doped GaAs in a laser diode, by the originators of the technique, Muralt et al. [11]. The edge of the interface was exposed by cleaving in ultrahigh vacuum, which formed a very flat surface. The authors identified six different regions near the active junction based on their potentiometric and I-V characteristics. They observed (1) n-type AlGaAs material, (2) a 15-nm depletion region just before the active interface, (3) a potential “waterfall” and (4) a 100-nm “plateau” in the active GaAs, (5) a drop to the p-doped GaAs, and (6) a region of strong I-V asymmetry in the GaAs away from the interface. The position of the active region was monitored as a function of lateral voltage, with changes around 10 nm for each 0.1 V. Figure 10 reproduces line scans across a p-n junction formed between boron and phosphorus-doped Si from Yu et al. [43]. The figure shows the threshold voltage, Vturn-on , required for the onset of tunneling for three values of the p-n junction voltage, Vpn . Vturn-on increases from the left to the right as the tip moves from n-type to p-type Si. The dashed line represents calculations based on a simple model of conduction and valence band positions solved by application of Poisson’s equation in one-dimension and then scaled to fit the data. The model accurately reproduces the STP profiles, suggesting the band positions can be measured in this way. Perhaps the most straightforward application of STP to p-n junctions was performed by Hersam et al. [44]. This group proposed exploiting STP’s spatial

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FIGURE 10. Voltage profiles from STP across a Si pn junction for three biases (solid) and calculated profiles (dashed). Reprinted with permission from E. T. Yu et al. [43]. Copyright 1992, American Institute of Physics.

resolution simply to locate the position of a p-n junction in Si as an alignment marker for nanoscale fabrication. The measured potential across the junction differed by two orders of magnitude and revealed a depletion region of about 20 nm. This provided a clear, well-defined location marker.

4 Outlook The 20th anniversary of the invention of scanning tunneling potentiometry is rapidly approaching. The technique has seen a number of variations and has been proven itself on a wide variety of materials and physical responses. And yet it is fair to say that STP is not a mainstream technique. One barrier is the modifications to conventional STM equipment needed to provide a properly balanced lateral voltage across the sample surface, with associated problems of contacts, and the additional apparatus and/or circuitry to differentiate topographical and potentiometric data. Second, in a review in 1996, Neddermeyer wrote that “the difficulty of surface preparation is probably one of the reasons for a comparative lack of relevant studies.” He also reported that “one complication in the data analysis was that the lateral position of characteristic details in the potential distribution was dependent on the voltage” [2]. With critiques of apparatus, samples, and analysis, one might conclude that the outlook for STP is bleak. However, commensurate with our abilities to fabricate

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and control materials the demand for characterization of electronic transport on a nanometer scale is now greater than ever. One alternative to STP is scanning surface potential microscopy, also known as Kelvin probe microscopy, which is closely related, but uses force feedback to determine the topography instead of electronic tunneling. For measurements at an atomic scale, STP still appears to offer better promise; both force- and tunneling-based approaches share the obstacles of additional apparatus, sample quality, and data interpretation, but tunneling generally provides much better lateral resolution. Clearly, improvements in STP need to continue to meet the demands of science and technology for an atomic scale understanding of current flow. Electronics, such as lock-in quality, and sample preparation are already far superior to those available at the inception of the technique. Little has been written about the theory of STP needed for a careful analysis of results. This is in part due to the complexity of combining electrical transport with the geometry of a tunneling microscope but also because the large length scale of many STP experiments is outside the range of first principles calculations. At smaller length scales, intriguing effects from quantum mechanics become important. In one of the few publications on the subject, Chu and Sorbello [45] have calculated interference effects between the tip and a surface defect. They found that the phase coherence between the electron wave reflected from a defect and the incident electron wave from the tip leads to Friedel-like oscillations in both the local transport field driving current and the observed tunneling voltage. In summary, 20 years have shown continuous improvements in scanning tunneling potentiometry. Several distinct approaches have been taken to distinguish topography from potentiometry, most notably simultaneous ac and dc, interrupted, and noise feedbacks. The technique has been successfully applied to a surprisingly diverse set of physical responses on metals, complex oxides, and semiconductors. The goal of mapping true atomic-scale conductivity has been elusive, but STP appears to offer the greatest promise.

Acknowledgments. Many thanks are due to the authors who have allowed their work to be reproduced in this review. I am also grateful for the support of my colleagues in the Low Dimensional Materials By Design Group, a part of the Condensed Matter Sciences Division at the Oak Ridge National Laboratory. Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract number DE-AC05-00OR22725.

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31. M. Fath, S. Freisem, A. A. Menovsky, Y. Tomioka, J. Aarts, and J. A. Mydosh, Science 285 (5433), 1540 (1999). 32. B. Grevin, I. Maggio-Aprile, A. Bentzen, O. Kuffer, I. Joumard, and O. Fischer, Applied Physics Letters 80 (21), 3979 (2002). 33. A. D. Kent, I. Maggio-Aprile, Ph Niedermann, and O. Fischer, Phys. Rev. B, Condens, Matter Mater. Phys. (USA) 39 (16), 12363 (1989); A. D. Kent, I. Maggio-Aprile, Ph Niedermann, Ch Renner, J. M. Triscone, M. G. Karkut, O. Brunner, L. Antognazza, and O. Fischer, Physica C: Superconductivity 162–64 (pt2), 1035 (1989); A. D. Kent, J. M. Triscone, L. Antognazza, O. Brunner, Ch Renner, Ph Niedermann, M. G. Karkut, and O. Fischer, Physica B: Condensed Matter 165–66 (2), 1503 (1990). 34. J. Besold, R. Kunze, and N. Matz, Journal of Vacuum Science & Technology B (Microelectronics and Nanometer Structures) 12 (3), 1764 (1994). 35. R. Landauer, IBM J. Res. Develop. 1, 223 (1957). 36. W. Zwerger, L. Bonig, and K. Schonhammer, Phys. Rev. B, Condens. Matter (USA) 43 (8), 6434 (1991). 37. R. M. Feenstra and B. G. Briner, Superlattices and Microstructures 23 (3–4), 699 (1998). 38. M. Kohler, Ann. Physik 38, 542 (1940). 39. J. Xu, B. Koslowski, R. Moller, K. Lauger, K. Dransfeld, and I. H. Wilson, Journal of Vacuum Science & Technology B (Microelectronics and Nanometer Structures) 12 (3), 2156 (1994). 40. D. Hoffmann, J. Seifritz, B. Weyers, and R. Moller, J. Electron Spectrosc. Relat. Phenom. 109 (1–2), 117 (2000). 41. D. G. Cahill and R. J. Hamers, Journal of Vacuum Science & Technology B (Microelectronics Processing and Phenomena) 9 (2), 564 (1991). 42. M. Tanimoto and K. Arai, Journal of Vacuum Science & Technology B (Microelectronics and Nanometer Structures) 12 (3), 2125 (1994). 43. E. T. Yu, M. B. Johnson, and J.-M. Halbout, Applied Physics Letters 61 (2), 201 (1992). 44. M. C. Hersam, N. P. Guisinger, and J. W. Lyding, J. Vac. Sci. Technol. A, Vac. Surf. Films (USA) 18 (4, pt. 1–2), 1349 (2000). 45. C. S. Chu and R. S. Sorbello, Phys. Rev. B, Condens. Matter (USA) 42 (8), 4928 (15).

I.2 Probing Semiconductor Technology and Devices with Scanning Spreading Resistance Microscopy P. EYBEN, W. VANDERVORST, D. ALVAREZ, M. XU, AND M. FOUCHIER

1 Introduction to Profiling Needs for Nanoscale Semiconductor Technology As the downscaling in semiconductor industry continues, the correct operation of devices becomes critically dependent on the precise location and activation of the dopants in two dimensions. For Si technology, Duane had already determined in 1996 that, in the 0.25-µm CMOS technology, a 10-nm decrease in the channel length was responsible for a more than 10% increase in the gate-to-drain overlap capacitance [1]. In the 65-nm devices processed today, effects of shifts in lateral position of a few nanometers or of variations in concentration of a few percent in the channel are drastically more pronounced. This necessitates the development of quantitative tools to measure the carrier distribution with a sufficient spatial resolution and accuracy. One-dimensional tools such as secondary ion mass spectroscopy (SIMS) [2] and spreading resistance probe (SRP) [3–5], or more recently carrier illumination [6], have been used successfully in the last few years to understand and calibrate the increasingly complex implantation, diffusion, and activation mechanisms involved in semiconductor processing and in particular CMOS technology processing. They have also been used to calibrate TCAD (technology computer-aided design) process simulators, which are used to generate accurate predictions of the spatial dopant distribution before the initiation of costly silicon processing. However, most recent devices are very sensitive to lateral diffusion mechanisms’ influencing the effective channel length and to implantations realized within the channel (as halo and threshold voltage adjustment implants), which cannot be studied with one-dimensional techniques. They are also sensitive to the stress and stress-induced lateral diffusion. Due to the complexity of the underlying physics, TCAD software typically involves a lot of process parameters, which need to be calibrated through direct two-dimensional (2D) dopant measurements before reliable TCAD predictions can be made. Therefore new methods are required to measure 2D carrier profiling. In addition, there is a growing need for techniques able to characterize specific devices on wafers in case of failure.

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Hence, the Semiconductor Industry Association (SIA) roadmap has pointed out the need for analysis techniques capable of measuring accurately the spatial (2D) electrical carrier (and dopant) profile with a high spatial resolution (2–3 nm), a high sensitivity (5%), and a large dynamic range (1015 to 1021 at/cm3 ).

2 Dopant Profiling in Si with SSRM 2.1 Basic Concepts of SSRM 2.1.1 Principle The scanning spreading resistance microscopy (SSRM) technique was conceived by Vandervorst et al. [7, 8] and implemented by De Wolf [9, 10] at IMEC starting in 1994. Different techniques have been proposed to measure the current flowing from a conducting AFM probe to a semiconductor sample [11]. The originality of the SSRM technique is the use of a high force. As a consequence, the measured resistance is dominated by the spreading resistance and not by the contact resistance. The SSRM concept is in fact born from the motivation to extend the capabilities of SRP by replacing the large SRP probes (1 µm) with a small probe (radius about 10 nm) mounted on an AFM system [9–12]. The motivation was to allow direct measurements on the sample cross sections (in order to avoid the beveling-related carrier-spilling effects) as well as two-dimensional carrier profiling without special test structures. In SSRM, a hard conductive probe is scanned in contact mode across the sample, while a dc bias is applied between a back-contact on the back side of the sample and the tip (see Figure 1). The resulting current is measured using a logarithmic current amplifier providing a typical range of 10 pA to 0.1 mA. The advent of SSRM is intimately linked with the use of silicon probes coated with doped diamond. These probes, mounted on stiff cantilevers (10 to 100 N.m), are the only ones that can survive the forces required for SSRM. In the last few years, the advent of solid diamond probes [13,14] has allowed significant progress in SSRM. The main characteristic of SSRM is, as previously explained, that the technique uses a high force (≥µN) to realize an intimate contact between the probe and the silicon sample such that spreading resistance dominates the contact resistance

FIGURE 1. Illustration of the SSRM basic scheme.

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resistance (a.u.)

FIGURE 2. Resistance measured as a function of load.

AF AFM/SCM M/ SC M 10 - 9

SSSSRM RM 10 - 6

10 - 3

force (N)

(Figure 2). Clarysse et al. have established that for such pressures, the probe punches through the silicon oxide and the underlying silicon undergoes a plastic deformation and phase transformation [15]. In analogy with SRP, the theoretical equation linking the measured resistance to the resistivity of the sample under the probe is then ρ R= (1) 4a where ρ is the resistivity of the silicon sample under the probe and a is the electrical radius of the probe. This simplistic model is, however, not fully satisfactory and contains various inaccuracies and deficiencies, as the electrical properties of the probe–semiconductor contact depend on many different parameters, such as the surface states’ density and their energy distribution, the exact probe shape, or the pressure. It is almost impossible to express mathematically all those non-idealities. Comparisons with calibration samples should therefore be performed, and the deviation from the ideal curve is classically expressed with a barrier resistance component Rbarrier as proposed by De Wolf et al. [16]: ρ + Rbarrier (ρ) (2) R= 4a Moreover, for non-uniformly doped samples, the resistance value at every position is no longer exclusively determined by the carrier concentration at this same place, as the spreading of the current might be influenced by neighboring conducting or insulating regions (see Figure 3). Hence, a correction factor (CF) is introduced, as proposed by De Wolf et al. [16]: ρ R = CF(a, ρ) + Rbarrier (ρ) (3) 4a Eyben et al. [17] have studied these phenomena in more detail, as discussed section 2.2.4. However, despite a few restrictions and corrections, the SSRM technique allows a direct link to the carrier distribution information and offers the possibility of

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FIGURE 3. Current distribution (solid lines) and potential contour lines (dashed lines) under a SSRM tip for three extreme situations: (a) nearby isolating boundary, (b) semi-infinite uniform layer, (c) nearby conducting boundary [16].

realizing an easy, first-order quantification of the measurements [18], as will be shown in section 2.3. Somewhat counterintuitively, but as demonstrated by Eyben et al. [19], one of the main advantages of the high-pressure SSRM technique is its unique spatial resolution (1–3 nm) and dopant gradient resolution (1–2 nm/dec) combined with an excellent signal-to-noise ratio (around 20) and adequate reproducibility (5–10%) as compared to all other low-force SPM-based techniques. The SSRM technique is also relatively robust and less sensitive to sample preparation conditions than SCM. The importance of a precise and specific SSRM sample preparation for high-resolution measurements has nevertheless been evidenced [20]. SSRM measurements may be performed on both polished and cleaved structures. Like SRP, SSRM benefits in theory from an extremely large dynamic range (1014 to 1021 at/cm3 ). In practice, this range is, however, limited in the highly doped range (>1020 at/cm3 ) by limited conductivity of the diamond probe, which is measured in series with the spreading resistance. Unlike the metallic SRP probe, the resistance of the AFM diamond probe is not negligible (about 1 k
). In low-doped areas (1020 at/cm3 ) and saturation is visible in the calibration curves (see Figure 5) as the probe resistance typically lies above 1 k
on Pt for a radius above 5 nm. Due to the final diamond deposition procedure, the outer surface of the diamondcoated tips is not flat but covered with sharp diamond crystals (see Figure 4(a)). The electrical contact is realized through one of those grains. Note that, since the contact is defined by the faceted diamond crystal, the effective electrical tip radius is better than the overall radius visible in the image (i.e., 3-nm-thick buried oxide layers have already been detected with a factor 2 resistance increase), but it is usually difficult to predict. Moreover, the probability of having a multiple contact is not negligible. As the silicon tip itself has a rather high aspect ratio, cleavage of the tip due to the high shear forces exerted is frequently observed. Increasing the diamond film thickness can reduce this effect at the expense of the tip radius as the thicker coating tends to become smoother [26]. In order to overcome these limitations, low-aspect tips have been developed [24]. They are molded pyramidal tips, and their outer diamond surface (deposited first within the mold) is smooth (see Figure 4(b)). Recent improvements of this process [14], have demonstrated a significantly enhanced spatial resolution (around 1 nm) at moderate forces (1–5 µN) [27] (see section 2.4 for details). Although they are superior in terms of spatial resolution, tip lifetime seems to be less as compared to the commercial diamond probes. Tip failures primarily

I.2. Probing Semiconductor Technology

37

occur due to small diamond grains’ being removed from the solid pyramid. Clearly improved diamond deposition is required, leading to a stronger cohesion of the diamond film. Faced with these limitations in tip lifetime, it is imperative to limit the shear force, i.e., providing a very well polished surface and working at very low force. The measurements also have to be done on small scan sizes (a few square microns maximum) and at low speed to reduce the damage to the probe.

2.2 Physics of SSRM 2.2.1 Introduction A major objective in scanning spreading resistance microscopy is to understand and (if possible) to describe quantitativaly the nature of the nanocontact between a probe and a semiconductor sample. The quantification procedure linking the macroscopic resistance measured with SSRM to the resistivity of the semiconductor under investigation is determined by the nature of the nanocontact. We will first present the electrical and mechanical properties before proceeding to a nanocontact modeling. 2.2.2 Experimental Observations 2.2.2.1 Electrical Properties of the SSRM Nanocontact r Calibration curves Scanning spreading resistance spectroscopy (SSRS) measurements (see [18]) performed on p-type and n-type staircase structures (in this case samples T8 and T9 [28]) are used for probe assessment and quantification and referred to further on as “calibration curves.” In Figure 5(a) and Figure 5(b), we may observe that the calibration curves are not linear and that they vary a lot with the bias (in this case between −700mV and +700mV). Moreover, non-monotonic calibration curves are observed on n-type material for all negative biases (applied to the sample). r Current-voltage curves From local I–V curves extracted from SSRS measurements—Figure 5(c) and Figure 5(d))—one notices that the contact varies from an ohmic-like shape (in highly doped areas) to a rectifying shape (in low-doped areas). Furthermore, surface states (SS) induced by the sample preparation affect the I–V curves [29]. This effect is particularly pronounced in low-doped p-type areas (see Figure 6). r Junction position Junction positions measured with SSRM on highly doped materials (source/well or drain/well implants) are in perfect agreement with the expected theoretical zero-field position, and a very good conformity with SIMS and SRP results can be obtained (see section 2.3.1.4)2 . When studying p+ n junctions with a 2

It should be stressed that SSRM measures the electrically active profile and thus the electrical junction (EJ) rather than the metallurgical junction (MJ) measured by SIMS.

38

P. Eyben et al. FIGURE 6. SSRM I–V curves on low-doped (10
.cm) p-type material measured on fresh and beveled surfaces.

low-doped side (source/substrate and well/substrate) a large shift of the SSRM electrical junction position away from the zero-field position towards the surface is, however, observed. For n+ p junctions, a complete disappearance of the junction peak can sometimes be observed (see Figure 15 and Figure 16). 2.2.2.2 Mechanical Properties of the SSRM Nanocontact r Radius of curvature The radius of curvature of the AFM probes (see R in Figure 7) can be determined using direct SEM observations or through measurements on SrTiO3 samples [30]. Such measurements were performed on different generations of diamondcoated and full diamond probes dedicated for SSRM, and typical radii varying between 20 and 50 nm were measured. For most recent generations of full diamond probes, radii of approximatively 10 nm were observed for the sharpest tips. r Spatial resolution The SSRM spatial resolution is difficult to determine quantitatively; however, it clearly appears to be drastically better than the radius of curvature of the probe.

FIGURE 7. Schematic diagram of a spherical SSRM indentation in a flat silicon surface with elastoplastic deformation and beta-tin Si(II) formation.

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FIGURE 8. Schematic representation of the various resistance components involved in SSRM measurements.

Experiments that have been realized on dedicated buried oxide structures (see section 2.4), as well as on device structures, demonstrate an SSRM spatial resolution clearly lying in the sub-5-nm range [20, 27]. Evidence for sub-nanometer spatial resolution has even been reported (see section 2.4) 2.2.3 Classical Ohmic Nanocontact Modeling Observations presented in the previous section show that the SSRM nanocontact is not ohmic. We, however, present in this section a classical ohmic nanocontact model as it is a simple analytical model and a reasonable first approximation in relatively highly doped materials (above 1018 at/cm3 ). 2.2.3.1 Maxwell Ohmic Nanocontact Modeling The total measured resistance Rtot in scanning spreading resistance microscopy experiments (see Figure 8) includes the resistance of the probe R p , the probe nanocontact resistance (also called spreading resistance) Rspr1 , the sample nanocontact resistance Rspr2 , the sample resistance Rsam ,, and the back-contact resistance Rb : Rtot = R p + Rspr1 + Rspr2 + Rsamp + Rb

(4)

The resistance of the probe (R p ) and of the sample (Rsamp ) are given by the classical Pouillet equation, L (5) A where ρ is the resistivity of the material (typically diamond for the tip and silicon for the sample), L its length, and A its area. The resistance of a macroscopic circular constriction (or nanocontact) separating two homogeneous conductors is described by the Maxwell formula [31], ρ1 ρ2 Rspr = Rspr1 + Rspr2 = + (6) 4a 4a where ρ1 , ρ2 are the resistivities of the materials in contact and a is the radius of the contact area (also called electrical radius). In appropriate conditions (see requirements on probe and back-contact in section 2.1), the dominant resistance in scanning spreading resistance microscopy measurements on silicon is nevertheless the sample nanocontact resistance (or R = ρ.

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P. Eyben et al. FIGURE 9. Simple calculation of the mean free path as a function of doping concentration for As-, P-, and B-doped silicon. Classical ohmic nanocontact modeling.

25

Mean free path (nm)

20

N-type As N-type P P-type B

15 10 5 0 1.E+14

1.E+16 1.E+18 1.E+20 Doping concentration (cm-3)

spreading resistance), and we obtain the classical Maxwell spreading resistance formula: ρsamp R= (7) 4a 2.2.3.2 Sharvin Ohmic Nanocontact Modeling The Maxwell formula is, however, only valid when the radius (a) is large compared to the mean free path of electrons and holes (λ). In Figure 9, the mean free path of electron and holes in silicon has been calculated for different concentrations of arsenic, phosphorus, and boron using simple mobility equations without electric field saturation [32]. The dependence of the mean free path on carrier type (electron or holes) and doping concentration (1014 to 1020 at/cm3 ) is illustrated (see also [33]). In the extreme situation of a contact area reduced to a few atoms, electron transport is ballistic, and the conductivity is described by the Landauer–B¨uttiker formula [34], Gc =

Nc 2e2
Ti h i=1

(8)

where Nc is the number of conductance channels through the contact and Ti is the transmission coefficient of the i-th channel. The number of conductance channels is proportional to the ratio of contact area to Fermi wavelength λF . Transmission coefficients are close to unity when no scattering sites such as impurities or grain boundaries are involved at the constriction. Quantized conductance can be observed for small contacts when only a few channels are involved. When the contact radius a is large compared to the Fermi wavelength λ F , the resistance converges to the Sharvin equation [35, 36]: RSharvin =

h λ2F 2e2 π 2 a 2

(9)

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The Sharvin resistance can be expressed in fully classical terms by substituting λ F with ρ and using the electron mean free path λ: RSharvin =

4ρλ 3πa 2

(10)

In Figure 10, the dependence of the Sharvin and Maxwell formulas on the contact radius is presented. We clearly observe that the Sharvin formula is dominant for small contacts (∼1 nm), whereas it becomes negligible compared to the Maxwell formula for large contacts (∼100 nm). In the transition region, both contributions are comparable. The increase in the quality of the measurement conditions (better probes and lower forces used) as well as latest experiments on electrical radius (see section 2.4.1) prove that the SSRM nanocontact size lies more in the Sharvin regime (at least in low-doped areas). Note that the Sharvin resistance equation has the same property as the Maxwell spreading resistance equation: the resistance increases monotonically with the sample resistivity, providing a highly sensitive method for carrier profiling (see Figure 11). Note also that the curvature present in the ballistic calibration curves is not sufficient to give explanation to the curvature in the experimental calibration curves. This curvature is mainly linked to influence of the surface states, as will be demonstrated in section 2.2.4. 2.2.4 Schottky Contact And Surface Modeling As discussed in section 2.2.2.1, experimental observations have revealed that the ohmic nanocontact modeling is not fully satisfactory. To understand the discrepancies between the classical ohmic theory and experimental observations, a more extended physical model of the contact and of the surface involving a Schottky-like contact with tunneling and surface states is introduced. Using this model (implemented in a device simulator [37]), the I-V curves, calibration curves, and even full SSRM profiles can be calculated. 2.2.4.1 Basic Description of the Model The introduction of the Schottky contact is based on the observation of rectified I-V curves (see Figure 5). The necessity to introduce this Schottky contact is not surprising given the nature of the materials involved in the SSRM nanocontact (diamond-coated probe, beta-tin phase of silicon, and silicon sample), none of which are real metals. The barrier height E b = eφm − eχ has been chosen to obtain a rectifying contact (eφ m < eφ s ) for all p-type impurity concentrations and a weakly rectifying contact (eφ m > eφ s ) for most n-type impurity concentrations (see Figure 12). In highly doped areas, the ohmic-like I-V curves observed experimentally (with large currents) may only be explained by the presence of a dominant tunneling current through the thin potential barrier of the contact.

100

1.E+04

1.E+05

1.E+06

1.E+07

1.E+02

1

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Radius a (nm )

10

100

100

Maxwell B Sharvin B Sum B

Boron (1e17 cm-3)

Radius a (nm)

10

Maxwell As Sharvin As Sum As

Arsenic (1e17cm-3)

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1

1

10

10 Radius a (nm)

Maxwell B Sharvin B Sum B

Boron (1e20 cm-3)

Radius a (nm)

Maxwell As Sharvin As Sum As

Arsenic (1e20cm-3)

100

100

FIGURE 10. Diffusive (RMaxwell ) and ballistic (RSharvin ) resistance as a function of the contact radius (a) for two different dopants (As and B) and three different doping levels (1014 , 1017 and 1020 at/cm3 ). The effective resistance is bounded by the sum (Rsum ) and the single values. The calculations assumed bulk resistivities for a contact between a perfect probe and silicon.

Radius a (nm)

1.E+02

10

100

1.E+05

Maxwell B Sharvin B Sum B

Boron (1e14cm-3)

Radius a (nm)

10

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+03

1

1

Maxwell As Sharvin As Sum As

Arsenic (1e14cm-3)

1.E+06

1.E+07

1.E+08

1.E+09

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1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

Resistance (ohm) Resistance (ohm)

Resistance (ohm)

Resistance (ohm)

Resistance (ohm) Resistance (ohm)

42 P. Eyben et al.

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1.E+10 1.E+09

1nm - Maxwell - As

1.E+08

1nm - Sharvin - As Resistance (ohm)

1.E+07

1nm - Maxwell - B

1.E+06

1nm - Sharvin - B

1.E+05

10nm - Maxwell - As 10nm - Sharvin - As

1.E+04

10nm - Maxwell - B 1.E+03

10nm - Sharvin - B

1.E+02 1.E+01 0.0001 0.001

0.01

0.1

1

10

100

1000

Resistivity (ohm.cm)

FIGURE 11. Diffusive (RMaxwell ) and ballistic (RSharvin ) resistance as a function of the resistivity (ρ) for two different dopants (As and B) and two different tip radii (1 nm and 10 nm).

FIGURE 12. Schematic representation of the contact model for a n-type silicon, where e φm is the metal work function, e φs the semiconductor work function, and eχ the semiconductor electron affinity. The SS zero-level is situated above the midband gap.

The sample preparation (polishing) has an important impact on the total SS concentration and distribution.3 It is common knowledge that the surface charges 3

At the surface of the silicon sample, the number of neighbor atoms is reduced (three instead of four) and each atom shows a non-saturated orbital called a dangling bond. Those dangling bonds generate two-dimensional energy bands in the band gap that form the socalled surface states (SS). SS are also created through the reconstruction of the surface (that can be compared to the Peierls’ transition). Besides these “intrinsic” states, “extrinsic” states are also present and play an important role in SSRM. They are typically linked to the presence of foreign atoms (like carbon or oxygen) and irregularities and defects at the surface.

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TABLE 1. Summary of the different parameters involved in the contact model Surface states Schottky contact Contact size

Parameters

Values

Zero-level SS concentration Schottky barrier E b = eφm − eχ Tunneling distance Tip radius

0.28 eV above mid-band gap energy 1013 eV/cm2 0.36 eV 10 nm 20 nm

create variations of doping concentration at the surface changing the I-V curves, shifting the junction and even creating inversion layers [38]. For the SS in our model we have chosen a zero-level above the mid-band gap in order to fit with the experimental observations showing a lower impact of SS on n-type silicon (see Figure 12) as compared to classical SS modeling [39]. 2.2.4.2 Calibration of the New Contact Modeling Based on the experimental observations and ISE/DESSIS device simulations [37], the different parameters have been extracted (see Table 1). 2.2.4.2.1 I-V Curves. The model parameters have been calibrated by comparing both experimental I-V and calibration curves. In highly doped areas, the effect of surface states (SS) is negligible, and the barrier is transparent, implying that the ohmic contact model is still applicable. The saturation (Figure 5) which can be observed for very high concentrations results from the fact that the probe tip resistance (which is not dependent on the silicon resistivity) and the spreading resistance are becoming the same order of magnitude. A good qualitative correspondence between measured and simulated curves (see Figure 13) can be obtained. Note that in order to simplify the comparison with the simulations, the bias in the x-coordinate 3.E-07

1.E-08

(a)

2.E-07

(b)

0.E+00

Current (A)

Current (A)

-1.E-08 1.E-07 0.E+00 -1.E-07 -2.E-07

-3.E-08 -4.E-08 -5.E-08 -6.E-08

Simulation Measurement

-3.E-07

-2.E-08

Simulation

-7.E-08

-4.E-07

Measurement

-8.E-08 -1

-0.5

0

0.5

Bias to the probe (V)

1

-1

-0.5

0

0.5

1

Bias to the probe (V)

FIGURE 13. Comparison between simulated and measured I-V curves in low-doped n-type (10.5
.cm) (a) and p-type (5.2
.cm) (b) homogeneous Si samples. A qualitative agreement may be observed.

I.2. Probing Semiconductor Technology

1.E+12

(a)

1.E+08

(b)

1.E+07

Resistance (Ω )

1.E+11 1.E+10

1.E+06

1.E+09 0.7V

1.E+08

1.E+06

-0.1V

1.E+05

-0.005V

1.E+04 0.001

1.E+05

0.28V 0.14V

1.E+07

0.01

0.1

1

Resistivity (Ω Ω .cm)

-0.28V -0.14V

1.E+04

Resistance (Ω )

1.E+13

45

-0.7V

10

0.001

0.01

0.1

1

10

1.E+03 100

Resistivity (Ω Ω .cm)

FIGURE 14. Simulated calibration curve. (a) simulation of the calibration curves on p-type Si for small negative biases to the back-contact. The non-linearity observed in experiments (see Figure 7) is reproduced. (b) simulation of the calibration curves on n-type Si for biases ranging from −700 mV to 700 mV. The qualitative agreement with the measured curves is once again clearly visible.

in Figure 13 is not the one applied to the sample Figure 5). The presence of large currents for negative biases to the probe in low-doped n-type samples is linked with the Schottky contact. 2.2.4.2.2 Calibration Curves. Applying the same model (parameters), to simulate calibration curves, the non-monotonic behavior for p-type samples can be observed (Figure 14(a)). The increase of the resistance (n-type) in lowdoped areas with decreasing bias is correctly reproduced when SS are included (Figure 14(b)). 2.2.4.2.3 Asymmetric Junction Structures. Using this model, we can elucidate the role of SS on the actual SSRM profiles. For this purpose, we present four typical p/n, n/p junction structures (Table 2). An SSRM measurement on the cross section of those structures was performed first. Then an SSRM measurement was simulated. For that purpose, we used the SIMS measurements (for B and As) as input dopant profiles for the ISE/DESSIS device simulator whereby full activation of the dopants was verified with SRP profiling. Then, the spreading resistance (in fact the current flowing from the TABLE 2. Measured and simulated SSRM electrical junction positions for the test structures: comparison with SIMS measurements and zero-field EJ Metall. junction Struct. p++ .n n++ .p p++ .n+ n++ .p+

SIMS meas. (nm) 660 650 180 210

Electrical junction on cross section ZF simul. (nm) 1040 780 215 210

SSRM meas. (nm) 340 ± 30 No peak 210 ± 10 230 ± 10

SSRM simul. (nm) 370 No peak 200 240

Au: “samples” ok here ?

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FIGURE 15. (a) Resistance profiles for p++ n. Comparison between experiment (SSRM on cross section) and simulations (with the new contact model). (b) Carrier density 2D map (500 × 500 nm) for sample p++ n as simulated with ISE/DESSIS for the new contact model.

probe to back-contacts on the back side of the sample for a given bias voltage) was simulated for different tip positions (on the cross section) using the new contact and surface model. The curve with all the simulated spreading resistances for the different lateral positions gives the simulated SSRM profile. To reduce the calculation time, we performed two-dimensional simulations. This has no influence on the junction position (our main concern here) but only on the resistance levels. Hence a quantitative comparison of the calculated resistance values is not possible. r Case 1 : p ++ n Sample p++ n is a p-type (B) implant (>1020 at/cm3 at the surface) on an n-type (As) substrate (4 × 1014 at/cm3 ). Figure 15(a) presents the measured and simulated SSRM profiles. Both show the same drastic shift of the junction peak toward the surface compared to the zero-field position (see Table 2). The latter can be understood by looking to Figure 15(b), which shows the calculated carrier density (holes/electrons) as a function of distance perpendicular to the cross-sectional plane. In this case, the large bending of the electrical junction position results in a much shallower junction position close to the cross-sectioned surface. Note that far from the surface, the surface states have no influence and the zero-field position for the electrical junction position is found. The displacement of the junction position due to surface states results from the accumulation induced in low-doped n-type material since in this case the SS zero-level. r Case 2 : n ++ p Sample n++ p is an n-type (As) implant (>1020 at/cm3 at the surface) on a p-type (B) substrate (2 × 1015 at/cm3 ). The experiment and simulation indicate the absence of junction peak. Only a slow gradual increase of the resistance with depth is observed (Figure 16(a)). This is caused by the fact that the surface

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FIGURE 16. (a) Resistance profiles for n++ p. Comparison between experiment (SSRM on cross section) and simulations (with the new contact model). (b) Carrier density 2D map (500 × 500 nm) for sample n++ p as simulated with ISE/DESSIS for the new contact model.

states induce an inversion layer along the cross section in the p-type region (see Figure 16(b)). The electrical junction does not intersect the cross-sectional surface of the sample and thus cannot be detected. Far from the surface, the surface states and the Schottky contact effect are minimal and the zero-field position for the electrical junction position is found. The disappearance of the junction due to surface states results from the inversion they induce in the low-doped p-type region. For p-type material, the Fermi level is below the SS zero-level, causing a transfer of electrons from the surface states to the bulk. Because of the low doping level in the bulk and because of a SS zero-level at 0.28 eV above the midband energy, a large depletion layer forms. Bands bend enough so that conduction electrons become the majority carriers near the surface and form the inversion layer. r Case 3 : p ++ n + Sample p++ n+ is a p-type (B) implant (>1020 at/cm 3 at the surface) on an n-type (As) implant (2 × 1017 at/cm3 ) similar to source/drain implant in an n-well. Due to the high doping levels, the surface states impact is drastically reduced and the difference between the zero-field and the simulated positions is negligible and lies within the error bar (Figure 22(b)). r Case 4 : n ++ p + Sample SRP1 is an n-type (As) implant (>1020 at/cm3 at the surface) on a p-type (B) highly doped substrate (5 × 1018 at/cm3 ) such as source/drain implant in p-well. As in the previous case, the difference between the zero-field and the simulated positions is almost negligible due to the high doping levels (Figure 22(a)). However, a small shift toward the depth remains visible. The conclusion of these simulations is that for junctions formed in low-doped substrate, the SS may influence the profile significantly (in particular in the junction

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region). At around 1017 at/cm3, this phenomenon becomes drastically reduced and the role of the SS disappears. It needs to be stressed that this phenomenon is true for any technique using cross sectioning as sample preparation. 2.2.4.3 Role of Pressure in Contact Modeling The SSRM contact modeling is a particularly challenging task: the contact size is extremely small (noticeably below 10 nm), the materials in contact are complex, and the current density in the nanocontact vicinity is extremely high. The good agreement between the new model and the measurements tends to prove that none of those parameters have a drastic influence. We will, however, in this section study the most striking missing parameter, the large pressure (in the GPa range) between the probe and the sample. All models within this section have (apparently) considered a zero-pressure situation. However, as it has been shown in section 2.1, one of the major characteristics of the SSRM technique is the use of high pressure (GPa) between the probe and the sample to penetrate the native silicon oxide and to obtain a stable electrical contact dominated by the sample spreading resistance. Experiments such as load–unload force versus penetration depth curves for spherical indenter [40] or electrical resistance measurements on rectifying goldchromium contacts on silicon [41] have demonstrated that as in the SRP situation, the large pressure involved in SSRM measurement was responsible for elastoplastic or even fully plastic deformations of the silicon sample indented and local phase transformation of silicon to so-called the β-tin phase [15]. The β-tin structure (also named Si(II)) is a denser structure than the cubic structure Si(I) (22% volume reduction) formed at moderately high pressures [42]. Under pure hydrostatic conditions, the transformation occurs at about 12 GPa, but this is reduced to values as low as 8 GPa when shear stresses are present (as is the case in the scanning contact mode SSRM) The Si(II) properties are substantially different from those of Si(I). In particular, this phase is metallic [43]. The electrical behavior of the point contact under pressure has been studied by measuring the current-voltage (I-V) characteristics at different loads for metal and silicon [44]. The presence of a larger threshold pressure necessary to obtain a stable resistance on silicon has been observed and interpreted as formation of Si(II) under the probe [45]. Contrary to an earlier suggestion by De Wolf [46], we believe that the presence of the “metallic” β-tin pocket under the probe does not result in crossover from Schottky to ohmic contact behavior. Indeed, if the contact between the probe and the Si-II is ohmic, the dominant SSRM nanocontact (linked to the silicon resistivity) is the contact between the Si(II) pocket and the Si(I) (see Figure 7). Realizing high force measurements (inducing a full plastic deformation under the indenter), Marchand et al. have demonstrated that such an internal contact was Schottky-like [47]. As discussed in section 2.4.1, the resolution of the SSRM technique is governed by the size of the β-tin pocket created under the probe, rather than by the

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FIGURE 17. Distribution of the plastic strain in the silicon as simulated with MARC. The radius of curvature is 5 nm and the force on the indenter is 5 µg. The grayscale pocket corresponds to the plastically deformed region and the black area to the elastically deformed region.

probe itself, giving an explanation to the nanometer spatial resolution of the SSRM technique. The β-tin pocket can thus be considered as a virtual SSRM probe. Nevertheless, the shape of the probe–sample contact is of crucial importance, as it will determine the stress distribution in the silicon sample. Two-dimensional (axisymetric) finite element simulations [48] provide the von Mises stress distribution under the probe for a typical probe configuration (see Figure 17) and three different radii of curvature (5, 10, and 50 nm). The simulations show three important steps: appearance of the plastic deformation, establishing of the contact between the probe and the plastically deformed pocket, and appearance of the fully plastic deformation. An important parameter obtained from the simulations is the ratio between the contact radius and the radius of the plastically deformed area, the latter determining the final resolution of the technique. The simulations show that the initial size of this pocket is almost independent from the radius of curvature of the probe and that it does form below the probe, rather than directly at the contact, in agreement with earlier observations by Laursen [49]. Note, however, that the pockets do not appear at the same depth when the radius of curvature is varying. A depth reduction is indeed observed when the radius of curvature is decreased implying that for a smaller radius, the contact tip-pocket will be established sooner ( = lower force). Since the size of the pocket increases with force, a smaller tip will lead to a smaller electrical contact. The most important result in Figure 18 is that the pocket is substantially smaller the tip radius (≈ 3× for tips varying between 5 and 50 nm).

2.3 Quantification 2.3.1 Calibration Curves 2.3.1.1 The Concept As pointed out in section 2.2, a straight convertion of spreading resistance (R) to local resistivity (ρ) can be made using the ideal (flat, pure-ohmic contact) formulas R = ρ/4a (Maxwell) or R = 4ρλ/3πa 2 (Sharvin), depending on the tip radius (a). The latter already provides a reasonable accuracy. In practice a true straight-line dependence is never observed, among other reasons due to the influence of the nanocontact nature (Schottky), the SS at the surface, and the

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probe resistance. Although these effects can be modeled (cf. above), taking them into account would make data conversions very slow. A more pragmatic approach is to perform quantification using of a look-up procedure based on calibration curves. Provided a high reproducibility is maintained (see section 2.4.2) this assures quantification accuracy as good as 20–30%. 2.3.1.2 The Implementation 2.3.1.2.1 Automatic Generation of Calibration Curves. As the probes used to measure on the unknown structures have varying characteristics, the first step of the quantification procedure is the acquisition of two calibration curves (for both impurity types) for each probe. Those calibration curves are constructed by collecting the resistances measured for different homogeneous calibration samples with a well-known resistivity. Whereas originally separate samples of different resistivity levels were used to establish the calibration curves (5–6 for each impurity type), dedicated epitaxial test-structures (one for each type) with a 1D staircase-structure are now used to obtain a complete calibration curve from a single scan. [28, 50]. This drastically reduces the time required to establish a calibration curve. In these structures, the resistivity levels range from 1 × 10−3 to 10
.cm (within concentration range of interest) as determined by the spreading resistance probe (SRP) and secondary ion mass spectrometry (SIMS) techniques. To eliminate the manual extraction of the resistances corresponding to each staircase step, a dedicated program, called MicroQuanti, was developed to build the calibration curves automatically based on the raw data collected for the staircase calibration structures. In Figure 19, an illustration of this procedure is presented for p-type (T8) and n-type (T9) staircase structures. The MicroQuanti routine has also been extended in order to perform automatic calibration procedure on other dedicated epitaxial test structures such as the MAYA structure [50].

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FIGURE 19. Screen shot from MicroQuanti illustrating the automatic generation of calibration curves for the T8 and T9 staircase structures.

2.3.1.2.2 Automatic Quantification for 1D And 2D Carrier Profiles. A fast and very easy way to obtain resistivity profiles from the raw resistance data is to use a calibration procedure. In this procedure, the resistance profile of the unknown sample is measured with the same probe, and using linear interpolation on the appropriate calibration curve (n- or p-type), the resistivity profile of the unknown sample can be reconstructed. The use of the experimental calibration curve obviously eliminates non-linearities due to the nature of the contact, the probe, and the back-contact resistance. In the MicroQuanti program a measured 1D or 2D spreading resistance profile is converted using the calibration curve, thereby ignoring all 2D-interactions. From the calculated resistivity profile, a carrier concentration profile is constructed using known values for the carrier mobility (Thurber mobility) [51]. This procedure is very fast and provides interesting quantitative information. In Figure 20, the one-dimensional quantification procedure for a lateral section through the channel of a 0.18-µm n-MOS transistor (with 0.25-µm gate size) is illustrated. In Figure 21, the two-dimensional quantification procedure for a 0.18-µm n-MOS transistor (with 0.25-µm gate size) is illustrated. The quantification software produces a two-dimensional active dopant (carrier) map using p-type calibration and conversion curves whereby the extension of the p-type halo implants within the channel are quantified.

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FIGURE 20. Screen shot from MicroQuanti illustrating the calibration quantification procedure for a one-dimensional profile.

2.3.1.3 Limitations For further quantitative refinements, a more complex (iterative) procedure is required to account for the current spreading effects induced by the dopant gradients. Improved contact and surface modeling also has to be taken into account (specially in low-doped areas), as explained in the next section, to explain carrier redistribution near the sample surface. 2.3.1.4 Application and Comparison with 1D Techniques Secondary ion mass spectroscopy (SIMS) is nowadays the standard reference technique for one-dimensional dopant profiling. A major difference between SSRM and SIMS is the fact that SIMS measures the position and the concentration of the dopant ions, rather than charge carriers. Even in the case of a fully activated profile, the dopant and the carrier distribution are not identical, due to the outdiffusion of the mobile carriers (difference between the EJ and the MJ). The classical procedure to compare SIMS and SSRM results is thus to calculate the carrier profile from the SIMS dopant profile solving the Poisson equation and then to compare this calculated profile with the SSRM quantified profile. In Figure 22(a) and Figure 22(b) corresponding, respectively, to n++ p+ and p++ n+ structures, very good agreement

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FIGURE 21. Screen shot from MicroQuanti illustrating the calibration quantification procedure for a two-dimensional profile.

in terms of concentration level and electrical junction position is observed between SIMS and quantified SSRM. The SRP technique is a carrier profiling tool similar to SSRM. However, SRP measurements are realized on beveled samples. As has been explained by Hu, the beveling procedure results in a shift of the junction (carrier spilling) [52]. SIMS MJ SIMS EJ SRP MJ SSRM EJ

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Comparison between cross-sectional SSRM or SIMS and on-bevel SRP profiles is thus not always straightforward. For a detailed discussion see [53]. In Figure 22(a) and Figure 22(b) good agreement between SRP and quantified SSRM (using MicroQuanti) in terms of carrier concentration is observed. The shallower junctions of SRP are representative of the carrier spilling effect that could not be completely corrected. Small differences between SIMS and SSRM exist in the most heavily doped part of the profiles (measured carrier concentration slightly lower with SSRM than with SIMS). SRP results evidence that this difference is linked to the presence of a not fully activated implant and not to a saturation problem of the technique (due to the predominance of the probe resistance). The profiles in the depletion zone also differ. The peak is less pronounced with SSRM than with SIMS. This is most probably linked to the perturbation of this zone by the voltage used in the SSRM measurements, resulting in non-zero carrier concentration. When the SSRM bias is increased the junction peak is further reduced. Overall, the agreement between SSRM and SIMS EJ positions (the latter being calculated from the SIMS MJ position) is very good, and one can conclude that SSRM is a technique for carrier profile determination with a very high spatial resolution (higher than SRP) and quantification accuracy. 2.3.2 2D Corrections 2.3.2.1 Influence of Current Flow For steep 2D profiles, additional corrections are necessary to account for the twodimensional current flow induced by nearby conductive or insulating layers (see Figure 3). Introduction of current flow correction factors (CF) had initially been developed for SRP [54]. Schumann and Gardner have proposed a deconvolution algorithm for on-bevel measurements [55]. In SSRM, the situation is different, since the measurements are performed on cross sections. Moreover, the gradient is drastically reduced, as the contact radius is two to three orders of magnitude smaller. De Wolf et al. have nevertheless developed and patented a special quantification procedure using a database containing correction factors for SSRM [56,57]. It is important to note that this quantification algorithm is based on the ohmic contact model thus limiting the applicability of this approach. Note that gradient correction factors are only important for distances of a few times the electrical probe radius. Moreover, preliminary calculations by De Wolf have shown that even then these are fairly limited (1 µN) should be relatively insensitive to small errors or inaccuracies in tip/sample contact. In other words, at high contact forces, the measured impedance values change little with small force variations. This hypothesis is further reinforced by the results in Figure 6. In Figure 6(a), 150 impedance measurements were collected while the AFM tip was held with a constant contact force on the gold film for approximately 0.5 h. The experiment was conducted at two different force set points: 0.50 µN and 1.25 µN. Use of a high (>1 µN) force set point dramatically improves data consistency. During nanoimpedance imaging, the tip is continually retracted and then extended point by point across a sample of interest. Under these conditions, although a constant force set point is maintained at each measurement point, the repeated establishment of new surface contacts combined with slight variations in the SPM z-scanner control and tip/surface interaction could affect the tip/sample contact and thus the measured impedance. The results of Figure 6(b) show that at least for Please check a smooth gold surface, this is not the case. These data were acquired for a stepwise third from scan (10 nm steps) on the same gold film as in Figure 6(a). last line in Both the absolute values and statistical variability of the scanned-tip data legend to (Figure 6(b)) are comparable to those of the fixed-tip data (Figure 6(a)), indicating Figure 5. that variations due to tip/sample contact fall within the experimental noise of the Something appears to be impedance measurement. Of course, a smooth gold film provides the almost ideal missing. case for repeatable tip/surface contact. Repeatability on rough samples or sharp topographical features will certainly be worse. In addition, dramatically softer or harder samples will likely exhibit very different force/impedance behavior, obligating larger or smaller force set points to acquire optimal contact nanoimpedance data.

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FIGURE 5. (a) Impedance modulus vs tip/sample contact force for a conductive diamond AFM tip in contact with a gold-coated silicon sample. The measured impedance quickly drops with increasing tip/sample contact force, and then stabilizes, suggesting that measurements at high force values are more repeatable. Reprinted with permission from [4]. (b) Impedance spectra with the frequency range from 40 Hz to 110 MHz of a tip/Au surface contact for a good tip-coating (•) and a damaged coating (
). Reprinted with permission from [3].

FIGURE 6. Variability of single point AFM impedance measurements for two different force set points between a conductive diamond AFM tip and a gold coated silicon sample. (a) Impedance measurements are acquired while the tip is held at a fixed position in contact with the gold film. (b) Impedance measurements are acquired while the tip is stepped in 10 nm increments across the gold surface. Reprinted with permission from [4].

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2.1.7 Measuring Speed and Resolution The absolute resolution limit of the nanoimpedance technique is set by the magnitude of the tip/sample contact spreading resistance. In practice, however, two other factors often conspire to limit the achievable detail of impedance images. These are (1) capacitive coupling between the sample and the extended tip and (2) the experimental measurement time. The constraints on measurement time are intimately linked to the problem of drift. Sample drift leads to an accumulating, time-related distortion in the acquired image data. To reduce measurement time and limit drift, it is therefore currently necessary to acquire two-dimensional (2D) impedance maps at a single measurement frequency (for example 100 Hz). As mentioned previously, full impedance spectra are first taken at several points across the surface to determine the primary frequencies of interest, i.e., characteristic frequencies that correspond to spectral peaks or valleys in the impedance spectra. Then, single-frequency impedance images are acquired at these frequencies. It is assumed that the critical frequencies do not shift significantly across the sample or in time. Measurement speed is currently 1–3 sec per point for frequencies greater than 10 Hz. At lower frequencies, the measurement time increases commensurately. This measurement time includes a settling period to allow the tip (which is stepping from pixel to pixel across the surface) to establish good contact with the sample. In our experience, the 50 × 50 pixel array size provides a good compromise between image detail and measurement time. Most of the 2D impedance images presented in the application section of this chapter are constructed from singlefrequency impedance scans taken in 50 × 50 pixel arrays. Typical measurement times for 50 × 50 pixel arrays are 1–4 h. The raw impedance modulus (Z 0 ) versus position and phase angle (φ) versus position data are post-processed in MATLAB (color range, contrast, pixel smoothing, interpolation) to produce 2D images.

2.2 Nanoimpedance Imaging of Polycrystalline ZnO A practical example of nanoimpedance imaging is provided by a study of grain/grain boundary transport in commercial polycrystalline ZnO varistors. Following Figure 7(a), the impedance of a cross-sectioned commercial ZnO varistor was probed laterally between the AFM tip and a bulk top electrode. Thus, in addition to the local impedance response at the AFM tip, non-local impedance contributions from any intervening grain boundaries between the tip and the bulk electrode were also probed. Coupled SEM, AFM topography deflection, and AFM Z 0 images from a 50-µm region of the ZnO varistor are shown in Figure 8. The Z 0 image was acquired with a 100-mV excitation signal under +5V dc bias at 1 kHz. Several distinct ZnO grains are visible in the images. The ZnO grains at the upper left of the image show purely ohmic behavior at a +5V dc bias. These grains are closest to the bulk top electrode, which was positioned approximately 30 µm above and to the left of the image field of view.

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The highly nonlinear I-V properties of ZnO varistors arise from double-Schottky like barriers formed at the grain boundaries of the material. Below a critical grainboundary breakdown voltage (typically 3–4 V), transport across the boundary is almost purely capacitive and the boundary is highly insulating. Above the critical voltage, however, transport across the grain boundary becomes ohmic [41,42]. Figure 9 shows a set of Z 0 and φ images for the same 50-µm area at five different bias voltages ranging from 0V dc to +8 V DC. (Measurements acquired at 1 kHz with a 100-mV excitation.) Note how individual grain boundary barriers break down sequentially during the dc bias voltage ramp, starting from the upper left with the grains closest to the electrode. This grain-by-grain cascade visibly demonstrates the highly nonlinear I-V characteristics of the polycrystalline varistor. The first grains to exhibit ohmic transport characteristics do so at 3–4 V DC, indicating 5V DC

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FIGURE 9. Impedance modulus (top row) and impedance phase (bottom row) images measured as a function of dc bias for the same 50 µm ZnO region documented in figure 8. From left to right, the images are acquired with increasing dc bias; 0 V, 3 V, 4 V, 5 V, 8 V. All images acquired at 1 kHz with a 100-mV excitation signal. Note the grain-by-grain “cascade” with increasing dc bias as the grains become conductive, starting with the grains on the upper left closest to the bulk electrode. Reprinted with permission from [4].

that they are removed by a single grain boundary from the top electrode. The other grains become ohmic between 5–8 V DC, indicating that they are probably separated by two grain boundaries from the top electrode. This result is reasonable given the varistor’s 40-µm average grain size and the location of the top electrode 30 µm above and to the left of the images. Figure 10 demonstrates the sub-micron resolution capabilities of the nanoimpedance imaging technique with a series of “zoom-in” magnifications on a ZnO triple junction. The small triangular shaped region at the junction between the three ZnO grains (clearly visible in the 6-µm image) is a Bi2 O3 second-phase inclusion, as confirmed by energy dispersive x-ray analysis (EDX). Bi2 O3 is added to ZnO varistors to control the grain-boundary properties of the material. Excess Bi2 O3 typically phase-segregates to the ZnO triple junctions, which is nonconductive. NIM point spectroscopy on a similar system is illustrated in Figure 11(a), showing single-point Cole–Cole (Nyquist) spectra from a ZnO ceramic. The experimental data can be well approximated by two RC elements in series, due to grain boundary and metal-semiconductor contact [3]. On increasing the dc bias, the curve collapses, indicative of the grain boundary breakdown. In comparison, shown in Figure 11(b) is the bias dependence of the local impedance measured at different separations from the macroscopic electrode contact corresponding to varying number of the grain boundaries between the two. Note that the breakdown voltage increases with increasing separation, as expected for an increasing number of grain boundaries between the two.

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FIGURE 10. AFM topography (top) and impedance modulus (bottom) images, increasing in magnification from left to right. (50 µm, 15 µm, and 6 µm scan regions, respectively.) Impedance-modulus images are acquired at 1 kHz with a 100 mV excitation signal and 5 V dc bias. The images “zoom” into a triple-junction region between 3 ZnO grains. The V-like intrusion between the 3 grains is a highly insulating Bi2 O3 second phase inclusion. (by EDX analysis.) Reprinted with permission from [4].

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2.3 Quantitative Nanoimpedance Measurement The nanoimpedance microscopy detailed in the previous section provided qualitative 2D maps or images of impedance variations across sample surfaces. In this section, a methodology for the extraction of quantitative data from the nanoimpedance technique is developed. Furthermore, this quantitative approach can be widely extended to a variety of other contact-based local-probe techniques, including SSRM, SSPM, and SCM. The methodology depends critically on the ability to characterize the AFM-tip/sample contact quantitatively. Using contact mechanics models, tip/sample contact forces measured in the AFM can be converted into tip/sample contact area estimates. Then, using a reasonable model for the tip/sample contact, quantitative impedance results may be extracted [5]. 2.3.1 Contact Area Estimation As mentioned above, the key to extracting quantitative impedance values is to determine tip/sample contact area accurately. Unfortunately, tip/sample contact area is not directly measurable in a standard AFM experiment. However, it can be estimated from known tip/sample contact forces. This methodology is now briefly described. Assuming that the hardness (H ) of a material is constant, contact area estimates can be obtained from contact force data using the standard hardness relation, H = P/A, where H = hardness (N/m2 ); P = applied load (applied normal force) (N); and A = projected or surface area of contact (m2 ) [43–45]. H is a constant for noncrystalline materials and geometrically similar probes (such as Vickers and Berkovich indenters). H is also constant for crystalline materials with small indentation size effect (ISE) [46]. However, hardness is tip-geometry dependent. Because the tips used in an SPM differ from the standard indenter geometries used in hardness experiments, a simple hardness relation like the one defined above is not immediately applicable. Instead, we require a hardness equation that explicitly accounts for the geometry of the tip. Thus, we define a tip-geometry dependant hardness function, H (θ), where: (H θ ) = P/Aproj . In this equation, the hardness H (θ) depends on the sharpness (θ = tip semi-angle) of the tip. For a given load and tip semi-angle, H (θ) pgay be used to determine the projected area of contact between the tip and the sample. A reasonable H (θ) function can be developed for most SPM tips by applying a conical approximation. Conical tips possess the property of geometric similarity; therefore a simplified version of Johnson’s expanding cavity model can be used to relate hardness to the materials properties of the sample and the sharpness of the tip [46]: ⎤ ⎡ E r + 4(1 − 2ν) 4 2 ⎥ 2Y ⎢ H (θ) = Y + Y ln ⎣ Y tan θ (2) [2 + ln(η)] ⎦= 3 3 6(1 − ν) 3 where H (θ) = material hardness measured by a conical tip of sharpness θ (N/m2 ); Y = yield strength of the sample (N/m2 ); Er = reduced modulus or indentation

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modulus (N/m2 ); θ = tip semi-angle from the vertical (◦ ); and ν = Poisson’s ratio of the sample. Er , the reduced modulus, is defined as 1 − νt2 1 − v2 1 = + Er Et E

(3)

where νt = Poisson’s ratio of the tip material; E t = Young’s modulus of the tip material (N/m2 ); ν = Poisson’s ratio of the sample; and E = Young’s modulus of the sample (N/m2 ). In general (especially for a diamond-coated SPM tip), E t >> E, so Er ≈ E/(1 − ν 2 ), and

1 E η≈ + 4(1 − 2ν) (4) 6(1 − ν) (1 − ν 2 )Y tan θ For most metallic materials, ν is ∼1/3; for most polymers, ν is about 0.5, thus for metals we have ηmetal ≈

1 9E + 32Y tan θ 3

(5)

and for polymers ηpolymer ≈

4E 9Y tan θ

(6)

Figure 12(a) shows H/Y versus tip semi-angle for different E/Y, based on Eq. (2). As the figure indicates, H decreases with increasing tip semi-angle. The figure also demonstrates that the results are insensitive to ν. For a specific tip semi-angle (70.3◦ ), Figure 12(b) shows curves of (H for ν)/(H for ν = 0.5) versus ν for various values of E/Y, indicating again that H is relatively insensitive to ν.

FIGURE 12. (a) H/Y and Hsurf /Y vs. the tip semi-angle for different E/Y ; E/Y = 10 (typical of polymers, ceramics), E/Y = 100, E/Y = 1000 (typical of ductile metals). Based on Eqs. (3) and (7). (b) (H for ν)/(H for ν 0.5) vs. ν for different materials tested with a Berkovich indenter. Reprinted with permission from [5].

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Since quantification of SPM measurements often requires an estimate of the true contact surface area between the tip and the sample rather than the projected contact area, an additional modification is required. We define Hsurf (θ) as a surfacearea related hardness value, which provides an estimate of the tip/sample contact surface area (rather than the projected area) for a given load: Hsurf (θ) = P/Asurf . In this definition, Asurf (m2 ) represents the true contact surface area between the tip and the sample. For the case of perfect conical tip geometry, we have Hsurf (θ) = H (θ ) sin θ

(6)

The second set of curves in Figure 12(a), then, are curves of Hsurf (θ) versus tip semiangle for different E/Y . As the indicates, a broad maximum occurs in the Hsurf (θ) curves. Around this maximum, Hsurf (θ) is fairly insensitive to the tip geometry. At E/Y = 10 and 30◦ < θ < 70◦ , for example, Hsurf (θ) is nearly constant. This fortuitous tip-geometry insensitivity is due to two opposing geometric correction factors that partially cancel one another out. This result implies that the contact area conversion methodology should be applicable for most SPM probe geometries if the SPM tip angle is not far from the curve maximum. Equations (2–6) provide the necessary adjustments to produce contact surface area estimates for conical SPM tips of arbitrary sharpness based on nanoindentation hardness measurements or materials properties. If the materials properties of the sample are well known, they can be inserted into Eqs. (2–5) to generate an approximate hardness function. More accurately, nanoindentation experiments on the sample of interest can be used to obtain Er and H(θ ) values at known tip angles θ. For example, Berkovich nanoindentation experiments give H = 70.3◦ . Estimating the Poisson’s ratio of the material, Eq. (2) may be solved to produce the yielding stress Y . Combining Eqs. (2) and (6), Hsurf (θ) estimates can then be obtained at any tip angle. Several significant assumptions have been made to derive these relations. Among the most important are the following: 1. AFM tip geometry is perfectly conical. 2. Hardness is constant (No ISE). 3. Material is elastic—perfectly plastic. Most materials reasonably satisfy assumption three. However, in the case of significant strain-hardening rates, modifications to the presented model can be applied [5]. For large contact depths (large contact areas), the first two assumptions are also satisfied. However, due to sample surface effects and the finite sharpness of real SPM tips, these assumptions become problematic for extremely small contacts. Most SPM tips have tip radii on the order of 10 nm. Therefore, for contacts below 10 nm (radius) in size, spherical rather than conical contact mechanics theory should likely be applied. Equation (2) may be replaced by [46]: 

 2Y Er r H (r ) = + 4(1 − 2ν) 6(1 − ν) (7) 2 + ln 3 YR where r = contact radius (m) and R = radius of the spherical tip (m).

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300 200

F = 3.4µN 100

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F = 5.4µN 100

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-Zimag (MΩ)

30 20

F = 3.4µN

10

F = 5.4µN 0

10

20

30

Zreal (MΩ)

FIGURE 13. (a) Example Nyquist impedance spectra results obtained at two different force settings from the Pt/Nafion experiment configuration described in Figure 7(b). The size of the impedance loop provides information on the kinetics of the oxygen reduction reaction occurring at the tip/Nafion interface. (b) Area-specific Nyquist impedance spectra converted from (a) based on the calculated area estimates for the tip/Nafion contacts.

At the 10-nm length scale, surface effects and sample roughness likely become significant. Thus, the methodology developed in this section is recommended only for contact sizes larger than about 10 nm (contact area >100 nm2 ). 2.3.2 Quantitative Nanoimpedance Measurement of ORR Kinetics An example application of the quantitative nanoimpedance measurement is provided by an investigation of the oxygen reduction reaction (ORR) kinetics at a nanoscale Pt/Nafion interface. Nafion is an important ionic conductor for fuel cell and electrolysis systems. The development of commercial fuel cell systems requires a nanoscale understanding of fuel cell reaction kinetics. A nanoscale impedance experiment, such as the one diagrammed in Figure 7(b), can help provide this kinetic understanding. In this experiment, a platinum-coated AFM tip is used as a local probe of the oxygen reduction kinetics on a Nafion 117 membrane. The impedance response measured in this experiment is related to the kinetics of the ORR. Figure 13(a) gives typical impedance measurement results at two different tip/sample contact force settings. Both Nyquist impedance spectra in this figure show a clear semicircular loop. The diameter of this semicircular loop provides information about the rate of the Faradaic charge transfer reaction at the tip/Nafion interface. However, because the two spectra were acquired at different tip/sample contact forces, they show drastically different loop diameters! In order to provide quantitative rate information we must normalize the impedance spectra in Figure 13(a) by tip/sample contact area. To arrive at an area-normalized version of Figure 13(a), tip/sample contact areas must be estimated for both measurements. Following the methodology outlined in the previous section, these tip/sample contact estimates can easily be produced. We briefly detail the procedure for the two impedance measurements above. First, from SEM inspection, the semi-angle of the AFM tip used in the above Nafion

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experiments is determined to be approximately 40◦ . Then, from a set of standard nanoindentation experiments on Nafion samples, an H(θ) curve for Nafion is established. (Alternatively, H(θ) for Nafion can be estimated from the E, Y , and ν for Nafion based on Eq. (2).) Using Eq. (6), the H(θ) curve is then converted into a Hsurf (θ ) curve, and Hsurf (40◦ ) is determined. For Nafion, Hsurf (40◦ ) is determined to be approximately 2.8 × 107 Pa [5]. Finally, knowing the applied force used in the measurement, the tip/sample contact area may be estimated as Asurf =

P Hsurf (θ )

(8)

The impedance spectra in Figure 13(a) were acquired with tip/sample contact forces F1 = 3.4 µN and F2 = 5.4 µN. Therefore Asurf,1 ≈ 0.12 µm2 and Asurf,2 ≈ 0.192 µm2 . Using these contact area estimates, the impedance spectra in Figure 13(a) (Z in units of
) can be converted to area-specific spectra (Z in units of
·cm2 ), as shown in Figure 13(b). As Figure 13(b) illustrates, the kinetic response of the system is virtually identical in the two experiments after contact area normalization. From either of these area-specific impedance spectra, the exchange current density, jo (an important kinetic parameter in fuel cell systems) can be extracted. The spectra in Figure 13(b) yield jo ≈ 2.6 × 10−7 A/cm2 [5]. This value lies well within the range of values obtained by macroscopic studies of Pt/Nafion ORR kinetics. The match between bulk kinetic measurements and those obtained by the nanoimpedance method affirm the quantitative capability of the nanoimpedance technique.

3 Noncontact SPM Impedance Measurement In the nanoimpedance microscopy and spectroscopy method discussed above the AFM tip acts as a moving current electrode, similar to conventional two-probe impedance measurements. However, in this case the total impedance is a sum of the system impedance and the impedance of the tip-surface contact coupled with the cantilever capacitance, which in most cases will dominate the response of the system. Alternatively, the SPM can be set-up in a four-probe impedance configuration, where the current is applied across the system using macroscopic electrodes and the SPM tip is used to detect the local amplitude and phase of voltage oscillations. This measurement configuration eliminates the tip-surface junction impedance. These measurements can be performed in the current detection mode as discussed in detail in chapter 3.1. However, this approach requires tip-surface impedance to be comparable to the input impedance of the voltmeter, limiting its applicability to highly conductive materials. An alternative approach, scanning impedance microscopy (SIM), is based on AFM force detection, where the AFM cantilever is used as a force sensor to detect periodic electrostatic forces between the tip and the surface. Principles, data interpretation, and resolution limits in SIM as well as applications to several materials systems are discussed below.

I.5. Frequency-Dependent Transport Imaging by Scanning Probe Microscopy 1ω

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Rd R R

R

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(e)

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(c)

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I2

nω

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nω A1nω ,ϕ1 A2nω , ϕ1 I nω

V2 Rd

R

R

R

V

(f) Rj

Vlat (b)

Vlat (d)

Cc

R

Rg

R

FIGURE 14. (a) Experimental set-up for dc and ac force-based SPM transport measurements. (b) Equivalent circuit for SSPM-based dc transport measurements. (c) Equivalent circuit for linear SIM measurements. (d) Equivalent circuit for non-linear SIM. (e,f) Experimental setup and equivalent circuit for current based SPM transport measurements. For clarity, only resistive components of the sample equivalent circuit are shown. Reprinted with permission from [55].

3.1 Principles In an SPM transport experiment, the experimental setup is configured similarly to standard four-probe resistance or impedance measurements, as illustrated in Figure 14(a), where the tip acts as a moving voltage electrode. In dc transport measurements by scanning surface potential microscopy (SSPM, also referred to as Kelvin probe force microscopy), the tip measures the dc potential distribution induced by a lateral bias applied across the sample, thus imaging resistive elements of the equivalent circuit (Figure 14(b)) [47–49]. In SIM, the tip measures the distribution of the phase and amplitude of the ac voltage, thus imaging both the resistive and capacitive elements of the equivalent circuit (Figure 14(c)) [1,2]. SIM can also be extended to the nonlinear domain, measuring the higher harmonics [50] or mixed-frequency signals [51] of potential oscillations in the sample generated due to frequency mixing on nonlinear interfaces. A corresponding equivalent circuit is shown in Figure 14(d), where a nonlinear interface acts as a current source at mixed-frequency harmonics of the applied bias. Note that c-AFM can also be configured for potential measurement techniques by nulling the tip-surface current (scanning potentiometry, or SP). However, the information obtained in SSPM and SP is different—the former measures electrochemical potential; the latter measures electrostatic potential.

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In the force-based techniques, acquisition of electrostatic force data requires contributions from elastic and Van der Waals interactions to be minimized. Correspondingly, SSPM and SIM are typically implemented in a dual-pass imaging mode. The tip scans the surface in the contact or intermittent contact mode, determining the position of the surface. Electrostatic data are then collected in the second scan, in which the tip retraces the topographic profile while maintaining a constant tip-surface separation. In SIM the tip is held at constant bias Vdc and a lateral bias Vlat = Vdc + Vac (x)cos(ωt) is applied across the sample. This lateral bias induces an oscillation in the sample surface potential Vsurf = Vs (x) + Vac (x) cos(ωt + ϕ(x)),

(9)

where ϕ(x) and Vac (x)are the position-dependent phase shift and voltage oscillation amplitude and Vs (x) is the dc surface potential. The variation in surface potential results in a capacitive force acting on the tip cap

F1ω (z) = C z′ (Vdc − Vs (x))Vac (x),

(10)

that results in a cantilever deflection detected by the optical beam-deflection system. The magnitude, A(ω), and phase, ϕc , of the cantilever response to the periodic force induced by the voltage are [52] A(ω) =

F1ω 1  2 2 m (ω − ωr c )2 + ω2 γ 2

and

tan(ϕc ) =

ω2

ωγ (11a,b) − ωr2c

where m is the effective mass, γ the damping coefficient, and ωr c is the resonant frequency of the cantilever. Equations (10) and (11) imply that the local phase shift between the applied voltage and the cantilever oscillation is ϕ(x) + ϕc and the oscillation amplitude A(ω) is proportional to the local voltage oscillation amplitude Vac (x). Therefore, variation in the phase shift (phase image) along the surface is equal to the variation of the true voltage phase shift with a constant offset due to the inertia between the sample and tip. The spatially resolved phase shift signal thus constitutes the SIM phase image of the device. The tip oscillation amplitude is proportional to the local voltage oscillation amplitude and constitutes the SIM amplitude image. SIM is complemented by scanning surface potential microscopy, which can access the dc potential distribution Vs (x) along the surface. In SSPM the tip is t t t biased directly by Vtip = Vdc is referred to as the (x) cos(ωt), where Vac + Vac driving voltage. The capacitive force between the tip and the surface is given by t is now position independent. Feedback is used to Eq. (10), where Vac (x) = Vac cap nullify F1ω by adjusting the dc component of tip bias and mapping the nulling t0 potential Vdc thus yields a surface potential image. Note that the force-nulling, rather than current-nulling mechanism in SSPM means that the measured potential t0 is Vdc = Vs +  CPD, where  CPD is the work function difference between the tip and the surface. In nonlinear SIM, higher harmonics of the tip deflection signal or a mixed frequency signal are detected [52,53]. In this case, the detection frequency is

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chosen so as to coincide with the resonance of the cantilever in order to amplify the otherwise weak mixed-frequency signal. To determine the absolute value of local amplitude, Vac (x), from SIM and NLSIM data, the microscope is reconfigured to the open-loop SSPM mode, in which the feedback is disengaged, and the tip oscillation response to the ac bias applied to the tip is determined. The local voltage oscillation amplitude is then  sspm  Vac Asim (x) Vsurf (x) − Vtip   Vac (x) = (12) sim Asspm (x) Vsurf (x) − Vtip where A is oscillation amplitude, Vtip is the tip dc bias, Vac is the tip ac bias, and sim and sspm refer to the SIM and open-loop SSPM modes, respectively. Vsurf (x) is the surface potential, which varies with x in the presence of a lateral bias and can be determined by SSPM. The driving frequency in SIM must be selected far from the resonant frequency of the cantilever to minimize the variations of the phase lag between tip and surface due to electrostatic force gradients related to the non-uniform surface potential. In practice, however, SIM is used to obtain frequency-dependent phase shift and amplitude; therefore, the data is acquired in a broad range of frequencies and the vicinity of the resonance can be excluded. The frequency range of SIM is limited by the bandwidth of the optical detector to 2–5 MHz. In addition, at high frequencies dynamic stiffening effects become important, minimizing response to electrostatic forces.

3.2 Quantification Here, we present the formalism to quantify the dc and ac transport properties from SSPM and SIM data. Unlike conventional two or four probe resistivity measurements, SSPM is sensitive to variations in local potential, while (local) current is generally unknown. However, for single interfaces such as in bicrystals or metalsemiconductor junctions, the system can be represented by a 1D equivalent circuit, which defines the current. In an SSPM transport experiment, a biased interface is connected to a voltage source in series with current limiting resistors to prevent accidental current flow to the tip. For a system with a single electroactive interface, the total resistivity of the sample R , is R = 2R + Rgb (Vgb ), where Vgb is the potential across the interface, Rgb (Vgb ) is the voltage-dependent resistivity of the interface and R is the resistivity of the current limiting resistors. The applied bias dependence of the potential drop at the interface is directly assessable by SSPM and is referred to as the voltage characteristic of the interface. To compensate for potential variations due to differences in local work function, images under applied lateral bias should be corrected by the grounded surface potential values. In general case, interface current-voltage characteristics, Igb (Vgb ), can then be obtained as     Igb Vgb = V − Vgb /2R, (13)

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provided the values of current limiting resistors are known. The current limiting resistors, R, can be varied to determine the presence of stray resistances in the circuit (e.g. contact and bulk resistances). Alternatively, the current, Igb , can be measured directly using a current-voltage converter. Similar analyses can be performed for the transport in multiple interface systems [53]. Given the unavoidable limitations for the resolution and precision of potential measurements by SPM, this approach for I-V curve reconstruction is applicable if the interface resistance and circuit termination resistance are well matched (i.e., Rgb /R ∼ 0.01 ÷ 1). For strongly nonlinear interfaces such as metal-semiconductor junctions, the I-V curve is highly asymmetric and effective resistance varies by many orders of magnitude. In this case, the analysis can be performed using the (known) analytical form for I-V curve. For transport across a Schottky barrier, the current is     q Vd Id = I0 exp − 1 + σ Vd (14) nkT where Vd is potential across the junction, q = 1.6 ·10−19 C is electron charge, n is ideality factor, k = 1.38 ·10−23 J/K is the Boltzmann constant, T is temperature, and σ is the leakage conductivity. In the limit of a large forward bias Eq. (13) simplifies to Vd = (kT /q) ln(Vdc /2R I0 ). Therefore, for a positively biased diode the potential drop at the interface is expected to be small and hardly detectable by SSPM. For a large negative bias, however, the potential drop occurs primarily at the interface. The crossover between the two regimes is expected at a lateral bias V = −2 RI0 and in this limit Eq. (13) becomes Vd = (V + 2R I0 )/(1 + 2Rσ )

(15)

Equation (15) implies that for finite conductivity in a reverse-biased diode, the potential drop occurs both at the diode and at current limiting resistors. Therefore, experimental voltage characteristics of the interface can be used to obtain both the saturation and leakage current components of diode resistivity. 3.2.1 ac Transport Properties by SIM For a single electroactive interface the analysis of the SIM-imaging mechanism is similar to that of SSPM. For the equivalent circuit in Figure 14(c) the total impedance of the circuit, Z  , is Z  = 2R + Z gb , where Z gb is the grain boundary impedance. The grain boundary equivalent circuit is represented by a par−1 −1 allel R-C element and the impedance is Z gb = Rgb + iωC gb , where Rgb and C gb are the voltage-dependent interface resistance and capacitance. Experimentally accessible and independent of the tip properties are the interface phase shift, ϕgb = ϕ2 − ϕ1 , and the amplitude ratio, A1 /A2 , across the interface. Interface phase shift is calculated from the ratio of impedances from each side of the interface, β = R/(Z gb + R), as tan(ϕgb ) = Im(β)/Re(β) (impedance divider effect). For the equivalent circuit in Figure 14(d) tan(ϕd ) =

ωCd Rd2 (R + Rd ) + Rω2 Cd2 Rd2

(16)

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TABLE 1. Frequency dependence of interface phase shift and amplitude ratio Frequency, ω Low-frequency limit, ω ≪ ωr High-frequency limit, ω ≪ ωr −1 −1  C gb 1 + Rgb /R Crossover frequency, ωr = Rgb

Phase shift, tan(ϕgb ) ωC gb

Amplitude ratio, A1 /A2

2 Rgb

(R + Rgb )

1 ωC gb R

Rgb  2 R(R + Rgb )

The voltage oscillation amplitude ratio, A1 /A2 = |β|−1 , is  2 (R + Rd ) + Rω2 Cd2 Rd2 + ω2 Cd2 Rd4 −2 β = 2  R 2 1 + ω2 Cd2 Rd2

R + Rgb R 1 

R + Rgb R

(17)

The high- and low-frequency limiting behaviors for Eqs. (16,17) are summarized in Table 1. In the high frequency limit phase shift at the interface is determined by the interface capacitance and circuit termination only. Thus, SIM phase imag−1 −1 ing at frequencies above the interface relaxation frequency, ω ≫ ωr = Rgb C gb , provides a quantitative measure of interface capacitance. Similarly to conventional impedance spectroscopy [54], the interface phase shift and the amplitude ratio can be used simultaneously to determine the interface transport properties. For frequency independent Rgb , C gb (Model 1), the frequency dependence of the interface phase shift and the amplitude ratio can be fitted to Eqs. (16,17), where C gb and Rgb are now fitting parameters. Alternatively, frequencydependent interface resistance and capacitance Rgb (ω), C gb (ω) (Model 2) can be calculated at each frequency from the experimental phase shift and amplitude ratio. Application of this analysis to frequency-dependent transport at electroactive interfaces in SrTiO3 is reported elsewhere [55]. Such data are expected to be particularly important for the characterization of interfaces possessing significant frequency dispersion of the interface transport properties, e.g., due to interface states or deep traps at semiconductor grain boundaries [56] or due to several relaxation processes in ionic conductors, for which interpretation of conventional impedance spectroscopy results is not straightforward.

3.3 Resolution One of the key characteristics of any SPM technique is spatial resolution. For current-based techniques, the resolution is ultimately determined by the contact area between the tip and the surface, which is on the order of several nanometers as discussed in section I. However, in force-based techniques such as SIM and SSPM, the probing volume is determined by relatively long range capacitive interactions between the tip and the surface. The algorithms for the determination of spatial resolution in SSPM and magnetic force microscopy have been extensively studied

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using both direct calculations from known probe geometry [57,58], mathematical modeling [59], and reconstruction methods [60]. The analysis of the image formation mechanism in SPM is greatly simplified if the imaging is linear, i.e., a measured image, I (x), where x is a set of spatial coordinates, can be represented as a convolution of the ideal image I0 (x − y) and the microscope resolution function, F(y), as  I (x) = I0 (x − y)F(y)dy + N (x) (18)

where N (x) is the noise function. The Fourier transform of Eq. (18) is I (q) = I0 (q)F(q) + N (q)



(19)

ikx

where I (q) = I (x)e dx, I0 (q), F(q) and N (q) are the Fourier transforms of the measured image, ideal image, resolution function, and noise, respectively. The instrument resolution function can be determined directly provided that the ideal image I0 (q) is known. Once the resolution function is determined for a known calibration standard, it can be used to evaluate the ideal image, I0 (x), from the measured image, I (x) for an arbitrary sample. The width of F(y) provides a quantitative measure of lateral resolution. From Eq. (19), the resolution function can be determined from suitable standard for which the ideal image is known. However, measurements in ambient are prone to the formation of conductive surface water layers and local contamination, resulting in a significant smearing of potential contrast even in well-defined systems such as interdigitated electrode systems, two-phase materials, or ferroelectric domains. An alternative approach for the calibration of resolution can be based on point-source type standards, such as carbon nanotubes [61]. In this case, the lateral size of the nanotubes is well below both the geometric and electrostatic radius of the tip, providing an ideal calibration standard of the tip properties. For a system consisting of carbon nanotubes on a substrate, the force between the tip and the surface can be written as [55] ′

′

′

2Fz = Cts (Vt − Vs )2 + Cns (Vn − Vs )2 + Ctn (Vt − Vn )2

(20)

where Vt is the tip potential, Vn is the nanotube potential and Vs is the surface potential, Cts is the tip-surface capacitance, Cns is the nanotube-surface capacitance and Ctn is the tip-nanotube capacitance, and the derivative is taken with respect to the z direction. When an ac bias is applied to the nanotubes (SIM), Vn = V0 + Vac cos(ωt) and Vs = V0 . Therefore, the first harmonic of tip-surface force is ′ F1ω = Ctn Vac (Vt − V0 )

(21)

In comparison, application of an ac bias to the tip, Vt = Vdc + Vac cos(ωt), yields ′ F1ω = Ctn Vac (Vdc − V0 ) + Cts′ Vac (Vdc − Vs )

(22)

Therefore, applying an ac bias directly to the carbon nanotube allows the tipsurface capacitance to be excluded from the overall force.

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Equation (21) can be generalized in terms of the tip-surface transfer function, F(x, y) = C z′ (x, y), defined for SIM and SSPM as the capacitance gradient between the tip and a region dxdy on the surface as F1ω = (Vt − V0 )  F(x, y)Vac (x, y) d x d y, which has the form of Eq. (18) for linear imaging. For a nanotube oriented in the y-direction and taking into account the small width, w0 , of the nanotube compared to the tip radius of curvature, Eq. (18) can be integrated as  F1ω (a) = w0 Vac (Vt − V0 ) F(a, y) d y (23)

where a is the distance between the projection of the tip on the surface and the nanotube. Assuming a rotationally invariant tip, the resolution function is  F(x, y) = F(r ), where r = x 2 + y 2 and Eq. (23) can be rewritten as a function of a single variable, a. Therefore, the resolution function can be found by numerically solving Eq. (23) using experimentally available force profiles across the nanotube, F1ω (a). The validity of the proposed standardization technique is illustrated in Figure 15. If the measurements are made sufficiently far (1–2 µm) from the biasing contact, the image background and potential distribution along the nanotube are uniform indicating the absence of contact-probe interactions. The height of the nanotube is a = 2.7 nm, while apparent width is H = 40 nm due √ to the convolution with the tip shape. Simple geometric considerations, H = 2 Ra, yield a tip radius of curvature of R ≈ 75 nm. The SIM amplitude profile is significantly broader, with a full width at half-maximum (FWHM) of at least ∼100 nm, which increases with tip-surface separation. Experimentally measured SIM amplitude profiles perpendicular to the nanotube, F1ω , were found to have Lorentzian shape, F1ω (x) = F0 +

w 2A , π 4(x − xc )2 + w 2

(24)

where F0 is an offset, A is the area below the peak, w is the peak width and xc is the position of the peak. The offset F0 provides a direct measure of the non-local contribution to the SPM signal due to the cantilever and conical part of the tip [51,62–64]. The distance dependence of peak height h = 2A/.π w for large tipsurface separations is h ∼ 1/d. The distance dependence of width, w, is shown in Figure 15(f) and is almost linear in distance for d > 100 nm. The integral Eq. (23) can be solved analytically and the radially symmetric resolution function in SIM/SSPM is 2A w F(r ) = (25) π (4r 2 + w 2 )3/.2 where A and w are z-dependent parameters determined in Eq. (25) and r is radial distance. Equation (25) can be used to determine the tip-shape contribution to electrostatic SPM measurements in systems with arbitrary surface potential distributions. For example, for a stepwise surface potential distribution such as grain boundary

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or metal-semiconductor interface, Vsurf = V1 + (V2 − V1 )θ(x), where θ (x) is a Heaviside step function, provided that the intrinsic interface width is significantly smaller than the microscope resolution. In this case, the measured potential profile will be Veff = V1 + V2 arctan (2x/w)/.π , provided that the cantilever contribution to the measured potential is small. Figure 15(f) shows the width of the SIM phase profile across a grain boundary in a Nb-doped SrTiO3 bicrystal. From independent measurements the double Schottky barrier width is 1

(17)

Selected values of the integral function I1 (n) are listed in Table 1. It can be shown that the accuracy of this approximation increases not only with larger oscillation amplitudes A, but also with larger values of n. A discussion on the accuracy of the different formulas can be found in [25].

3 Application of Dynamic Force Microscopy 3.1 Mechanisms of DFM Contrast Formation on Semiconductors Semiconductors were the first class of material to be resolved with atomic resolution using DFM [2,3]. Even though semiconductors can quite easily be imaged down to the atomic scale by alternative methods such as scanning tunneling microscopy (STM), they are still frequently investigated by DFM due to the complementary information obtained. Moreover, semiconductors are likely to be

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515

[001]

height (pm)

[110]

0 -10 0

10 nm

a)

10

b)

1 2 3 4 lateral position (nm)

FIGURE 5. (a) Atomic-scale FM-DFM image of InAs(110) with missing protrusions, which can be identified as As vacancies [26]. The size of an individual unit cell is 0.606 nm x 0.427 nm. (b) Section along the white line with the double arrow. It was taken across one of the vacancies, which manifests as a depression of about 15pm depth.

the class of materials where the DFM contrast mechanism is best understood due to numerous theoretical studies, including computer simulations that target semiconducting surfaces. Therefore, we will first discuss the DFM contrast formation on semiconductors before we generalize for other surfaces. To illustrate the various aspects of contrast formation, we will concentrate on III-V semiconductors as a model system in general and indium arsenide in particular. 3.1.1 Basic principles: Imaging the Total Charge Density with Non-Reactive Tips The measurement presented in Figure 5 demonstrates the level of resolution that can be achieved with DFM applied in ultrahigh vacuum. The data has been obtained on the (110) surface of an n-doped InAs single crystal (sulfur ≈ 3 × 1018 cm−3 ), which has been cleaved in ultrahigh vacuum [26]. Figure 5(a) represents a topographic image, where each of the protrusions reflects an arsenic atom. Individual defects are readily visible. The cross section presented in Figure 5(b) shows that the noise level is below 2 pm rms. InAs crystallizes in the ZnS structure, i.e., the (110) surface is made up of zigzag chains of alternating In and As atoms along the -direction. Therefore, one might expect that both atomic species, In and As, should be visible. According to the bond rotation model, however, which is valid for most III-V semiconductors, the As atoms relax outward and the In atoms inward, lifting the As sublattice by 80 pm above the In sublattice (cf. Figure 6(a)) [26]. As a result, the In atoms are not visible, and the rows of bright protrusions can be identified as the As atoms where the total valence charge density has its maximum (Figures 5(a) and 6(b)) [26,27]. A similar observation was made by Ohta et al. on InP [28]. More detailed analysis ˚ reveals that the observed contrast is essentially caused by short-range (3–6 A) interaction forces between tip and sample, which are mainly governed by the total electron density at the surface. Thus, if the probe tip only negligibly influences the electron density of the sample surface, as it does in Figs. 5 and 6(b), the resulting

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In relaxed In As

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FIGURE 6. (a) Relaxed (110) surface of InAs according to the bond rotation model for IIIV semiconductors (side view). The In atoms, having empty dangling bonds, are located about 80 pm lower than the As atoms featuring filled dangling bonds. (b) DFM image of the InAs(110) surface acquired with a non-reactive tip. Only one feature per unit cell is visible. The bright protrusions can be identified as As atoms [27]. (c, d) Two examples of dynamic mode SFM images where two features per surface unit cell are resolved on InAs(110)-(1 × 1). The second feature, an additional protrusion in (c) and a depression in (d), is located between the bright protrusions and can be attributed to the presence of the lower lying In atoms.

DFM image can be interpreted as a map of the total electron density at the sample surface, which is usually regarded as representing the “topography” of the sample. 3.1.2 Imaging with Reactive tips: Orbital Hybridization and the Onset of Bond Formation In many cases, however, the atom at the tip apex exhibits reactive bonds, which are likely to interact with electron orbitals of surface atoms. In this case, the electron density at the sample surface will be significantly disturbed by the presence of the tip at close tip-sample distances. The images presented in Figure 6(c) and 6(d) can be explained by such an interaction. In both images, a second feature emerges at exactly the position where the In atom is located [26,29]. The nature of this second feature, however, is quite different: It manifests as an additional protrusion or “shoulder” in (c), while depressions are observed in (d). This at the first sight puzzling contradiction can be solved by assuming different types of tips (e.g., tips that have either an In atom, a Si atom, or an As atom at the tip end), which exhibit very different ways of interacting with the surface atoms of the sample. More information on this subject can be found in [26, 27]; computer simulations for the very similar case of GaAs are presented in [30, 31]. Later, the effect was confirmed for GaAs by Uehara et al. [32,33]. Using distance-dependent DFM imaging, they also showed that effects arising from In atoms are only visible at small tip-sample distances. As a result, we can conclude that atomically resolved DFM images represent a mixture between the sample topography (i.e., the total electron density at the sample surface) and the reactivity of the tip with specific sites at the sample surface, which is usually very short-range. This reactivity is essentially due to orbital hybridization [34,35], which is sometimes also regarded as reflecting the

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onset of chemical bonding [36]. In the present case, this feature allows to visualize positions of atoms which are hidden under normal circumstances. To summarize, the presence of the tip near the sample surface is a factor that can significantly influence properties such as the electron distribution at the sample surface. The varying interaction strength between tip and sample during approach can then lead to a significant distance-dependence of the image contrast: at “larger” distances, where the onset of atomic resolution during tip-sample approach takes place, comparatively long-range electrostatic and van der Waals forces dominate the image contrast. Upon further approach, increasing levels of orbital hybridization involving both tip- and sample states might give rise to different contrasts on samples at intermediate and close distances. Experiments performed √ √ tip-sample by Morita et al. on the Si(111) 3 × 3-Ag surface, for example, illustrate this behavior elegantly [34,35]. This general mechanism gets even more complex if the atom at the tip end is replaced by another chemical species that exhibits different interaction strengths with the atoms at the sample surface; examples are given in [35,37,38]. 3.1.3 Tip-Induced Surface Relaxation and Adhesion Hysteresis Another important effect influencing atomic-scale contrast formation is the tipsample interaction that not only can alter the electron distribution at the surface, but also the actual location of the surface atoms. Attractive and repulsive forces acting between tip and sample can lead to a tip-induced relaxation of the position of the surface atoms relative to the bulk atoms, which increases with decreasing tipsample distance. Even though this effect is significant, it is difficult to quantify from experimental data since all surface atoms visible in an image are likely to relax in the same manner. As a consequence, effects due to surface atom relaxation cannot easily be separated from the “regular” increase in resolution caused by the reduced tip-surface separation. However, such effects might get evident near defects, where some atoms are more weakerly bonded to the bulk then others. This is the case in Figure 7, where a point defect on InAs is shown that has been imaged at two different tip-sample distances [26]. As discussed above, the protrusions reflect the positions of the As atoms. The two neighboring As lattice sites marked with X exhibit a different corrugation amplitude compared to their surrounding. We also note that the contrast inverts from (a) to (b) relative to the surrounding As atoms after the tip-sample distance has been decreased (resulting in an increase of the magnitude of the tip-sample interaction). From the symmetry with respect to the As atoms, it can be concluded that the point defect is located on the In sub-lattice. The observed distance dependence of the contrast indicates the presence of an In vacancy in the surface layer [26]. A missing In atom reduces the number of bonds of two neighboring surface As atoms from three to two. According to calculations carried out for GaAs(110), this results in an inward relaxation for surface cation vacancies [39]. With the tip approaching the surface, the additional attractive tip-sample interaction provides enough energy to pull the two weakly bonded As atoms toward the tip, e.g., into the vacuum region. Although

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Udo D. Schwarz and Hendrik H¨olscher FIGURE 7. DFM images of the same point defect on InAs(110) acquired at two different tipsample distances. The position of the two As lattice sites, which are influenced by the defect, are marked with X (X-sites). The symmetry suggests that the defect is located on an In lattice site, and the distance dependence indicates a surface In vacancy. The effective relaxation of the X-site As atoms with respect to the undisturbed As sublattice, as explained in more detail in the text, is influenced by the magnitude of the tip-sample interaction (see the line sections and the corresponding sketches below).

only the relaxation of sample atoms around a defect relative to the plane defined by the other surface As atoms can be directly observed in DFM, all other surface atoms will also relax due to the tip-sample interaction. In particular, relaxation of the foremost atom at the tip apex has to be considered, because of its exposed position. This has been confirmed by ab initio calculations for GaAs(110), where the tip atoms as well as the atoms of the defect free surface were allowed to relax [30]. Additional complication of the described effect occurs if the tip and the surface deform in such a way during an individual oscillation cycle that the force felt by the tip during approach and retraction is different. This does not only have an effect on the observed contrast that is difficult to quantify, it also can give rise to a significant energy dissipation mechanism [27]. Denoted as adhesion hysteresis, it has been numerously discussed in theoretical work about DFM (see also Section 4.3 or [40,41] for reviews), but experimental proof has been difficult so far [42–44]. 3.1.4 Charge Imaging Like all forces acting between tip and sample, electrostatic forces cause a shift of the resonance frequency if the oscillating tip approaches the surface.

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FIGURE 8. Large-scale DFM image acquired on an atomically flat terrace of n-InAs(110) [46]. The image has been taken directly after cleavage under ultrahigh vacuum conditions. No bias voltage has been applied during data acquisition. The observed corrugation is on the order of 0.1–0.2 nm and can be attributed to the presence of near-surface doping atoms, which lead to a locally varying electrostatic tip-sample interaction.

As a consequence, they are readily detectable by DFM. In most cases, electrostatic forces exist even if both tip and sample are grounded or on the exact same potential. This is because tip and sample can be regarded as two electrodes of a capacitor. If they are electrically connected via their back sides and have different work functions, electrons will flow between tip and sample until their Fermi levels are equalized. As a result, an electric field, and consequently, an attractive electrostatic force, exists between them at zero bias. This contact potential difference can be balanced by applying an appropriate bias voltage [45]. But even then, local variations in the surface potential can cause a local variation of the resonance frequency that has a visible effect on DFM images. Again, we will explore this aspect with the example of InAs. As mentioned earlier, the InAs sample shown in Figs. 5 to 7 has been doped with sulfur in a concentration of approximately 3 × 1018 cm−3 . Assuming an equal distribution of sulfur everywhere in the crystal, this is equivalent to a separation of 7 nm between individual sulfur atoms. In reality, however, sulfur atoms are statistically distributed, leading to a variation of the dopant density on the nanometer scale. Since sulfur acts as electron donor, this causes a modulation of the electron density on the same scale, which modifies the surface potential and thus shows up in DFM images. An example for this effect is given in Figure 8 [46]. The 2 × 2 - µm image shows an atomically flat terrace on n-InAs, which appears to have a corrugation of around 0.1–0.2 nm. We can interpret this “apparent corrugation” according to the above discussion as reflecting the modulation of the electron density (charge imaging). In the present case, this is equivalent with the distribution of the doping atoms. The “brightness” of the contrast is influenced by how close the doping atoms are to the surface. The cloudy structure arises from the fact that the screening length, i.e., the distance on which an individual doping atom significantly disturbs the charge density, is 8 nm in sulfur-doped n-InAs. This distance is larger than the mean distance between individual sulfur atoms of 7 nm. Therefore, the charge

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FIGURE 9. Upper-left: Large-scale DFM image (120 × 120 nm) of p-InAs(110) with a monoatomic step on the left hand side. The most prominent features are the approximately 150 bright spots, which can be identified as being caused by the Coulomb potentials of individual near surface doping atoms. Lower-left: Atomically resolved DFM image of the same sample displayed in a quasi-3D-representation. Image size is 16 × 10 nm. Bright areas with an intact atomic structure (see the cross section along (a)) correspond again to ionized (negatively charged) near surface doping atoms (acceptors). Dark areas, in contrast, have at least one missing protrusion in their center (cf. (b)) and can be attributed to positively charged As vacancies.

clouds around the doping atoms overlap, which leads to the observed “cloudy” contrast. Even though the charge distribution in Figure 8 is on the nanometer scale, the high resolution of DFM operated in ultrahigh vacuum allows charge imaging down to the atomic scale, if an appropriate sample is investigated. On p-InAs, screening lengths are shorter than on n-InAs (2 nm), so that charge clouds around doping atoms should not overlap on p-InAs if the sample crystal exhibits a similar doping concentration than the crystal imaged in Figure 8. This can be seen in Figure 9. The picture in the upper-left corner represents an 120 × 120-nm area of the sample. The ∼150 different white spots belong to individual zinc doping atoms (concentration: ≈4–6 × 1018 cm−3 ) located at different depths below the surface (up to a maximum distance of about 2 nm, which is determined by the screening length). The lower-left image in Figure 9 represents a zoom to the atomic scale. The regular atomic corrugation is modulated by bright and dark areas. Bright areas

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FIGURE 10. Series of images demonstrating the bias dependence of the frequency shift at identical sample locations, which can be interpreted by the presence of an accumulation, depletion, or inversion zone underneath the probe tip. Bias voltages are applied with respect to the grounded cantilever. A detailed description of the experiment can be found in [46].

feature an intact atomic structure and correspond to ionized (negatively charged) near surface doping atoms (acceptors). As they attract holes, which represent the majority carriers on p-InAs, the surface appears elevated (see the cross section along line a). Dark areas have at least one missing protrusion in their center (see Figure (b)), therefore representing As vacancies. Since As vacancies on p-InAs are known to be positively charged (in contrast to As vacancies on n-InAs as the ones shown in Figure 5, which are neutral), they repel holes and thus appear dark. A more detailed discussion of the contrast formation can be found in [46]. An apparent problem in charge imaging is that effects due to topography and charge are difficult to distinguish in the images presented above. In contrast to all other forces acting between tip and sample, however, the electrostatic interaction is easily modified by applying appropriate bias voltages. This has significant influence on the electrostatic surface potential, but not on the topography. Therefore, information acquired at different bias voltages can be used to separate electrostatic interactions from other interactions. An example illustrating the bias dependence is shown in Figure 10. The sample is the same n-doped InAs crystal that has already been presented in Figs. 5 to 8. The contrast variation within the encircled area is used to discuss how an externally applied bias voltage Ubias influences the image contrast. This bias dependence of the contrast can be interpreted by the presence of an accumulation, depletion, or inversion zone underneath the probe tip. (a) At Ubias = −2.22 V, electrons (majority carriers) are accumulated at the surface. Bright areas correspond to a high density of doping atoms. (b) The contrast becomes weaker at smaller absolute values of Ubias . (c) At Ubias = +0.50 V, the contrast vanishes. The surface is depopulated of mobile charge carriers. (d) At Ubias = +2.75 V, holes (minority carriers) are generated near the surface. Inversion occurs and the contrast inverts. By subtracting images acquired with vanishing electrostatic contrast (compensated contact potential) from images acquired with substantial applied bias voltage, charge accumulations or depletions can be visualized, as it has been shown by Sugawara et al. [47] and Morita et al. [48] for Si-doped n-GaAs. A useful further discussion of the bias dependence of DFM images is given by Arai and Tomitori in [49].

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Finally, we would like to close this section with mentioning that a very convenient way of visualizing directly charge distributions at surfaces using DFM techniques has been developed with the so-called Kelvin probe microscopy, which involves the oscillation of the applied bias voltage. Using lock-in methods, the changing contribution caused by surface charges can be separated from the constant topography part. A detailed discussion of Kelvin probe microscopy is provided in contribution by Glatzel.

3.2 Insulators While the general mechanism of contrast formation in FM-DFM is very similar for all materials, there are differences due to the chemical nature of the specimen investigated. Most insulators do not feature dangling bonds in the way that semiconductors do, and the details of atomic-scale contrast mechanisms vary from material to material. Ionic crystals, e.g., are bonded by Coulomb interactions. Therefore, direct Coulomb interaction replaces orbital hybridization as the main interaction responsible for atomic scale contrast on ionic crystals. Other sources of interaction that have to be considered are image forces (the charge of ionized surface atoms induces a polarization in the conducting tip), capacitance forces, and forces due to tip and surface charging. While tip charging is usually not a major problem for conducting tips, charging of the sample surface might be significant on highly insulating ionic crystals due to charge separation during the cleavage process. As an example, DFM images acquired on NiO(110) are presented. In Figure 11(a), atomic resolution at a step edge is shown [50]. The step height is 0.22 nm, which is equivalent to a monoatomic step or, with other words, half of a unit cell. Atomic resolution is visible both on the upper and on the lower terrace. In addition, a defect that comprises at least three atoms is located in the upper right corner. Figure l1(b) displays a high resolution image of the atomic structure

FIGURE 11. (a) Atomically resolved step edge of NiO(001). In the upper-right corner, a defect comprising at least three missing atoms is visible. (b) High-resolution image of NiO(001). In the center of the image, an impurity atom that is 10 pm higher that the surrounding atoms is visible.

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on NiO. The atom right in the center is about 10 pm higher that all surrounding atoms, i.e., it reflects an impurity atom of a different chemical species. Its exact nature, however, cannot be further specified. Moreover, we note that in both images Figures. 11(a) and 11(b), only one atom per unit cell is visible. Without knowledge of the exact tip structure, it is not possible to determine which one of the ions— nickel or oxygen—is imaged [51]. The unambiguous interpretation of atomically resolved DFM images on insulators has so far only been achieved in very few cases, such as, e.g., for some experiments performed on the CaF2 (111) surface [52].

3.3 Van der Waals Materials On most materials, atomic resolution is enabled by strong short-range interactions such as Coulomb forces or chemical forces arising from orbital hybridization. As a last example for contrast mechanisms in DFM, we will explore in this section what resolution can be achieved on weakly interacting surfaces such as van der Waals materials. Due to the weak interaction strength, atomic resolution has not yet been observed on van der Waals materials at room temperature due to the insufficient signal-to-noise ratio of FM-DFM at these temperatures, which is most prominently caused by thermal drift and thermally induced cantilever oscillations. If the microscope is cooled to low temperatures, however, these noise sources can be suppressed, so that the sensitivity becomes sufficient to image the atomic structure. A first example is given in Figure 12(a), which shows an atomic-scale image of graphite. In graphite, a layered material, the carbon atoms are covalently bonded and arranged in a honeycomb structure within the (0001) plane. In the highresolution DFM images presented in Figure 12(a), however, a large maximum and two different minima have been resolved instead of the expected hexagonally arranged protrusions [53]. A simulation using the Lennard–Jones potential, in which the attractive part is given by the short-range interatomic van der Waals force,

FIGURE 12. (a) Atomic-scale image of graphite(0001). Note that the protrusions reflect the locations of the minima of the surface potential (hollow sites), while the atoms are situated in the apparent depressions (see text for details). (b) Atomically resolved image of xenon. Here, protrusions actually mark the locations of the individual xenon atoms. Both images are 5.3 nm x 5.3 nm in size and have been acquired at a temperature of T = 22K .

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explained this finding: the large maximum could be assigned to the hollow site, while the minima represented the locations of the atoms [54,55]. The two different types of minima reflect whether the carbon atom has a neighbor in the layer below or not. In other words, the contrast on graphite is inverted: atoms manifest as depressions, while the highest protrusion indicates the location of the potential minima. This surprising finding arises from the fact that the nearest-neighbor distance in graphite is only 142 pm and thus very small. As a result, the attractive force on the foremost tip atom is maximal if it is positioned directly in the center of the hexagon, where all six carbon atoms forming the hexagon attract the probing apex atom simultaneously. On the other hand, the attraction is minimal if the tip is positioned directly above a surface atom. This mechanism should be again distancedependent: if the tip is approached further and further, forces above the locations of the atoms should get larger than the forces at the hollow sites, and hexagonally arranged protrusions that actually reflect the atomic positions should become visible. This assumption agrees with the results of Hembacher et al. [56], who observed the complete hexagonal rings of carbon atoms as maxima at close distances. While experiments on graphite basically take advantage of the increased stability and signal-to-noise ratio at low temperatures, solid xenon, a pure van der Waals crystal, can only be observed at sufficiently low temperatures due to its melting temperature of 161 K [57]. Since xenon is additionally a good insulator, DFM applied in ultrahigh vacuum is the only real space method available today that allows the study of solid xenon on the atomic scale. Figure 12(b) presents an atomically resolved image of a well-ordered xenon film adsorbed on graphite(0001). The sixfold symmetry and the distance between the protrusions corresponds well with the nearest neighbor distance in the closed packed (111) plane of bulk xenon, which crystallizes in the face centered cubic structure. A comparison between experiment and simulation confirmed that the protrusions correspond to the position of the xenon atoms [58].

4 Dynamic Force Spectroscopy Ever since it has been invented in 1986, atomic force microscope has been widely used to study tip-sample interactions for various material combinations. If performed as a function of the tip-sample separation, such measurements are referred to as force spectroscopy. Unfortunately, force spectroscopy is often strongly complicated by an instantaneous jump of the tip to the sample surface. The origin of this “jump to contact” is an instability in the effective tip-sample potential at the position where the actual force gradient of the tip-sample interaction is larger than the spring constant of the cantilever [59]. This problem is avoided when operating the AFM in FM mode. If the oscillation amplitude is large enough, the “jump to contact” of the tip is prevented by the restoring force of the cantilever [23]. In section 2.3, we showed how the frequency shift can be calculated for a given tip-sample interaction law. In general, however, the inverse problem will be of more interest: How can the tip-sample interaction

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FIGURE 13. Example for the application of dynamic force spectroscopy. The gray symbols reflect the tip-sample force as calculated from the experimental data shown in Figure 3 using Eq. (18). The force Fts Eq. (19) is plotted by a dashed-dotted line; the solid line represents the best fit based on the contact force Fc Eq. (20). The border between “contact” and “noncontact” force is marked by the position z 0 ; Fad indicates the adhesion force (cf. Sect. 4.2).

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be determined from frequency shift data? The answer to this question is given in this section and will lead us to the dynamic force spectroscopy (DFS) technique, which is a direct extension of FM-DFM.

4.1 Determining Forces from Frequencies For typical DFM setups, it is straightforward to measure the frequency shift with a fixed oscillation amplitude A as a function of the actual tip-sample distance D (i.e., the distance of closest approach of the tip during an individual oscillation cycle). An example of such behavior is illustrated in Figure 13 (see section 2.3). The calculation of the tip-sample interactions from such data sets is possible by reversing the integral in Eq. (14). As shown by D¨urig [24], this results in Fts (D) =

∞ √ cz A3/2 ∂   f (z) dz, 2 √ f0 ∂ D z−D

(18)

D

allowing a direct calculation of the tip-sample interaction force from frequency shift versus distance curves. Application of this formula to the experimental frequency shift versus distance curves presented in section 2.2 is shown in Figure 13. The obtained force curves are almost identical although obtained with different oscillation amplitudes. The fact that tip-sample potentials and forces can be determined with this accuracy without “jump-to-contact” demonstrates the advantage of dynamic force spectroscopy compared to force-distance curves acquired without oscillating the cantilever, as DFS can probe the complete attractive and repulsive regime of the force curves without discontinuity. Since Eq. (14) was derived with the condition that the oscillation amplitude is considerably larger than the decay length of the tip-sample interaction,

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the same restriction applies to Eq. (18). However, using more advanced algorithms it is also possible to determine forces from dynamic force spectroscopy experiments without restriction to large amplitudes. The numerical approach of Gotsmann et al. [18,60], e.g., works in every regime, as do the semianalytical methods introduced by D¨urig [61], Giessibl [62], and Sader and Jarvis [63]. Not only is the z-resolution of DFS remarkable—if highly stable DFM setups such as microscopes operated at low temperatures are used, the lateral resolution of dynamic force spectroscopy can be driven down to the atomic scale. Lantz et al. [64] measured frequency shift versus distance curves at different lattice sites of the Si(111)-(7 × 7) surface (see Figure 14). In this way, they were able to distinguish differences in the bonding forces between inequivalent adatoms of the 7 × 7 surface reconstruction of silicon.

FIGURE 14. Dynamic force spectroscopy performed with atomic resolution on Si(111)-(7 × 7). The frequency shift versus distance curves plotted in (A) were measured at the positions marked in the topographical image shown in (B). The atoms labeled “2” and “3” represent inequivalent adatoms (cf. also the cross section displayed in C); DFS is able to distinguish differences in their bonding strength (see insert in A). Experiments have been performed at a temperature of T = 7.2 K. (Reprinted with permission from [64]. Copyright 2001, AAAS.) (See also Plate 3 in the Color Plate Section.)

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FIGURE 15. (a) Principle of 3D force spectroscopy with the example of NiO(110) (cf. Sect. 3.2). The cantilever oscillates near the sample surface and measures the frequency shift at all locations defined by a dense raster grid inside an x yz-box. The surface topography of the NiO sample, as obtained immediately before recording the spectroscopy field, is displayed ˚ × 10 A). ˚ (b) The reconstructed force field in a perspective representation (image size: 10 A of NiO(001) taken along the line indicated in a). The positions of the atoms are clearly visible.

This concept can be extended to achieve true three-dimensional force spectroscopy by mapping the complete force field above the sample surface [16]. Figure 15(a) illustrates the measurement principle. Frequency shift vs. distance curves are recorded on a matrix of points perpendicular to the sample surface. Using Eq. (18), the complete three-dimensional force field between tip and sample can be recovered with atomic resolution. Figure 15(b) shows a cut through the force field as a two-dimensional map, from which the decay of the force field into the vacuum can be recovered. Recently, it became possible to use dynamic force microscopy for nanomanipulation. Atomic-scale manipulation has been demonstrated by Oyabu et al. [44], who removed individual atoms from a Si(111)-7 × 7 surface with the AFM tip. Subsequently, they were able to re-deposit the same atoms from the tip back onto the surface. Loppacher et al. [65] achieved pushing on different parts of an isolated Cu-TBBP molecule, which is known to possess four rotatable legs. They measured force-distance curves while one of the legs was pushed by the AFM tip and turned by 90◦ . By this means, they were able to quantify the energy that was dissipated during the “switching” of this molecule between different conformational states. The possibility simultaneously to exert and measure forces during single-atom or -molecule manipulation represents an exciting future application for high-resolution DFM experiments.

4.2 Analysis of Tip-Sample Interaction Forces Since the above-presented DFS methods can be used to measure tip-sample interactions with high resolution, this approach opens a direct way to compare experiments

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with theoretical models and predictions. As an example, we will analyze the force curves presented in Figure 13. Following a suggestion by Giessibl [23], we describe the force between tip and sample by a combination of a long-range (van der Waals) and a short-range (Lennard–Jones) term. The long-range part reflects the van der Waals interaction of the tip with the sample, modeled as a sphere with radius R above an atomically flat, infinitely extended plane. The short-range Lennard–Jones part represents the interaction of the last tip apex atom with the surface. With these assumptions, we obtain   AH R 12E 0  r0 13  r0 7 Fts (z) = − 2 + . (19) − 6z * r z z ' () () * ' 0 long−range

short−range

AH is the Hamaker constant, and E 0 and r0 are the binding energy and the equilibrium distance of the Lennard–Jones force, respectively. Note that this approach does not consider elastic contact forces between tip and sample. Therefore, we will call Fts the “noncontact force” in the following. A fit of this equation to the experimental tip-sample force data is indicated in Figure 13 by a dashed-dotted line; the parameters used are AH R = 2.4 × 10−27 ˚ and E 0 = 3 eV [15]. The regime right from the minimum fits well Jm, r0 = 3.4 A, to the experimental results, but the deep and wide minimum of the experimental curves cannot be described accurately with the noncontact force. This is caused by the steep increase of the Lennard-Jones force in the repulsive regime (Fts ∝ 1/r 13 for z < r0 ), which does not consider elastic deformation. Left of the minimum, however, the tip-sample force is mainly determined by elastic contact forces, as the tip starts to tap on the surface. This elastic contact behavior can be described with the assumption that the overall shape of tip and sample changes only slightly until point contact is reached and that, after the formation of this point contact, the tip-sample forces are given by the well-known Hertz theory (see, e.g., [66,67]). The Hertz theory considers only the repulsive elastic force between tip and sample, but no additional deformation due to attractive forces (see, e.g., [68] for a discussion about this topic). The easiest way to consider attractive forces is by a simple offset (Hertz-plus-offset model). This approach coincides with Maugis’ approximation [69] to a model introduced earlier by Derjaguin, Muller, and Toporov (DMT model) [70]. It results in a force law of the type Fc = G 0 (z 0 − z)3/2 + Fad

for

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(20)

The first term in this equation describes the elastic behavior of a Hertzian contact, where z 0 is the point of contact and G 0 a constant that depends on the elasticity of tip and sample and on the shape of the tip [67]. The offset Fad is the adhesion force between tip and sample surface. Since the experimentally measured tipsample force shows a reasonable agreement with the noncontact force Fts until it reaches its minimum, we define the contact point by this minimum, i.e., z 0 = ˚ and therefore Fad = Fts (z 0 ) = −6.7nN. With this choice, the min{Fts (z)} = 3.7A,

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connection between noncontact and contact force and their corresponding force gradients is continuous. A fit of Eq. (20) to the experimental data is given in Figure 13 by a solid line (G 0 = 5.8 × 105 nN/m3/2 ). The experimental force curves agree well with the contact force law for distances D < z 0 . Therefore, we can summarize that the overall behavior of the experimentally obtained force curves can be adequately explained by a combination of long-range (van der Waals), short-range (Lennard– Jones), and contact (Hertz/DMT) forces. Furthermore, this result demonstrates that not only noncontact, but also elastic contact forces can be quantitatively measured by dynamic force spectroscopy.

4.3 Measurement of Energy Dissipation Besides the measurement of tip-sample forces, another physical mechanism exists that can be analyzed with dynamic mode microscopy. As explained in section 2.3, the gain factor g (and thus the excitation amplitude aexc , which is directly proportional to g) represents a measure for the energy dissipation due to non-conservative tip-sample interactions. It can be shown that in self-excitation mode, conservative and dissipative interactions can be strictly separated if the time delay t0 has been adjusted to match an excitation-oscillation phase difference of 90◦ [19,22]. Energy dissipation is partially caused by the cantilever itself (intrinsic damping). More interestingly, however, energy is “lost” due to the tip-sample interaction. Conservative forces acting at the tip-sample junction can, at least in vacuum, be understood in terms combinations of van der Waals, electrostatic and chemical interactions. In contrast, the dissipative processes taking place when the tip comes close to the sample surface are comparatively poorly understood. Stowe et al. [72] modified the experimental setup of an dynamic force microscope and oscillated the cantilever parallel to the sample surface. They observed that if a voltage potential is applied between tip and sample, charges are induced in the sample surface, which will follow the tip motion. Due to the finite resistance of the sample material, energy will be dissipated during the charge movement. This effect has been used to image the doping level of semiconductors. But even in absence of external electromagnetic fields, energy dissipation was observed if tip and sample approached each other within less than about one nanometer. Clearly, mechanical surface relaxations must give rise to energy losses. One could think of the AFM tip as a small hammer, hitting the surface and inducing phonon excitations. From a continuum mechanics point of view, we assume that the mechanical relaxation of the surface is not only governed by elastic responses. Viscoelastic effects of soft surfaces are also likely to render a significant contribution to energy dissipation. In the atomistic view, the last tip atom can be envisaged changing position while yielding to the tip-sample force field. A fully reversible change of position would not result in a loss of energy. Still, it has been pointed out by Sasaki and Tsukada [73] that a change in atom position would result in a change in the force interaction itself. Therefore, it is possible that the tip atom changes position at different tip-surface distances during approach and retraction, effectively causing an

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FIGURE 16. FM-DFM image of the Si(111)-(7 × 7) surface. The atomic structure can be seen simultaneously in the topography (a), the tunneling current (b), and the dissipation channel (c). Defects are marked by circles and visible in all three channels. (Reprinted with permission from [71]. Copyright 2000, Elsevier.)

atomic-scale hysteresis to develop. This model has been extended by Kantorovich and Trevethan [74], who included thermal activation processes. The dissipation channel (i.e., the recorded values of either the gain factor g or the excitation amplitude aexc , respectively, as a function of the lateral position) can be also used to image surfaces with atomic resolution as shown by L¨uthi et al. [75] and Guggisberg et al. [45]. Instead of feedbacking the distance on the frequency shift, the excitation amplitude in FM mode can even be used as the control signal. The DFM image of the Si(111)-(7 × 7) reconstruction shown in Figure 16 was successfully recorded this mode. The step edges of monoatomic NaCl islands on single crystalline copper have also rendered atomic resolution contrast in the dissipation channel [76].

Acknowledgments. The authors would like to thank Wolf Allers, Alexander Schwarz, and Shenja Langkat for their experimental results presented throughout this chapter. This contribution was prepared during the stay of U. D. Schwarz at the Center for Nanotechnology (CeNTech) of the University of M¨unster. H. H¨olscher acknowledges financial support from the German Federal Ministry of Education and Research (BMBF) (grant No. 03N8704) and the Deutsche Forschungsgemeinschaft (DFG) (grant No. HO 2237/2-1), U. D. Schwarz from the National Science Foundation (grant No. DMR-0414944) and the Petroleum Research Fund (grant No. 42259-AC5).

References 1. 2. 3. 4. 5. 6.

G. Binnig, C. F. Quate, and C. Gerber, Phys. Rev. Lett. 56, 930 (1986). F.-J. Giessibl, Science 267, 68 (1995). Y. Sugawara, M. Otha, H. Ueyama, and S. Morita, Science 270, 1646 (1995). T. Albrecht, P. Gr¨utter, D. Horne, and D. Rugar, J. Appl. Phys. 69, 668 (1991). R. Garcia and R. P´erez, Surf. Sci. Rep. 47, 197 (2002). Noncontact Atomic Force Microscopy, edited by S. Morita, R. Wiesendanger, and E. Meyer (Springer-Verlag, Heidelberg, 2002).

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7. F.-J. Giessibl, Rev. Mod. Phys. 75, 949 (2003). 8. H. H¨olscher and A. Schirmeisen, in Advances in Imaging and Electron Physics, edited by P. W. Hawkes (Academic Press Ltd., London, 2005). 9. Q. D. Zhong, D. Inniss, K. Kjoller, and V. B. Elings, Surf. Sci. Lett. 290, L688 (1993). 10. P. K. Hansma, J. P. Cleveland, M. Radmacher, D. A. Walters, P. E. Hillner, M. Bezanilla, M. Fritz, D. Vie, H. G. Hansma, C. B. Prater, J. Massie, L. Fukunaga, L. Gurley, and V. B. Elings, Appl. Phys. Lett. 64, 1738 (1994). 11. C. A. J. Putman, K. O. Vanderwerf, B. G. Degrooth, N. F. Vanhulst, and J. Greve, Appl. Phys. Lett. 64, 2454 (1994). 12. H. Ueyama, Y. Sugawara, and S. Morita, Appl. Phys. A 66, S295 (1998). 13. C. Loppacher, M. Bammerlin, F. Battiston, M. Guggisberg, D. M¨uller, R. L. H. R. Hidber, E. Meyer, and H.-J. G¨untherodt, Appl. Phys. A. 66, S215 (1998). 14. W. Allers, A. Schwarz, U. D. Schwarz, and R. Wiesendanger, Rev. Sci. Instrum. 69, 221 (1998). 15. H. H¨olscher, A. Schwarz, W. Allers, U. D. Schwarz, and R. Wiesendanger, Phys. Rev. B 61, 12678 (2000). 16. H. H¨olscher, B. Gotsmann, W. Allers, U. D. Schwarz, H. Fuchs, and R. Wiesendanger, Phys. Rev. Lett. 88, 019601 (2002). 17. B. Gotsmann, D. Kr¨uger, and H. Fuchs, Europhys. Lett. 39, 153 (1997); ibid 41, 581 (1998). 18. B. Gotsmann, B. Ancykowski, C. Seidel, and H. Fuchs, Appl. Surf. Sci. 140, 314 (1999). 19. H. H¨olscher, B. Gotsmann, W. Allers, U. D. Schwarz, H. Fuchs, and R. Wiesendanger, Phys. Rev. B 64, 75402 (2001). 20. B. Gotsmann and H. Fuchs, Appl. Surf. Sci. 188, 355 (2002). 21. H. H¨olscher, B. Gotsmann, and A. Schirmeisen, Phys. Rev. B 68, 153401 (2003). 22. U. D¨urig, N. J. of Phys. 2, 5.1 (2000). 23. F.-J. Giessibl, Phys. Rev. B 56, 16010 (1997). 24. U. D¨urig, Appl. Phys. Lett. 75, 433 (1999). 25. H. H¨olscher, U. D. Schwarz, and R. Wiesendanger, Appl. Surf. Sci. 140, 344 (1999). 26. A. Schwarz, W. Allers, U. D. Schwarz, and R. Wiesendanger, Phys. Rev. B 61, 2837 (2000). 27. V. Caciuc, H. H¨olscher, S. Bl¨ugel, and H. Fuchs, Nanotechnology 16, S59 (2005). 28. M. Ohta, H. Ueyama, Y. Sugawara, and S. Morita, Jpn. J. Appl. Phys. 34, L1692 (1995). 29. A. Schwarz, W. Allers, U. D. Schwarz, and R. Wiesendanger, Appl. Surf. Sci. 140, 293 (1999). ˇ 30. S. H. Ke, T. Uda, R. P´erez, I. Stich, and K. Terakura, Phys. Rev. B 60, 11631 (1999). ˇ 31. S. H. Ke, T. Uda, I. Stich, and K. Terakura, Phys. Rev. B 63, 245323 (2001). 32. N. Uehara, H. Hosoi, K. Sueoka, and K. Mukasa, Nanotechnology 15, S97 (2004). 33. N. Uehara, H. Hosoi, K. Sueoka, and K. Mukasa, Jap. J. Appl. Phys. 43, 4676 (2004). 34. T. Minobe, T. Uchihashi, T. Tsukamoto, S. Orisaka, Y. Sugawara, and S. Morita, Appl. Surf. Sci. 140, 298 (1999). 35. S. Morita and Y. Sugawara, Ultramicroscopy 91, 89 (2002). ˇ 36. R. P´erez, I. Stich, M. C. Payne, and K. Terakura, Phys. Rev. B 58, 10835 (1998). 37. K. Yokoyama, T. Ochi, Y. Sugawara, and S. Morita, Phys. Rev. Lett. 83, 5023 (1999). 38. S. Morita and Y. Sugawara, in Noncontact Atomic Force Microscopy, edited by S. Morita, R. Wiesendanger, and E. Meyer (Springer-Verlag, Heidelberg, Germany, 2002), pp. 47–77. 39. G. Schwarz, A. Kley, J. Neugebauer, and M. Scheffler, Phys. Rev. B 58, 1392 (1998).

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40. M. Gauthier, L. Kantorovich, and M. Tsukada, in Noncontact Atomic Force Microscopy, edited by S. Morita, R. Wiesendanger, and E. Meyer (Springer-Verlag, Heidelberg, Germany, 2002), pp. 371–394. 41. H.-J. Hug and A. Baratoff, in Noncontact Atomic Force Microscopy, edited by S. Morita, R. Wiesendanger, and E. Meyer (Springer-Verlag, Heidelberg, Germany, 2002), pp. 395–431. 42. T. Uchihashi, Y. Sugawara, T. Tsukamoto, M. Otha, S. Morita, and M. Suzuki, Phys. Rev. B 56, 9834 (1997). 43. S. Morita, Y. Sugawara, K. Yokoyama, and T. Uchihashi, Nanotechnology 11, 120 (2000). 44. N. Oyabu, O. Custance, I. Yi, Y. Sugawara, and S. Morita, Phys. Rev. Lett. 90, 176102 (2003). 45. M. Guggisberg, M. Bammerlin, C. Loppacher, O. Pfeiffer, A. Abdurixit, V. Barwich, R. Bennewitz, A. Baratoff, E. Meyer, and H.-J. G¨untherodt, Phys. Rev. B 61, 11151 (2000). 46. A. Schwarz, W. Allers, U. D. Schwarz, and R. Wiesendanger, Phys. Rev. B 62, 13617 (2000). 47. Y. Sugawara, T. Uchihashi, M. Abe, and S. Morita, Appl. Surf. Sci. 140, 371 (1999). 48. S. Morita, M. Abe, K. Yokoyama, and Y. Sugawara, J. Cryst. Growth 210, 408 (2000). 49. T. Arai and M. Tomitori, in Noncontact Atomic Force Microscopy, edited by S. Morita, R. Wiesendanger, and E. Meyer (Springer-Verlag, Heidelberg, Germany, 2002), pp. 79– 92. 50. W. Allers, S. Langkat, and R. Wiesendanger, Appl. Phys. A 72, S27 (2001). 51. A. S. Foster and A. L. Shluger, Surf. Sci. 490, 211 (2001). 52. A. S. Foster, C. Barth, A. L. Shluger, and M. Reichling, Phys. Rev. Lett. 86, 2373 (2001). 53. W. Allers, A. Schwarz, U. D. Schwarz, and R. Wiesendanger, Appl. Surf. Sci. 140, 247 (1999). 54. H. H¨olscher, W. Allers, U. D. Schwarz, A. Schwarz, and R. Wiesendanger, Phys. Rev. B. 62, 6967 (2000). 55. M. Ashino, A. Schwarz, H. H¨olscher, U. D. Schwarz, and R. Wiesendanger, Nanotechnology 16, S134 (2005). 56. S. Hembacher, F. J. Giessibl, J. Mannhart, and C. F. Quate, Proc. Natl. Acad. Sci. 100, 12539 (2003). 57. W. Allers, A. Schwarz, U. D. Schwarz, and R. Wiesendanger, Europhys. Lett. 49, 276 (1999). 58. H¨olscher, W. Allers, U. D. Schwarz, A. Schwarz, and R. Wiesendanger, Appl. Phys. A 72, S35 (2001). 59. N. A. Burnham and R. J. Colton, J. Vac. Sci. Technol. A. 60. B. Gotsmann and H. Fuchs, Phys. Rev. Lett. 86, 2597 (2001). 61. U. D¨urig, Appl. Phys. Lett. 76, 1203 (2000). 62. F.-J. Giessibl, Appl. Phys. Lett. 78, 123 (2001). 63. J. E. Sader and S. P. Jarvis, Appl. Phys. Lett. 84, 1801 (2004). 64. M. A. Lantz, H. Hug, R. Hoffmann, P. J. A. van Schendel, P. Kappenberger, S. Martin, A. Baratoff, and H.-J. G¨untherodt, Science 291, 2580 (2001). 65. C. Loppacher, M. Guggisberg, O. Pfeiffer, E. Meyer, M. Bammerlin, R. L¨uthi, R. Schlittler, J. K. Gimzewski, H. Tang, and C. Joachim, Phys. Rev. Lett. 90, 066107 (2003).

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66. K. L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, UK, 1985). 67. L. D. Landau and E. M. Lifschitz, Lehrbuch der theoretischen Physik VII: Elastizit¨atstheorie (Akademie-Verlag, Berlin, 1991). 68. U. D. Schwarz, J. Colloid Interface Sci. 261, 99 (2003). 69. D. Maugis, J. Colloid Interface Sci. 150, 243 (1992). 70. B. V. Derjaguin, V. M. Muller, and Y. P. Toporov, J. Colloid Interface Sci. 53, 314 (1975). 71. M. Guggisberg, M. Bammerlin, A. Baratoff, R. L¨uthi, C. Loppacher, F. Battiston, J. L¨u, R. Bennewitz, E. Meyer, and H.-J. G¨untherodt, Surf. Sci. 461, 255 (2000). 72. T. Stowe, T. W. Kenny, D. J. Thomson, and D. Rugar, Appl. Phys. Lett. 75, 2785 (1999). 73. N. Sasaki and M. Tsukada, Jpn. J. Appl. Phys 39, L1334 (2000). 74. L. N. Kantorovich and T. Trevethan, Phys. Rev. Lett. 93, 236102 (2004). 75. R. L¨uthi, E. Meyer, M. Bammerlin, A. Baratoff, L. Howald, C. Gerber, and H.-J. G¨untherodt, Surf. Rev. Lett. 4, 1025 (1997). 76. R. Bennewitz, A. S. Foster, L. N. Kantorovich, M. Bammerlin, C. Loppacher, S. Sch¨ar, M. Guggisberg, E. Meyer, and A. L. Shluger, Phys. Rev. B 62, 2074 (2000).

II.9 Scanning Tunneling Microscopy and Spectroscopy of Manganites CHRISTOPH RENNER AND HENRIK M. R ONNOW /

The quest to unravel the properties of manganites has fueled several important concepts in contemporary solid-state physics, involving intricately coupled degrees of freedom (lattice, charge, spin and orbital) and electronic inhomogeneity or phase separation between states of different electronic character. With simultaneous spatial and spectral resolution, scanning tunneling microscopy (STM) can provide direct information on each of these states and on their spatial extent. Here we highlight some recent advances and outline the potential for further STM studies of manganites.

1 Introduction Manganese oxides (manganites) have been the focus of revived interest [1–3] following the rediscovery of a very large (colossal) negative magnetoresistance (CMR), i.e., an orders of magnitude reduction in resistance upon applying a magnetic field, in some manganites in the early 1990s [4–7]. Beyond their technological prospects [8], manganites are challenging the established understanding of the electronic behavior of materials. Along with the high-temperature superconducting copper oxides, they have spurred the development of novel concepts of confinement, phase separation, and electronic inhomogeneity as central topics for transition metal oxides (TMOs) in which strong electron correlation leads to novel electronic properties. Manganites belong to the Ruddlesden–Popper series [9] with the general formula Tn−nx D1+nx Mnn O3n+1 , where T is a trivalent metal or lanthanide cation (e.g., Bi, La, Pr, Nd) and D is a divalent metal or alkaline-earth cation (e.g., Pb, Ca, Sr, Ba). They can be viewed as a stacking of n layers of corner sharing MnO6 octahedra cut from the perovskite structure (n = ∞) and separated by cation oxide rock-salt layers (Figure 1). The remarkable properties of the manganites derive from the outer d-shell electrons. With increasing divalent cation doping, x, the Mn valency is shifted from Mn3+ toward Mn4+ . While both ions hold three electrons in the t2g orbitals, Mn3+ has one extra electron in the eg orbital that is unstable toward a Jahn–Teller 534

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FIGURE 1. Generic structure of the n = 1, n = 2, and n = ∞ members of the Ruddlesden– Popper series Tn−nx D1+nx Mnn O3n+1 of manganese oxides (manganites). The oxygen octahedra are each centered on a Mn ion, and the black spheres represent the trivalent lanthanide (T ) and divalent alkaline-earth (D) cation lattice sites. The n = ∞ compounds with perovskite structure do not cleave, making them very difficult to study by STM, whereas n = 1 and n = 2 compounds do have cleaving planes (CP) within the rock-salt oxide layers, making them ideal for STM investigations.

distortion. Due to strong Hund’s coupling, both ions are in high-spin states, S = 3/2 in Mn4+ and S = 2 in Mn3+ . It immediately becomes apparent how systems of mixed-valence between these two types of ions are likely to host a series of intertwined degrees of freedom: lattice, charge, spin, and orbital. The competition between the typical energy scales associated with each of these degrees of freedom leads to a rich phase diagram1 dominated by different-ordered phases with distinct effects on the electronic transport properties, and several metal-insulator transitions (MITs), both as a function of doping and temperature. CMR essentially results as a proximity effect to these transitions, in the vicinity of which even moderate magnetic fields are sufficient to influence the phase lines and domain structure on microscopic or macroscopic length scales. The proposal of electronic phase separation (EPS) [10] challenges most experimental techniques which average over macroscopic sample sizes. In contrast, local probes like STM have the potential to search directly for such inhomogeneities and to investigate the intrinsic properties of the different phases involved. As such, the manganites provide an ideal arena for developing scanning probe techniques as an important tool in unraveling the physics of complex correlated electron materials. This article aims at providing a snapshot of the key issues related to the understanding of the remarkable properties and possible electronic inhomogeneities of manganites, and how they can be addressed by local probe techniques. It is not intended as a comprehensive review of scanning tunneling probe studies of 1

Several examples of phase diagrams—with references—for manganites with n = 1, n = 2 and n = ∞ can be found in Dagotto et al [10].

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manganites and a colossal magnetoresistance. We shall mainly focus on STM, describing its particular capabilities as well as some of the potential pitfalls one should keep in mind when evaluating these very sensitive experiments. Spatial resolution is the main thrust of this article. We start the discussion at the lowest resolution in section 2, with temperature-dependent tunneling spectroscopy of the various gap features appearing around the Fermi energy. In section 3, we introduce scanning tunneling spectroscopy and scanning tunneling potentiometry, two spatially resolved spectroscopic techniques especially suitable for tackling the question of electronic phase separation. Section 4 is devoted to atomic-scale imaging of manganites, the ultimate resolution needed to study the Jahn–Teller–driven lattice distortions, the various phases of ordered electronic degrees of freedom (charge, spin and orbital), and possible electronic (in-)homogeneities in real space. Finally, in section 5 we conclude with a summary of the current experimental situation and a brief outlook on where STM investigations of manganites may lead in the future.

2 Temperature-Dependent Tunneling Spectroscopy Tunneling spectroscopy is undoubtedly one of the most powerful techniques for probing the electronic density of states (DOS) in the vicinity of the Fermi energy, E F . While photoemission [11] can only measure the occupied DOS below E F with limited energy resolution and no direct spatial resolution,2 local probe tunneling spectroscopy can resolve the occupied (eV ≤ E F ) and unoccupied (eV > E F ) DOS3 with very high spatial resolution (∼0.1 nm) and optimal energy resolution (∼ kB T ). We refer the reader to other publications [14, 15] for detailed descriptions of basic STM imaging and spectroscopy applications. The complex phase diagram of manganites contains a range of electronic phases and phase transitions, many of them separating a metallic from an insulating phase. The most fiercely debated metal-insulator transitions are those associated with charge ordering in Mn4+ rich manganites (x ≥ 0.5, section 2.1), and with CMR in manganites with dilute Mn4+ concentrations (0.2 < x < 0.5, section 2.2). It may seem ill-advised to study such phase transitions by STM spectroscopy, since in principle the STM cannot operate on insulating samples. However, it turns out that a number of MITs in manganites can be readily probed by STM, in a temperature range where the insulating phase is not too resistive (ρ < 1
cm) and the gap at E F in the local DOS is not too large.

2

The unoccupied DOS above E F can in principle be accessed by inverse photoemission [12], though with much coarser energy resolution. 3 That STM spectroscopy is measuring the local DOS is justified, e.g., by Tersoff and Hamann [13], though their simple model neglects electronic correlations and therefore does not a priori hold for strongly correlated systems. This question definitely deserves future attention. However, for the purpose of the present discussion, we shall assume that a similar relationship to the one-particle spectral function holds for correlated systems.

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FIGURE 2. Temperaturedependent tunneling spectroscopy of polycrystalline Nd0.5 Sr0.5 Mn O3 . (a) I (V ) characteristics measured by STM. (b) Numerical derivatives d I /d V (V ) of the measured I (V ) spectra. Spectra at T > 79 K are offset by 0.2 nA and 1 nA/V, respectively. Adapted with permission from [16]. Copyright 1997, Institute of Physics.

The central goal of temperature dependent tunneling experiments is to detect the gap, , around the Fermi energy associated with the insulating phase in the current-voltage, I (V ), tunneling characteristics, and/or in the differential tunneling conductance, dI/dV(V). In this article, we define the gap  as the energy range around E F where the tunneling conductance does not depend on bias voltage and is equal to zero. Incidentally, this is the gap probed by optical spectroscopy involving electron-hole excitations across the gap. In the tunneling spectra, E F corresponds to the bias voltage V = 0.

2.1 Charge-Ordering Metal-Insulator Phase Transition A number of STM spectroscopy studies of manganites are concerned with the charge-ordering MIT in compounds with x ≥ 0.5. Biswas et al. [16] measured I (V ) characteristics on polycrystalline Nd0.5 Sr0.5 MnO3 (NSMO) as a function of temperature (Figure 2(a)). Below the charge ordering transition temperature, TCO ≃ 130 K, the tunneling spectra reveal a gap  ≃ 0.5 eV in the local DOS around E F . As the temperature is increased above 79 K, Biswas et al. observe a gradual reduction of the gap. By the time the temperature exceeds TCO , the I (V ) characteristics acquire a finite slope at V = 0, which Biswas et al. contend marks the closing of the gap. Because this happens near TCO and since  compares well with the nearest-neighbor Coulomb repulsion energy [17], they ascribe it to the charge-ordered state. However, upon further increasing the temperature, a new gap appears to be opening in the 214 K and 245 K spectra. This is below the Curie temperature Tc = 250 K, where the sample should be metallic, and the origin of this gap remains to be explained. Yao et al. [18] measured a very similar temperature dependence of the I (V ) characteristics on Pr0.5 Sr0.5 MnO3 epitaxial thin films, another manganite with a charge-ordering MIT, deposited on LaAlO3 (100) substrates. Similarly to the above results on NSMO, they measured a gap  ≃ 0.4 eV, which closes at TN ≃ 160 K

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and another unexplained gap which opens below Tc = 260 K. Yao et al. question if a gap in the tunneling spectrum below TCO is sufficient to infer the existence of a charge-ordered state. Indeed, in the absence of any complementary measurements, such as atomic-scale topographic STM imaging discussed in section 4, the observation of a gap around E F is not indisputable proof of charge ordering by itself. In an effort to gather independent and more robust evidence of the origin of the gap around E F at T < TCO , Biswas et al. [19] studied the magnetic field dependence of  in NSMO. The charge-ordered state was shown to melt in response to an applied magnetic field [20], and they indeed observed the collapse of the gap, giving them confidence that  is really associated with charge ordering. The above results are based on a graphical analysis of the differential tunneling conductance curves obtained by computing the numerical derivative of the measured I (V ) spectra (Figure 2(b)). The analysis is simple and straightforward: with increasing temperature, the conductance at zero bias eventually becomes finite, which is interpreted as the closing of a gap in the local DOS around E F . However, such an interpretation neglects the impact of thermal smearing, possible tip-induced effects at large tunneling bias, and collective effects due to electron correlations. It may be justified in a band-gap insulator, where the single-electron gap remains essentially unaltered by temperature, and thermal smearing only becomes significant when the temperature reaches values comparable to the gap amplitude. This would be the case, for example, in a semiconductor, where states thermally excited from the valence into the conduction band account for the increasing conductance with increasing temperature. In this case, a finite slope in the I (V ) curves at V = 0 does not imply that states have been transferred into the gap nor that the material has become metallic. In Mott–Hubbard insulators with strong electron–electron and electron–phonon interactions, like manganites, the situation is even more complex. In this case, the gap is a collective result of strongly correlated electrons, and is itself damped by temperature. This is what has been dubbed the “bad insulator” crossover by Kotliar and Vollhardt [22]. The upshot is a remarkably stronger temperature dependence. This is illustrated in Figure 3, where the zero-bias slope of the I (V ) curve, σ0 , is nonzero at elevated temperature although the gap remains constant over the entire temperature range shown. Therefore, σ0 > 0 is not a reliable measure of the local metallicity of the sample surface. Note that the pseudogap in high-temperature superconductors shows a similar enhanced temperature dependence [23,24], leading to the appealing suggestion they both are a consequence of strong correlation and not a band structure effect.

2.2 Colossal Magnetoresistance Metal-Insulator Phase Transition Colossal magnetoresistance is one of the main reasons behind the surge of interest in manganites. Several STM experiments focus on the MIT associated with this phenomenon in dilute Mn4+ compounds with x < 0.5. Spectroscopy of

II.9. Scanning Tunneling Microscopy and Spectroscopy of Manganites 0.04

283 K 44 K → 283 K × 2.5 44 K → 283 K 44 K

0.03 dI/dV (pA/mV)

539

0.02 0.01 0 −300

−200

−100

0 100 Bias (mV)

200

300

FIGURE 3. Tunneling spectra of a gapped manganite measured at 44K (solid line) and at 283 K (dashed line) [21]. Transforming the 44 K spectrum by the regular Fermi–Dirac function for 283 K (dotted line) has little effect, but allowing 2.5 times more smearing (i.e., taking the Fermi–Dirac function with an effective temperature of 700 K) for this Mott– Hubbard-type system produces remarkable agreement (dot-dashed line) with the measured 283K spectrum, which should therefore not be interpreted as metallic.

La1−x Cax MnO3 (LCMO) [25] and La1−x Srx MnO3 (LSMO) [26] thin films with x = 0.3 reveal a gap around E F at high temperature which vanishes upon cooling the sample below the ferromagnetic transition temperature Tc . A similar gap was measured in LCMO with x = 0.3 and LSMO with x = 0.3 and x = 0.33 by Wei et al. [27]. However, in contrast with these former two studies, in the experiments by Wei et al. the gap persists at all temperatures, including in the low-temperature ferromagnetic metallic phase. Wei et al. contend this gap is a measure of the Jahn– Teller distortions, corroborating their argument with the fact that the gap amplitude compares well with the calculated Jahn–Teller coupling energy. Further investigations are needed for a full understanding of this gap feature and the apparent discrepancy between the above tunneling experiments. Double exchange, in conjunction with strong electron–phonon interactions, has been proposed as a possible mechanism for CMR and the concomitant ferromagnetic state. A direct consequence of double exchange and the Jahn–Teller lattice distortions is a large spin splitting of the conduction band. The ensuing well separated minority and majority spin subbands result in a half-metallic conduction band, with nearly perfectly spin polarized electrons in the ground state. This idea is supported by different theoretical approaches, and the half-metallic DOS has been calculated [28] for LCMO with x = 0.25. Peaks in the local DOS (near ±1.75 V in Figure 4(a)) compatible with this theoretical description have been reported by Wei et al. [27] on LCMO (x = 0.3) thin films in the ferromagnetic state at 77 K. Similar peaks were measured in LSMO (x = 0.33) thin films [29], which also exhibit CMR. As expected within the double exchange scenario, these peaks are absent from tunneling spectra of LaMnO3 thin films, which do not exhibit CMR

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(dI/dV) / (I/V)

10 8

(a) LCMO at 77K (FM )

(b) LMO at 77K (AFM )

6 4 2 0

-4

-2

0 2 V (volts)

4

-4

-2

0 2 V (volts)

4

FIGURE 4. STM tunneling spectra at 77 K of a (a) ferromagnetic (FM) La0.7 Ca0.3 MnO3 thin film and (b) antiferromagnetic (AFM) LaMnO3 thin film. Reprinted with permission from [27]. Copyright 1997, American Physical Society.

(Figure 4(b)). Likewise, the half-metallic peaks in LCMO consistently disappear in the paramagnetic metallic state. However, in LSMO they have already vanished unexpectedly at room temperature [29], which is well below the Curie temperature of this compound, Tc = 360 K. This inconsistency as well as the absence of such peaks in other STM spectra measured on similar compounds [25,26] calls for further scrutiny to determine the origin of the high energy peaks in the tunneling DOS.

3 Spatially Resolved Tunneling Spectroscopy Electronic phase separation (EPS) is the subject of a vivid debate prompted by theoretical models which ascribe to such inhomogeneities a key role in the occurrence of colossal magnetoresistance in manganites [10] and high-temperature superconductivity in cuprates [30], two of the most challenging problems in contemporary solid-state physics. Both in the manganites and the cuprates, the debated EPS involves spatial segregation of electronic charges, where the local carrier density is enhanced in some regions and depleted in others. The charge segregation can be over nanometer distances as well as microns. Owing to its combined topographic and spectroscopic resolution, STM is optimally suited to study EPS—as long as each phase remains sufficiently conducting (ρ < 1
cm). STM offers two ways of probing EPS in real space: Firstly, scanning tunneling spectroscopy (STS, section 3.1), which consists of measuring the local tunneling characteristics and plotting the gap at E F [31] or the differential tunneling conductance at a given energy eV [25] as a function of position. Secondly, scanning tunneling potentiometry (STP, section 3.2), whose output is a map of the local surface potential shaped by the path of an electric current traversing the sample.

3.1 Scanning Tunneling Spectroscopy Electronic phase separation (EPS) can be visualized in real space with very high spatial resolution using scanning tunneling spectroscopy (STS). However, because

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FIGURE 5. Linear I (V ) tunneling characteristics (dashed line) expected over metallic regions and nonlinear I (V ) characteristics (solid line) expected over regions with a gap in the local DOS when using an ideal free electron metal STM tip for voltages small compared to the work function. All spectra pass through the origin and the set point (SP) of the STM tunnel junction. Note that the corresponding dI/dV(V) curves do cross at |V | < |V sp| (see Figure 10).

of the operating principle of the STM, metallic regions only distinguished by their local DOS cannot be delineated in this way. When both the sample and the tip are metallic and at small voltages compared with the local work function, the differential tunneling conductance, d I /d V (V ), is independent of the bias voltage and equal to the junction conductance σt ≡ ISP /VSP , where ISP and VSP are the setpoint current and voltage, respectively (Figure 5). During normal operation, the STM feedback loop is regulating the tip-to-sample distance in order to maintain a constant current at the setpoint voltage. Hence, σt and dI/dV(V) are independent of position along the sample surface, and any EPS will only generate contrast in topographic micrographs.4 For nonlinear tunneling characteristics on the other hand, the local differential tunneling conductance is mostly different from σt . In this case, EPS will produce contrast both in STS maps and topographic micrographs at some appropriately selected bias voltage (e.g., V = VSP or V = 0—suitable for STS maps only—in Figure 5). Different types of EPS have been reported and are being considered theoretically: EPS may either take the form of a granular patchwork of sizable regions with distinct electronic properties [10], implying charge segregation over large distances, or charge stripes [32], where charge segregation is limited to a few lattice sites. The Coulomb energy cost, which is a major argument against the formation of large domains, is greatly reduced in the stripe configuration. However, the observation of stripe-like EPS by STM has so far only been reported in a few isolated instances in manganites [33] and HTS cuprates [34]. The majority of STM experiments claiming to find evidence of EPS, both in manganites [25,26] and cuprates [31], conclude that granular phase separation oc4

Besides topography, an alternative method to probe EPS in this case is scanning tunneling potentiometry discussed in section 3.2.

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FIGURE 6. STS micrographs suggesting granular electronic phase separation. (a) 610 × 610 nm2 STS images of an epitaxial La0.73 Ca0.27 MnO3 thin film measured as a function of magnetic field just below the Curie temperature (scale bar: 100 nm). The gray scale represents the slope of the tunneling I (V ) characteristics at V = 3V. Adapted with permission from [25]. Copyright 1999, AAAS. (b) 500 × 500 nm2 STS images of an epitaxial La0.7 Sr0.3 MnO3 thin film measured as a function of temperature in zero magnetic field. The contrast is derived from the slope σ0 of the tunneling I (V ) characteristics at V = 0, black corresponding to σ0 > 5.9 × 10−3 nA/V and white to σ0 < 5.9 × 10−3 nA/V. Adapted with permission from [26]. Copyright 2002, American Physical Society.

curs, with coexisting nanometer- to micrometer-size regions exhibiting different electronic characters as illustrated in Figure 6. F¨ath et al. [25] measured dI/dV(V) maps at V = 3V as a function of magnetic field slightly below the Curie temperature on La.73 Ca0.27 MnO3 thin films grown on SrTiO3 substrates with and without a YBa2 Cu3 Oy buffer layer. They interpret the inhomogeneous conductance maps they measure (Figure 6(a)) in terms of a percolative phase transition [35,36]. They argue that, because the spatially averaged conductance maps and bulk CMR values are in excellent agreement, the STM results are representative of the bulk EPS. However, in a percolative MIT transition, the net conductance is determined by the least resistive percolation path, and is not expected to scale with the spatial average over all local conductances. Furthermore, if the conductance maps were to show percolation linked to the bulk transport, their granular structure should evolve with magnetic field, unlike the nearly field-independent texture revealed in Figure 6(a). A step toward a more quantitative analysis was taken by Becker et al. [26], who mapped the zero-bias conductivity of La0.7 Sr0.3 MnO3 thin films grown on MgO substrates as a function of temperature (Figure 6(b)). By introducing a zerobias conductance threshold criterion to distinguish metallic and insulating regions,

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the authors argued that they had observed the formation of percolating networks, which they could fit to bulk resistivity data through resistor-network simulations. However, the use of a threshold criteria to partition the scanned area into two types of regions can be misleading. Any statistical conductance distribution with a finite width, whose average value is shifting with temperature, will seem to show percolation at a temperature that can be chosen arbitrarily by tuning the threshold value. Undisputable evidence of the coexistence of two phases with distinct electronic properties would be provided by a temperature dependent distribution, rather than a threshold, of a selected tunneling feature, such as the conductance at zero bias or the gap, which becomes bimodal near the phase transition [37]. Scanning tunneling spectroscopy can be extremely sensitive to the surface morphology [38,39]. Therefore, one should pay particular attention to possible correlations between spatial inhomogeneities in the local tunneling conductance and the surface texture, especially the local surface gradients, to avoid mistaking topography-induced fluctuations for intrinsic phase separation or percolation. Both STS studies discussed above were performed on thin films exhibiting granular surfaces, with a substantial (on the length scale typical for STM) peak-to-peak roughness of about 20 nm. The importance of a very flat surface to differentiate spectroscopic inhomogeneities induced by topography and those intrinsic to the metal-insulator transition is illustrated in a recent study by Akiyama et al. [38]. They measured STS conductance maps at V = 2 V on the very smooth surface of 20–30 nm thick epitaxial LSMO (x = 0.3) films deposited by laser-MBE on Nb doped SrTiO3 (100) substrates (Figure 7). Within the terraces, they find extremely homogeneous STS maps (Figure 7(b)). The few fluctuations they observe are all

FIGURE 7. (a) STM micrograph of a 20–30 nm thick epitaxial La0.7 Sr0.3 MnO3 film deposited by laser-MBE on a Nb-SrTiO3 (100) substrate measured at 300 K. (b) Simultaneously recorded STS dI/dV(V) map measured at V = 2 V. Note the remarkable homogeneity of the STS map, showing absolutely no structure except at the unit-cell high (≃0.4 nm) steps. The amplitude profiles shown in the lower panels are measured along the white line in each corresponding image. Reprinted with permission from [38]. Copyright 2001, American Institute of Physics.

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correlated with the unit-cell high (≃0.4 nm) steps (Figure 7(a)) delimiting the terraces. Interestingly, the largest effect is found at steps running perpendicular to the scanning direction, with the sign depending on whether it is an up or a down step. Almost no spectroscopic contrast is seen along steps running parallel to the scanning (horizontal) direction. This result is a striking illustration of the real possibility that spectroscopic inhomogeneities are entirely attributable to the surface morphology. It clearly excludes static mesoscopic electronic phase separation as a generic feature of CMR manganites.

3.2 Scanning Tunneling Potentiometry In a homogeneous sample, the local potential associated with the transport current will drop uniformly throughout the sample, with a constant gradient parallel to the applied electric field. On the other hand, if the sample is phase separated into lowand high-resistance regions, the current will channel along some path of lowest resistance. In that case, the surface potential will not drop homogeneously through the sample, and its gradient will vary both in amplitude and direction as a function of position. Scanning tunneling potentiometry (STP), first introduced by Muralt and Pohl [40] in 1986, enables the mapping of the local surface potential, Vloc , with high resolution. The principle of STP is depicted schematically in Figure 8(a). A floating potential Vs is applied to two opposite sides of the sample, and the resulting electric field drives the current through the sample. The tunneling bias voltage, Vb , is applied to the sample via a bridge circuit while the STM tip is grounded. Experimentally, Vloc is defined as the tunneling bias voltage Vb one has to apply to the tunnel junction in order for the tunneling current, It , to be zero. Vloc can be measured in two ways (Figure 8(b)): (i) An entire I (Vb ) spectrum is acquired at each sampling point along the specimen surface, and Vloc is calculated from the intersection with the It = 0 axis (according to the definition It (Vloc ) = 0). (ii) A single point It (Vb = 0) is acquired at each sampling point along the sample surface, and Vloc is calculated by a linear extrapolation Vloc = Rt · It (0). Method (i) relies on the acquisition of a full spectrum for each data point in the STP map, making it rather slow. But it is extremely robust and does not rely on any particular assumptions, neither on the nature of the local tunnel junction, nor on the line shape of the I (V ) characteristics. Method (ii) requires only the measurement of

FIGURE 8. (a) Principle of scanning tunneling potentiometry (see text for details). (b) The tunneling I (V ) characteristics shift as the surface potential, Vloc , changes depending on position (1– 3) along the sample surface. Reprinted with permission from [41]. Copyright 2002, American Institute of Physics.

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a single point for each data point in the STP map, and is therefore much faster. However, it is susceptible to noise and spatial variations in the junction resistance Rt , and only works in the linear regime of the I (V ) characteristics. In both cases, the spatial resolution of the surface potential maps is limited by the accuracy with which the voltage can be measured, not by the spatial resolution of the STM. Nonuniform STP maps measured on polycrystalline [42] and textured epitaxial [43] La0.7 Sr0.3 MnO3 thin films grown on MgO substrates were ascribed to electronic phase separation. STP images of the room temperature ferromagnetic metallic phase of those specimens revealed extended areas where Vloc was essentially constant, separated by sharp steps where Vloc changes abruptly. These steps were found to correlate with topographic features, predominantly the grain boundaries, indicating the nonuniform drop of the surface potential is not due to EPS but to the granular structure of the sample. Inhomogeneous current flow in thin films was also found to be caused by strain, as studied by Paranjape et al. [44] in an experiment where they tuned the amount of strain in La0.7 Ca0.3 MnO3 (LCMO) by selecting different substrates and varying the film thickness. They measured 50 and 200 nm thin films grown epitaxially on SrTiO3 (STO) and NdGaO3 (NGO) substrates by pulsed laser deposition. The 50 nm thick LCMO film grown on STO was subject to the largest strain due to the lattice mismatch between the film and the substrate. Relaxed, nearly strain-free LCMO films were obtained either by growing thicker films (200 nm) on STO or growing the thin films (50 nm) on the lattice-matched NGO substrate. Paranjape et al. observed a direct correlation between the amount of strain and the degree of inhomogeneity in the surface potential. An important result of their work is that, even within flat terraces, local strain fluctuations can cause inhomogeneities which therefore do not necessarily reflect intrinsic EPS. Strain induced inhomogeneities of the local transport properties were also observed in La0.67 Ca0.33 MnO3 thin films at low temperature using magnetic force microscopy [45]. In contrast to the inhomogeneous surface potential distribution found in polycrystalline and epitaxial textured or strained thin films, very uniform surface potential maps were measured on epitaxial La0.7 Sr0.3 MnO3 (LSMO) thin films [41,42]. Gr´evin et al. [41] investigated single crystalline LSMO thin films (26 nm thick) grown in situ on SrTiO3 (110) substrates by magnetron sputtering. The key findings of their measurements, done in ultrahigh vacuum at room temperature, are presented in Figure 9. STP maps of the metallic ferromagnetic state (Figure 9(b)) show essentially no correlation to topographic features such as steps (Figure 9(a)). Except for a small voltage drop near x = 170 nm due to a large structural defect, Vloc decreases linearly from left to right (Figure 9(c)), with a slope (13mV over 500 nm), in good agreement with the gradient expected from the applied voltage (263 V/cm). The above STP experiments on epitaxial LSMO (x = 0.3) thin films [41] are in perfect agreement with STS experiments in similar epitaxial thin films [38], but are entirely at odds with the picture emerging from the STS experiments on granular LCMO (x = 0.3) [25] and granular LSMO (x = 0.3) [26] thin films discussed in section 3.1. In particular, the uniform voltage drop observed over 500 nm on several occasions in LSMO epitaxial thin films [41,42] precludes the existence of

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FIGURE 9. Room temperature STP of an epitaxial La0.7 Sr0.3 MnO3 thin film grown in situ. (a) 500 × 500 nm2 area topography and (b) simultaneously measured map of the surface potential Vloc (x,y). (c) Topographic (top) and surface potential (bottom) traces extracted along the line shown in the corresponding images. Adapted with permission from [41]. Copyright 2002, American Institute of Physics.

an intricate network of metallic and more insulating clusters on this length scale. However, they do not exclude the existence of nanometer-scale (cluster size below the spatial resolution of STP) or dynamic (cluster fluctuating on a time scale too fast to be resolved by STP) phase separation in these systems. In any case, STP experiments on LSMO epitaxial thin films (like the STS experiments discussed in section 3.1) clearly exclude static mesoscopic electronic phase separation as a generic feature of CMR manganites.

4 Atomic-Scale Topographic Imaging Under optimal conditions, scanning tunneling microscopy offers the unique ability to uncover structural, spectroscopic, and magnetic features with subnanometer length scale resolution in real space. This capability is of particular interest in manganites, which host a wide variety of crystalline, electronic, and magnetic phases that often exhibit some degree of atomic-scale order. Atomic-scale STM imaging has been achieved on a number of transition metal oxides (TMOs) [46–48], but despite extensive efforts, it remains elusive on most CMR and HTS transition metal oxides.5 In manganites, this finest resolution has only been achieved on

5

Colossal magnetoresistance and high-temperature superconductor transition metal oxides which have been imaged with atomic-scale resolution by STM include Bi0.24 Ca0.76 MnO3 [49], La1.4 Sr1.6 Mn2 O7 [21], Bi2 Sr2 Cu2 O6 [50,51], Bi2 Sr2 CaCu2 O8 [52,53], Bi2 Sr2 Ca2 Cu3 O10 [54] and YBa2 Cu3 O7 [55,56], mostly on single crystals.

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single crystals of the pseudocubic perovskite [49,57] T1−x Dx MnO3 (section 4.1) and its bilayer T2−2x D1+2x Mn2 O7 polymorph [21] (section 4.2). No high-resolution imaging has been published on manganite thin films to date, including epitaxial thin films.

4.1 Pseudocubic Perovskite Manganites (n = ∞)

The perovskite structure does not have a natural cleaving plane, making it very challenging to prepare a flat and clean surface suitable for STM experiments. However, against all odds, atomic resolution micrographs were first achieved on the pseudocubic member (n = ∞) of the manganese oxide Ruddlesden–Popper series. Biswas et al. [57] obtained some atomic-scale contrast on a La0.6 Pb0.4 MnO3 single crystal at 320 K. Very systematic and reproducible atomic-scale resolution was reported by Renner et al. [49] on Bi1−x Cax MnO3 (BCMO) single crystals grown by the self flux method at a nominal doping of x = 0.76. Mn4+ -rich BCMO (x = 0.76) exhibits a charge-ordering metal-insulator phase transition at TCO = 250 K, which was characterized with unprecedented high resolution by Renner et al. [49] using scanning tunneling microscopy and spectroscopy. They achieved atomic resolution imaging in ultra-high vacuum between 88 K and 300 K on as grown surfaces, gently cleaned in air without any additional in situ conditioning. Depending on temperature and tip position along the surface, the STM micrographs revealed three √ distinct atomic-scale patterns: a square lattice √ ˚ a 2a0 × 2a0 checkerboard lattice, and stripes with a periwith a0 ≃ 3.8 A, √ odicity of about 2 2a0 . The square lattice was found to be characteristic of the paramagnetic metallic phase at T > TCO , whereas the other two patterns were associated with the charge-ordered insulating phase at T < TCO [33,49]. 4.1.1 Checkerboard Charge-Ordered Phase The topographic micrographs and tunneling spectra of Bi0.24 Ca0.76 MnO3 both change remarkably as a function of temperature in the vicinity of TCO . STM micrographs of the paramagnetic (PM) metallic phase above TCO revealed a square ˚ consistent with the pseudocubic coordination of the Mn lattice (a0 = 3.8 ± 0.1 A) ions (Figure 10(a)). The tunneling I (V ) characteristics (Figure 10(d)) measured in those regions exhibit a finite differential conductance at V = 0, consistent with the metallic nature √ of BCMO at T = 299 K [58]. When BCMO is cooled below TCO , √ a 2a0 × 2a0 checkerboard lattice develops in the topography, with a doubling of the unit cell along the diagonal (Figure 10(b)), and the I (V ) characteristics turn insulating, with a gap on the order of 700 meV becoming clearly visible at E F (Figure 10(d,e)). Upon closer examination, the low-temperature micrographs (Figure 10(b)) revealed substantial distortions, both in lateral position and amplitude (Figure 11). The lattice sites in Figure 11(a) are shifted away from the vertices ˚ and long of a regular square lattice into a bimodal distribution of short (3.0 ± 0.1 A) ˚ nearest-neighbor distances (Figure 11(c)). Remarkably, these short (4.5 ± 0.1 A) and long interatomic distances are not randomly distributed, but alternate regularly

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FIGURE 10. Nanometer-scale STM characterization of the charge-ordering phase transition in Bi0.24 Ca0.76 MnO3 single crystals (TCO = 250 K). 4.5 × 3.5 nm2 constant, current micrographs measured in (a) the paramagnetic metallic phase at 299 K, and the charge-ordered ˚ unit insulating phase (b) at 146 K and (c) at 299 K. The white squares depict the a0 = 3.8 A cell. (d) I (V ) characteristics measured in the paramagnetic metallic phase at 299 K (gray line) and in the insulating charge-ordered state at 146 K (black line). (e) Logarithmic plot of the differential tunneling conductance (numerical derivatives of measured I (V ) curves normalized to the 299 K junction conductance R = V /I ) demonstrating that the gap is essentially the same (≃ 0.7 eV) in the charge-ordered phases at 299 K (black lines) and 146 K (gray lines). Adapted with permission from [49]. Copyright 2002, Nature Publishing.

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FIGURE 11. Lattice distortions (small polarons) observed by STM in the charge-ordered phase of Bi0.24 Ca0.76 MnO3 single crystals at 146 K. (a) 3 × 3 nm2 constant current STM micrograph. The dashed line highlights one of the long range-order zig-zag structures obtained when connecting short interatomic distances, and the white square shows the a0 unit cell. (b) Amplitude profiles measured along the vertical (gray line) and horizontal (black line) solid lines in (a). Arrows emphasize alternating short and long interatomic ˚ and distances. (c) Bimodal distribution of the lattice distortions into short (3.0 ± 0.1A) ˚ interatomic distances (a0 = 3.77A). ˚ Adapted with permission from [49]. long (4.5 ± 0.1A) Copyright 2002, Nature Publishing.

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across the entire imaged area, as shown in Figure 11(b), to form long-range ordered zig-zag chains running along the diagonal of the square basal plane (Figure 11(a)). Note that this charge and structural zig-zag is different from the spin and orbital zig-zag proposed by Goodenough [59] for the CE-type antiferromagnetic phase found in x = 0.5 compounds [60,61]. Its amplitude and periodicity are half those of the spin and orbital zig-zag. The height profiles reveal a concomitant change in the relative amplitude of neighbouring atomic sites (Figure 11(b)). Renner et al. [49] ascribe the checkerboard pattern to alternating Mn3+ and Mn4+ , as posited in (integer charge) description of mixed-valence √ the simplest √ manganites.6 The 2a0 × 2a0 modulation resolved in the STM micrographs below TCO (Figures. 10 and 11) is the first and only real space atomic-scale observation of the charge-ordered phase in a manganite. It graphically illustrates the existence of a checkerboard charge-ordered phase in a doped Mott insulator. ˚ are too large to ascribe the However, the lateral distortions, in excess of 0.5 A, STM contrast to the Mn ions alone. X-ray structural analysis of charge-ordered La0.5 Ca0.5 MnO3 single crystals [63], which are isostructural to BCMO, showed that the Jahn–Teller distorted MnO6 octa hedra were tilted by an angle θ ≃ 10◦ , thus shifting the apical oxygen away from the vertices of the square lattice by a ˚ where aMO = 1.94 A ˚ is the Mn-O bond length. distance d|| ≡ aMO sin θ = 0.34 A, Assuming that tunneling occurs through the apical oxygen, Renner et al. explained the bimodal distribution shown in Figure 11(c) in terms of the non-uniform tilting of the octahedra along the zig-zag chains seen by X-ray diffraction [63], where neighboring apical oxygens are either brought closer or moved apart by roughly ˚ the displaced 2d . Given that the undistorted lattice parameter is equal to 3.77 A, ˚ oxygens should generate a lattice with alternating interatomic distances of 3.09 A ˚ and 4.45 A, in excellent agreement with the STM findings [49]. The contrast in constant-current STM micrographs is a convolution of atomic structure and density of states. Hence, two contributions may account for the nearest-neighbor amplitude difference which develops in the charge-ordered phase (Figure 11(b)): (i) the minute difference in the distance separating the apical oxygen from the Mn ion between a Jahn–Teller distorted MnO6 octahedron centered on Mn3+ and an undistorted one centered on Mn4+ , and (ii) the local charge difference between a MnO6 octahedron centered on a Mn3+ ion and a Mn4+ ion. The ˚ the effecJahn–Teller distortion can at most account for a modulation of 0.1 A, tive contribution to the topography being further reduced due to the 10◦ tilting of the octahedra. Hence, because the actual average amplitude modulation exceeds ˚ it must entail some contribution from the distinctive spatial charge modu0.1 A, lation of the charge-ordered phase.

6

The exact distribution of charge around the Mn ions and the possibility of fractional valence is under discussion (see, e.g., Herrero-Martin et al. [62]). We simply name the two distinct ionization states observed by STM using the non-hybridized labels Mn3+ and Mn4+ .

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4.1.2 Stripe Charge-Ordered Phase The high-resolution STM micrographs of BCMO discussed in the previous paragraph are not consistent with the nominal doping (x = 0.76) of the single crystals investigated by Renner et al. [49]. The checkerboard shown in Figure 10(b,c) suggests that Mn4+ and Mn3+ are present in a ratio of 1:1, corresponding to x = 0.5. Diffraction data [64] for crystals with the same nominal doping prepared following √ 2a instead of the same procedure show double stripes with a periodicity of ∼ 4 0 √ the 2a0 periodicity seen by STM. This apparent discrepancy was pointed out by Renner et al. [49], who suggested two possible explanations. One is that the surface is stabilizing the checker-board phase. Theory indeed shows the checkerboard to be energetically more favorable, even in systems away from half doping [65]. Another possibility is that, even though the samples studied by Renner et al. have a bulk charge-ordering transition as sharp as any reported, the doping may not be x = 0.76 in all regions at the surface. The observation of stripe-like charge ordering in BCMO (Figure 12) by Renner et al. [33] suggests the doping may indeed be different in some locations. Commensurate single stripes built from a 3:1 ratio of Mn4+ to Mn3+ , running parallel or diagonal √ to the square Mn lattice in the ab-plane, would have a periodicity of 4a0 or 2 2a0 , respectively. The stripes seen by STM have a periodicity of the order of 1.1 nm (Figure 12(b)), which is consistent with diagonal single stripes. However, a detailed assessment of the stripe structure can only be done based on atomically resolved micrographs. So far, STM has been unable to resolve atoms in the striped regions, and the meandering shown in Figure 12(a) indicates the latter may have a more complex registration to the √ lattice. However, Figure 12 is definitely not consistent with the double stripes 4 2a0 inferred from high-resolution X-ray scattering√[64] and low-energy electron diffraction [66]. The modulation periodicity of 2 2a0 observed by STM clearly suggests single stripes. STM tunneling spectroscopy of the stripes reveals a gap around E F that is smaller than the (a)

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FIGURE 12. (a) 5 × 5 nm2 constant-current STM micrograph revealing stripes in Bi0.24 Ca0.76 MnO3 at 145 K. (b) Amplitude √ profile extracted along the white line in showing the stripe periodicity to be 1.1 nm ≃2 2a0 . (c) Logarithmic plot of the differential tunneling conductance to highlight the ∼0.3 eV gap measured in √ regions with the stripe phase. √ For comparison, the ∼0.7 eV gap measured in the 2a0 × 2a0 checkerboard regions is also shown. Reprinted with permission from [33]. Copyright 2005, Elsevier B.V.

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gap measured in the checkerboard phase [33] (Figure 12(c)), which is consistent with the checkerboard ground state being energetically more favorable than the stripe configuration. 4.1.3 Electronic Phase Separation

√ √ STM micrographs acquired below TCO predominantly show the 2a0 × 2a0 checkerboard, whereas the more homogeneous a0 square lattice is primarily seen above TCO . However, occasionally a checkerboard pattern is observed at room temperature [49] (Figure 10(c)). STM data (Figure 10) indisputably shows that the checkerboards seen above and below TCO are the signature of one and the same phase. They are identical from a structural (Figure 10(b,c)) and from a spectroscopic (Figure 10(e)) point of view, exhibiting the same topographic contrast and ∼700 meV gap at the Fermi energy. It is not surprising to find the high and low temperature phases coexisting. The first-order nature of the transition means that even far above TCO , the charge-ordered phase can be locally nucleated by, for example, surface geometry and defects. Note that the interface separating the two phases (Figure 13(a), dashed line) is atomically sharp—the transition from one spatial charge distribution to the other occurs over one lattice distance a0 —and stable in time. The simultaneous observation of the PM metallic and charge-ordered insulating phases in a single STM micrograph above TCO (Figure 13) provides further insight into the charge-ordering MIT and the nature of the checkerboard phase [49]. On an atomically flat and clean surface, constant-current STM is primarily sensitive to the local DOS as a function of position. The amplitude profile shown in Figure 13(b) graphically illustrates how the homogeneous charge density of the PM √ metallic phase is redistributed (charge-ordered) over atomic lengths scales in the 2a0 × √ 2a0 checkerboard region. Indeed, the amplitude is almost equal on each lattice site in the PM metallic region (position >2 nm in Figure 13(b)), and alternates between high and low on nearest-neighboring lattice sites in the charge-ordered

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FIGURE 13. (a) 3.5 × 3.5 nm2 constant current STM micrograph of Bi0.24 Ca0.76 MnO3 at 299 K. It shows the atomically sharp boundary separating coexisting paramagnetic metallic and charge-ordered insulating regions. (b) Amplitude profile extracted along the black line in graphically illustrating the charge redistribution on the nearest-neighboring lattice sites in the charge-ordered phase. The dashed line depicts the atomically sharp domain boundary. Adapted with permission from [49]. Copyright 2002, Nature Publishing.

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region (position 0.1 mV) and the lateral resolution ( 4 : 1) in the center that we attribute to a protein fibril embedded within a non-piezoelectric matrix (Figure 4(b,c)). The spatial resolution of PFM, determined as the half-width of the boundary between piezoelectric regions with different orientation, is about 5 nm. Note that the resolution achieved is an order of magnitude better than 50–100 nm typical for single crystals and is comparable to the best results achieved to date for thin films of ferroelectric perovskites. In PFM in the strong indentation regime [34], the resolution is limited by the tip-surface

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contact area. For a tip-surface indentation force on the order of ∼100 nN, the contact radius can be estimated as ∼5–20 nm depending on the tip radius of curvature and effective Young’s modulus of the material. Here, this limit is achieved for a biological material. Given the strong orientation dependence of the PFM signal, this opens a pathway to molecular orientation imaging at comparable resolution. Comparison of the VPFM and LPFM images shows a different pattern of piezoelectric domains, suggesting a complicated fibril structure, most likely consisting of several protein strands. The vector PFM approach allows combined representation of the VPFM and LPFM data within one image [37]. In this approach, VPFM and LPFM images are normalized with respect to the maximum and minimum values of the signal amplitude so that the intensity changes between −1 and 1. Using commercial software (Mathematica 5.0, Wolfram Research) these 2D vector data (vpr, lpr ) are converted to the amplitude/angle pair, A2D = Abs(vpr + I lpr), θ2D = Arg(vpr + I lpr). These sets of data can be plotted in one image using color representation so that the color will correspond to the orientation of the piezoresponse vector in the plane perpendicular to the cantilever axis (Figure 4(d), color inset) and thus will serve as a measure of the local protein fibril orientation. Color intensity in this case will correspond to the magnitude of the piezoresponse signal according to the color wheel diagram. The color encoded vector PFM map, shown in Figure 4(d), clearly delineates a helical structure, visualizing the electromechanically active protein fibril conformation in real space [49]. Note the additional details (complex spiral shape of the molecule) that can be visualized in the 2D vector PFM map, as compared to the original data sets. Vertical and lateral PFM signals provide complementary information on the orientation of protein fibrils in dentin, thus allowing statistical description of the microstructure. Shown in Figure 5(a,b) are the VPFM and LPFM images of the 3x3 µm2 area of dentin, respectively, which exhibit strong PFM contrast due to the presence of protein rich regions. Figure 5(c) shows the double histogram of normalized VPFM and LPFM signals in the same dentin area, representing the count number of points with the signal level in the interval (vpr + δv, lpr + δl), where vpr, lpr ∈ (−1, 1). Shown in Figure 5(d,e) are the amplitude and angle signal distributions. These data suggest that there are two primary antiparallel orientations of the piezoresponse vector. Thus, the local dentin microstructure can be well represented by axially ordered antiparallel protein fibers, as shown in inset on Figure 5(f). The characteristic fiber size can be determined using self-correlation function analysis, as is illustrated in Figure 5(f). The normalized experimental function can be well approximated using a simple phenomenological form C(x) = A exp(−x/ξ ), where characteristic domain size ξ is 160 ± 2 nm. This analysis illustrates the reconstruction of local microstructure of peritubular dentin from the PFM data.

3.4 Molecular Orientation in PFM The analysis described above can be further extended to create a semiquantitative nanoscale map of local molecular orientation. The electromechanical properties

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FIGURE 5. (a) VPFM and (b) LPFM phase images of the 3 × 3 µm2 region of dentin. (c) Double histogram of the vertical and lateral PFM signals of the same area of dentin shown in (a) and (b). (d) Amplitude and (e) phase distribution of the piezoresponse vector. (d) Selfcorrelation function for the PFM signal. Dotted line is a fitting using C(x) = A exp(−x/ξ ), where characteristic domain size ξ is 160 nm. The inset shows the simplified nanostructural model for dentin formed by antiparallel protein fibrils. Reprinted with permission from [36]. Copyright 2005, American Institute of Physics.

of solids are characterized by a piezoelectric tensor, di j , where tensor elements are determined in the coordinate system linked to the principal crystallographic axes. On the other hand, the experimentally measured VPFM and LPFM signals l l are determined by the coefficients d33 and d34 of the piezoelectric tensor, dil j , in the laboratory coordinate system [48]. The two coordinate systems are related by a set of three Euler rotation angles, (θ, ψ, ϕ) [50] that uniquely defines the local crystallographic orientation in the laboratory coordinate system. The relationship between the dil j tensor in the laboratory coordinate system and the di j tensor in the crystal coordinate system is [50]: dil j = Aik dkl Nl j ,

(5)

where Ni j and Ai j are the rotation matrices. For materials with a known di j tensor, the local crystallographic orientation (φi , θi , ψi ) can be derived by solving Eq. (5). The detailed theoretical analysis of electromechanical orientational imaging by vector PFM including approaches to calibration and measurement artifacts is developed elsewhere [48]. For the protein fibril studied in this work, only partial information on the electromechanical response vector is available from VPFM and LPFM data. Assuming

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that the fibril is formed by collagen,1 the di j matrix has the form as shown in Eq. (4). Thus, from Eq. (5), the components of the piezoelectric tensor proportional to the PFM signal can be written as l d33 = 0.5 cos θ(d15 + d31 + d33 − (d15 + d31 − d33 ) cos 2θ), (6) l d34 = −((d31 − d33 + (d15 + d31 − d33 ) cos 2θ) cos ψ + d14 cos θ sin ψ) sin θ, (7) l d34 = −((d31 − d33 + (d15 + d31 − d33 ) cos 2θ) sin ψ − d14 cos θ sin ψ) sin θ.

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In this case, the molecule is rotationally invariant and the response is independent on the third Euler angle, ϕ. Orientation dependence of PFM signal surfaces are shown in Figure 6. Note that while the exact shape of response surfaces are strongly dependent on the di j , values the nodes are dependent only on the crystal symmetry and should be universal for most biological systems, which generally exhibit shear piezoelectricity. For rotationally invariant molecules, the combination of VPFM and LPFM data is sufficient for reconstruction of molecular orientation. To calculate the effective electromechanical response measured in our PFM experiment, we use the di j values (in pm/V) for tendon reported by Gunjian [17]: ⎡ ⎤ 0 0 0 −2.66 1.40 0 ⎣ 0 0 0 1.40 2.66 0 ⎦. (9) 0.067 0.067 0.087 0 0 0

Neglecting the d33 and d13 coefficients, we obtain that the VPFM and LPFM sigl l nals are proportional to d33 = 0.7 cos θ(1 − cos 2θ) and d34 = (2.66 cos θ sin ψ − 1.4 cos 2θ cos ψ) sin θ, respectively. By solving these two linearly independent 1

Note that collagen is chosen only as an example since there is no direct proof that the observed protein is indeed collagen.

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equations, we can determine angles θ and ψ. Given the large degree of uncertainty in published values for di j and lack of absolute calibration, the VPFM and lmax l l max LPFM signals were normalized by taking d33 = max[d33 (θ, ψ)] and d34 = l max[d34 (θ, ψ)], where (θ, ψ) ∪ (0, 2π ). This provides a semi-quantitative calibration of the measured PFM signal that can be related to the local electromechanical properties of the collagen. It should be noted that due to the absence of reliable piezoelectric data and incomplete information on the electromechanical response vector (only 2 of 3 orthogonal components have been measured) only semiquantitative analysis of the orientational imaging could be performed in this case. However, we expect that the potential for orientation imaging of biological systems at the nanoscale level will stimulate further experimental development of this approach (e.g., using complete 3D PFM data), and theoretical modeling of the electromechanical coupling coefficients for complex biomolecules, which can potentially open a pathway to molecular identification.

4 Electromechanical Properties of the Butterfly Wings Butterfly wings exhibit a complex microstructure that is designed to generate certain color and pattern effects, provide flexural stiffness and deformability of the wing, control heat transformation, etc. [51–55]. The wings are covered by thousands of chitin scales that vary in shape, size and color. Scale microstructure has been the subject of numerous studies by optical and electron microscopy techniques [56, 57]. Examination of the wing structure yields information on the interference and diffraction mechanisms that produce certain color patterns of the wings. Furthermore, the intricate wing structure also provides an inspiration for engineering of complex light-weight deformable structures that can be used in micromechanical devices. In this section, we demonstrate how the SPM-based approach for characterization of butterfly wings can go beyond visualization of the scale structure and can actually allow evaluation of their elastic and electromechanical properties on the length scales from 50 µm to 10 nm. Examination of the piezoelectric properties of the butterfly wings at the nanoscale can be used as a way for elucidation of their ultrastructure by employing the electromechanical activity of the chitin fibers. A sample used in this study has been cut from the dorsal forewing of Vanessa virginiensis butterfly (Figure 7(a)). The sample has been mounted on the SiO2 /Si wafer using silver paint. Optical micrograph in Figure 7(b) shows a number of white-pigmented scales covering the area of the wing that was subsequently inspected by SPM. Mesh-like structure of longitudinal lamellae connected by crossribs can be seen in the topographic images (Figure 7(c)). It is believed that this structure is a basis for high structural stability of the scale. Figure 7(d) shows another image of the same area of the wing as in Figure 7(c) acquired by AFAM. The AFAM signal is directly related to the mechanical properties of the sample below the tip, providing an approach to visualize, if not quantify,

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A. Gruverman, B. J. Rodriguez, and S. V. Kalinin FIGURE 7. (a) Optical photograph of Vanessa virginiensis (courtesy of Jeffrey Pippen, Duke University) and (b) optical micrograph of the wing scales. (c) AFM surface topography of the wing (vertical scale is 1 µm). (d) AFAM elasticity image (vertical scale is 18% of the average signal) of the wing obtained simultaneously with (c). (See also Plate 5 in the Color Plate Section.)

the variations in mechanical properties at the nanometer scale. Figure 6(d) shows significant variations in the elastic constant within an individual ridge that appear as regions of different contrast, suggesting an internal structural inhomogeneity. Regions of higher contrast in AFAM correspond to harder material. Note the difference between effective resolution on the topographic and AFAM images—while no features smaller than 100 nm can be distinguished in the topographic image, the AFAM image shows details with sub-10-nm resolution. This result illustrates the possibility of addressing the structural differences in the protein-chitin matrix constituting the scale by means of various modes of SPM. Butterfly wings, like exoskeletons of most insects, represent a form of biological composite made of chitin fibers in a protein matrix. Similar to many other polysaccharide-based biopolymers, chitin is reported to be piezoelectric [58–60]. However, the complex nanoscale structure and lack of macroscopic samples have previously hindered studies of piezoelectricity in such systems. Here, the electromechanical properties of the butterfly wing have been probed by PFM by scanning a 2 × 2-µm2 wing region. Remarkably, vertical PFM image in Figure 8(a) clearly shows piezoelectric contrast that we attribute to the electromechanical behavior of chitin. Vertical PFM (VPFM) measurements have been complemented by the lateral LPFM imaging, providing the information on two components of electromechanical response vector. Shown in Figure 8(b) is the LPFM image obtained from the same area of the wing as the VPFM in Figure 8(a). In Figure 8(c), the 2D-vector PFM image illustrates the position-dependent piezoelectric properties: the magnitude and orientation of the electromechanical response vector of the wing scale in the plane perpendicular to the cantilever long axis (color inset). Here, red color corresponds to the preferential orientation of chitin fibers in the direction normal to the surface while green color indicates the primarily in-plane orientation of

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the fibers. If we assume that the piezoelectric tensor of chitin exhibits shear piezoelectric response (as in collagen), then the non-zero VPFM signal observed in the butterfly wing should lead to a conclusion that the chitin molecules are oriented at some angle to the surface. Note also that color is virtually uniform within the ridge and cross-rib, while varying between these structural elements indicating an orientational difference of about 90o . The histogram analysis of angle distribution of the 2D PFM signal in Figure 8(c) reveals two peaks corresponding to two main orientations of chitin fibers within lamellae and cross-ribs, respectively (Figure 8(d)). No quantitative data has been obtained yet, however, we estimate the effective piezoelectric constant to be just below 1 pm/V. How essential are the piezoelectric properties for functionality of the butterfly wings is an open question that needs to be addressed in future research. In the meantime, the piezoelectric properties of the wing can be utilized to examine its local structure at the micro- and nanoscale. The obtained results demonstrate that the SPM-based methods have a great potential in improving the understanding the structure-property-functionality relationship

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FIGURE 9. Surface topography (a) and vector PFM images (b,c) of deer antler. Vector PFM illustrates finer details of internal antler structure, including the presence of region with different keratin orientation. The characteristic keratin fiber size in PFM image is ∼200 nm. Note that there is no correlation between PFM and topographic images, suggesting absence of cross-talk. Reprinted with permission from [42]. Copyright 2006, Elsevier, Inc. (See also Plate 7 in the Color Plate Section.)

in biological systems, as well as in the development and testing of biologically inspired micromechanical devices, such as biomimetic wings.

5 Wider Applicability of PFM to Bioelectromechanical Imaging Data shown below illustrate the applicability of PFM for structural characterization to a broader range of materials system. Figure 9(a) illustrates surface topography of a longitudinal cross-section of the deer antler. Unlike teeth, this material contains lipids, which can diffuse to the surface thus forming a non-conductive layer and significantly complicating PFM imaging. This necessitates the use of cantilevers with relatively high spring constants (>5 N/m) to penetrate the contamination layer. To visualize electromechanical response data, we again employ color representation of the PFM signal acquired from the same area (Figure 9(b), color inset), which allows visualization of otherwise invisible microstructural elements. Vector PFM image of a smaller area (Figure 9(c)) clearly shows elongated regions of homogeneous contrast (marked by white ellipses) about 2–3 µm long and 200–300 nm wide which are presumably due to the keratin fibrils of different orientation.

FIGURE 10. (a) Surface topography and vertical PFM (b) amplitude and (c) phase images of the microtomed canine femoral cartilage. The scan size is 2 × 2 µm2 .

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Finally, shown in Figure 10 is a set of topographic and PFM images of canine femur cartilage. The surface is formed by multiple mounds with characteristic size of 100–200 nm, formed during the drying and shrinking of the cartilage surface. Vertical PFM phase and amplitude images clearly indicate that the surface is piezoelectric. Bright regions in the PFM amplitude image are associated with the piezoelectrically active collagen embedded in the extracellular matrix.

6 Conclusion To summarize, piezoresponse force microscopy is shown to be a powerful tool for real-space imaging of electromechanically active proteins in calcified and connective tissues with nanoscale resolution. PFM allows differentiation between organic and mineral components and is not sensitive to topographic cross-talk, thus significantly simplifying the interpretation of image contrast in terms of materials microstructure. It has been shown that application of PFM provides an additional insight into the composition and structure of dental tissues. It is suggested that PFM can be used to study internal structure and orientation of the protein microfibrils in the calcified matrix. PFM thus holds a great promise for imaging and elucidating the structure/property relationship in biological tissues as well as in the development and testing of biologically inspired materials and devices.

References 1. V. A. Bazhenov, Piezoelectric Properties Of Wood (Consultants Bureau, New York, 1961). 2. E. Fukada and I. Yasuda, J. Phys. Soc. Jpn. 12, 1158 (1957). 3. M. A. El Messiery, IEE Proc. 128 A, 336 (1980). 4. E. Fukada, J. Phys. Jpn. 10, 149 (1955). 5. E. Fukada, Biorheology 5, 199 (1968). 6. E. Fukada, Biorheology 32, 593 (1995). 7. M. H. Shamos, and L. S. Lavine, J. Clin. Orthop. 35,177 (1966). 8. W. Williams, and L. Breger, J. Biomech. 8, 407 (1975). 9. A. J. Bur, J. Biomech. 9, 495 (1977). 10. W. G. Cady, Piezoelectricity: An Introduction to the Theory and Applications of Electromechanical Phenomena in Crystals (New York: Dover Publications, 1964). 11. A. V. Shubnikov, Piezoelectric textures, USSR Academy of Sciences, Moscow, 1946. 12. E. Fukada, Rep. Progress in Polymer Phys. Jpn. 3, 163 (1960). 13. E. Fukada, J. Phys. Soc. Jpn. 12, 1301 (1956). 14. M. Yamauchi, Advances in Tissue Banking 6, 445 (2002). 15. G. N. Ramachandran and G. Kartha, Nature 174, 269 (1954). 16. A. A. Marino, and R. O. Becker, Calc. Tissue Res. 8, 177 (1971). 17. A. A. Gundjian, and H. L. Chen, IEEE Transactions on Biomedical Engineering 21 (3), 177 (1974). 18. S. B. Lang, Nature 212, 704 (1966). 19. A. R. Liboff, and M. Frust, Ann. NY Acad. Sci. 238, 26 (1974).

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20. S. Mascarenhas, in Electric Charge Storage, ed. by M. Perlman (The Electroemechanical Society Inc.,1972), pp. 650–656. 21. H. Athenstadt, Naturwiss 48, 465 (1961). 22. J. C.Anderson, and C. Eriksson, Nature 227, 491 (1970). 23. T. G. Netto, and R. L. Zimmerman, Biophysical J. 15, 573 (1975) 24. C. A. L. Bassett, Calc. Tiss. Res. 1, 252 (1968). 25. A. Gjelsvik, J. Biomech. 6, 69 (1973). 26. C. T. Brighton, Z. B. Friedenberg, E. I. Mitchell, and R. E. Booth, Clin. Orthop. Relat. Res. 124, 106 (1977). 27. S. Weiner and H. D. Wagner, Annu. Rev. Mater. Res. 28, 271 (1998). 28. H. Athenstadt, Nature 238, 830 (1970). 29. W. S. Williams, M. Johnson, and D. Gross, in Electrical Properties of Bone and Cartilage, ed. by Brighton, Black and Pollack (Grune and Stratton, 1979). 30. E. Korostoff, J. Biomech. 10, 41 (1977). 31. A. Gruverman, in Encyclopedia of Nanoscience and Nanotechnology, ed. by H. S. Nalwa, Vol. 3, pp. 359–375 (American Scientific Publishers, Los Angeles, 2004). 32. A. Gruverman, O. Auciello, and H. Tokumoto, Annu. Rev. Mat. Sci. 28, 101 (1998). 33. Nanoscale Characterization of Ferroelectric Materials, ed. by M. Alexe and A. Gruverman (Springer-Verlag, Berlin 2004). 34. S. V. Kalinin, E. Karapetian, and M. Kachanov, Phys. Rev. B 70, 184101 (2004). 35. L. M. Eng, H.-J. Guntherodt, G. A. Schneider, U. Kopke and J. M. Saldana, Appl. Phys. Lett. 74, 233 (1999). 36. S. V. Kalinin, B. J. Rodriguez, S. Jesse, T. Thundat, and A. Gruverman, Appl. Phys. Lett. 87, 053901 (2005). 37. S. V. Kalinin, B. J. Rodriguez, J. Shin, S. Jesse, V. Grichko, T. Thundat, A. P. Baddorf, and A. Gruverman, Ultramicroscopy 106, 334 (2006). 38. C. Halperin, S. Mutchnik, A. Agronin, M. Molotskii, P. Urenski, M. Salai, and G. Rosenman, Nano Letters 4, 1253 (2004). 39. U. Rabe, M. Kopycinska, S. Hiserkorn, J. Munoz-Saldana, G.A. Schneider, and W. Arnold, J. Phys. D 35, 2621 (2002). 40. M. Goldberg, M. Takagi, Histochem. J. 25, 781 (1993). 41. A. Linde, S. P. Robins, Coll. Relat. Res. 8, 443 (1988). 42. B. J. Rodriguez, S. V. Kalinin, J. Shin, S. Jesse, V. Grichko, T. Thundat, A. P. Baddorf, and A. Gruverman, J. Struct. Biol. 153, 151 (2006). 43. A. A. Marino, B. D. Gros, Archs. Oral Biol. 34, 507 (1989). 44. S. Habelitz, M. Balooch, S. J. Marshall, G Balooch, G. W. Marshall, J. Struct. Biol. 138, 227 (2002). 45. J. H. Kinney, M. Balooch, G. W. Marshall, S. J. Marshall, Arch. Oral Biol. 44, 813 (1999). 46. H. Sano, B. Ciucchi, W. G. Matthews, D. H. Pashley, J. Dent. Res. 73, 1205 (1994). 47. M. A. Elmessiery, G.W. Hastings, and S. Rakowsky, J. Biomed. Eng. 1, 63 (1979). 48. S. V. Kalinin, B. J. Rodriguez, S. Jesse, J. Shin, A. P. Baddorf, P. Gupta, H. Jain, D. B. Williams, and A. Gruverman, Microscopy and Microanalysis 12, 206 (2006). 49. J. W. Smith, Nature 219, 157 (1968). 50. R. E. Newnham, Properties of Materials: Anisotropy, Symmetry, Structure, Oxford University Press, 2005. 51. R. J. Wootton, Scient. Am. 262, 114 (1990). 52. C. P. Ellington, J. Exp. Biology 202, 3439 (1999). 53. R. J. Wootton, Proc. R. Soc. Lond. B 262, 181 (1995).

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R. Dudley, J. Exp. Biol. 150, 37 (1990). S. J. Steppan, J. Res. Lepidoptera 35, 61 (2000). H. Tada, S. E. Mann, L. N. Miaoulis, and P. Y. Wong, Applied Optics 37, 579 (1998). P. Y. Wong, T. H. Gupta, M. C. B. Robins, and T. L. Levendusky, Optics Letters 28, 19 (2003). 58. C. C. Silva, C. G. A. Lima, A. G. Pinheiro, J. C. Goes, S. D. Figueiro, and A. S. B. Sombra, Phys. Chem. Chem. Phys. 3, 4154 (2001). 59. H. Maeda, Biophysical J. 56, 861 (1989). 60. E. Fukada, R. L. Zimmerman, and S. Mascarenhas, Biochem. Biophys. Res. Comm. 62, 415 (1975).

III.4 Scanning Capacitance Microscopy Applications in Failure Analysis, Active Device Imaging, and Radiation Effects C. Y. NAKAKURA, P. TANGYUNYONG, AND M. L. ANDERSON

Though most widely used as a two-dimensional (2D) dopant-profiling tool, scanning capacitance microscopy (SCM) has a diverse array of applications in the semiconductor industry. This chapter highlights three emerging applications of SCM: failure analysis of semiconductor devices, imaging of device operation, and the visualization of radiation effects. Each application is described in detail, providing practical experimental details and a number of examples.

1 Introduction The drive for each successive generation of metal-oxide-semiconductor field-effect transistors (MOSFETs) to have decreasing critical dimensions has created a growing need for high-resolution, two-dimensional dopant profiling techniques [1–5]. As a result, scanning capacitance microscopy (SCM) has rapidly matured to an established device characterization method in the semiconductor industry [6–14]. The SCM measurement uses an atomic force microscope (AFM) in contact mode with a resonant capacitance sensor coupled to the tip [15–18]. A time-varying bias voltage (dV) applied between the tip and sample induces changes in capacitance (dC/dV), which reflect the local carrier concentration in the sample. By mapping the capacitance changes as a function of tip location, a 2D image of the free carrier concentration can be generated. In its most basic application, SCM is used as a quantitative metrology tool to measure 2D carrier profiles in cross-sectioned MOSFETs, providing important device parameters such as the effective channel length and junction depth [11]. These profiles, in turn, can be used to extract 2D dopant profiles for the calibration of process models [19–27]. While the bulk of SCM studies have focused on establishing a reliable methodology for quantitative dopant profiling, a handful of new applications in the semiconductor industry have emerged. In failure analysis (FA) of integrated circuits, SCM has been used to identify failure mechanisms, such as regions of incorrect doping and electrical shorts, thereby indicating the appropriate corrective actions required to remedy the device [28–33]. Because sample preparation and data interpretation are relatively straightforward, FA applications of SCM can be performed 634

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with quick turnaround and with few of the ambiguities that can arise in quantitative applications. Scanning capacitance microscopy has also been used in active MOSFET imaging, where cross-sectional SCM images are acquired while incrementally biasing the device between non-conducting (off) and conducting (on) states [34–38]. This application allows the opportunity to investigate basic device physics using a 2D imaging technique for real space visualization of device operation. Finally, SCM has been used to image the effects of radiation exposure on carrier distribution in a MOSFET structure, providing a method to form 2D maps of radiation effects that could previously only be inferred from electrical measurements. This chapter is divided into three sections that focus on the three SCM applications outlined above, highlighting work performed at Sandia National Laboratories. The first section introduces the use of SCM as a failure analysis tool. Methods of isolating the failure site are discussed, as well as sample preparation and strategies of root cause determination using SCM. The second section focuses on active MOSFET imaging, with emphasis on the key experimental details that enable such measurements. The third section introduces the application of SCM to the visualization of radiation effects. Because the operation of microelectronic devices in harsh radiation environments (e.g., satellites in space orbit) is sensitive to radiation exposure, the ability to image these effects with SCM is important to the development of new device structures that are resistant to radiation-induced degradation and failures. Practical experimental details will be highlighted for each SCM application, and several examples will be presented.

2 Failure Analysis of Integrated Circuits Failure analysis is a key component of the development of new semiconductor technologies. During the initial stages of process development and integration, feedback from FA studies is paramount to identifying root causes of device failures and providing the subsequent process, integration, or design changes that are necessary to eliminate the observed failure mechanism. Failure analysis uses a wide array of analytical tools to isolate and then characterize the failure site physically, electrically, and chemically [39]. Scanning capacitance microscopy has attracted increasing attention as a failure analysis tool because of its ability to provide 2D free carrier profiles in a semiconductor device, yielding information that, in many cases, cannot be obtained with other analysis techniques [40–42]. Quantitative dopant profiling of pn junctions [11], while the most active area of SCM research in recent years, suffers from a number of complicating factors that have limited the use of SCM. Some of these factors include difficulty in reproducing data—which in many cases is attributed to the sensitivity of SCM to sample surface preparation and degradation of tip coating materials—tip-sample interactions at the pn junction, and bias voltage effects [9,34,43–51]. In contrast, FA applications of SCM are largely qualitative. Typically, data from non-defect sites are compared with those from defect sites to identify any differences in the

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carrier profiles. In most cases, the differences between the two sites are obvious, allowing the discrepancies to then be attributed to the defects provided that the SCM imaging is performed under identical experimental conditions. In certain instances, it is possible to identify the failure mechanism with a single SCM sample [32], making this a convenient, high-impact analytical tool. This section focuses on the practical application of using SCM as a failure analysis tool. Strategies for isolating failure sites with complementary FA techniques will be discussed, in addition to sample preparation procedures for the SCM measurement. A number of case studies, which cover the entire FA process, will be introduced to illustrate the implementation of SCM in failure analysis applications.

2.1 Isolating the Failure Site & Preparing for SCM Before the root cause of a failure can be determined and addressed, the failure site must first be isolated. In the manufacture of integrated circuits, wafer-level electrical testing is performed after wafer processing is complete to determine the yield of that particular lot, or batch, of wafers. An automated set of qualifying measurements are designed to exercise and test all parts of the circuitry. The presence of a failing device or circuit is first identified with these qualifying electrical tests. When a failure occurs, testing is repeated to confirm that the defect can be reproduced and understood electrically. Subsequent electrical testing is performed to further isolate the defect within the circuitry, at which point optical microscopy can be used to verify whether the failing site can be observed. If optical inspection fails to locate the cause of the defect, an assortment of analytical FA techniques can be subsequently used. For the SCM case studies outlined in this section, light emission microscopy was the most useful technique for fault isolation. Light emission microscopy is a nondestructive method for localizing defective pn junctions [52]. As current flows across anomalous pn junctions, light emission occurs by radiative electron-hole recombination at or near the junctions. The wavelengths of the emitted photons are in both the visible and near-infrared spectra and can be detected by a liquid nitrogen-cooled, charge-coupled device (CCD) camera. The result is a real-space image of the device array with a bright region highlighting the defect. Following isolation with light emission microscopy, additional fault characterization can be performed destructively by deprocessing the sample and then imaging with an optical microscope, scanning electron microscope (SEM), or transmission electron microscope (TEM). After isolating and identifying the site to be imaged with SCM, the sample must be prepared for either top-down or cross-sectional imaging. In either case, it is sometimes necessary to mark the device of interest to facilitate coarse positioning of the SCM tip. Laser scribes are well suited for this because the scribe mark can be precisely positioned using a microscope, and the depth of the scribe can be adjusted by varying the laser energy and duration. This allows one to mark a defect whether it is buried under several levels of metal interconnects (see Figure 1(a,b)) or if it is exposed at the topmost layer. In the work presented in this chapter, top-down

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FIGURE 1. (a,c,e) Schematic cross sections of an integrated circuit and (b,d,f) corresponding top-down optical images during various stages of sample preparation for top-down SCM.

samples were prepared by immersing the die of interest in a 50% hydrofluoric acid solution (HF) for approximately 10–60 seconds to remove the back-end metal interconnect and interlayer dielectric (ILD) levels [53]. Following the HF dip, the samples were thoroughly rinsed with de-ionized water and dried with nitrogen. Although the aluminum lines, tungsten contacts, and dielectric layers were removed during the HF dip, the polysilicon lines remain intact, as shown in Figure 1(c,d). The polysilicon lines were subsequently delaminated from the substrate with adhesive tape to reveal the bare MOSFET islands. Finally, the samples were rinsed and ultrasonically cleaned in isopropyl alcohol before imaging with SCM (Figure 1(e,f)). Cross-sectional samples were prepared by standard polishing procedures using diamond-coated lapping films on a polishing wheel. Failed devices were isolated by electrical testing and then marked with a laser scribe to ensure the device of interest was correctly targeted. Next, the die containing the defect site was mounted on a polishing stub using hot wax, and then polished with lapping films, starting with a 15-µm particle size disk and incrementally reducing the particle size to 0.1 µm. The final polish was performed with colloidal silica slurries to obtain a

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scratch-free surface and form the passivating oxide layer. Site-specific preparation requires repeated optical inspection and careful attention so that a finished surface is obtained at the site of interest without cutting past the device. After polishing, the sample and polish stub were attached to a custom-made sample holder that was mounted directly on the SCM system for imaging [54].

2.2 Case Studies 2.2.1 Error in Starting Material This first case study illustrates the use of SCM to identify a global failure mechanism [32]. In a recent 0.5 µm, radiation hardened, bulk Si technology lot, a 100% failure rate in the static-random access memory (SRAM) devices was observed at functional test. Electrical testing indicated that all the devices had a quiescent power supply current (IDDQ ) in excess of 100 µA; however, no localized thermal defects were detected. Instead, failure analysis data showed global heating across the die. Top-down SCM was used to analyze several transistors from this lot, as well as those from a lot that passed functional test. Representative results are shown in Figure 2. The gray-scale for the SCM images is shown at the bottom of the figure, where p-type regions appear at the dark side of the scale, and n-type regions are at the light side. Regions where there is no change in capacitance, or dC/d V = 0, are plotted at the center of the gray-scale and correspond to both insulating and highly conductive parts of the sample. Figure 2 shows that there are distinct differences in SCM contrast between the functional and failed devices, particularly in the p-type metal-oxidesemiconductor (PMOS) transistor islands on the lower right-hand side of the images. The functional devices in Figure 2(a) exhibit SCM features that one would

FIGURE 2. Top-down SCM images of bulk Si transistor islands within an SRAM device from both (a) functional and (b) failed product lots.

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expect for properly functioning transistors—the heavily implanted source/drain regions do not show any appreciable difference in contrast between PMOS and NMOS devices since they both have high carrier concentrations (dC/dV = 0). In addition, each transistor island clearly shows the source/drain regions separated by lightly doped well regions: p-type (dark) for the NMOStransistors and n-type (white) for the PMOS transistors. The SCM image of the failed devices in Figure 2(b), however, shows that the n-well regions of the PMOS islands appear darker in contrast and, therefore, are more heavily doped than those of the functional devices. The SCM data in Figure 2 strongly suggest that the failed lot contained an error in the doping type of the epitaxial silicon layer of the starting material. This was independently confirmed using other analytical techniques, which showed the epitaxial silicon layer of the starting material was doped n − instead of p − . Therefore, the difference in SCM contrast observed for the PMOS islands is explained as follows. For the functional lot, with the correct p − epitaxial layer, n-well formation resulted in a lightly doped n-well with carrier concentration in the range of 1016 cm−3 . In the failed lot, however, n-well formation resulted in a higher doping level (in the range of 1017 cm−3 ), which is expected since the starting epitaxial material was n-type. The SCM contrast in the n-well regions of the failed devices, therefore, is closer in the gray-scale to dC/d V = 0, indicating that it is more heavily doped relative to the functional lot. 2.2.2 Dislocation Induced Device Short Dislocations are crystalline defects that can significantly change the electrical properties of semiconductor materials. Although they can originate from the bulk crystal growth process [55], the majority of dislocations in semiconductor devices are created during fabrication processes such as ion implantation and film growth. High temperature processing steps, in particular, can produce substantial mechanical and thermal stresses that contribute to dislocation formation. Dislocations can lead to considerable current leakage in devices and degrade performance or cause electrical test failures. The presence of dislocations can also cause major yield losses in production and reliability concerns. The exact mechanisms of dislocation formation are still not well understood [56]. Characterizing dislocations, however, provides important information that can be helpful in optimizing fabrication steps to reduce stresses and dislocation formation. Wet chemical delineation etching [57] and TEM are the two major techniques that have been used to characterize dislocations in silicon. Scanning capacitance microscopy provides unique information that is not obtainable from wet etching and TEM, particularly the carrier profiles at or near the dislocation. These profiles can shed light on the mechanisms of dislocation formation as they are likely to be different from the surrounding non-defect areas. Dislocations are known to be good getters of both impurities and dopants, resulting in anomalous pn junctions in semiconductor devices. This makes light emission microscopy an ideally suited technique for isolating dislocation-induced

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C. Y. Nakakura, P. Tangyunyong, and M. L. Anderson FIGURE 3. (a) Light emission microscopy image showing a spot of intense photon emission, attributed to a dislocation in the buried silicon layer. (b) Optical microscopy image of the transistor island in (a) following deprocessing in aqueous HF. The arrow denotes the location of the defect. (c) Topographical AFM image of defect site (denoted by arrow) and (d) corresponding SCM image showing the location of the dislocation-induced short. Inset shows a higher magnification image of the short.

defects prior to performing SCM. Figure 3(a) shows the light emission from a dislocation site (denoted by arrow) near the heavily doped n + drain region of an n-channel MOSFET at the edge of an island of MOSFETs. The failure site was marked with a laser scribe, and the sample was subsequently deprocessed to expose the underlying silicon islands to be imaged with SCM, as seen in the optical microscopy image in Figure 3(b). The four dark, rectangular features around the island are pits formed by the laser scribe. The top-down AFM in Figure 3(c) shows the topography of the defective MOSFET (denoted by arrow) and its adjacent, functioning neighbors. The corresponding carrier distribution is seen in the SCM image in Figure 3(d). No differences were observed between defective and functioning MOSFETs in the topographical AFM image in Figure 3(c); however, the SCM image (Figure 3(d)) distinctly shows an anomalous region in the defective MOSFET. The heavily doped n + source/drain regions of the neighboring, functioning devices are gray in the SCM image (dC/dV = 0) and separated by clearly defined lightly doped p-type channel regions (dark SCM contrast). In contrast, the defective MOSFET exhibits a moderately doped n region in the p-type channel, connecting the source and drain regions (labeled “short” in Figure 3(d)). The location of this anomalous region coincides with the location of the observed bright spot in the light emission image of Figure 3(a). The abnormal dopants in the channel region resulted from a dislocation generated in this area, which was confirmed using TEM. The dislocation distorted the dopants in the area, resulting in an electrical short between the adjacent source and drain regions. This electrical short created an elevated current leakage (several microamperes) in the defective

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MOSFET, compared to the leakage of sub-nanoamperes in the neighboring MOSFETs. 2.2.3 Abnormal Titanium Silicide Growth The previous two case studies illustrated the application of top-down SCM in characterizing IC failure sites. The following case demonstrates the limitations of top-down measurements and how complementary, cross-sectional SCM images can provide additional detail as to the root cause of a failure [32]. A recent 0.35 µm, radiation hardened, silicon-on-insulator (SOI) technology lot exhibited a low yield of static random access memory (SRAM) devices. Electrical testing, however, indicated that the quiescent power supply current (IDDQ ) on these devices was within the nominal limit. The failure sites of several of these SRAMs were identified with electrical testing, and these devices were subsequently deprocessed for both top-down and cross-sectional SCM measurements. The location of all the failures in this lot was isolated to the VSS contact region of the NMOS islands, shown as the rectangular feature near the center of the topographical AFM image in Figure 4(a); therefore, this region was imaged with SCM for functioning and failed devices. The density of failed VSS contact sites was relatively low, typically one or two sites in a 64 K SRAM array. The low failure density allowed several “good” devices to be imaged from areas adjacent to the failed devices on a single sample, eliminating any question as to whether experimental conditions were contributing to differences in the SCM images. The top-down images in Figure 4 show the (a) topography and (b) carrier distribution of a functioning NMOS island. There are several regions in the topographical image of Figure 4(a) that are dark gray and appear as depressions in the otherwise raised island. These regions correspond to areas of titanium silicide (TiSi2 ) formation that were removed by the HF etch during sample preparation. The TiSi2

FIGURE 4. Top-down images of an NMOS island in a functioning SRAM array showing (a) topography (AFM) and (b) carrier distribution (SCM) at the VSS contact region.

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FIGURE 5. Top-down (a) AFM and (b) SCM images of the VSS contact region of a defect-ive NMOS island in a SRAM array that failed functional testing. (c) Topographical line scan across the VSS contact showing the defect as a discontinuity in the silicide layer (denoted by arrow).

areas provide electrical contact to the source and drain regions of the transistor island and are separated by areas that were previously covered by polysilicon gates. The SCM image of Figure 4(b) shows the corresponding carrier distribution for the functioning NMOS island. The heavily implanted n + source/drain regions are clearly defined and isolated from one another by the lightly doped p-body region. The SCM image also shows the VSS contact being comprised of a p + body tie sandwiched between two n + source areas of adjacent transistors. Even though all regions in the VSS contact are heavily doped, the darker SCM contrast in p + body tie region is clearly distinguishable from the lighter contrast in the n + source areas. Both AFM and SCM images of the device in Figure 4 are representative of numerous functioning NMOS islands acquired from both “good” areas of this lot, as well as other equivalent product lots that do not exhibit this failure. In contrast, Figure 5 shows top-down (a) topographical and (b) capacitance images of a failure site in an island adjacent to the NMOS island in Figure 4. The AFM image of the failed device (Figure 5(a)) shows a discontinuity, or break, in the silicide layer at the VSS contact region. The break is a raised feature as indicated by the arrow in the topographical line scan of Figure 5(c), and appears to be the result of incomplete silicide growth. Transmission electron microscopy data confirmed that the break corresponded to a region of no TiSi2 growth [33]. In addition, this feature is centered approximately at the interface between the n + source and p + body tie. Accompanying the break in the silicide is an anomalous spreading of

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FIGURE 6. (a) Schematic drawing of the cross-section through the VSS contact region of an NMOS island. Cross-sectional SCM images across the VSS contact from (b) functional and (c) failed SRAM devices.

carriers, seen in the SCM image of Figure 5(b). These carriers appear to spread through the lightly doped channel region of the adjacent NMOS transistor. Although the results of the top-down SCM images identify the signature of the failed SRAM cells, they do not fully explain the actual failure mechanism. To address this, cross-sectional SCM imaging of both functional and defective NMOS islands was performed, and the results can be seen in Figure 6. The cross section was taken along the edge of a row of NMOS islands, including one island with a defect site in the TiSi2 as seen in Figure 5. Figure 6(a) is a schematic representation of the device cross section that shows the two adjacent n-type MOSFETs separated by a p + body tie region on an NMOS island. The source/drain implants are shallow relative to the thickness of the device silicon layer and do not extend to the Si/buried oxide interface. The SCM image in Figure 6(b) shows a pair of transistors at the edge of a defect-free NMOS island. Very similar to the schematic in Figure 6(a), the SCM image of Figure 6(b) shows two pairs of light, n-type source/drain regions separated by a dark p-body, each pair corresponding to an NMOS transistor. The two transistors are separated from each other by the p + body tie at the center of

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the image. In contrast, the defect site in Figure 6(c) has a marked difference in SCM contrast at the source area of one of the transistors adjacent to the defect. The location of the defect (highlighted by the arrow) shows a discontinuity in carrier distribution, while the contrast to the right of the defect suggests that ptype carriers dominate at the source and are encroaching on the channel of the transistor. This carrier encroachment changes the dopant profiles of the active device region by converting the n-type region to p-type, thus causing the SRAM cell to fail functionally. This change in carrier type may be attributed to the diffusion of p-type dopants from the overlying ILD, which is made of silicon dioxide doped with phosphorous and boron and is more commonly known as borophosphosilicate glass (BPSG). In this model, boron from the BPSG diffuses through the break in the silicide layer and into the source and channel regions of the adjacent transistor, changing the carrier distribution in the device. The corrective action taken to deal with the anomalous silicide growth was to replace the existing BPSG oxide layer with an undoped, high-density plasma (HDP) silicon dioxide layer. The initial reason for choosing the HDP oxide was the absence of dopants in the film, eliminating the possibility of dopants diffusing through the silicide break. In addition, the HDP oxide is deposited at a much lower substrate temperature of ∼450 ◦ C, versus ∼850 ◦ C for the BPSG. After implementing the process change to HDP oxide, yield on the SRAM devices increased significantly. Breaks in the TiSi2 layer at the VSS contacts were no longer observed, and the anomalous silicide growth was eliminated. The elimination of silicide breaks by switching to the HDP oxide suggests that the difference in process temperature contributed to the break formation; however, the consistent location of the breaks at the VSS contact suggests that device layout also plays a role in forming this defect. As previously mentioned, the VSS contact consists of a p + body tie region sandwiched between two n + source regions of the adjacent transistors; therefore, the contact has two n + / p + junctions on either side of the body tie. The two junctions are identical except for very slight lithographic misalignments due to the inherent overlay tolerance of the lithographic tool. This results in a slight overlap between the n + and p + regions on one of the n + / p + junctions and a slight “underlap” (or separation) on the other junction. Interestingly, all the breaks observed in the silicide layers from all the failed SRAM cells occur only on the overlapped junctions, which was confirmed by TEM analysis. This suggests that the silicide growth in the VSS contact is significantly affected by the dopant distribution at this junction. 2.2.4 Bipolar Junction Transistor Development The previous section showed how top-down and cross-sectional SCM imaging can complement one another in the characterization of IC failure sites. While combining these two imaging strategies is powerful in root cause analysis, the ability to identify failure mechanisms with just one is preferential to reduce turnaround time. In this section, the failure mechanisms for two different npn bipolar junction transistor (BJT) lots were identified using top-down and cross-sectional SCM

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FIGURE 7. Top-down SCM image of a failed npn bipolar junction transistor. Discontinuities at the emitter/base interface are attributed to electrical shorts, highlighted by arrows.

imaging individually. Electrical isolation problems were revealed in the first lot using a straightforward top-down approach, while cross-sectional imaging uncovered dopant discrepancies in the second lot. Operational npn BJT’s require electrical isolation between the adjacent n + emitter and p-type base contacts, which can be adequately accomplished using a dielectric film to separate regions of titanium silicide growth. In an npn BJT development lot, a dielectric layer was omitted from the process flow to speed the lot’s movement through the line. In final electrical test, however, all of the devices failed due to shorting, and the omission of the dielectric was the suspected root cause of the problem. Since the contact region was located at the top layer of the device, top-down SCM imaging was employed. Figure 7 shows a top-down capacitance image of the npn BJT. The n + emitter and p-type base are clearly distinguished in the SCM image. The heavily doped n + emitter is imaged near the middle of the gray-scale, whereas the surrounding p-type base is slightly darker (corresponding to moderately doped p-type). The SCM image in Figure 7 also reveals several discontinuities at the interface between the emitter and base that show little capacitance change (i.e., dC/d V = 0). Although zero capacitance change corresponds to insulating as well as highly conductive regions, the emitter-base short found during final electrical test suggested that these discontinuities were the sources of conduction between the emitter and base. Upon review of the process flow, it was found that what was originally believed to be a redundant layer of silicon nitride was also used as a break to separate the titanium silicide growth on the adjacent emitter and base. In subsequent development lots, this silicon nitride layer was reinserted into the process flow, and the shorting problem was no longer observed. In the previous example, top-down imaging was necessary to identify failures in electrical isolation. Since these shorts were randomly located around the emitter, it is unlikely that cross-sectional imaging would have identified these sites.

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C. Y. Nakakura, P. Tangyunyong, and M. L. Anderson FIGURE 8. (a) Schematic drawing of the cross-section through an npn bipolar junction device. (b) Cross-sectional SCM image of the same area of the BJT device.

This would have required the prepared cross-section to have fortuitously included one of the shorting locations. However, for certain failure mechanisms, top-down imaging does not provide conclusive information, and cross-sectional SCM is necessary. For example, cross-sectional SCM was used to identify a doping error in a subsequent npn BJT lot. Although the problem with electrical shorts had been resolved, the npn transistors failed electrical tests. Scanning electron microscopy and cross-sectional AFM images confirmed the physical layout was correct; therefore, a more elusive failure mechanism was responsible for the problems observed during electrical testing. A schematic drawing of the cross section of the npn transistor is shown in Figure 8(a), while Figure 8(b) is the corresponding SCM image of a functioning device. As expected, the lightly-doped n-type collector appears light in the capacitance image, the p-type base is dark (moderately-doped p-type), and the n + and two p + contacts are imaged as heavily doped (center of the grayscale). The feature above the center of the n + contact in (b) is a tungsten plug and does not affect the capacitance signal near the device region. With the proper doping of the collector, base, and emitter, this device passed electrical tests. In contrast, Figure 9 shows SCM images of the defective device, and the cause of the failure can be readily seen when compared to the images of the functioning device in Figure 8. The collector shows the expected light colored n-type doping, and heavily doped n + / p + /n + contacts; however, the base region is light in the gray-scale, corresponding to a moderately doped n-type material. The SCM results suggested additional electrical testing to confirm the failure mechanism. Subsequently, it was determined that the base was indeed doped n-type rather than p-type. Cross-sectional SCM was well suited for this particular failure analysis application because it allowed all regions of the device to be imaged simultaneously, facilitating an accurate comparison of the carrier profiles among all the device regions.

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FIGURE 9. (a) Cross-sectional SCM image from a failed npn BJT product lot, showing all device regions. (b) Higher-magnification SCM image of the region marked in (a), showing the incorrect doping profile of the base.

3 Active Device Imaging Early SCM development was driven largely by the semiconductor industry’s growing need for high-resolution, quantitative 2D dopant profiling techniques. As a result, a large body of work focuses on using SCM to characterize cross-sectioned, state-of-the-art MOSFETs [6–14]. While this particular application of SCM is used primarily on static devices that are grounded, the ability to measure electrically active devices [3,34–38,58–61] is attractive because it can provide insight into basic device physics and validate theories of dynamic process, such as channel formation. In addition, the ability to image active devices provides a link between dopant distributions in the device as fabricated with its carrier distribution during operation. This section will focus on the application of SCM for imaging active device cross sections, particularly the experimental aspects that are required to perform these measurements [34–36]. The power of having device bias as an additional degree of freedom during SCM characterization will be demonstrated. Examples of active SCM measurements on two different types of MOSFET structures—one, a bulk Si technology and the other, an SOI technology—will be presented.

3.1 Experimental Considerations The realization of active device imaging using SCM has been slow in part due to limitations of commercially available instruments. The standard configuration of

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C. Y. Nakakura, P. Tangyunyong, and M. L. Anderson FIGURE 10. Schematic of the SCM measurement of the cross-section of an active p-channel, bulk Si MOSFET.

most SCM systems applies the capacitance modulating bias voltage to the sample while holding the conductive tip at ground. To facilitate electrical contact to the sample, the use of metallic paint or deposited metal is recommended to create a robust electrode for applying the bias voltage [62]. The result is that all regions of the device must be shorted to one another, prohibiting the use of external voltages to bias the device into operation. This can be overcome either by using an SCM system with tip-biasing capability (custom or commercial) [63], or by modifying a standard configuration commercial system [36]. Figure 10 shows the configuration of the SCM system used to image the devices presented in this section. The commercial SCM system was modified to allow the capacitance modulation voltage (dV) to be applied directly to the tip, instead of the typical tip-grounded configuration. Applying this ac bias voltage to the tip frees the connection to the sample, allowing independent, external dc bias voltages to be applied to separate device regions in order to change the carrier distribution in the device. An added benefit to the tip-biasing configuration is that it allows top-down SCM measurements of SOI devices [32], which is particularly helpful in FA applications. As shown in Figure 10, an HP 4145 semiconductor parameter analyzer biases test structures during the SCM measurements. Four independent voltages are applied to four separate regions: drain (VD ), gate (VG ), source (VS ) and well (VW for bulk devices) or body (VB for SOI devices). By varying these four voltages, the devices can be switched between conducting and non-conducting states. Although a standard dc power supply can alternatively be used to provide the bias voltages that control the devices, the parametric analyzer allows the currents associated with each device region (I D , IG , I S , and IW /I B ) to be measured before, after, and during the SCM measurements. The ability to monitor the device currents during the SCM measurement is critical to verify device functionality, as well as to ensure a one-to-one correspondence between SCM images and macroscopic electrical behavior.

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FIGURE 11. (a) Drawing of the test structure layout. (b) Photograph of the packaged SCM sample. The test structure in (a) is circled and mounted hanging off the edge of the package to allow access to the device for polishing.

In addition to the hardware modifications outlined above, the use of novel test structures and packaging techniques is required to perform reproducible, active SCM measurements. Two key design elements are included in the layout of the test structure, shown in Figure 11(a). First, the device channel width is exaggerated at 100 µm (compared to several µm) to facilitate sample preparation when crosssectioning the device. Because SCM cross-sections are prepared by mechanical polishing, site-specific preparation requires careful attention to prevent polishing past the device location of interest. Increasing the length of the test structure serves to relax this constraint on the polishing procedure. The second key element to the test structure layout is the position of the bond pads, which are located on the side of the device opposite to the cross-sectioned edge to avoid damage while polishing. These pads provide electrical access to the independent regions of the sample to supply the dc bias voltages to operate the device. The design is a simple module that can be included on photolithography reticles for any product lot we wish to evaluate with active SCM measurements; in addition, the same design considerations can be used to fabricate devices other than MOSFETs (e.g., diodes or bipolar transistors). The die containing the test structures is mounted to a cut, 16-pin dual in-line package (DIP) using conductive epoxy, and then wire-bonded to attach the device bond pads to the package leads (see Figure 11(b)). The die is mounted to the package cantilevered off the cut side to allow mechanical access to the edge for polishing. Since the exposed bonding wires are extremely fragile, they are coated with epoxy to prevent them from breaking free during polishing and handling. This packaging procedure provides a compact, rigid sample assembly that can be easily handled and transferred from sample preparation area to the measurement area. Preparation of active SCM samples uses the same cross-sectioning techniques used for static SCM samples, with the exception of a modified sample holder [36]. Cross-sectioning is performed on a polishing wheel using diamond-coated lapping films, starting with a 15-µm particle size disk and incrementally reducing the medium size to 0.1 µm, followed by a final polish using CMP colloidal silica slurries. Because the test structures are electrically active, the impact crosssectioning the device has on the electrical characteristics can be evaluated by

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C. Y. Nakakura, P. Tangyunyong, and M. L. Anderson FIGURE 12. Plot of off-state drain current as a function of the polish step during sample preparation of a bulk Si, pchannel MOSFET.

recording current-voltage curves (drain current, I D , vs. gate voltage, VG ) before, during, and after polishing. Figure 12 shows the off-state drain leakage current for a 0.5-µm, bulk silicon p-channel MOSFET as a function of polishing step (measured with VD = −0.1 V; VS = VW = 0 V at VG = 1 V) [64]. The drain current remained in the sub-picoampere range from the pre-polished sample (step 1) through polishing with the 1-µm disk (step 6). This is not surprising since none of these polish steps, as determined by optical microscopy, cut into the device itself and so should not have affected its I-V characteristics. Once the cross section was exposed (steps 7 and 8), the current increased into the nanoampere range. However, after performing the final polishing step with silica-based slurries, the drain current decreased back down to the sub-picoampere range. The final polish is used to remove all the surface scratches caused by the previous polishing steps. This suggests that the increase in device leakage is the result of scratches in the device cross section. Therefore, being able to electrically monitor the sample during the polishing procedure provides a secondary check for the quality of the sample surface prior to imaging it with the SCM. In addition, these measurements can be used as an indicator of when the device of interest is reached, since a dramatic increase in leakage current is measured when the device edge is first exposed. And, lastly, monitoring the drive current provides an estimate of the new width of the crosssectioned device since the drive current scales with this dimension. Once a finished cross section is obtained, the sample is transferred to the SCM for imaging.

3.2 Examples 3.2.1 Bulk Silicon MOSFET A series of active SCM images for a typical bulk silicon MOSFET is shown in Figure 13. The bulk device was fabricated at the Microelectronics Development Laboratory in a 5 V, 0.5-µm (effective channel length) CMOS technology that uses shallow trench isolation and CMP planarization [65]. The SCM images of

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FIGURE 13. Sequence of SCM images of a bulk Si, p-channel test structure with gate voltages of (a) 0 V, (b) −1.05 V, and (c) −1.75 V. (d) An I D –VG curve of the bulk Si, p-channel test structure generated from point-by-point electrical measurements taken during SCM measurements.

the device are plotted as a function of gate voltage, with VD = −0.1 V and the remaining connections grounded. This low drain bias was selected to operate the device in the linear region and also to minimize any artifacts that could result from a higher bias voltage. The gray-scale shows the p-type regions at the dark side of the scale, and n-type regions at the light side of the scale, while regions where there is no change in capacitance (dC/d V = 0) are plotted at the center of the gray-scale and correspond to both insulating and highly conductive parts of the sample. The layout of the cross section for this particular device was shown previously in the schematic drawing in Figure 10, where the p + source and drain regions are implanted in an n-well. Figure 13(a) shows an SCM image of the device in the non-conducting state, where the gate voltage was held at VG = 0 V. In addition to the interlayer dielectric, the top of the image contains the polysilicon gate, Si3 N4 spacers, and TiSi2 contacts, shown in outline; all regions are imaged at dC/dV = 0 since they are either insulating or metallic. As expected for a device in the nonconducting state, Figure 13(a) shows the p-type source and drain curving upward and terminating beneath the gate while being isolated from each other by a region of light gray, corresponding to the lightly doped, n-type well. The source/drain regions in this image have dC/dV = 0 at the top-most layer, indicating a heavy implant, while the lower region of the junction is dark, indicating a lightly doped, p-type region. Qualitatively, the junction exhibits dark-light-dark contrast banding from top to bottom. This banding of dC/dV response in the intermediate junction areas is similar to what has been observed by other groups [44,47]and is attributed

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to tip-induced motion of carriers near the depletion region edge [10]. It has been shown that the extent of this tip-sample interaction has a complex dependence on the SCM bias voltage [10,47]; however, for the scope of this chapter it is sufficient to note that this contrast is the signature of a p + n junction. The electrical characteristics of the device were measured while recording the SCM images, and the results are shown in the I D vs.VG curve in Figure 13(d). The large circles are labeled with letters corresponding to the SCM images in Figure 13 (a–c). Increasing the gate voltage to VG = −1.05 V, the separation between the upwardly curved regions of the source and drain decreased, as shown in Figure 13(b). This gate bias brings the device near the threshold voltage, and the drain current increases an order of magnitude, from 1.6 × 10−8 A to 1.6 × 10−7 A, as seen in Figure 13(d). Further increasing the gate voltage to −1.75 V, the SCM image (Figure 13(c)) shows the source and drain connected to one another, while the electrical measurement yields a device current of 0.26 mA. The contrast signature of the p-n junction can be seen in the channel region of Figure 13(c), which is not surprising since there is a high concentration of p-type carriers (inversion layer) adjacent to the n-well. 3.2.2 SOI MOSFET Figure 14 shows SCM images of an active SOI MOSFET fabricated in a 3.3 V, 0.35-µm (effective channel length) CMOS technology line using an SOI substrate.

FIGURE 14. Series of SCM images of a p-channel silicon on insulator MOSFET, with gate voltages of (a) 0 V, (b) −0.75 V, and (c) −1.25 V. (d) An ID –VG curve of the device generated from point-by-point electrical measurements taken during SCM measurements.

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The sequence demonstrates device operation, with VD = −0.1 V, VB = VS = 0 V, and dc voltages incrementally applied to the gate. In Figure 14(a), the p-channel device was in a non-conducting state with VG = 0 V. The different device layers are clearly differentiated by SCM. The white region at the bottom of the SCM images corresponds to the silicon substrate. The gray region directly above substrate is outlined with dashed lines and exhibits dC/d V = 0, as expected for the buried oxide. The light SCM contrast above the buried oxide, in the center of the device layer, corresponds to a lightly doped n-type region. This light region separates the source from drain, and corresponds to the body of the SOI device, analogous to the well region of a bulk MOSFET. On either side of the n-body are the gray (heavily doped) p + source and drain. The source and drain exhibit dark-light-dark contrast banding, which is the signature of a p + n junction as noted in the previous section. Finally, the top of the image, which contains the gate, contacts, spacers, and ILD, was imaged in the middle of the gray-scale since they are either insulating or metallic. The characteristics in the SCM image of this device are similar to the bulk silicon MOSFET, except that the source, body, and drain are truncated by the insulating buried oxide. In this series of SCM images (Figure 14(a–c)), device operation was observed while the corresponding electrical characteristics were measured (Figure 14(d)). From Figure 14(a) to (b), the gate voltage was decreased from 0 V to −0.75 V. As a result, in Figure 14(b), the upwardly curved source and drain regions elongated and are no longer terminated at the gate oxide. The separation between the source and drain decreased while the measured drain current increased five orders of magnitude, as seen at point (b) in Figure 14(d). At a gate voltage of −1.25 V, the source and drain are no longer separated by the body and are continuous in Figure 14(c). The device current increased further to 5 × 10−4 A and, therefore, the source and drain are shorted. Throughout the sequence, the thickness of the gray middle band of the drain is smaller than that of the source. This apparent asymmetry of the source and drain is due to the two p + n junctions being biased differently. At the source/body junction, 0 V was applied, while the body/drain junction was reversed biased at 0.1 V. This leads to the two junctions having different depletion widths, resulting in the asymmetric imaging by SCM. Often, this effect is not visible at such low drain voltages, as was the case with the bulk Si device in Figure 13; however, favorable conditions of the prepared sample cross section and SCM tip enabled this observation. It is important to reemphasize that the key aspect of our methodology is the ability to measure device current while acquiring each SCM image, which provides a means to verify that the active SCM images indeed represent a functioning device. We have observed cases in which electrically damaged transistors yield SCM images that change as a function of bias; however, the manner in which they change is considerably different from a damage-free device. Therefore, the ability to produce a one-to-one correlation between active SCM image and measured device current is critical to acquiring meaningful SCM data.

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4 Radiation Effects Exposure of MOS devices to ionizing radiation can have adverse effects on device operation and performance [66]. Understanding these effects is critical to the development of radiation-hardened integrated circuits, designed for use in harsh environments such as outer space travel, earth orbit, and nuclear environments. When an MOS device is exposed to radiation, electron-hole pairs are generated as photons travel through the semiconductor and insulator layers. In the SiO2 regions of the device, high-mobility electrons are quickly swept into the electrode with positive bias (time scale 10−12 sec) [67], while holes are transported 109 –1012 times more slowly [68] until becoming trapped at the Si/SiO2 interface, which typically has a high density of charge trapping [69]. The net positive charge on the oxide causes electrons in the adjacent Si to accumulate at the Si/SiO2 interface. As a result, n-channel MOS devices are susceptible to leakage paths generated by negative charge accumulation in the p-type regions separating the source and drain junctions [70]. While a number of undesirable radiation-induced failures are possible in a silicon based MOSFET, this section will focus on total dose effects caused by long term charge buildup in the insulating device layers. The extended lifetime of total dose effects enables the use of SCM for their study since measurements are performed ex-situ following radiation exposure. The development of radiation-hardened technologies requires charge sensitive characterization tools. Electrical testing of semiconductor parameters, where particular electrical characteristics (e.g., threshold voltage) are measured as a function of radiation exposure, is the most widely used technique [70]. While this approach yields ample information, a complementary, charge sensitive imaging technique would be ideal to directly observe radiation effects and confirm models inferred from non-imaging electrical measurements [71]. This would have particular utility in cases where the devices are sufficiently hardened to the extent that electrical measurements do not show any dependence on exposure [72], leaving the user without a direct result showing the mechanism for successful radiation hardening. Scanning capacitance microscopy is attractive for this application because it is a charge sensitive imaging technique. Because it yields 2D carrier maps, SCM is able to show real space images of radiation effects on cross-sectioned MOS devices, complementing models extracted from electrical measurements. This section will introduce the application of SCM in studying radiation effects on crosssectioned MOSFETs. Building on the previous section on active device imaging, this section presents SCM images of an active device before and after exposure to radiation, and the changes in the images resulting from radiation exposure are discussed.

4.1 The Body-Under-Source FET (BUSFET) Silicon-on-insulator substrates are attractive for radiation hardened ICs because the thin Si device layer yields a smaller volume for carrier generation upon

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FIGURE 15. (a) Schematic drawing of an n-channel SOI MOSFET fabricated with deep implants for both source and drain. (b) Schematic showing the effect of a net positive charge on the buried oxide post radiation exposure. The conductive back channel shorting the source to drain is highlighted.

exposure [73–75]. When both junctions of the MOSFET are deep implants such as the device shown previously in Figure 14, however, the body region is electrically isolated, without any direct external connection [74]. This leaves the device susceptible to shorting after prolonged exposure leaves a net charge on the buried oxide layer and inverts the lower part of the body, creating a back channel that shorts the source and drain, in n-channel SOI MOSFETs [76]. This process is illustrated in Figure 15, which shows an n-channel SOI MOSFET (a) before exposure to radiation and (b) after exposure to an arbitrary amount of radiation sufficient to switch on the back channel. As a net positive charge builds up on the buried oxide layer, electrons accumulate at the p-body interface until this region inverts, forming a back channel between source and drain, as shown in Figure 15(b). The formation of this conductive back channel results in an increase in the off-state leakage current, which increases with the total radiation dose [72]. To address this limitation of SOI MOSFETs, a new type of device was developed called a body under source field-effect transistor, or BUSFET [76]. Figure 16 shows a schematic of an n-channel BUSFET, which consists of a field-effect transistor built on an SOI substrate with a deep implant at the n + drain, extending down to the buried oxide, and a shallow implant at the n + source. The shallow implant at the source

FIGURE 16. Schematic drawing of an n-channel BUSFET. The shallow implant at the source avoids the radiation-induced back channel from shorting the drain to the source.

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FIGURE 17. Sequence of SCM images of an n-channel BUSFET recorded with gate voltages of (a) 0 V, (b) 0.4 V, and (c) 0.75 V. (d) An I D –VG curve of the BUSFET generated from in situ electrical measurements taken while recording SCM images.

prevents source/drain shorting after radiation exposure creates a back channel, while allowing electrical contact to the body. The series of active SCM images for a 0.35-µm n-channel BUSFET is shown in Figure 17(a–c), while the corresponding electrical measurements taken while imaging are shown in Figure 17(d) [37]. As with the sample previously presented, these images were recorded as a function of gate voltage, while applying a low drain bias (0.1 V) and grounding all other connections. The SCM image for the device in its “off” state (VG = 0 V) is shown in Figure 17(a). The top part of the image exhibits the shade corresponding to dC/dV = 0 since this region contains insulating and highly conductive features. The silicon substrate, at the bottom of the figure, appears dark in the SCM image, which confirms that this is a p-type substrate, as specified by the wafer manufacturer. In addition, the buried oxide layer just above the substrate appears at the center of the gray-scale (dC/d V = 0), which is expected since this is an insulating region. On the left side of Figure 17(a), the shallow source implant is gray at the top layer, indicating a heavy carrier concentration, and white near the bottom, indicating a lightly doped n-type region. In contrast, the drain appears uniformly gray through the entire Si layer down to the buried oxide interface, showing that the heavy implant at the drain is indeed deep, as the design of the BUSFET requires. In addition, the area of the n + drain that borders the p-body exhibits banding similar to what was observed for the p + n junction of the bulk p-channel MOSFET, but at the opposite end of

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the gray-scale. This is, again, attributed to tip-induced carrier movement, and the dark/light banding is assigned the SCM signature of an n + p junction. Note that this contrast is identical to the entire region at the lower boundary of the source. This suggests that the contrast at the source is due to the p-type body not only being adjacent to the edge of the source beneath the gate, but also underneath the entire source implant. Therefore, the source implant only partially penetrates the Si layer, leaving a layer of the body beneath it, in accordance with the design of the BUSFET. Unfortunately, the layer of the p-body beneath the source could not be resolved because the SCM junction signature extends down the entire Si layer to the buried oxide. Further studies that investigate the bias dependence of this apparent junction depth are in progress to determine the optimum conditions for resolving the body underneath the source. Lastly, Figure 17(a) shows that both the source and drain are isolated from each other, separated by the moderately dark region representing the p-type body, as expected for a device in the non-conducting state. As the gate voltage was increased to VG = 0.4 V, the curved portions of the source and drain began to extend toward one another (Figure 17(b)), while the device current modestly increased (Figure 17(d)). As the gate bias was increased further to VG = 0.75 V, the SCM image of Figure 17(c) shows the two curved regions of the source and drain overlap to form a continuous path between source and drain. The functionality of the device is confirmed in Figure 17(d), which shows that the drain current has increased to I D = 11.6 µA. Therefore, the continuous path in the SCM image represents the formation of the BUSFET conduction channel.

4.2 Post-Irradiation SCM Exposing active SCM samples to radiation presents a number of experimental complications. The additional handling, as well as the use of X-ray radiation sources, leaves devices susceptible to electrical damage. Moreover, post-irradiation charge buildup on the native oxide covering the device cross section, where the device is imaged, can obscure results. To limit the possibility of damage during transport and irradiation, great care was taken to prevent electrostatic discharge. Radiation exposure was performed in an ARACOR 4100 semiconductor irradiator using a 10 keV X-ray source, equipped with an HP 4062 parametric analyzer [77]. This allowed the testing of device functionality immediately following radiation exposure. Charging of the native oxide at the device cross section was addressed by re-polishing the sample post-irradiation. This ensured that the device cross section had a fresh, unexposed native SiO2 layer. Since this oxide is used by the SCM as the insulating layer for the capacitance measurement, it is critical that it be free from any charge buildup from the radiation exposure. Following exposure, functional testing, and re-polishing, the irradiated sample was immediately transferred to the SCM for imaging. Figure 18(a–c) shows the active SCM measurements following a total radiation dose of 500 krad (SiO2 ) [78]

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FIGURE 18. Sequence of SCM images of an n-channel BUSFET following 500 krad exposure. Images recorded with gate voltages of (a) 0 V, (b) 0.4 V, and (c) 0.75 V. (d) An I D –VG curve of the irradiated BUSFET (solid) plotted along with pre-exposure data (open), both generated from in situ electrical measurements. (See also Plate 8 in the Color Plate Section.)

as a function of gate bias (VD = 0.1 V, VW = VS = 0 V). The off-state image in Figure 18(a) exhibits enhanced contrast at the source/drain n + p junctions compared to the corresponding image without radiation exposure (Figure 17(a)). This is likely due to charge redistribution in the body region resulting from the net positive charge on the buried oxide; however, the limited resolution on this preliminary data does not provide sufficient detail to elaborate on this effect. The most notable difference between the pre/post-SCM images can be seen at the buried oxide/substrate interface. Figure 18(a) shows that the topmost region of the substrate is no longer dark, corresponding to a lightly doped p-type Si. Instead, this region appears gray to light gray in the SCM gray-scale, corresponding to lightly doped n-type material. This would occur if electrons in the substrate were accumulating at the buried oxide/substrate interface. Therefore, the observed contrast at the top of the substrate was the direct result of positive charge buildup on the buried oxide, causing the substrate to invert just below the buried oxide.

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The subsequent two SCM images show the effect of increasing the gate bias to (b) 0.4 V and (c) 0.75 V. The I D -VG curve in Figure 18(d) shows post-exposure current measurements taken simultaneous to the SCM images (solid squares) superimposed on the I -V data for the pre-exposure BUSFET (open squares, data taken from Figure 17(d)). The large circles correspond to data points acquired for the SCM images shown. The curve in Figure 18(d) shows that 500 krad (SiO2 ) of exposure did not change the general I -V characteristics of the device. The offset in off-state leakage current (VG = 0 to 0.5 V) between pre- and post-exposure data is due to slight differences in the AFM laser alignment, causing different concentrations of photogenerated carriers [37]. When the gate bias is increased to 0.4 V, the SCM image in Figure 18(b) shows the same generalities that all the previous active SCM examples have shown: the source/drain separation decreases. The device current in Figure 18(d) shows that at this near-threshold gate voltage, the current increased from ∼400 pA to 3.3 nA. Increasing the gate voltage to 0.75 V resulted in the source/drain in the SCM image (Figure 18(c)) forming a single, continuous feature. The current increased to 10.8 µA, and so the bright feature connecting the source and drain represents the formation of the channel. In comparison to the analogous pre-exposure image in Figure 17(c), the post-exposure BUSFET in the conducting state (Figure 18 (c)) has a distinctly straight boundary between the channel and the body. This is most likely related to the presence of an inversion layer in the p-body, similar to what was seen in the p-substrate, except at the body/buried oxide interface. Studies to improve the SCM resolution of the body under source region are currently underway to find evidence supporting this argument.

5 Summary Scanning capacitance microscopy is a powerful characterization tool with a wide range of applications in the microelectronics industry. This chapter introduced three relatively new applications of SCM: failure analysis of integrated circuits, active device imaging, and the visualization of radiation effects. Each of these diverse applications are enabled by the SCM’s unique ability to image free carrier concentrations in two dimensions. Although SCM has gradually become an established technique in failure analysis, its application to the study of device operation and radiation effects is still preliminary. The impact of visualizing these dynamic processes, as shown in this chapter, will hopefully inspire more researchers to join this field.

Acknowledgments. The authors thank all of their colleagues at the Microelectronics Development Laboratory (MDL) at Sandia National Laboratories, Albuquerque, who have supported the SCM applications team through the years. We are grateful to D. L. Hetherington and M. R. Shaneyfelt for all their efforts in the early stages of the project, in addition to L. M. Cecchi and R. E. Anderson for

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management support. The authors also extend their gratitude to the Fab personnel for fabricating the devices shown in this chapter. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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III.5 Kelvin Probe Force Microscopy of Semiconductors Y. ROSENWAKS, S. SARAF, O. TAL, A. SCHWARZMAN, TH. GLATZEL, AND M.CH. LUX-STEINER

1 III-V Semiconductors Due to their technological importance, III-V compound semiconductors have been widely studied. While extensive work has been done on their geometric and electronic structure, Kelvin probe force microscopy (KPFM) in ultrahigh vacuum (UHV) creates the possibility to study the electronic structure of the surfaces on a nanometer scale [1]. The work function is one of the most important values characterizing the property of a surface. Chemical and physical phenomena taking place at the surface are strongly affected by the work function. In turn, the work function variation reflects physical and chemical changes of surface conditions [2]. For example, due to a localized dipole at atomic steps, the averaged work function on a metal surface decreases in proportion to the step density [3]. If molecules or atoms are adsorbed on a surface, the work function changes depending on the magnitude of the electric dipole formed by the adsorbates [2]. Although the work function is defined as a macroscopic concept, it is necessary to consider its microscopic local variations in understanding the details of the formation of semiconductor interfaces and device behavior. In the first subsection, KPFM measurements of the surfaces of UHV-cleaved nand p-type doped GaAs and GaP will be presented. The discussion will be focused on the work function variations at step edges; for p-type materials an increase and for n-type doped semiconductors a decrease of the work function at step edges can be determined. The impact on the work function difference measured at a UHV cleaved GaP pn-homojunction will be discussed. Nowadays, low-dimensional systems, such as quantum wells, are conventional features widely incorporated in to optoelectronics devices. Electrical characterization of such low-dimensional structures can ideally be performed using atomic force microscopy (AFM)-based techniques such as scanning capacitance microscopy (SCM) [4], scanning spreading resistance microscopy (SSRM) [5], or KPFM. These include detection and profiling of new types of carrier distribution, the determination of materials properties such as band offsets, and the evaluation of the spatial resolution in these AFM-based techniques. Very recently, carriers confined in quantum wells (QWs) have been investigated by cross-sectional SCM 663

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[6], SSRM [7], and KPFM [8]. All methods were capable of imaging the confined carriers in the quantum wells. In the last subsection, UHV-KPFM measurements of multi-quantum-well structures are presented. The work function of the individual InGaAs quantum wells was measured in the temperature range of 29–300 K. The measurements were conducted on a GaAs-based ternary compound layer structure with multiple quantum wells, used for high-efficiency solar cells. The experimentally obtained potential profiles were found to be in a good agreement with a secondary electron emission profile obtained using high-resolution scanning electron microscopy and numerical simulations of the contact potential difference.

1.1 Surface Defects and Surface Band Bending The applicability of semiconductors in electronic devices and technology is strongly influenced by the uncontrolled and unintentional formation of defects during growth and processing of semiconductor crystals, because these defects eventually counteract the desired effects of dopant atoms. Therefore, considerable research efforts were focused on the physics governing the formation of defects and the incorporation behavior of impurities as well as their respective electronic properties. Mostly indirect methods have been applied for such studies relying on the interpretation of macroscopic data of differently processed crystals or of signals integrating over a large amount of usually unknown defects. Atomic-scale properties of defects and steps have been achieved by scanning tunneling microscopy (STM) [9–12]. Unfortunately, quantification of the measured values by STM is difficult. Sommerhalter et al. [13] presented, for the first time, KPFM measurements on GaAs(110) surfaces, which qualitatively show surface band bending at step edges and the influence of single localized charges at dopant sites on the surface potential. Recently Glatzel et al. published a detailed KPFM analysis of III-V semiconductor surfaces [14]. The KPFM used was a modified Omicron UHVAFM/STM ( p < 10−10 mbar) capable of simultaneously measuring topography and work function. The principle of KPFM in vacuum and the experimental setup were described in details in our first chapter. To measure the electrostatic forces, an acbias (Vac = 100 mV) at the second resonance frequency of the cantilever was superimposed on the tip-sample voltage. This setup allows the independent and energy-sensitive determination of the contact potential (CP). Furthermore, with these low ac voltages, a significant tip-induced band bending at semiconductor surfaces can be excluded [15]. To determine the surface photovoltage (SPV) of the semiconductors, defined as the work function difference between the dark and illuminated sample surface, the sample was illuminated with a HeCd laser (λ = 442 nm) or a laser diode (λ = 675 nm). All other measurements were performed under dark conditions. Well-defined III-V semiconductor (110) surfaces were obtained by cleavage in UHV. Doping concentration of the GaAs samples were p ≈ 2 × 1018 cm−3 and n ≈ 1 × 1017 cm−3 for the p- and n-type material, respectively. The

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GaP pn-homojunction was also cleaved in UHV and both sides of the junction were in electrical contact. Figure 1 shows the topography and the work function of the KPFM measurements on p- and n-type doped GaAs(110) surfaces, respectively. Additionally, line profiles are plotted. These profiles are averaged values from all lines through the images perpendicular to the step edges. The work function changes are associated with the monolayer steps, a depression on the p-type sample, whereas the n-type GaAs(110) shows a work function increase along the step edge. This indicates that the steps are the source of a localized charge-induced downward or upward band bending. Thus, on the samples investigated the steps are found to be positively charged on p-type-doped and negatively charged on n-type-doped materials. This effect was already observed with STM analysis [12], but with the KPFM it is possible to measure and quantify the potential, induced by charges localized at step edges. Very recently it has been shown that the charge located at steps on a GaP surface could be quantitatively extracted from a KPFM measurement using a 3D Poisson simulation [15]. Due to the relaxation of surface atoms, no surface states exist within the band gap for most (110) surfaces of III-V semiconductors [16]. Thus, the position of the Fermi energy at the surface is determined by the bulk doping; the surface is in flat band condition. In contrast, surface states within the band gap appear at the

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FIGURE 2. KPFM measurement on UHV cleaved GaP pn-homojunction without illumination. The topography (a) and the simultaneously measured work function (b) shows the band bending at the pn-homojunction. The profiles in (c) show an average value of the work function data perpendicular to the step edge. We illuminated the sample with a HeCd laser (λ = 442 nm) with two different intensities [14].

step edges. Due to localized charges in these defect states a band bending occurs, influencing the work function; in the case of n-type or p-type material the work function is increased or decreased, respectively. Consistent with the measurements presented in Figure 1(b,e), Laar et al. proposed a defect state near the conduction band which would imply a stronger band bending for n-type material [17]. This is also confirmed by the KPFM measurements presented in Figure 1. In Figure 2 KPFM images of a UHV-cleaved GaP pn-homojunction are presented. In the topographic image the two sides can be distinguished due to a different morphology. The n-type-doped side shows atomically flat areas between a few steps, whereas the p-type side exhibits a large number of steps; the morphology difference is attributed to the liquid phase epitaxy growth of the p-type side. Under illumination with a HeCd laser a reduction of the potential drop across the pnjunction was observed. Figure 2(c) shows the averaged work function profiles perpendicular to the interface for three different light intensities. With the maximum intensity available nearly flat band conditions across the interface are observed. The difference in Fermi level position at single p- and n-type GaP surfaces were determined to be E fs = 1.40 eV. In comparison with the band-gap energy of the bulk, E g = 2.26 eV, and the doping concentrations of the samples, this seems to be too small. Huijser et al. [16] found in photoemission measurements, that the band gap on GaP(110) surfaces is free of filled surface states and a band of empty surface states starting at 0.55 eV below the conduction band edge. On ntype material, the Fermi energy at the surface is pinned at this position. Therefore, only a difference in Fermi level position of E fs,max = 1.76 eV could be expected. With this knowledge the measured GaP pn-homojunction can be explained. At the interface between the materials a band bending of up to the band gap energy is expected. The work function difference between the two sides in Figure 2(b) averages only  pn = 1.20 eV. The main reason of this reduction is the pinning

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FIGURE 3. Representative KPFM measurement on the InGaAs/InP QW sample showing two QWs. (a) CP image (contrast  CP = 230 mV). (b) Typical line scan showing the variation of CP across the structure. QW2 is closer to the cleaved edge [8].

of the Fermi energy at the defect level within the band gap of the n-type doped material as we discussed above. A further reduction of the potential difference is caused by the heavily stepped surface of the p-type doped side. Furthermore, the influence of the cantilever should be considered. Due to the long range nature of the electrostatic force an averaging effect of the whole cantilever is possible [18,19].

1.2 Quantum-Well Structures Just recently the detection and characterization of InGaAs/InP quantum wells (QWs) as narrow as 5 nm by UHV-KPFM was published by Douheret et al. [8]. It was shown that the characteristic peaks in the KPFM data carry the signature of carriers accumulated in the quantum wells. In Figure 3 the KPFM measurement on In0.53 Ga0.47 As/InP (lattice matched) QW samples are shown. The two InGaAs wells, 20 nm and 5 nm wide, were separated by 400-nm n-type (Si doped) InP barriers. In the line scan (Figure 3(b)) well defined peaks in the KPFM signal are seen at the QWs, indicating a significant potential difference between the wells and the barriers. Moreover, the peak for the 5-nm QW is smaller in height and width than the peak for the 20 nm QW. As a first interpretation, the origin of the observed peaks can be related both to the conduction band offset between InP and InGaAs and electron accumulation in the QW. While the electron accumulation is directly responsible for the peak-like contrast, the influence of the band offset will be contained in the magnitude of the peak. Within a simple 1D Poisson/Schr¨odinger simulation the observed behavior was confirmed and furthermore the measured peak widths and peak height are comparable to the the ones from the simulation. In another recent study, Glatzel et al. [20] reported on low-temperature UHVKPFM measurements of multi-quantum-well structures. The work function of the individual InGaAs quantum wells was measured in the temperature range

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FIGURE 4. Contact potential image of a GaAs multi-quantum well structure with 20 InGaAs quantum wells each 7.5 nm wide measured by UHV-KPFM at a temperature of T = 30 K. The averaged linescan across the QWs shows a reduced contact potential (CP ≈ 5 mV) at the position of the QWs.

of 29–300 K. The measurements were conducted on a GaAs-based ternary compound layer structure with multiple quantum wells, used for high-efficiency solar cells. Strain-balanced quantum well solar cell (QWSC) contain an i-region which is inserted into a conventional pn-solar cell to extend the built-in field. A number of QWs formed with Inx Ga1−x As wells and GaAs1−y Py , barriers as compressively strained wells and tensile strained barriers [21,22]. The QWs extend the absorption below the bulk band-gap. If the field is maintained across the i-region, the carriers produced in the wells escape efficiently at room temperature to the bulk cell and contribute extra current. There is some loss of voltage, but it was demonstrated, that the current enhancement of the QWs is sufficient to overcome the voltage loss [23,24]. In these strain-balanced systems the wells can enhance efficiency compared with conventional cells with the bulk band-gap. In Figure 4 the KPFM measurement at 30 K of a strain-balanced QWSC formed with 20 In0.17 GaAs wells (width ≈ 8 nm) and GaAsP0.06 barriers (width ≈ 45 nm) grown on an n-type GaAs wafer with a 1.4-µm-thick p-type GaAs top layer is shown. The barriers as well as the single QWs are clearly visible. The potential gradient from the left to the right of the image are raised from the potential drop within the enlarged i-region of the pn-junction. From the averaged line scan on the right it can be deduced, that the QWs induce a potential drop of around 5 mV which is in good agreement with ID Poisson/Schr¨odinger simulation of the QWSC. The experimentally obtained potential profiles were also found to be in a good agreement with a secondary electron emission profile obtained using high-resolution scanning electron microscopy [25].

2 Chalcopyrite Solar Cells Nowadays, the necessity of alternative energy use is widely recognized. In solarenergy technology crystalline silicon cells are well established. Beside these, the thin-film solar technology based on the chalocopyrites Cu(In(1−x) Gax )(Sy Se1−y )2 with 0 < x < 1 and 0 < y < 1 is very promising due to lower production costs and

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shorter energy payback times. At present, detailed knowledge about devices especially with high band-gap absorber material is limited, and further improvement of solar cell parameters will require a better understanding of the electronic and structural properties of the devices. An important issue for improving the device performance is an appropriate electronic band alignment at the various interfaces of the different layers that compose the heterostructure [26]. Typical chalcopyrite thin-film solar cells consist of a Mo back-contact on soda lime glass, the p-type absorber layer, a thin buffer layer, and a n-type window layer. A variety of KPFM studies on chalcopyrite solar cell materials have been performed [27–40]. In this section, these studies will be briefly described and discussed. In the first subsection, KPFM study resolved work function differences for differently oriented facets on single grains of CuGaSe2 will be reviewed. The next subsection will present recent achievements based on KPFM characterization of grain boundaries within the polycrystalline absorber material. Finally UHV-KPFM measurements on a cross section through a complete solar cell structure will be discussed. Absolute work function values of the different material surfaces forming the device were observed. Detailed information was obtained especially on the interfaces and was used to optimize the devices.

2.1 Surface Orientation Sadewasser et al. [35] studied the band alignment between a ZnSe single crystal and a CuGaSe2 absorber layer, as a model system for the absorber/buffer interface in chalcopyrite solar cells. By studying the electronic properties of the substrate and the absorber surface, i.e., the work function and the SPV, the band offset between absorber and buffer material was estimated using a formalism initially proposed by Kronik et al. [41] for macroscopic SPV measurements. In the same study the authors found lateral inhomogeneities in the CuGaSe2 film, which became evident through a negative SPV of one grain, whereas the rest of the surface showed a positive SPV. Another study was performed on the surface of p-type CuGaSe2 absorber material, also grown on a ZnSe(110) substrate by metal-organic vapor phase epitaxy [37]. The film was of polycrystalline nature; however, x-ray diffraction showed its orientation along the (220) direction. Figure 5 shows the surface of this CuGaSe2 /ZnSe sample. 2D color-scale images of the topography and the work function are shown in Figure 5(a,b), respectively. In Figure 5(c) both images are merged into one 3D representation; the 3D image reveals the topographical information, whereas the magnitude of is given by the color scale. It is clearly seen that different crystal facets exhibit distinct values of the work function with differences between the facets as small as 30 meV up to 255 meV. Since AFM data supply truly 3D information, the crystal orientation of the different facets can be indexed using an analysis of the angles between the facets of single grains and the surface normal. Comparison between the topography and the work function clearly shows that for each facet adopts a distinct and constant value. Comparing the angles of the facets with those expected for the CuGaSe2 crystal

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FIGURE 5. KPFM measurement of a CuGaSe2 thin film grown on a freshly cleaved single crystalline ZnSe(110) substrate. (a) The topography image shows distinct crystal facets on the (220) oriented CuGaSe2 film. The scale corresponds to height differences of 384 nm. (b) Representation of the simultaneously measured work function ( = 4.85 − 5.09 eV). The crystallographic orientation of the facets is assigned based on the angles to other facets and to the surface normal. (c) 3D image merging the topography (as the 3D effect) and the work function represented by the color scale. The origin corresponds to the lower left corner in the 2D images [37].

structure (tetragonal) results in an assignment of the crystallographic orientation of the facets. The result of the analysis of several grains is included in Figure 5(b). The (112) surface develops preferentially during crystal growth and thus, is likely to be found frequently in the present sample. The various work function values for different facets were explained by a surface dipole characteristic for each orientation. The atomic arrangement at the surface, i.e., surface relaxation and reconstruction, varies with surface orientation. Therefore the atoms and ions will form a surface dipole which depends on the orientation. It should be pointed out that for the observation of small work function differences, as for example the difference of 30 meV between the (111) and the (102)

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planes, the KPFM represents an ideal tool which in addition to its high energy resolution (≈ 5 meV) also provides exceptional lateral resolution (≈ 25 nm). Previous studies of work function differences for differently oriented surfaces employed photoemission spectroscopy on single crystals, with inferior energy resolution (100–300 meV). In view of the application of semiconductors in heterostructures, the observation of laterally different work function values is of importance because the energy band alignment (i.e. band offsets) in these heterostructures will vary with the exposed surface. This can have a detrimental effect on the efficiency of solar cell devices [26]. High-efficiency Cu(In,Ga)Se2 solar cells are achieved using an absorber material with a (220)/(204) preferential orientation [42]. Thus, according to the KPFM results on the related material CuGaSe2 , the orientation could be an important criterion for obtaining high efficiencies, for example, due to an improved band alignment.

2.2 Grain Boundaries Very recently Hanna et al. reported on the influence from surface orientation of Cu(In,Ga)Se2 absorber material on the electrical behavior of the grain boundaries [40]. In this work, the authors investigated two samples with a different surface texture ((220/204) and random texture) by KPFM. Figure 6 shows the topography

FIGURE 6. KPFM measurements on (a) a Cu(In,Ga)Se2 film with random orientation and (b) a (220/204)-textured Cu(In,Ga)Se2 film. The two-dimensional mappings show the topography z (with (a) z = 269 nm; (b) z = 238 nm) and the measured contact potential CP (with (a) CP = 841–1300 mV, (b) CP = 838–1,329 mV) of both samples. Lighter gray scales represent high values in the maps. The line scans display the measured height z of the sample surfaces (dashed lines) and the work function (solid lines) as determined from the CP along the lines printed in the maps. A strong dip of marks the position of the grain boundary (GB) in the sample with random texture. In contrast, the GB of the (220/204)-textured sample is marked by a maximum of [40].

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and contact potential (CP) of the film surface measured with KPFM of the two samples. The contact potential of the grains and their grain boundaries (GBs) are identified by comparing the maps of the topography with that of the CP. Clearly, the CP varies significantly with the texture of the films. The sample with the random texture displays lower CP values around the grain boundaries than at the grains, as seen by the dark line in the contact potential map between the two grains in Figure 6(a). The surfaces of the two adjacent grains seem to have the same CP (white areas). At the sample with a (220/204) texture (Figure 6(b)), the CP of the GBs does not strongly differ from the CP of the grains that are adjacent to the GBs. Instead, the contact potential varies from grain to grain at the (220/204)-textured samples or between different surface areas on one single grain. Apparently, the GBs of the (220/204)-textured sample mainly represent a step between two areas of constant CP belonging to the grains. The lower part of Figure 6 shows one-dimensional line scans across a GB for the topography and the simultaneously measured work function . The latter is extracted from the measured contact potential as described in the experimental section. Note that varies between 5.0–5.5 eV in both samples. In the sample with a random texture the line scan of in Figure 6(a) has a dip of about 400 meV at the GB, while, on both grain’s surfaces it is at a level of about 5.44 eV. In the (220/204)-textured sample (Figure 6(b)), exhibits no comparable dips at the GB. Instead, the GB rather seems to consists of two oppositely tilted surfaces, each having a different but constant value of . Together with the other two surfaces,

passes four different plateaus (indicated by dotted lines in Figure 6(b)) when crossing one GB as seen in scan 1 of Figure 6(b). Also, small spikes in are observed when crossing a GB in the (220/204)-textured sample (see scan 2 of Figure 6(b)). So far in recent reports, the influence of a possible surface band bending on the KPFM evaluation has not always been considered. Because surface charges and the charge of the surface depletion region may partly screen the GB charges, a surface band bending might influence quantitative conclusions that are drawn from the KPFM results on the GBs [28]. In the presented experimental situation, surface band bending was concluded to be negligibly small based on two experimental findings. Firstly, the samples do not exhibit a surface photovoltage; i.e., the values of measured under illumination equal the values measured under dark conditions. Secondly, the measured values of the work function are in good agreement with the values obtained by other characterization methods [43]. Thus, from the KPFM measurements, not only qualitative differences between GBs of (220/204)- and (112)-textured films were observed but also quantitative values as the net doping N A of the Cu(In,Ga)Se2 film as well as the areal density of charges n G B present at the GB were obtained [40].

2.3 Cross-Sectional Studies on Complete Devices The analysis of cross sections from complete devices allows the direct determination of interface properties and growth peculiarities by KPFM. Furthermore a

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FIGURE 7. KPFM measurement of a CuGaSe2 solar cell cross section: (a) topography (gray scale z = 65 nm) and (b) work function ( = 3.92 − 4.86 eV) [31].

direct correlation with macroscopic solar cell parameters is possible. In recent studies, Glatzel et al. [31,44] investigated the cross section through complete solar cell devices. The samples for the KPFM investigation were prepared by polishing, successfully avoiding the problem of large topographical height differences. To obtain clean surface conditions for the measurement of representative work function values, the samples were cleaned in UHV by argon sputtering. The topography (a) and the work function (b) of the CuGaSe2 cross section after Argon sputter cleaning are shown in Figure 7. From the lower left corner up to the upper right side the Mo back contact, the CuGaSe2 absorber, and the ZnO window layer on the top can be seen. The work function image shows a clearer contrast of up to 940 meV between the different layers under dark conditions. Between the absorber and the Mo back-contact an additional layer of about 100-nm thickness with a distinct work function is observed. The additional contrast between Mo and absorber layer was attributed to a MoSe2 intermediate layer, which is in agreement with high resolution transmission electron microscopy and scanning energy dispersive X-ray detection measurements [45]. Based on the results, the authors were able to propose a schematic band diagram [31]. In another study Glatzel et al. reported on the substitution of the i-ZnO in the window layer by sputtered Zn1−x Mgx O alloy which enabled efficient buffer- and especially CdS-free solar cells [30,32,44]. The authors demonstrated that the use of Zn1−x Mgx O influences the conduction band offset towards the Cu(In,Ga)(S,Se)2 absorber. In Figure 8 the topography (a) and the work function (b) of a cross section from such a thin-film solar cell with Zn0.70 Mg0.30 O obtained by UHV-KPFM are presented. On the left side of the illustrations the ZnG:Ga window layer and on the right side the absorber can be seen. In Figure 8(c) the data are represented along the arrow in (a) for the topography, the work function, and the electrical field strength, respectively. The KPFM measurement (Figure 8(b)) shows a reduced

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FIGURE 8. KPFM measurement of the Cu(In,Ga)(S,Se)2 /(Zn,Mg)O/ZnO:Ga interface, (a) the topography and (b) the work function. In (c) the data are plotted along the arrow in (a), for the topography (top), the work function (center) and the electrical field strength computed from the smoothed potential (bottom) [44].

work function (≈ 110 meV) for the Zn0.70 Mg0.30 O layer in comparison with the ZnO:Ga. The average work functions of the ZnO:Ga layer, of the absorber and of the Zn0.70 Mg0.30 O layer are ZnO:Ga = (4.21 ± 0.06) eV, CIGSSe = (4.75 ± 0.04) eV, and (Zn,Mg)O = (4.10 ± 0.04) eV, respectively. In the plot of the electrical field (Figure 8(c)), both material transitions between absorber and Zn0.70 Mg0.30 O as well as between Zn0.70 Mg0.30 O and ZnO:Ga are clearly resolved. This result agrees very well with the predicted reduction of the band offset at the absorber/window interface as well as the capability of UHV-KPFM characterization to laterally resolve surface potential variations in the nanometer range. The measured potential differences can be used under the given prerequisites as a minimum for the actual diffusion voltage of the device. From performed electrical simulations in comparison with the experimental data a diffusion voltage of VD = 900–1,000 mV was extracted. Furthermore, the space charge region of the Zn0.70 Mg0.30 O/absorber transition can be determined from the measured data (cf. Figure 8(c)). Its larger portion extends into the absorber (W p = 100 ± 40 nm and Wn = 70 ± 40 nm) which leads to a hole charge carrier density of p ≈ 2 × 1016 cm−3 for the Cu(In,Ga)(S,Se)2 absorber. A slightly higher electron charge carrier density n ≈ 3 × 1016 cm−3 is formed for the i-ZnO or Zn0.70 Mg0.30 O layers due to the smaller space charge region width.

3 Measurement of Semiconductor Surface States 3.1 Absolute Band Bending and Surface Charge Measurements Probably the most important semiconductor surface electronic properties are the equilibrium surface band bending, VS , and the concentration of the surface states

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within the semiconductor band-gap. The former is a very important parameter for example in the formation of metal-semiconductor interfaces [46], oxidation, etc. In addition, in recent years, the knowledge of the surface states energy distribution (presented in the next section), density, and the surface band bending is essential in order quantify accurately two-dimensional (2D) carrier profiling with high spatial resolution using scanning capacitance microscopy (SCM) [47,48] and scanning spreading resistance microscopy (SSRM) [49]. Surface photovoltage spectroscopy (SPS) [50] is probably the only wellestablished technique for such measurements but it has three main drawbacks: it relies on photoinduced transitions that make the determination of the equilibrium surface charge density possible only in very few cases, it does not work well for small and/or indirect band gap semiconductors like Si, and it does not have high spatial resolution. In this section we show that KPFM can measure the equilibrium surface band bending and surface charge in semiconductors. The method is based on cross-sectional surface potential measurements of very asymmetric p ++ n or n ++ p junctions. The measured built-in voltage on the surface of the junction is used to derive the spatial distribution of the diode surface band bending, and the total surface charge density on the low-doped side of the junction. Figure 9(a) shows a 2D numerical calculation of the potential distribution of a symmetric Si pn junction (dopant concentration of 1 · 1017 cm−3 ) with a density of 1 · 1012 cm−2 (5 · 1012 cm−2 ) donor (acceptor) states located at an energy of 0.7 eV (0.8 eV) above the valence band maximum, E V . The lower junction built-in potential on the surface, Vbis compared with the built in potential in the bulk, Vbib , observed at the “back” of the figure, is due to charged surface states; surface states trap holes (electrons) on the cleaved surface of the p(n) side of the junction, creating depletion-type band bending opposite in sign on each side of the junction. Thus the bands will bend up (down) in the n( p) doped region, with the net result being a reduction of Vbis (relative to Vbib ). In the case of an asymmetric diode (with a density of 7.7 · 1011 cm12 (3.2 · 1012 cm−2 ) donor (acceptor) states located at an energy

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of 0.6 eV (0.336 eV) above E v ) shown in Figure 9(b), the degenerate side of the junction serves as a potential reference since the band bending on this side is negligible. Vs is then determined as the difference between the calculated bulk potential and the (simulated and fitted to the measured contact potential difference (CPD)) surface potential, calculated from a 2D numerical solution of Poisson and Laplace equations for a semiconductor-air system. The surface charge and band bending were extracted from the following boundary condition at the semiconductor—air interface [51]: εSC E SC − εair E air = Q SS , where ε is the dielectric constant, E is the electric field and Q SS —the surface charge, is a function of the surface band bending given by (for the case of a single acceptor state): Q SS = −q Nt

1

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(1)

where Nt is the surface states density, E t is the surface state level, the subscript b denotes bulk values, and the other symbols have their usual meaning. The surface (110) band bending and charge of an air cleaved n ++ p Si diode ntype (As-doped) implanted with a maximal dopant concentration of 2.1 · 1020 cm−3 on a p-type (B-doped) substrate with a dopant concentration of 1.8 · 1015 cm−3 ), resulting from the fitting procedure are shown in Figure 10(a,b). The diode was cleaved using a specially designed cleaving machine (SELA Inc.), the doping was performed by ion implantation and measured by secondary ion mass spectroscopy (SIMS) in IMEC, Belgium. Figure 10(a) shows the “deconvolved” CPD profile (symbols) taken from the measured 2D CPD image, the calculated (and fitted to the measurement) surface potential (solid line) and the surface charge (dashed line). Figure 10(b) shows the calculated surface (dotted line) and bulk (dashed line) potential and surface band bending (solid line) obtained from subtracting the surface from the bulk potential. As shown in Figure 10(b) the surface band bending is initially zero on the degenerate part of the junction as expected; then it increases due to a decrease of the doping concentration, reaches a maximum,

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FIGURE 11. Calculated 2D band structure of a n ++ p Si diode based on the measured surface potential.

and then sharply decreases. This sharp change, which gives rise to the peak in the CPD curve, is due to a sharp decrease of the negative surface charge (marked with an arrow in Figure 10(a)). This may result from a depopulation of donor surface states that move above the Fermi level as they follow the potential change along the pn-junction. The surface band bending (surface charge) then decreases to zero in the vicinity of the metallurgical junction and increases again until reaching a constant value of 0.32 eV (8.63 1010 q·cm−2 where q is the elementary charge) in the neutral p-region. The error in the surface band bending is determined by the noise level of the measured CPD, typically ±10 mV in our system, the error of the SIMS measurement to obtain the dopants concentration, and the error of the numerical calculation, which has the smallest effect. Therefore we estimate that the accuracy of the surface band bending is ±20 meV. The error of the surface charge density depends on to the error of the surface band bending; for example, for a band bending of 0.32 eV the error is ca. ±3.1 · 109 q · cm−2 . The knowledge of the junction surface potential allows to obtain the 3D band structure of the n ++ p diode shown in Figure 11. This is because once the surface charge is determined, the potential at each point in the structure is known from the solution of Poisson equation. Apart from the band bending, the figure also shows the spatial distribution and width of the surface space charge region.

3.2 Measuring the Surface States Energy Distribution The electronic properties of semiconductor surfaces are determined by the surface state energy distribution, NSS (E) within their bandgap. This distribution is essential in determining the properties of semiconductor junctions [46], the phenomenon of Fermi level pinning, surface passivation [52], molecules adsorption [53], leakage current in metal-oxide-semiconductor (MOS) transistors [54], etc. The importance of contacts in molecular electronics [55] suggests that semiconductor electrodes may play an important role [56], thus the knowledge of the surface states distribution is crucial in determining the charge transfer processes and the current in such devices.

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Y. Rosenwaks et al. FIGURE 12. Schematic description of measuring the surface states energy distribution using KPFM. As the tip scans the junction surface (inset), the surface states population decreases thereby changing the measured surface potential.

A widely used method to measure the surface states energy distribution is photoemission spectroscopy (PES), and angle-resolved PES [2]. Interface states energy distribution is measured using capacitance-voltage (C-V) method [57], where the capacitance of a metal-insulator-semiconductor (MIS) structure is measured as a function of metal bias. The main disadvantage of the C-V method stems from the fact that it requires a top contact; thus measuring of bare surfaces (i.e., surface versus interface states) is impossible. Kronik et al. [50] have suggested a contactless method to measure the energy distribution of surface states using surface photovoltage spectroscopy (SPS) with a tunable laser as the excitation source [58]. All the above methods (and others not mentioned here) share a common drawback: they have low spatial resolution. Scanning tunneling microscopy (STM) has been widely used in the last decade to measure local density of surface states [59], but it is limited mainly to highly conductive samples and very clean surfaces. We present here a method, based on Kelvin probe force microscopy (KPFM), to measure surface states energy distribution on a local scale with very high sensitivity (≥ 1 · 109 cm−2 eV−1 ). The method is demonstrated by extracting the states distribution on polished oxidized Si (110) surface. The method is based on measuring the surface potential on a cross-sectional pn junction using KPFM as shown schematically in Figure 12. As the tip scans the junction surface, the surface states depopulate, thereby changing the measured surface potential. The energy distribution is then obtained by equating the position derivative of the surface and the space charge region (SCR) charge (Q SS and Q SC respectively), as described in detail in the Appendix. A key factor in this calculation is the knowledge of the absolute surface band bending, Vs , at each point on the surface [60]. Figure 13(a) shows the measured (symbols) surface potential of a polished and oxidized p ++ n Si diode (p-type (B doped) implant with a maximum dopant concentration of ∼1.75 · 1020 cm−3 on a n-type (As doped) substrate with a dopant concentration of ∼2.9 · 10−14 cm−3 ). The KPFM measurements were conducted using a commercial atomic force microscope (Autoprobe CP, Veeco, Inc.) operating in the noncontact mode. The KPFM measurements (based on a setup described previously [61]) were conducted inside a nitrogen containing ( n coalescence > n LEO ), while KPFM highlighted differences in impurity incorporation and defect structure [15]. Charge rearrangement near defects due to strain relaxation in both Ga- and N-face GaN were investigated by Bridger et al. [16] using EFM. In N-face GaN,

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FIGURE 7. (a) EFM and (b) topography images (and associated line profiles) of N-face GaN demonstrating charge accumulation near the edge of steps, and (c) EFM and (d) topography images (and associated line profiles) of Ga-face GaN showing that charge accumulates near the edge of hexagonal pits. The arrows represent the spatial extent (60 nm) of the screening charge associated with the defect structure. Reprinted with permission from [16]. Copyright 1999, American Institute of Physics.

charge accumulates at the edge of steps, while in Ga-face GaN, charge accumulates near the edge of hexagonal pits, as shown in Figure 7. In both cases, they found the charge rearrangement to occur over 60 nm, which is approximately equal to the calculated Debye length (electron concentration ≥ 1015 cm−3 ), suggesting that the observed charge is truly a screening charge. KPFM has also been used to determine defect type. Ku et al. [31] measured lower E F by 0.2 eV on V-shaped defects on AlGaN/GaN films, reflecting characteristics

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FIGURE 8. (a) 5 × 5 µm2 topography and (b) KPFM images of an oxidized GaN surface, and (c) topography and (d) KPFM images of a different area immediately after the sample was cleaned in 160◦ C H3 PO4 for 5 minutes. Dark regions in (d) indicate the presence of excess negative charge and correspond to domain boundaries or pits in (c) as indicated by arrows. Reprinted with permission from [21]. Copyright 2002, American Institute of Physics.

of acceptor type defects. Koley et al. [23] observed negatively charged dislocations in n-GaN and AlGaN surface potential variations of 0.1–0.2 V and 0.3–0.5 V, respectively. In addition, Choia et al. [32] measured negatively charged extended dislocations with 0.04–0.2 V higher potential than the surrounding region. Hsu et al. [21] demonstrated a surface potential dependence on surface treatment, as mentioned previously. Topography and KPFM images of a GaN surface before and after a hot H3 PO4 surface treatment are shown in Figure 8(a,b) and Figure 8(c,d), respectively. Interestingly, they observed a potential variation associated with defects only after cleaning the GaN surface in hot H3 PO4 . Using KPFM, a lower surface potential was detected near dislocations located at domain boundaries, which is consistent with a local excess of fixed negative charge. They did not observe KPFM contrast near screw dislocations, suggesting screw dislocations might have gap states near the conduction band edge. Not only is KPFM a function of surface treatment, but it also can be modified by ultraviolet (UV) illumination, since photogenerated carries will redistribute to screen electric fields near the surface. This technique is often called surface photovoltage microscopy [65]. Using super-band-gap photons, Bozek et al. [28] observed nano- and microscale variations which they attributed to threading dislocations with a screw component and strain dislocations, respectively. Simpkins et al. [35] correlated C-AFM with KPFM after UV illumination to demonstrate that dislocations exhibit decreased conductivity and larger decreases in KPFM after illumination. They attribute this result to Mg segregation to dislocation cores. Previously, Bridger et al. [18] also observed a dependence on illumination and further demonstrated that KPFM can be modified by the external application of strain. The relation between surface potential and dislocations in GaN films with different doping levels has been explored by Krtschil et al. [29,30]. Using KPFM,

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they determined that the defect is either negatively charged or neutral depending on the type of doping atoms in the layers. They proposed that the dislocations are decorated by an accumulation of charge. In the final part of this section, we explore how C-AFM can be used to establish a correlation between defect type and leakage current. High reverse bias gate leakage limits device performance, and C-AFM has been employed by several groups to determine if defects contribute to the leakage, and to identify electrically active defects. Hsu et al. [39] used C-AFM to measure reverse bias leakage in GaN films and found that non-zero current was detected primarily on hillocks, suggesting that leakage occurs primarily at dislocations with a screw component. In addition, two samples were examined which had a similar total dislocation density but with screw dislocation densities that differed by an order of magnitude [38]. They found that the sample with a higher density of screw dislocations had a higher density of reverse-bias leakage paths, corroborating that screw dislocations have a greater impact on leakage than do edge or mixed dislocations. More recently, several other groups have also employed C-AFM for current mapping of GaN films. Dong [44] attributed a reduction in leakage current as measured by C-AFM to the incorporation of hydrogen during growth. Pomarico et al. [45] reported increased conduction on off-axis facet planes. Using KPFM, Gu et al. [33] also found etched pits and as-grown islands to have lower surface potential, higher workfunction, and increased electrical activity. Spradlin et al. [46] observed a correlation between screw dislocations associated with hillocks and increased leakage current. Furthermore, they investigated both forward and reverse current conduction and measured local I -V curves on these dislocations, revealing a Frenkel-Poole mechanism for forward conduction. On the other hand, Shiojima et al. [43] employed the tip as a probe to measure current-voltage characteristics on submicron Schottky contacts on n-GaN and found that dislocations did not affect I -V characteristics. Simpkins et al. [35] have taken electrical characterization of defects by SPM one step further, employing KPFM and C-AFM of the same surface in order to establish a direct correlation between leakage current and the charge state of these leakage paths as shown in Figure 9. The analysis demonstrated that threading dislocations are negatively charged and do not contribute to leakage current, while pure screw type dislocations are not charged and are indeed the source of leakage current. Thus, SPM techniques allow establishment of a direct correlation between charge and defect structure. SPM-based techniques have even offered scanning modification methods to reduce the effect of leakage current in Schottky diodes. Miller et al. [41] also observed dislocation-related leakage paths in AlGaN/GaN heterostructures. In addition, they demonstrated that the process of scanning with a voltage applied between the tip and sample can lead to the formation of an insulating layer (of gallium oxide) [42] over the dislocation. This layer grows to a thickness of 2-3 nm and eventually blocks the leakage current. As evidence, they measured I -V characteristics of Schottky diodes fabricated on an AFM-modified area, and found that the surface modification reduced the reverse-bias leakage by a factor of two.

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FIGURE 9. (a) Topography and (b) surface potential of a 10 × 10 µm2 area of a GaN surface demonstrating the lack of correlation between leakage paths (highlighted by squares) and negatively charged features. Reprinted with permission from [24]. Copyright 2003, American Institute of Physics.

It has been demonstrated that SPM can be used to identify defects, to measure the charge associated with defects, and to modify the surface and block leakage associated with defects. One future challenge would be to use SPM-based techniques to measure the charge distribution and electrical properties near a defect in an operating III-nitride device.

4 Measurement of Polarity Effects by SPM For polarity-based devices, one of the most detrimental defects is an inversion domain—a region within the film that has opposite polarity. Devices based on polarization effects such as HEMTs depend on uniform polarity, and the presence of inversion domains limits the charge density that can be achieved, while the density of inversion domains limits the size of the devices that can be fabricated. SPM techniques, such as PFM and EFM, can be used to locate these inversion domains and to measure the density of defects, thus playing an important role in improving device performance and reliability. As discussed in the introduction, the surface charge and hence the screening charge is intrinsically related to the polarity. Therefore, any discussion of surface charge or polarization screening relates to polarity effects. Thus the distinction between the measurement of electronic properties and polarity effects is somewhat arbitrary. In this section, we distinguish between the two by focusing on the determination of polarity and on polarity screening effects. The determination of polarity has long been a challenge for the III-nitride community [9,10]. While etching can reveal the presence of inversion domains, the method is destructive [69,70]. In addition, while the presence of inversion domains can often be deduced from growth conditions and surface topography, these techniques infer polarity rather than measure it directly. Scanning probe techniques, with their abilities to measure surface charge, surface potential, and piezoelectric response (piezoresponse) to an applied field, can

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FIGURE 10. (a) Topography and (b) EFM of Ga- and N-face regions, half of which are covered by Pt (right side of dotted line).

be used to determine polarity. In particular, EFM is a measure of the net surface charge and the polarity can be deduced if the screening charge is known. Figure 10(a,b) shows topography and EFM, respectively, of Ga- and N-face regions of a GaN-LPH sample, the right half of which is covered by Pt. Note that while no contrast exists in the EFM image across the inversion domain boundary on the Pt top electrode (suggesting that the metal effectively screens the surface charge), there is polarity-dependent contrast between the two domains in the uncoated region. Similarly, KPFM can potentially be used to deduce polarity since the contact potential is expected to vary for different polar faces [34]. However, the value obtained for contact potential difference depends strongly on the surface condition [19,25]. KPFM and the associated topographic image of a 10 × 10 µm2 area of a GaN-LPH surface are shown in Figure 11(a) and 11(b), respectively, demonstrating

FIGURE 11. (a) Topography and (b) KPFM of a 10 × 10 µm2 area of a GaN-LPH surface. (c) Topography and (d) KPFM images (15 × 15 µm2 ) of an AlN bulk crystal. GaN sample courtesy of O. Ambacher and R. Dmitrov. AlN sample courtesy of R. Dalmau and Z. Sitar.

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FIGURE 12. (a) Topography and (b) KPFM of a GaN surface showing an inversion domain. Reprinted with permission from [19]. Copyright 2001, American Institute of Physics.

that Ga- and N-face regions have opposite KPFM contrast related to the polarity. In Figure 11(c) and 11(d), topography and KPFM images of a 15 × 15 µm2 area on the surface of an AlN bulk crystal are presented, also demonstrating polaritydependent KPFM contrast. Polarity contrast can also be observed by KPFM on the nanoscale, as shown in Figure 12, which illustrates an inversion domain in a GaN thin film. Inverted domains can also be imaged by another SPM technique, PFM, which measures the electromechanical response of the sample when electrostatic forces are minimized (by using a stiff cantilever). In this manner, PFM can be used as a direct measure of polarity [71,72]. In PFM, originally developed for delineation of ferroelectric domains, a periodic electrical bias is applied to a conductive SPM tip, resulting in a periodic displacement of the surface that can be measured with sub-Angstrom precision [73]. The strength and direction of the local electromechanical response reveals the amplitude and phase, respectively, of the subsequent cantilever oscillations. Whereas with EFM the tip deflection is due to the electrostatic interaction between the tip and the net surface charge, with PFM, the tip deflection is due to the mechanical surface displacement and is related to the bulk properties (i.e., sample crystallographic orientation and polarization direction) as illustrated in Figure 13. Furthermore, unlike the piezoresponse of perovskite ferroelectrics (with well-defined crystallographic orientation [74,75]) which can be used to evaluate spontaneous polarization [76], for pyroelectric materials such as the III-nitrides, the magnitude of the spontaneous polarization is a second order correction to the piezoresponse [77,78]. PFM has been employed to determine the polarity in III-nitride thin films and bulk crystals [47–49]. PFM of a GaN-based LPH is shown in Figure 14. The phase contrast is directly related to the polarity of the GaN, while the PFM magnitude is nearly the same for the two opposite domains. Figure 15(a) shows PFM of an inversion domain in a sputtered AlN thin film. From the PFM amplitude and phase images (Figure 15(b,c)), it is evident that the two regions have similar piezoresponse and different phase response, suggesting that the composition is the same, but with different orientation. These images demonstrate the ability of PFM

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FIGURE 13. A schematic demonstrating the response of a material (d33 > 0) to an applied electric field (a) parallel to the Z-axis and (b) antiparallel to the Z-axis. By convention, an electric field applied parallel to the Z-axis will cause a piezoelectric material to expand for d33 > 0. We define in-phase to mean a sample expands when the applied field is generated by a positively biased tip. A sample with d33 > 0 will therefore oscillate out-of-phase with the modulation voltage. The sign of d33 is related to the crystallographic orientation of the sample, which also defines the direction of spontaneous polarization in III-nitrides. Therefore, a measurement of the sign of d33 (from PFM phase) is also a measurement of crystal polarity and polarization direction. Dotted line represents sample shape before application of electric field.

to determine polarity and identify inversion domains. PFM offers a significant advantage compared to macroscopic techniques in measuring the properties of piezoelectric films since PFM can resolve nanometer variations in the piezoelectric properties of a sample. In addition, PFM directly measures electromechanical response, a material property essential to the employment of piezoelectrics such as III-nitrides in microelectromechanical systems. PFM has also been used to measure the magnitude of the piezoelectric response and thus the effective longitudinal piezoelectric coefficient, d33 , of III-nitride thin films, and the results are consistent with literature values [49]. For measurements of d33 using epitaxial GaN/AlN and AlN layers prepared by organo-metallic vapor phase epitaxy on SiC, a frequency of 1 kHz was used and

FIGURE 14. Topographic (a), PFM magnitude (b) and PFM phase (c) images of a GaN-based LPH. The innermost 5 × 5 µm2 square is a Ga-face region. The N-face region has a higher piezoresponse magnitude as indicated by contrast, and there is a sharp contrast difference in the phase image, demonstrating inversions in film polarity. Reprinted with permission from [47]. Copyright 2002, American Institute of Physics.

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FIGURE 15. (a) Topography, (b) PFM magnitude, and (c) PFM phase images of AlN/Si antiphase domains in a predominantly N-face sample. Reprinted with permission from [48].

a modulation voltage (0.5–5.0 V) was applied to 80-nm-thick Pt top electrodes of 100 and 200 µm diameters. In this case, the generated field is uniform and the quantitative determination of d33 becomes possible [71,75]. The electrodes should be small enough to minimize any wafer-bending that may occur upon application of the electric field [79]. In order to determine the effective piezoelectric coefficient, once a piezoresponse magnitude image was obtained, a histogram was generated, and the peak value determined. For GaN/AlN/SiC films we observe d33 = 2 ± 1 pm/V, and for AlN/SiC, we observe 3 ± 1 pm/V. The standard deviation measured from the image histogram indicates the variation in piezoelectric properties across the surface of a film. The results of these microscopic measurements can be compared to data of macroscopic methods such as interferometric techniques. Using an interferometric method, Lueng et al. [80] reported d33 = 3.9 ± 0.1 pm/V for AlN/Si(111) and 2.7 ± 0.1 pm/V for both GaN/AlN/Si(100) and GaN/AlN/Si(111) heterostructures (all films were prepared by MBE). Guy et al. [81] reported 2.0 ± 0 .1 pm/V for polycrystalline GaN/Si(100) grown by laser assisted chemical vapor deposition (CVD); 2.8 ± 0.1 pm/V for single crystal GaN/SiC grown by hydride vapor phase epitaxy; and 3.2 ± 0.3 pm/V and 4.0 ± 0.1 pm/V for polycrystalline AlN/Si(100) heterostructures grown by plasma-assisted and laser-assisted CVD, respectively. In order to understand the screening mechanism in III-nitrides and the role screening plays on band bending and surface potential, EFM and KPFM have been employed by Rodriguez et al. [20] on the same surface before and after an HCL surface treatment which is known to remove oxide. In measurements of the as-received sample, the KPFM revealed a surface potential (relative to Pt) of 0.3 V for the Ga face and 0.9 V for the N-face for a potential difference of 0.6 V as shown in Figure 16. Following an HCl treatment, the surface potential did not change for the Ga-face and decreased to 0.6 V for the N-face (Figure 16(c)). Under the assumptions that (1) there is a dc bias that equalizes the force on the tip, and (2) that ∂Ct ∂z has the same magnitude but opposite sign for the polar faces, the difference in surface charge density between the polar faces can

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FIGURE 16. (a) Topography of a 20 × 20-µm2 area, (b) KPFM (with line profile) of a GaNLPH prior to surface treatment, and (c) KPFM of the same area after surface treatment. Reprinted with permission from [20]. Copyright 2005, American Institute of Physics.

be obtained. From Eq. (1), it can be shown that:    N   Ga  ε0 (1 + κ) ∂Ct  ′  σ  − σ  = 2Vdc − VsN − VsGa , Ct ∂z

(3)

′ is the value of dc bias that equalizes the forces. where Vdc The EFM (Vdc = 0) of the same area before the surface treatment revealed that the electrostatic force on the tip is larger on the N-face than the Ga-face GaN. The EFM phase measurements indicated that the net surface charge (superposition of polarization and screening charge) is positive for the N-face surface and negative for the Ga-face surface. Following the surface treatment, the electrostatic force for the N-face further increased, while the EFM phase measurements revealed that the net surface charge remained positive for the N-face surface and negative for the Ga-face surface. Figure 17(a–c) shows EFM phase images and Figure 17(d–f) shows EFM magnitude images for tip biases of 0 V, 1 V, and 2 V, respectively, of the as-received

FIGURE 17. (a–c) EFM phase and (d–f) EFM magnitude images of a 10 × 10-µm2 region on the GaN-LPH sample with a dc bias of 0 V, 1 V and 2 V, respectively. Reprinted with permission from [20]. Copyright 2005, American Institute of Physics.

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FIGURE 18. Plot of electrostatic force as a function of applied dc bias demonstrating that the electrostatic force on the tip is greater for the N-face GaN when no bias is applied and greater for the Ga-face GaN when the bias is greater than 1.5 V. Reprinted with permission from [20]. Copyright 2005, American Institute of Physics.

surface. The results indicate that a tip bias of 1.5 V equalizes the electrostatic force on the tip from the Ga- and N-face regions, and the contrast reverses for a tip bias above 1.5 V. At 0 V bias, the tip responds to a net negative charge on the Ga-face GaN and a net positive charge on the N-face GaN. At this bias, the magnitude of the EFM signal indicates that the net surface charge on the N-face is greater, suggesting that the screening charge (both external and internal) is greater on the Ga face. If both faces are assumed to have roughly the same degree of internal screening, the results suggest the Ga-face surface has more adsorbed charge. As the bias (Vdc ) is increased, the second term in Eq. (1) is reduced for the N-face but increased for the Ga-face, which explains the change in magnitude contrast. This is demonstrated graphically in Figure 18. Using the method of image charge approach and assuming the manufacturer specified tip radius R = 50 nm and the chosen operating tip-sample distance z = 70 nm, 7 × 10−18 F and –1.6 × 10−11 F/m are obtained for Ct and ∂Ct /∂z, respectively [53,82]. Using Eq. (3), the net surface charge density difference can be determined to be |σ N | − |σ Ga | = 3.6 ± 0.4 × 10−5 C/m2 prior to the surface treatment and |σ N | − |σ Ga | = 6.2 ± 0.8 × 10−5 C/m2 after the surface treatment, indicating a net increase in the surface charge density difference between faces. Since the surface potential for the Ga-face remained the same, the change in the difference in surface charge density is attributed to the N-face only. The corresponding increase in surface charge density for the N-face is roughly (1.6 ± 0.5) × 1010 electrons/cm2 , corresponding to a small fraction of the bound polarization charge (σ P = 2.1 × 1013 cm−2 ). This slight increase of the surface charge has a negligible effect on the percentage of screening, which is close to 99.9% in both cases. Since a reduction in net (positive) surface charge is observed and the electrostatic force on the tip changes only for the N-face GaN, it is reasonable to conclude that the surface treatment added adsorbed charge to the N-face regions. The band bending at the as-received N-face surface is initially flat or bent slightly upward and increases as a result of the HCl treatment. Because the deduced net charge is not large enough to account for the observed change in surface potential, surface states or defects must be present near the surface to receive the excess negative charge to allow the upward band bending. Since these measurements were performed in air as opposed to a vacuum environment, it is impossible to establish the relative contribution from the band bending and surface dipole. EFM and KPFM techniques were used to evaluate the surface charge density of a GaN-LPH by determining the potential difference and the tip bias that

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equated the electrostatic force due to both polar faces. Unlike most ferroelectric oxide surfaces, for which internal screening is secondary to screening by adsorbed species [83], GaN is primarily screened by internal charge (Nd = 4.1 × 1017 cm−3 ) [84]. It has been found that the Ga-face surface was unaffected by the HCl surface treatment, while the surface potential of the N-face GaN was reduced in the process.

5 Summary and Outlook In this review, the impact of electrical characterization by SPM on the III-nitride material system has been presented. From the determination of polarity in films and bulk crystals alike, to the measurement of d33 , and to the elucidation of the screening mechanism in Ga- and N-face GaN, it has been established that SPMbased electrical characterization methods can be used to investigate polarity effects in III-nitrides and nitride-based devices and address critical issues such as band bending, barrier heights, and defect-related degradation effects. SPM techniques have played an important role in the development and advancement of III-nitrides and are certain to continue to have an impact. Information gained by SPM opens the door to the development of novel devices which make use of the polarization in IIInitrides, including HEMTs, capable of employing either 2DEGs or 2 dimensional hole gases, and detection sensors based on changes in measured 2DEG density resulting from changes in adsorbed charge. There are several clear avenues for continued impact. First, vacuum or controlled ambient measurements are needed. Only then can the surface be modified in a controlled way. Second, measurements should be performed on active devices. In this manner, device performance and defect type can be related in an operating device, a possibility first demonstrated by Hsu et al. [51] using scanning gate microscopy on AlGaN/GaN transistors to correlate threading dislocations with lower 2DEG density. Third, SPM is ideally suited to address issues related to III-nitride/ferroelectric heterostructure fabrication and device design, which has recently attracted interest [85–90]. Lastly, while some devices have been developed that exploit the polarization in these materials, the potential has yet to be fully realized. It is intriguing to suggest that the large surface-bound polarization charge in the III-nitrides can be used to drive self-assembly of charged molecules.

Acknowledgments. The authors would like to thank O. Ambacher and R. Dmitrov for the LPH-GaN sample, R. Dalmau and Z. Sitar for the AlN bulk crystal, and V. Lebedev for the AlN on Si thin film. We would also like to acknowledge S. V. Kalinin for providing instrument time to obtain the images in Figure 11 and T. C. Blair for useful discussions. We extend our gratitude to B. S. Simpkins for useful comments related to this chapter and also to J. W. P. Hsu, H. Morko¸c, E. T. Yu, and M. G. Spencer for kindly discussing their results. We gratefully acknowledge the support of the Office of Naval Research MURI on Polarization Electronics Contract

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No. N00014-99-1-0729 and the National Science Foundation (Grant No. 0403871, NIRT on Nanopatterned Polar Surfaces and Grant No. DMR02-35632).

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III.7 Electron Flow Through Molecular Structures SIDNEY R. COHEN

In this chapter, a perspective is given on some aspects of electron flow through molecular bridges. The advent of molecular electronics, drive to understand charge transfer in biological systems, and functioning of devices such as organic lightemitting diodes and dye-sensitized solar cells all require deeper understanding of this topic. Application of SPM to such studies has opened the possibility of true single-molecule measurements, but has also introduced a number of artifacts and complications into the work, notably perturbations due to the force and local electric field applied by the tip. Additional chapters in this book provide specific studies of electron flow in thiolated hydrocarbons and of electrical and electromechanical measurements on biomolecules. Here, SPM measurements on two specific systems—electron flow through DNA, and STM measurements of isolated molecules on a semiconductor surface, are developed in detail. These studies are presented in the general context of electron flow measurements through single molecules, and are compared with parallel, non-SPM techniques. The strength of SPM to combine imaging with the electrical measurement is emphasized.

1 Background and Theory Electron flow through a molecule involves two distinct and widely studied events: intramolecular charge transport and electron exchange with the surroundings. These two processes cannot be unambiguously separated since the interface of a molecule with an adjacent electrode, or ionic solution can have profound influence on the molecular properties and hence conductivity. This is certainly true for SPM measurements where at least one of the electrical contacts is made with a sharp tip, so that effects of a strong electric field, high forces, pressure, and effective contact resistance will contribute to the experimental observation. Refinement of both SPM, and alternate measurement techniques, and comparison with both calculations and modeling, has greatly furthered the understanding of the complexities of this problem [1]. In this introductory section, the basic considerations and terminology relevant to SPM measurements of electron flow will be developed. The molecule through which the current flows is referred to as a molecular bridge, 715

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and it interacts with solid electrodes, one of which being the SPM tip. The movement of electrons through this structure is termed charge transport, or transfer. These terms are used loosely here, although there are differing formal definitions in the literature: Jortner et al. [2] link transport to multistep, resonance-enhanced processes and transfer to a unistep donor-acceptor electron-hole process, whereas Zhu [3] assigns the terms to different communities—transport being the motion of unlocalized charges in matter as used by physicists, and transfer referring to electron movement between two localized states as used in chemical and biological communities.

1.1 Different Modes of Electron Flow and Energy Loss Any investigation of electron transport at the molecular level must reflect the fact that energy dissipation to the surroundings will be of a different nature than for classic, macroscopic systems. Both experiment and theory have shown that single molecules can bear a fraction of a nA of current without being destroyed. At such current densities, scattering-dominated transport applying macroscopic heat capacities would lead to local heating of hundreds of degrees [4]. These local temperatures would generally destroy the delicate organic molecules. The largely ballistic character of electron flow over short molecular distances can be invoked to understand why the molecules nonetheless remain intact. At the single molecule level, comparing molecules with different intramolecular bonding illustrates this point. Under appropriate conditions, it has been observed that unsaturated molecular bridges are destroyed by the current flow under conditions where saturated ones are not [5,6]. This can be understood if electron transfer through the saturated system proceeds by direct tunneling, whereas in the unsaturated system there is a possibility of vibronic coupling because of electron delocalization. In the simplest view, electron flow through the molecule can be divided into mechanisms which are thermally activated (e.g., thermionic emission and hopping), and those that are not (ballistic transport—direct tunneling, either low bias or high bias) [7]. Longer residence times and paths allow energy exchange between the electron and vibronic manifold of the bridge. This leads to a weaker distance dependence and in addition some form of temperature dependence. These distinctions are often not sharp. For instance, transport associated with hopping often shows a weak, but finite distance dependence. Characteristic decay lengths β are a convenient way to characterize a molecular current path, and exponential decay of the form I ∝ Pe−βd with d being the molecular length is valid for a wide range of systems [8]. The prefactor P is inversely proportional to d for low bias, and to d2 ˚ −1 as for high bias. The exponential decay β ranges roughly between 0.3 to 2.5 A the gap is modified from highly conjugated organic bridges to free space [9]. In general, low values of β, on the order of a few tenths of an inverse Angstrom rep˚ −1 and above resent thermally activated processes, whereas larger β values of 1 A correspond to direct tunneling. The exponential decay with distance is well known in the Marcus theory of donor-acceptor electron transfer at a distance, which has been long applied to charge transport in biological systems [10].

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A consequence of interaction with the surroundings is a change in phase of the injected electron. A necessary condition for the existence of coherent tunneling is that there is no strong interaction with the vibrations in the molecular wire, so that electron energy and phase can be conserved. In this case, the efficiency of the transport is governed by the quantum exchange rate, as for the particular case of superexchange where a hole or electron injected at one end of the molecule is removed by electron or hole transfer on the other end. Here, the intermediate bridge consists of a series of overlapping orbitals which do not resonate with the donor or acceptor orbitals. This direct tunneling is favored when the Fermi level of the metal electrode lies between the molecular HOMO and LUMO levels. DNA contains multiple donor–acceptor pairs with varied interactions between them, modified by the myriad of possible structural arrangements. It is therefore a model system for study of charge transfer through a molecular bridge, and decades of experiments and theoretical studies have examined the distinction between the two extremes of charge transport. Unistep superexchange mediated hole transfer ˚ −1 < β < 1.6 A ˚ −1 ) [11]. in DNA has been assigned to short decay lengths ( 1.2 A −1 ˚ On the other end of the scale, short decay lengths of 0.2 A have been assigned to hopping transport, generally considered to be mediated by polarons [12,13], as opposed to a simpler molecule which may have only one donor and acceptor site which could be tunneled between, DNA has many such pairs. In this case, tunneling from one end of the bridge to the other is precluded, so that even if tunneling is involved, it must be combined with a hopping mechanism [14]. It is not only the distance between donor and acceptor, but also the overall length of the bridge determines the charge transport. For extended transport distances, the sequence of base-pair sites is critical. Electron-rich G bases have the lowest oxidation potential at 1.49 V [15] and provide a stable site for transient charges. At one extreme, charge flow could occur between discrete ionic sites by superexchange transfer across adjacent T:A pairs from the G:C pairs or multiples of them, or it could follow the thermal process of phonon-assisted hopping. Alternatively, the charged species could delocalize to form a polaron, and then propagate through the DNA by phonon-assisted hopping. The distinction between pure charge transfer (one step superexchange), and charge transport (hopping) was considered in a theoretical study [2]. Charge transport in DNA requires that the ion pair travel sequentially along many adjacent bases, enhancing the vibronic coupling. Vibronic coupling is enhanced as the time that the electron is in contact with the tunnel barrier rises. This time is given by [5]: τ=

h¯ N E b − E in j

(1)

Where N is related to chain length, Eb is the energy level of the molecular bridge, and Einj is the electron energy on incidence. For an incident energy close to that of the bridge energy, as in resonant tunneling, or for long molecules, the time becomes long and energy transfer more efficient. Transit time for the barrier has ˚ and height of 1 eV, the transit been described fully [9]. For a barrier width of 10 A time is on the order of a femtosecond, which is too fast to allow coupling with

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FIGURE 1. Schematic picture of conformation for molecules bridging tip and surface. In (a) it is seen that a variety of molecular conformations should exist in the contact zone under a compressive situation. Comparison of (b) and (c) for stretching or break-junction configurations shows that even a single molecule could have different bond orientation at the surface.

nuclear motion (tens or hundreds of fs). When the barrier is lower, distances longer, or resonances are involved, energy loss could occur. In addition to investigations of influence of molecular length and barrier height, vibronic effects as they relate to conformation have also been calculated by taking “snapshots” for different Born–Oppenheimer geometries [16].

1.2 Molecule-Electrode Junction Calculation of effective resistance of the molecule-metal junction must account for atomistic structure of the electrode, molecular conformation, and chemical binding effects, or overlap of molecular and electrode wavefunctions [17]. The configuration of an SPM measurement is somewhat ill-defined. For instance, whereas molecular conformation has been shown to influence the contact resistance [18,19], the unknown tip shape means that the molecules in the junction could be trapped in any of a number of non-optimal molecular configurations. Thus, the actual configuration of the molecular bridge may be difficult to ascertain, and when there are several such bridges in the contact, they may adopt different configurations (see Figure 1(a)). Conductivities of conjugated molecular wire systems have been calculated by the electron-scattering quantum chemistry (ESQC) technique using a planar metalinsulator-metal structure [20]. The calculations showed small but potentially measurable currents for low (0.1 V) bias and molecular chain length of several tens of Angstroms. Particular attention was paid to the influence of the molecule-surface bond. It was shown that changing the specific adsorption site—for instance from hollow site to on-top site—has a small but significant influence on the current. The difference in conductance between the sites ranged from under a factor of two for oligo(phenylbutadiyne) to more than a factor of three for oligo(phenylethynylene). Furthermore, the nature of the barrier plays a critical role: here, a symmetric junction was constructed by choosing identical sites on either side of the bridge structure. An asymmetric tunnel junction would be expected to greatly increase

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the resistance. Ideally symmetric junctions are difficult to achieve experimentally, and unlikely to be the case when an SPM tip probes a molecule bound to a flat electrode. The bridge system where a thiol or dithiol is bound to one or two gold electrodes through the Au-S covalent bond, while being convenient to assemble experimentally, is apparently less favorable than other available binding choices. Calculations of conductivity through a benzene 1,4 dithiolate molecule have demonstrated qualitative, but not quantitative agreement with experiment [21,22]. By adding a single gold atom between the flat electrode and molecule, calculated values dropped to within an order of magnitude of those experimentally determined. A very high barrier exists at the Au-S contact due to the low density of states. A further impediment to electron flow is the orbital orientation: Au has s-orbitals at the Fermi level which do not couple to the sulfur p orbitals parallel to the Au. Thus, the π -channel, which is the transport path in the benzene ring, is broken here. In contrast, the calculation for an aluminum atomic contact, which has p-orbitals at the Fermi level, yielded significantly higher conductivity, since p-levels parallel to the electrode surface are able to form π states. This result is supported by a Green function approach comparing metals of groups 10 (Ni, Pd, Pt) with those of group 11 (Cu, Ag, Au) [23]. Both thio and isonitrile binding to the metal were compared. The collinear orientation of the CN-metal bond was shown to favor transmission. For S, collinear orientation is not achieved with any of the metals, and the differences between the metals are due to alignment of the Fermi level EF with the molecular states. Again, the Au-S couple was seen to be the least favorable, whereas Pd followed by Pt were the optimal choices of the metals studied. Little difference was seen between Au and Ag. Since the current is sensitive to local geometry and configuration, situations leading to molecular disorder in the monolayer film such as domain boundaries or steps at the metal substrate might be expected to yield strong current variations. Again, SPM tips are unlikely to present an ideal lattice or geometry. It should be noted that these concepts are not universally accepted. In a work which theoretically investigated the influence of molecule-electrode binding on electron flow, a Au contact was estimated to provide conductance five times better than one of Ag [24]. This same work also found almost no influence on current of the bond angle. However, the thiol linkage was estimated to be a poor one: substituting Se for S increased the conductivity by a factor of 25. Although it may seem intuitive from the above that a more robust metal-molecule contact will facilitate the current flow, a study of carbon chains showed that current may actually increase for the weaker C-metal bond [25]. Furthermore, the calculations indicated that the current could rise for a longer bridge because of the increasing remoteness of the perturbing effect of the metal electrodes on the bridge.

1.3 Mechanical and Conformational Effects The issue of the mechanical stability of the delicate tip-molecule interface is not a simple one. As opposed to the case of a molecule bound to a fixed surface, the

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tip-molecule interaction has two additional complications: the highly stepped tip apex is less amenable to ordered bonding than a smooth electrode surface, and the longer-range tip-surface interaction and system compliance can lead to high, disruptive forces between tip and molecule. These forces are not easily modeled due to the irregular shape of the tip and range of forces applied. In contrast, the simpler situation of a molecular film adsorbed to a perfect crystalline surface is amenable to computational techniques. Figure 1a illustrates how different degrees of molecular compression should exist under such a rough tip. These issues were broached early in the developmental stages of AFM in order to consider the limits of resolution and interpretation of force-distance plots in the AFM [26,27]. In principle, direct application of contact mechanics, which relies on a continuum model, should be inappropriate at the molecular scale. In practice, it has shown surprisingly good agreement with experiments indicating that the continuum approach is relevant down to the near-atomic limit. There are several different manifestations of this approach, the difference between them being related to the relative magnitude of the effective elastic modulus and interfacial energy of the contact [28,29]. Using the JKR model [30], which accounts for surface adhesion, the contact area between a metal tip and a Langmuir– Blodgett (LB) film was found to be several times larger than when a purely elastic Herzian model was applied for low imaging force [31]. Molecular dynamics simulations, which have the capability to predict the atomic-scale rearrangements at the contact, show an instability of surface atoms at very small separations, meaning that it may be impossible to maintain the initial tip and surface character upon contact [32]. This instability could dominate the nature of the contact, although it may not be present at the passivated organic monolayer/metal electrode surface [33]. The calculations must also presume a well-defined tip conformation, often modeled on a single crystal facet. Real tips may be quite irregular and often change during the course of an experiment. As the tip approaches to contact with the surface, van der Waals attractions can dominate the nature of the interaction, as discussed in references 28–30. The potentially strong effect of more distance points in the tip profile, coupled with an irregular macroscopic tip shape may be intractable in the exact solutions. For instance, the molecular dynamics study ˚ [32], much smaller than the cited used an effective tip radius of curvature of 30 A 20–50-nm radius typical for metal-coated tips. The probes presently used in SPM current measurements have a characteristically large volume close to the apex due to the bulky metal coating, which may also be of irregular shape. Development of a stable, well-defined, and small conducting tip would be a welcome development. Capillary forces can be significantly larger than the inherent van der Waals forces, pointing to an advantage of performing experiments in a controlled environment such as vacuum, dry nitrogen, or liquid. Molecular conformation effects can appear subtly in slight twists or rotations of the molecule. The effect of molecular conformation on electron transport through molecules containing benzene rings was probed using a Green’s function-based method [34]. The Landauer formula was applied, i.e., inelastic processes were not

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accounted for. Variations with ring orientation were profound—a three-order-ofmagnitude increase in resistance was predicted when adjusting the relative rotation from a coplanar arrangement to 90 degree misalignment due to decreased overlap. As indicated in Figure 1, conformational variations might be expected even when a single molecule is bridged between the tip and surface, and certainly many different conformations could exist simultaneously in the contact region for an ensemble of molecules in the gap.

1.4 Alignment of Molecular and Substrate Electron Energy Levels The act of molecular binding to the surface imposes an equilibrium between the chemical potential (Fermi level) of the molecule, and that of the surface. Consequently, the spectrum of molecular energy levels will take on a new correspondence with respect to the surface energy bands. Even when a formal chemical bond is not formed, polarization from electrons spilling outside the metal electrode will lead to a strong interaction between substrate and adsorbate [35]. The repulsion between molecule and surface electrons leads to a lowering of the substrate workfunction, and hence formation of a surface dipole layer [36]. The existence of this dipole requires that the substrate and molecular vacuum levels are not aligned, and an intrinsic barrier for charge transfer exists. The relative positioning of the molecular levels determines the relevant parameters governing charge flow such as the tunneling barrier height in direct tunneling, or the availability of molecular levels for resonant tunneling. Alignment of molecular energy levels with the surface states thus determines the nature of electron flow, and can be illustrated through relatively simple notions and schemes. While this is no replacement for the formal calculations described above, it can be informative. Dipole formation and influence of charge reorganization in adsorbed films is currently of high interest [35]. Many such studies relate to molecules bound to metal electrodes [37], whereby one of the electrodes could be the SPM tip. The picture may be very different when the molecule is adsorbed to a semiconducting, rather than metallic substrate [38]. Here, effects of substrate band-bending, surface states and size of energy gap can dominate the behavior. These considerations and their influence on STM measurements of individual molecules adsorbed to semiconducting surfaces are outlined here. Figure 2 shows a hypothetical band energy diagram exhibiting electron energy levels or bands in an isolated n-type semiconductor and remote molecule (a), and some possible changes upon bringing them together (b). Further modifications occur due to the bias applied in the STM measurement (c–e). The first stage in deriving these schemes is to determine the isolated molecular Fermi level—which can be approximated to reside halfway between the HOMO and LUMO levels. In the hypothetical nonequilibrium state without electrical contact between molecule and substrate, initially inequivalent Fermi levels do not align. The energy level positions can then be assigned by aligning the vacuum levels. Here, the ionization potential of the molecule, and HOMO-LUMO

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FIGURE 2. Examples of changes in band alignment for a molecule adsorbed at an n-type semiconductor surface, unperturbed and in the presence of biased tip. (a) Isolated molecule and surface. Ev, s/t is the vacuum level of surface/tip, EF, s/t the Fermi level of surface/tip. CB and VB are the surface conduction and valence band edges, respectively. HOMO is the highest occupied molecular orbital and LUMO the lowest unoccupied molecular orbital. (b) Molecule adsorbed and equilibrated at surface, resulting in a negative charge on the molecule, and local charge reorganization. The consequent surface band bending is depicted, as well as two sub-gap states ml1 and ml2, which are formed as result of hybridization between molecule and surface. In (c) and (d), a negative bias is applied to the sample, represented here as + bias on the adjacent tip. The potential through the molecule could be flat, or exhibit a gradient, as shown by the heavy and light vacuum level contours and shift of molecular levels (see text). Larger (c) and smaller (d) negative sample biases depicted. In (e), a positive sample bias is shown, which results in large band bending for the n-type surface.

gap would determine the molecular levels of the adsorbate, while the electron affinity, work function, and band gap, those of the substrate. Equilibration of the Fermi levels of substrate and molecule requires charge flow, resulting in a surface dipole.

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Charge transfer between molecule and substrate results in a charged molecular site, which can be modeled as a defect on the surface. Figure 2(b) illustrates how molecular adsorption and surface charge redistribution can realign the molecular and substrate levels relative to those existing at a distance. Formation of a net negative charge on the molecule is demonstrated. A charge at the surface will necessarily affect the local workfunction. The electrostatic image force can significantly stabilize the charge: ionization potential reduction on the order of 0.5 eV has been observed [39]. This surface charge can cause local depletion of free carriers in the semiconductor and hence band-bending. The well-known Schottky barrier which can develop at a metal-semiconductor surface [40] has a molecular analogy. However, whereas the semiconductor levels shift uniformly for the former, for the latter discrete molecular levels will shift by different amounts, depending on the extent of participation in bonding with the substrate [41]. Charge transfer resulting from the molecular interface can result in a significant compression of the HOMO and LUMO states—an order of magnitude lowering of the HOMO-LUMO gap has been reported [42]. Thus, after equilibration, not only will the vacuum levels be unaligned due to the surface dipole, but the internal molecular levels could shift dramatically. Finally, new hybrid states could appear due to binding to the surface, indicated as the levels ml1,2 in Figure 2(b–e). Introduction of an opposing electrode, the tip, will impose a local field which is a function of the tip shape and distance from surface. The magnitude of the bias and surface doping levels determines the overall potential profile between the electrodes. In the STM experiment, the sample is biased relative to the tip. A negative (positive) bias applied at the back contact could lead to downward (upward) band-bending, as the free carriers accumulate, or are depleted from the surface. Accumulation is indicated in Figure 2(c,d), which in this example counters the surface band-bending due only to the charged molecule. Depending on the direction of the surface dipole associated with the molecule, the barrier for electron injection from substrate to tip could be diminished or augmented relative to that on the bare surface. Although most of the bias drops at the two junctions, a portion could fall over the molecular bridge itself, providing an additional source for shifting of the energy-levels which, as noted above, could vary independently for the different molecular energy levels. The details of the potential drop between the two electrodes will vary strongly depending on the specific system. For the n-type semiconductor shown, depletion will be a stronger effect (Figure 2e). In this case, the larger band-bending and concomitant widening of the space charge region could push a significant fraction of the potential drop into the substrate. It can be shown that for some STM measurements, with small molecules in good electrical contact to a metal surface, the potential drop resulting from bias between tip and substrate occurs largely in the tip-surface vacuum gap [43]. For conducting probe AFM measurements, semiconducting substrates with small band bending [44], and for long molecular bridges, a substantial portion of the potential drop occurs within the molecule. Even though the electrochemical potential (Fermi level) of the molecule may be equivalent to that of the substrate, the electrostatic potential could vary sharply inside the

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molecule. Datta and coworkers examine this for a α, α ′ -xylyl dithiol molecule bound to a gold electrode and measured by STM [45]. In order to conform to experiment, they conclude that the potential falls steeply near both contact points, not just the tip-molecule junction, and then remains flat through the molecule. The form of any potential drop which does exist within the molecule could be quite irregular. Di Ventra et al. calculated that even for a simple benzene dithiol bound to gold, different ring atoms are at different potentials [46]. In Figure 2(c,d), the two different magnitudes of negative bias demonstrate how molecular levels could shift into or out of resonance with the free electrons lying at the bottom of the conduction band as the bias is varied (see right-arrow line). A secondary influence of the bias is broadening of the molecular levels: As the negative bias grows in magnitude, the tunneling barrier becomes smaller and the finite barrier size then leads to the appearance of continuum molecular states. The result of this change is a broader molecular level and hence enhanced tunneling relative to the discrete states which exist when the barrier is essentially infinite.

1.5 Kinetic Factors Changes in the internal molecular level occupancy could arise from other sources. The equilibrium situation which existed without current flow is replaced by the dynamics of the tunneling process. A molecular level which would be occupied under equilibrium can be depleted of its electrons in the steady-state conditions established during tunneling [47]. Varying the tunneling conditions would then alter the current flow and thus state occupancy, resulting in changes in the charge state. The electron occupation of the molecular level is then given by the steadystate condition [47,48]: f =

e p + cn n W + e p + en + c p p + cn n

(2)

where n and p are the concentration of free electrons and holes, respectively, emission and capture probabilities for electrons (holes) are en (e p ) and cn (c p ), and W is the transfer probability of an electron from the tip to the surface. Figure 3 shows the relevant parameters for tunneling through a molecular level with negative sample bias. The molecular level is then filled by capture of electrons from the conduction band, or emission of holes to the valence band. This is balanced by

FIGURE 3. Kinetic parameters for tunneling through molecular state on n-type surface at negative sample bias. cn , capture probability of electrons from conduction band, e p , emission rate of holes to valence band, W transfer rate of electron from molecular state to tip.

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ejection of electrons to the tip. The minority processes of electron emission and hole capture are not depicted.

1.6 Issues with Isolated Single Molecules The push toward single molecule devices presents unique problems which are quite amenable to SPM study. Specifically, the capability of the SPM to perform electrical measurements on isolated individual molecules bound in a specific configuration to the substrate can be fully exploited. This capability enables observation of phenomena which cannot be measured by techniques that examine average molecular properties of a film. The charging energy of an ionized molecule on a surface can be substantially stabilized when it is in a film [39]. An isolated charged molecule at an interface cannot benefit from this stabilization. Even though the metallic or semiconducting substrate will undergo charge reorganization to stabilize the charge, this screening from below will be less effective than screening originating inside of a film in which the charge rests, since the electrostatic field drops by 1/r2 for a dielectric, and by exp (−λd), λ the Debye length, if free carriers are available. Further, coupling to other molecules opens a larger number of charge transfer pathways. For instance, combined through-space and throughbond mechanisms for electron transfer in a film [4] would not be possible for single isolated molecules. Finally, the nature of the spatial confinement may be quite different for a molecule in a film, due to steric factors, which are relaxed for isolated molecules. Due to these considerations, prediction of behavior of single molecule transport based on studies of molecular films should be made with caution. Nonetheless, clear identification of isolated molecules on a surface by SPM is elusive, and the necessity to prepare the molecule in a specific conformation may require preparing it as a film. This was essential in the DNA studies described in section 3.1. Nonetheless, the new insights obtained by study of isolated molecules, particularly in STM work, are beginning to give a glimpse of the isolated molecule behavior.

2 Experimental Measurements As is evident from the background material presented above, a “clean” SPM measurement must take into account many factors which could contribute to the electron flow: The molecular orientation is of supreme importance, both that of the bonds at the substrate or tip interface, and that along the intermediate backbone region. Orientation is particularly hard to control in SPM measurements, where molecules constrained between the flat surface and an irregular tip could undergo considerable molecular distortion. The question of the nature of binding to the adjacent electrode is also difficult to monitor in SPM. Chemical binding of the molecule to the substrate can be ascertained by well-documented procedures, and can verified through surface analysis techniques which address a large ensemble of molecules, notably photoelectron and photoemission spectroscopy. This is to be

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compared with SPM, where the existence of a dynamic chemical bond to the tip must be inferred indirectly from current or force traces observed in the SPM itself.

2.1 Comparison with Other Techniques As discussed above, the experimental constraints of an SPM measurement may introduce undesired complications in understanding and interpretation of the results. Whereas SPM measurements carry the distinct advantage of providing topographical information at the atomic or molecular level, other techniques have been used successfully in recent years to investigate transmission through molecules. It is instructive to review some of these techniques in order to focus the strengths and pitfalls of SPM-based measurements. Break junctions, first realized by Reed and Tour in 1997, have several distinct advantages [22]. They involve symmetrical chemical bonds at the two electrodes; the environment is easily modified from liquid to ambient to vacuum; the inter-electrode distance can be finely controlled which allows making and breaking the contact at will, or altering molecular conformation; and a limited number (as low as one) of molecules can be trapped and investigated. The initial demonstration of this technique was made using a notched Au wire with a minute bending controlled by a contrasting force applied from a piezoelectric transducer. Using this technique, such subtleties as the influence of molecular symmetry on electron transmission have been reported [49]. In the crossed-wires technique, the Lorentz field from an induced current in thin, crossed Au wires was used to exert fine deflections on the wires, one coated with an organic monolayer, while recording current [50]. The distance/force between wires can be accurately controlled. This technique does not address individual molecules, but an ensemble numbering about one thousand. The rounded geometry with curvature radius much larger than molecular dimensions should allow a wellordered monolayer film to form and simplify the contact geometry. Unfortunately, due to striations in the extruded wire, the geometrical form is not a perfect cylinder. Preparation of perfectly cylindrical wires would have a clear benefit: Given a wellcharacterized molecular packing, the convenient geometry of crossed-cylinders allows accurate estimation of the area of the contact region. Thus, given the relevant elastic constants, the average deformation of the molecules at each force could be estimated from readily available formulae [51]. In particular, for cylinders of equal radii, the interaction formulae reduce to those for a sphere on flat, for which analytical contact mechanics relations exist [52]. Suitable application of lithography combined with evaporation under gentle conditions was used to produce nanopores, with the molecules sandwiched between two gold electrodes [53]. Here, the measurements are not made on individual molecules—ensembles of thousands of molecules are measured; however, the advantage of a well-defined planar geometry exists. Shadow-evaporation at controlled angle around tip structures has also been used to create electrodes of molecular spacings [54]. Electron-beam deposition can also provide closely spaced gaps [55]. In these cases, single molecule conditions were achievable.

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Contacting a hanging Hg drop with a Au surface, with both surfaces coated with self-assembled monolayers, also introduces a large ensemble of molecules in the junction, but allows the possibility to control several experimental parameters [56,57]. First, a molecular contact can be made using two different thiols, rather than one dithiol. This enables investigation of the transmission across touching molecular tails, and comparison of a series of molecules under identical conditions. Further, the junction can be varied more easily, for instance using a mixed thiol on the Hg electrode and alkylsilane on a bottom Si electrode. Whereas many measurements have been performed under ambient conditions, the hanging Hg drop is also amenable to studies under liquid. This enables study of electrontransfer in redox couples in general, and biological systems in particular [58]. The liquid monolayer formed on Hg provides additional variability of measurement parameters. The 30 degree alkanethiol tilt angle which exists on Au is governed by S-Au epitaxy which is not a factor on a liquid Hg surface where the angle is close to 0 degrees. By changing the size of the Hg droplet, the molecular packing and hence orientation can be changed controllably. The formation of a fully liquid monolayer on the Hg is supported by evidence that the volume of the monolayer remains constant as the mercury drop expands (as was determined from the dependence of capacitance on area). As the monolayer volume was constant, current as function of monolayer height could then be continuously monitored by expansion of the mercury drop [58]. In this way, decay constants were observed similar to those derived for thioalkanes under other conditions. It is not completely clear that such measurements, performed in aqueous solution, are relevant to the dry tip-monolayer-electrode configuration since the known ordering of water at the interface can influence the conformation of the monolayer outer functionality. Interchain coupling is found to be a significant pathway in addition to the (predominant) sigma through-bond flow, in agreement with some SPM measurements. This effect was correlated with deformation of the chains due to electrostriction at higher applied potential, leading to dominance of through-space over through-bond tunneling [57]. Some spectroscopic techniques have provided information on the adsorbed molecule electronic structure. Photoelectron spectroscopy can provide precise information on the electronic structure of thin films, and even partial monolayers [59]. In two-photon photoemission spectroscopy, an electron is sequentially excited from an occupied to an unoccupied state, then beyond the vacuum level. It allows probing the energy, momentum, and time domains, enabling us to determine molecular orbital level alignment, charge redistribution, and coupling strength [3]. Chemically resolved electrical measurements (CREM) [60] utilizes shifts in the electron kinetic energy in photoelectron spectroscopy to identify the variations in potential at specific nodes (i.e., positions) along the molecule. This allows determination of not only the integral potential drop across the entire molecule, but further gives the drop between any two points. The effect of the back contact is accounted for by monitoring the shift of the surface bond, and there are no issues of mechanical contact at the outer surface. This technique is suitable for molecules that allow assignment of a unique chemical (spectroscopic) signature

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to a specific molecular location. It also allows for independent monitoring of any chemical changes occurring during the course of the measurement, for instance, due to radiation damage.

2.2 Importance of Molecular Conformation in an SPM Junction Molecular bridges have been studied both by STM and AFM. Whereas the former is generally acknowledged to provide superior resolution, allowing not only molecular, but often sub-molecular features to be monitored, the actual force exerted on the molecule is unknown. A number of techniques have been devised to surmount this difficulty. Some of these techniques are predicated on the premise that no significant electron flow occurs when there is no mechanical contact between tip and molecule. Haiss et al. were able to infer the formation of a molecular bridge of viologen-containing molecule through a thiol linkage to a Au tip [61]. After achieving tunneling contact, the tip was retracted from the surface during which a plateau in the current was observed. Decay of this current plateau was associated with rupture of the contact, and found to occur at a distance corresponding to the length of the stretched molecule. Xu and Tao have made a similar STM measurement, examining molecules expressing both thiol and pyridyl linkage [62]. By operating at very high tunneling impedance, it has been suggested that the tip may be constrained to remain outside of the film boundary [63]. Here, a structured inhomogeneous film consisting of distinct islands of different alkanethiol heights was studied. Presuming a two-layer junction model with junction 1 being the vacuum and junction 2 being the trans-molecule gap, the decay constant β across the molecule could be estimated relative to that over the vacuum (α) by comparison of the apparent step height between the two regions. If β and α were equal, then no height difference would be registered. When β is equal to zero, as for a perfectly conducting molecular bridge, the STM topography should reflect the true height of the molecule. When β is nonzero but less than α, the measured molecular height would be less than the true height, and proportionate to the ratio of the two different decay constants. The influence of molecular geometry affects both the efficiency of tunneling through the molecule, and the predominance of alternate pathways. Experiments and calculations have shown that films of highly tilted alkanes have significantly higher tunneling rates than those with lower tilt [19]. This is explained in terms of interchain hopping, which is very sensitive to tilt angle, combined with superexchange tunneling. The latter varies with the electrode material which will in turn influence the barrier height: a higher work function of the electrode material leads to higher tunneling probability for hole-induced superexchange. Interchain hopping can significantly lower the total tunneling distance. Application of these principles gives good qualitative correspondence between predicted and measured values, but the agreement is not quantitative.

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Whereas the STM measurements on alkanethiols cited above have found significant tunneling current without tip-molecule contact [63], measurement of force and current simultaneously on such monolayers indicate that substantial molecular deformation must occur before current flows. A specialized surface-force apparatus allowing continuous measurement of the development of current and force from noncontact to point-contact and through molecule deformation provides an understanding of the changes in current with stress [64]. This work, performed in ambient conditions, compares well with a previous study performed with a wellcharacterized interface in ultra-high vacuum which reached a similar conclusion: significant applied stress is required before current flows through the monoalkane film [65]. A similar result was obtained for a variety of self-assembled monolayers in ambient using a tunneling tip attached to a tuning fork-based force sensor [66]. The requirement for molecular deformation was explained as follows [64]: If the Fermi level is in the midpoint of the HOMO-LUMO gap of 9 eV for these alkanethiols, then the barrier height for tunneling is half this, 4.5 eV [34]. This barrier is very similar to that of the Au-Au barrier with no intervening monolayer, 4.7 eV. Vacuum tunneling at separations corresponding to the length of the thioalkane should not give a measurable current. Therefore, in order to bring the molecular levels within the gap and allow current to flow at gap distances close to that of the molecular height, a stress-induced narrowing of the band gap must occur, which leads to overlap of the tails of the HOMO and LUMO levels. This model is contrasted with a different study, in which the current through a similar goldmolecule-gold tunnel junction was studied as function of distance and molecular compression [67]. This work also seems to indicate that measurable current only flows after compressive contact (Figure 5, in [67]). The results were modeled using quantum chemistry electron scattering theory, treating the molecular chain, tip, and tip-methyl gaps as scattering impurities. Noncontact tunneling current was calculated to be enhanced by a factor of 5 for each additional C atom in the chain, relative to a bare Au surface, indicating a lowered tunneling barrier in the presence of the molecules. Current enhancement upon tip contact was explained by bending of the chains. Qualitative, but not quantitative agreement was observed between theory and accompanying experiment. Molecular-resolution imaging of alkanethiols as a function of force shows a clear pressure-induced disorder at high scanning forces [68]. This transition has been invoked to explain a bimodal dependence of current on load, with two different slopes correlated with the ordered and disordered film [69]. It is presently not clear what force, if any, is required to observe current flow through relatively long thioalkanes, nor is there general agreement on the theoretical effect of such a force. The seeming controversy between the different calculations and measurements are likely due to the very factors which are being considered here, namely the extreme sensitivity to molecular conformation and electrode structure. The current state-of-the-art of SPM dictates that these factors are not perfectly controlled or defined, which can go a long ways toward explaining any quantitative differences between experiment and theory. Achievement of true molecularly resolved images in combination with current measurements, should

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in principle allow monitoring the molecular configuration simultaneously with the current monitoring. This would allow controlled variation of the important experimental factors, and provide new insights on the subject. The capability to obtain atomic and molecular resolution in noncontact AFM [70] may be developed to achieve this goal. Control of the contact force leading to molecular deformation is possibly the hardest factor to control. The force measured in AFM is only that which results in deflection of the cantilever, and cannot observe the distribution of forces which may exist under an irregular tip apex contacting many molecules simultaneously (see Figure 1). Another matter which should be considered is that the point of the tip which exerts the force may not be the same locale that transmits the current. Even under clean UHV conditions, conductance through the small contact area can be blocked by (un)fortuitously placed contaminants or oxide [71].

2.3 Quality of Molecular Contacts in SPM Measurements The mobile SPM probe, which moves across the surface imaging and making electrical contact at different positions, carries obvious advantages compared to the static techniques described in section 2.1. This benefit must be weighed against the uncertainty in the quality of the electrical contact between tip and molecule. Several AFM studies have addressed the issue of reliability of the bonding contact between tip and molecule. Cui et al. showed that touching the conducting tip to a gold nanoparticle (GNP) covalently bound to the upper end of an alkanethiol, which is in turn bound at the bottom end to a gold electrode provides a stable molecule-electrode contact which greatly increases the stability and consistency of the recorded current [72,73]. By eliminating the tip-GNP barrier and creating a chemical bond directly between the tip and an exposed thiol on the molecule, the contact barrier can be reduced even further [62]. The contact resistance for the electrode–alkanethiol-tip system was shown to be one to three orders of magnitude larger than that measured when the alkanethiol was replaced by an alkanedithiol, which binds to both electrodes simultaneously [74]. The nature of such “dynamic” chemical bonding to the tip is unclear. The thiolate–metal bond is generally prepared in solution, and requires minutes to hours to assure full adsorption. Current measurements through a simple physical contact between the tails of alkanethiols adsorbed to both tip and surface hints that this physical contact provides no larger barrier than the chemical Au-S bond. Such assemblies yielded a contact resistance of 10 k
, which can be compared to trans-molecular resistance of 100 M
for ˚ length [75]. alkanethiol of 10 A In further works with conducting probe AFM (CP-AFM), Frisbie and coworkers have investigated the influence of specific metal composition of the electrode, and type of chemical binding to the surface [76]. Whereas there was only a small reduction of 10% in resistance, when replacing the thiol linkage by a isonitrile, larger variations existed between different metals. Pt, with the highest work function, gave the lowest resistance, followed by Pd, Au and Ag, pointing to the conclusion that lower work functions yield higher resistance. The decrease of resistance with increasing metal work function was ascribed to “hole tunneling”, which is favored

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as the metal Fermi level is pushed down closer to the molecular HOMO level. Interestingly, the contact resistance barrier in this work seems to be no larger for a physical contact such as metalized tip touching the end of molecule, or even contact of two molecular end groups in a bilayer configuration [69], than for the chemical (e.g., thiol) linkage to the electrode. This is clearly in contrast to some of the concepts developed in section 1 and requires further study. Comparison of the experimental trends of electron flow in these aliphatic molecules on various metals with theoretical predictions on aromatic systems underscores the dominating influence of molecular orbitals and Fermi levels of the molecular wire. For instance, Pt electrode performs better than Pd contrary to theory, although both are better than Au and Ag as predicted [23]. Furthermore, the significantly better performance of Au electrode in comparison with Ag [24] is not born out quantitatively. Given the uncertainty in the precise role of type and quality of contact, it is clear that a means to standardize measurements is needed in order to achieve some degree of reproducibility. Attaching an upper GNP to the molecule not only improves the quality of the chemical contact, but gives a good degree of control over the lateral extent of the contact and thus the local pressure, since the GNP is large enough so that it should be the only feature in contact with the tip. We have recently extended this idea to measurements on short DNA chains, a system which has long eluded reliable and consistent experimental determination, as will be discussed below.

3 Specific Systems The insights on electron flow through molecules gained by SPM have greatly advanced our understanding of the various systems studied. Two of these systems are summarized here.

3.1 DNA 3.1.1 Concepts in Measurement of DNA Conductivity Whereas the study of electron or charge transport in DNA has been pursued over several decades, the ability to probe characterized individual strands has only been achieved in the past few years. In addition to the difficulties already summarized here in measuring transport in small organic molecules, DNA carries the added difficulties of molecular complexity impacting several factors: the longer molecular lengths; 3D tertiary structure; possibility of ionic transport outside the strands; tendency toward denaturization when the environment is changed, and the sensitivity to variations in the base types and sequence. Reaching reproducible and well-defined measurement conditions is therefore not a trivial task. It is partly for this reason that reports on DNA conductivity span behavior ranging from insulating to superconducting. Various means have been employed to measure the electron flow in DNA. Several works have manipulated DNA to chemically or physically attach it to patterned

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gold electrodes on a surface. Predominantly, the current measurements under such a setup show that except for very short strands 1 TΩ 1 MΩ

d 500 x 500 nm

>1 TΩ

FIGURE 11. Local conductivity scan on platinum measured with a conductive Pt-coated AFM cantilever. Parts (a) and (b) show the topography and current image with contamination; parts (c) and (d) show the same sample after thermal treatment.

would suspect to obtain a homogeneous result over the specimen. This is not the case as can be seen in the top images of Figure 11. Apart from a deteriorating tip, a contamination layer on top of the sample could influence the measurement significantly. This assumption is supported by the fact that the current increases drastically after heating the sample at 200◦ C for five minutes as presented in the bottom images of Figure 11. 1.3.2 Surface-Layer Analysis The presented measurements raise the question whether samples are generally covered by some sort of contamination layer. The best was to analyze this is by surface sensitive methods like X-ray photolectron spectroscopy (XPS) or Auger spectroscopy [11]. To avoid surface charging in XPS a neutralizer is utilized. In order to have a stoichiometric composition, a BTO single crystal is used as a model material. The O 1s core line measured by XPS at room temperature is shown in Figure 12. In case of an ideally clean surface, only the lattice oxygen with an energy of E 1 = 529.8 eV exists. The two additional components with an energy of E 2 = 531.5 eV and E 3 = 533.8 eV indicate the existence of oxygen with different binding energies. According to [12] the component E 2 can be identified as chemisorbed CO or CO2 , and the component E 3 can be assumed to be physisorbed OH or H2 O. Due to the fact that the lattice oxygen can be detected, the thickness of the contamination layer is estimated to be a few nanometers. Measurements at different angles show that under grazing incidence the intensity of the physisorbed layer is increased indicating that this peak comes from the topmost layer of the

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FIGURE 12. O 1s core lines of a BaTiO3 (BTO) single crystal measured by XPS at room temperature.

crystal. A schematic cross-section of the stacked layers of the covered substrate is given in Figure 13(a). 1.3.3 Sample Treatment to Reduce Contamination As one of the layers is physisorbed OH or H2 O, it should be possible to evaporate it, at least partially. Heating of a BTO single crystal under ultra high vacuum (UHV) conditions is necessary so that no new physisorbates form from the moisture in

a) Physisorbates Chemisorbates Perovskite Lattice

normalized intensity

b)

1.0 0.8

lattice oxygen CO or CO2 H2O or OH

0.6 0.4 0.2 0.0 0

100 200 300 400 500 600 700 800 temperature (°C)

FIGURE 13. Model of adsorbate layers (a) on a perovskite type material and XPS results (b) showing the influence of heating under UHV on the adsorbates (reprinted with permission from [13]).

K. Szot et al. 250

250

200

200

150 100 50 0

Ambient

High vacuum

Piezoactivity (%)

Piezoactivity (%)

760

150 100 50 0

High vacuum after heating to 350°C

Ambient after heating cycle

FIGURE 14. Average piezoelectric activity under different measurement conditions.

the air. In situ XPS measurements show that above ≈ 350 ◦ C, H2 O and OH is largely removed (Figure 13(b). Increasing the temperature up to 800 ◦ C leads to a reduction of the chemisorbed layer. The relative high temperature suggests that the OH groups and the last monolayers of BTO form a chemical bond. After heating the sample in UHV to 800 ◦ C it is cooled down in situ. No change in the core lines can be detected after cooling. A short exposure to ambient surrounding results in a restoration of the physisorbate layer of the surface similar to the condition before heating [13]. Here we present experimental results of the impact of the adsorbates on piezoactivity measurements. Similar results and further influences are reported in [14–16]. The influence of the adsorbates can be quantified by comparing the average piezoactivity of a large area before and after the heat treatment. Measurements are performed on a BTO single crystal which is heated and cooled under high vacuum (3 · 10−5 mbar) conditions. For the piezoresponse measurements a voltage of U = 50 Vpp at 7 kHz is applied to the sample via a conducting cantilever. During the experiment the crystal is heated above the Curie temperature Tc of 120 ◦ C where new domains might be created. The inherent or created domains are relatively large, justifying the assumption that the measured area is in a single-domain state. The sequence of the measurements is as follows: at first a piezoresponce force microscope (PFM) scan is performed under ambient surroundings. After reaching high vacuum a second scan is performed. To be in line with XPS measurements, the sample is then heated under high vacuum to 350 ◦ C and kept at this temperature for 5 min. As we are unable to measure piezoresponse at elevated temperatures, the sample is cooled down. As soon as room temperature is reached, a third scan is done. The fourth measurement is performed again under ambient conditions. In this order the domain structure is identical between the first two and the last two scans. The total piezoelectric activity is calculated as the average of the absolute value of each measurement point and the normalized values are shown in Figure 14. The chemi- and physisorbate layer on top of the BTO single crystal leads to a potential drop between the tip and the sample [17, 18]. In comparison with the

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80 Polarization (µm/cm2)

60 40 20 0 −20 −40 −60 −80 −6

−4

−2

0 Voltage (V)

2

4

6

FIGURE 15. Single-shot hysteresis measurement after pre-polarization of a PZT thin film with electrode size of 300 × 300 nm.

partly adsorbate free case, this results in an effective piezoactivity of 250%. Thus, if quantitative values like the piezoelectric coefficent are to be determined by PFM, the sample has to be cleaned in situ of the physi- and chemisorbates. Measurement surroundings can be optimized by utilizing high vacume (HV) or preferably UHV AFM systems.

2 Measurement Results 2.1 Polarization P(V) and Capacitance C(V) Measurements The aforementioned challenges are limiting the minimum top electrode size for hysteresis measurements. Up to now the smallest electrode size used for hysteresis measurements is the 300 × 300 nm shown by Schmitz et al. [19]. For these results the compensation of parasitic capacitance and leakage current is required in order to derive the ferroelectric properties. Generally we can state that direct electrical measurements are limited by the area as opposed to piezoresponse investigations, where the thickness of the material is the limiting factor; Figure 15 shows electrical hysteresis measurements of a 150-nm-thick PZT thin film with a 300 × 300 nm electrode. This small size is realized by focused ion beam milling. The excitation frequency for the measurement is chosen as 100 Hz. Figure 16(a) presents a small signal capacitance measurement on a PZT thin film. An ac signal of 500 mV at 200 Hz and a large excitation signal of 4 V at 100 mHz is used. Other small signal measurements utilizing a lock-in amplifier include those used to determine the piezoelectric coefficient. Results of a 130 nm PZT thin film are given in Figure 16(b).

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a)

b)

100 80 60

30

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FIGURE 16. (a) Single-shot measurement of PZT thin film with electrode size of 2 × 2 µm and (b) CV and d33 measurement on a 130-nm PZT thin film performed with an aixACCT double-beam laser interferometer on a 0.36-mm2 electrode.

In contrast to the ferroelectric measurements, the challenging aspect here is not reducing the electrode size but detecting a deformation of a thin film, as this is only a few picometers for ultra thin films.

2.2 Scanning Potential Measurements Besides measuring the leakage current through the sample, the knowledge of the potential at the surface is of interest. The surface potential can be measured by an enhanced electrometer amplifier. Two main challenges have to be overcome when using an electrometer in connection with high ohmic samples. On the one hand, the input capacitance and the sample resistance form a low-pass filter, reducing the bandwidth of the system. On the other hand, an input resistance lower than the sample resistance distorts the result considerably. Due to the high resistance of perovskite-type materials it is essential to use an amplifier with an extremely small input capacitance and a high input resistance. If the previous points have been considered the bandwidth is sufficient to use this set-up in combination with a scanning probe microscope (SPM). This enables a fast scan speed so that the thermal drift of the SPM can be neglected. A unity gain electrometer amplifier is used for charge or voltage measurements, where the amplifier is connected in parallel to the device under test (DUT) or to a reference component. This amplifier type does not require frequency stabilization but is affected by parasitic capacitance and insulation resistance of the input cable. For small charges or voltages the in-coupling of noise and ground bouncing is one of the major challenges. A high-speed unity gain amplifier has been utilized to perform these measurements on dielectric materials. Figure 17 shows the topography and the surface potential scan of a BTO thin film. A field is applied across the surface by two planar electrodes 4 µm apart on top of the sample [20].

Piezo Coefficient (nm/V)

Capacitance (nF)

120 Capacitance (fF)

Piezo Coefficient Capacitance

35

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FIGURE 17. Surface potential scan of a BTO thin film.

These measurements show that the grains build plateaus of equal potential. The occurrence of these plateaus suggest that the grain boundaries are limiting the electrical transport.

2.3 Conductivity Measurements on Materials with Perovskite Structure of ABO3 Type in the Nanoscale Regime The nature of electric transport phenomena in perovskite-type materials is still a subject of discussion. Recent investigations indicate that structural defects in ternary oxides are not statistically distributed. High-resolution transmission electron microscope (HRTEM) studies using spherical aberration correction revealed that oxygen vacancies in stoichiometric SrTiO3 (STO) can accumulate [21]. This effect was also observed by Muller et al. on epitaxial STO thin films deposited under varying oxygen partial pressures [22, 23]. Other types of defects which induce a local symmetry breaking and electronic structure modulation are extended defects. The analysis at the core of edge dislocations show the existence of new phases such as TiO2 - or SrO-rich regions [24]. Electron energy-loss spectroscopy (EELS) studies of dislocations in STO show oxygen deficiency and reduction of titanium valency [25]. The high dislocation density of around 6 · 109 cm−2 in STO single crystals [26,27,64] supports the idea that dislocations play an important role as easy diffusion paths for oxygen vacancies. This can increase in thin films where the dislocation densities can easily be up to two orders of magnitude higher. These diffusion paths support the self-doping process by d-electrons during reduction under low oxygen partial pressure. Although the electric properties of perovskite materials with ABO3 structure have been investigated for a long time, the different conduction mechanisms (electronic, polaron, ionic) are still of major interest. With the lateral resolution of SPM and high-bandwidth measuring techniques introduced in section 1, it is possible to study the electrical transport with an AFM on a nanometer scale. Measurements performed with these tools might give new insight required to resolve some of the outstanding issues regarding electrical properties

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FIGURE 18. Principle of local conductivity measurements on a macroscopic electrode (right tip) and with a mobile electrode (left tip) in an AFM.

of these d 0 band insulators. In contrast to electron beam-induced current (EBIC), the stoichiometry is retained as no high-energy electrons are injected [28–30]. The Au: the analysis of electrical properties using macro-electrodes gives only averaged inforhigh-electron mation about the nanosized local properties. A higher macroscopic conductivity electrons” might be understood as a homogeneous conductivity of the material or as caused currect? by heterogeneous local properties. Reducing the size of the electrode enhances the local selectivity of this measurement. An extremely small electrode can be provided by an AFM tip used as a movable electrode. As can be seen in the enlarged view of Figure 18, the main potential drop is located directly below the tip. This justifies the use of an AFM tip as a mobile nano-electrode for investigations on perovskite-type materials [31–33]. Using a mobile electrode opens the way to study electrical properties with near atomic resolution. For example, in conductivity measurements of polycrystalline thin films this enables a differentiation of the grain resistance and the grain boundary resistance in ferroelectric films. 2.3.1 Relevance of Local Conductivity Measurements An example of the influence of nanosized charge transport on the macroscopically measured current flow is given in Figure 19. The images show local conductivity atomic force microscope (LC-AFM) measurements on an epitaxial PZT thin film with uniformly distributed 0.8 × 1.4 µm electrodes under high vacuum conditions. After dc polarization with 2.1 V, a bias of −0.9 V is applied to the sample. Unexpectedly, the measured current on identical electrodes varies by more than three orders of magnitude. To investigate this effect in more detail, the material should be analyzed without top electrodes. The contact between the conducting AFM tip and the electrode-free surface of the film provides this possibility [35,36,64]. With this method it should be possible to distinguish between nanometer sized areas of different conductivity.

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FIGURE 19. Topography (left) and current (right) measured on a 4 nm epitaxial PZT thin film with micro-electrodes [34].

2.3.2 Local Conductivity in Materials with Perovskite Structure of ABO3 Type Although PZT is of great technical relevance, difficulties controlling the chemical homogeneity persist [37]. Therefore, it is advantageous to study model materials. As a representative we chose BTO for a material in the ferroelectric phase and STO for a material in the paraelectric phase at room temperature [38]. 2.3.2.1 Conductivity Measurements on Epitaxial Thin Films In analogy to Figure 19 LC-AFM measurements on stoichiometric, epitaxially grown thin films were performed. The left part of Figure 20 shows the topography of a BTO sample, and the right part the corresponding current image. A bias of 1.35 V is applied. A 200 × 200-nm scan of an epitaxial STO film is presented in Figure 21. For the current observation a voltage of −10 V is applied to the cantilever. The current images show an inhomogeneous distribution with high

520 MΩ

12 nm

250 × 250 µm

0 nm

250 × 250 µm

>140 GΩ

FIGURE 20. Topography (left) and resistivity (right) measured on a epitaxial BTO thin film with a mobile electrode.

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FIGURE 21. Topography (left) and resistivity (right) measured on a epitaxial STO thin film.

conductive filaments for both BTO and STO epitaxial thin films. A similar effect for polycrystalline PZT films was studied in [35]. Further measurements show that the density of good conducting channels of 1010 cm−2 correlates with the density of dislocations in thin films [26, 27]. Local crystallographic perturbations such as edge or screw dislocations may lead to a change in the chemical composition close to the core of these dislocations inducing a higher local conductivity [27,39,40]. However, the global ideal stoichiometry has been shown by XPS and single ion mass spectromerty (SIMS). This phenomenon of inhomogeneously distributed current paths in epitaxial perovskite thin films has been observed to be typical for this class of materials [41]. The presented LC-AFM measurements show the dominance of conducting filaments. This data supports the idea that the existance of conducting current paths can be generalized for other ternary oxides of the ABO3 type with perovskite structure. 2.3.2.2 Conductivity Measurements on Polycrystalline Thin Films In applications for micro- and nano-electronics perovskite-type materials are mostly used as polycrystalline thin films [42–47]. The question arises whether a difference in a local electrical transport between apparently perfect epitaxial films and—from a crystallographic point of view—imperfect polycrystalline films can be observed. The influence of the crystallites on the electric and dielectric properties is discussed extensively [48–52]. Similarly, the role of the grain-grain and grain-boundary interfaces is hotly debated [53]. The following measurements add a further aspect to these discussions. In Figure 22 the local conductivity of a polycrystalline BTO thin film is measured with an applied dc voltage of 5.5 V. A bias of 4 V is used to measure the conductivity of a STO polycrystalline thin film presented in Figure 23. For these experiments, columnar grown polycrystalline films on conducting substrates are used. Due to the film morphology, it is possible to distinguish between the partial conductivity of columns and grain boundaries. Surprisingly, conducting regions on the grains

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FIGURE 22. Topography (left) and resistivity (right) measured on a polycrystalline BTO thin film.

and the boundaries can be observed. The variations in electrical conductivity reach many orders of magnitude. Up to now we have presented conductivity measurements on epitaxial and polycrystalline thin films. In these films an interface should influence thinner films more than thicker films or even single crystals [54–56]. The question arises how strong the substrate-film interface affects the conducting mechanisms. Due to the misfit in lattice parameter, strain, and different work functions for the substrate-film interface an influence on local conductivity (LC) is expected.

FIGURE 23. Topography (left) and resistivity (right) measured on a polycrystalline STO thin film.

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FIGURE 24. Topography (left) and resistivity (right) measured on a BTO single crystal.

2.3.2.3 Conductivity Measurements on Single Crystals Here, we extend the LC-AFM measurements of perovskite single crystals. The conductivity of stoichiometric crystals with ABO3 type at room temperature is very low, resulting in extremely high requirements on the current sensitivity of the I/V converter. As a consequence, published results are often obtained on self-doped samples (see section 2.3.2) in order to decrease the resistance [57]. Alternatively, the high sensitivity of enhanced current amplifiers enables us to examine even single crystals at comparable low voltages of below 500 V, depending on their thickness. The following measurements present some LC investigation on single crystals. LC measurements of untreated BTO and STO single crystals performed under high vacuum conditions are shown in Figure 24 and Figure 25. In the case of BTO, a 0.1 mm-thick (100) orientated single crystal epi-polished on both sides is used. For the current measurement, a bias of 100 V is applied to the sample. Figure 25 shows the topography and current response of a 0.5 mm-thick STO (100)

FIGURE 25. Topography (left) and resistivity (right) measured on a STO single crystal.

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FIGURE 26. Topography (left) and resistivity (right) measured on a self-doped BTO single crystal.

epi-polished single crystal while applying a dc voltage of 280 V to the cantilever. In the inset a cross section of a 3-nm-wide conducting filament is given. These LC-AFM measurements show that in both materials the character of local conductivity is comparable to epitaxial and polycrystalline thin films. 2.3.2.4 Local Conductivity of Self-Doped Samples Conductivity measurements on single crystals are challenging even with specialized current amplifiers designed for high-resistive current sources. The concentration of mobile charges in perovskites can be enhanced by a redox process called self-doping. This means that the concentration of oxygen vacancies is increased by reduction under low oxygen partial pressure. Simultaneously, the number of transition metal ions with reduced valences (d 1 , d 2 , d 3 ) increases [58,59]. In this way a stoichiometric perovskite crystal, normally a d 0 band insulator, can be transformed into the metallic state. A short reducing time leads to semi-conducting behavior. The question arises whether this reduction process influences the resistivity homogeneously. The following images present LC-AFM measurements of selfdoped samples. Figure 26 shows a BTO single crystal reduced for 48 h at 900◦ C. A low resistive path of only 5 M
can be observed on some crystallites. After reduction for 30 min at 700 ◦ C and a H2 pressure of 1,000 mbar, the resistivity of a 10 nm-thick polycrystalline BTO film is locally reduced to 25 M
(Figure 27). An example of a self-doped polycrystalline STO crystal is given in Figure 28.

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35 nm

1.9 x 1.9 µm

0 nm

1.9 x 1.9 µm

> 5 GΩ

FIGURE 27. Topography (left) and resistivity (right) measured on a 10 nm polycrystalline self-doped BTO thin film.

30 nm

500 x 500 nm

0 nm

1.5 GΩ

500 x 500 nm

> 350 GΩ

FIGURE 28. Topography (left) and resistivity (right) measured on a self-doped STO thin film.

Effusion measurements are used to determine the critical concentration of oxygen vacancies required to transform a band insulator like a STO single crystal into the metallic state. The concentration is determined to be 1014 oxygen atoms per cm3 [27,64]. This value is four orders of magnitude smaller than the ≈ 5 · 1018 cm−3 predicted by the Mott criterion [60]. A possible reason is a local accumulation of oxygen vacancies conglomerated at extended defects. On the basis of SIMS measurements utilizing tracer techniques (18 O2 ) it has been shown that extended defects provide easy diffusion paths for oxygen [27]. We hypothesize that these defects significantly influence the diffusion as well as the electrical conductivity. HRTEM studies with atomic resolution of STO show that the local symmetry is broken along edge dislocations. Additionally the cores of the dislocations are enriched with either SrO or TiO2 [24]. A high conducting path can be obtained at grains and at grain boundaries.

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dc source photo diode

adder

LASER mirror

sample

cantilever

~ ac small signal low pass

AFM stage

current amplifier

insulator LockIn amplifier

Vref

FIGURE 29. Setup for simultaneous measurement of local conductivity and piezoresponse.

2.3.3 Local Conductivity in Combination with Piezoresponse Force Microscope The previous results of this chapter show that the macroscopically measured current flows in localized filaments rather than through the total volume beneath the top electrode. The question arises whether a correlation between these filaments and the piezoelectric activity exists. A combination of local conductivity measurements and the PFM method could provide an answer [61]. 2.3.3.1 Measurement Setup The local conductivity piezoresponse force microscope (LC-PFM) is an enhancement of a standard AFM operating in PFM mode (Figure 29) [62, 63]. The dc bias for the current measurement is superposed by the ac signal required for the PFM. If this excitation voltage is applied externally, the stage as well as the cantilever has to be totally insulated from the ground potential of the AFM system. This can be achieved, for example, by mounting the specimen on a quartz plate. The excitation signal is connected to the bottom electrode of the sample. The dc bias has to be supplied by a low-noise precision voltage source, whereas the ac signal can be provided by the built-in generator of the lock-in amplifier. Both signals are superposed by an analog adder. A conductive cantilever is used as a nano-probe to locally contact the specimen. The bottom electrode is connected to a virtual ground amplifier. Due to the ac signal the sample exhibits piezoresponse, leading to a varying deflection of the AFM laser beam. This deflection is sensed by the four-sector photodiode connected to a selective lock-in amplifier. Simultaneously, the current is measured by a sensitive current amplifier. In order to minimize the influence of the mechanical drift in the AFM system the measurements have to be carried out in a short time. These require a current

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FIGURE 30. (LC-PFM) measurement on a 20-nm BTO thin film (a) and on a BTO ceramic (b). The background color represents the piezoresponse and the lines show the current contours.

amplifier with a high cut-off frequency. Additionally this amplifier must also be capable of performing these high-speed measurements on extremely resistive sources, as is the case in ternary oxides with perovskite structure. A low-pass filter is inserted to reduce the influence of the ac signal to the measured current signal. The PFM frequency has to be less than the resonance frequency of the cantilever. In this case a strong mechanical coupling exists between the movement of the cantilever and the displacement of the samples. On the other hand this frequency should be more than ten times larger than the scanning frequency of the AFM to reduce its influence. 2.3.3.2 Measurement Results Results are given in Figure 30. Both illustrations show a superposition of the contour lines of LC and the PFM results for thin film Figure 30(a) and ceramic Figure 30(b) BTO. The presented images are acquired at an ac excitation signal of 1 Veff at 7 kHz. For the current measurement a dc bias of 4 V is applied. In Figure 30(a) the results of a BTO 20-nm chemical solution deposition thin film with platinum bottom electrode are depicted, whereas Figure 30(b) is obtained from a 0.5-mm-thick BTO ceramic sample. The measurements are performed under high vacuum conditions (4 · 10−3 Pa). The presented results show areas with a varying degree of correlation between the local conductivity and the piezoresponse. This method opens the door to investigating the ferroic order parameter and the local conductivity of high resistance ternary oxides in a more detailed way.

3 Conclusions Enhanced SPM methods such as LC-AFM facilitate a more detailed investigation of electrical transport phenomena in metallic, semiconducting, and insulating materials. Due to the extremely high lateral resolution provided by these techniques,

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the heterogeneity of materials can be detected and the influence of the measuring equipment on the material properties has to be taken into account. Therefore, a sophisticated amplifier with a reduced input capacitance, an extremely high input resistance, and a minimized polarization current has to be used to investigate materials at these challenging dimensions. To guarantee a proper contact when utilizing a cantilever as a nanoprobe, a special pretreatment of the sample is necessary and the measurements have to be performed under vacuum conditions. Measurements show that the intuitive assumption of homogeneity for macroscopic materials can not be applied at the nanoscale. Conducting filaments are found by LC-AFM for single crystals, epitaxial, and polycrystalline thin films of perovskite-type materials with ABO3 structure. These conducting paths seem to be coupled to extended defects. Simultaneous measurements of local current as well as piezoresponse—LC-PFM—draw a similar heterogeneous picture. Measuring methods based on enhanced SPM techniques establish new possibilities for mapping macroscopic material propperties in more detail on the nanoscale.

Acknowledgments. The authors thank all their colleagues at the Institute of Solid State Research, Research Center J¨ulich, who have supported the activities of the SPM group throughout the years. We are indebted to Dr. Hermann Kohlstedt for providing PZT samples with micro-electrodes. Special thanks are due to Dr. Regina Dittmann for preparing epitaxial BTO and STO samples and Dr. Theo Schneller for supplying Chemical Solution Deposition (CSD) thin films. The authors are obliged to Dr. Klaus Prume for providing FEM simulations and for fruitful discussions.

References 1. C. B. Sawyer and C. H. Tower, Physical Review 35, 269–275 (1930). 2. K. Prume, T. Schmitz, and S. Tiedke, Polar Oxides—Properties, Characterization, and Imaging. Wiley-VCH (2005). 3. S. Tiedke, T. Schmitz, K. Prume, A. Roelofs, T. Schneller, U. Kall, R. Waser, C. S. Ganspule, V. Nagarajan, A. Stanishevsky, and R. Ramesh, Applied Physics Letters, 79(22), 3678 (2001). 4. K. Amanuma, S. Kobayashi, T. Tatsumi, Y. Maejima, H. Hada, J. Yamada, T. Miwa, H. Koike, H. Toyoshima, and T. Kunio, Applied Physics Letters 79(22), 2098 (2001). 5. K. Prume, T. Schmitz, B. Reichenberg, S. Tiedke, and R. Waser, Japanese Journal of Applied Physics 41, 7198 (2002). 6. E. Bonaccurso and G. Gillies, Langmuir 20(26), 11824 (2004). 7. M. Kawasaki, A. Ohtomo, T. Arakane, K. Takahashi, M. Yoshimoto, and H. Koinuma, Applied Surface Science 107, 102 (1995). 8. C. J. Lu, A. X. Kuang, and G. Y. Huang, Journal of Applied Physics 80(1), 202 (1996). 9. H. M. Duiker, P. D. Beale, J. F. Scott, C. A. Paz de Araujo, B. M. Melnick, J. D. Cuchiaro, and L. D. McMillan, Journal of Applied Physics 68(11), 5783 (1990). 10. K. Szot, W. Speier, S. Cramm, J. Herion, Ch. Freiburg, R. Waser, M. Pawelczyk, and W. Eberhard, Journal of Physics and Chemistry of Solids 57, 1765 (1996).

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11. D. Brune, R. Helmborg, H. J. Whitlow, and O. Hunderi, Surface Characterization. Wiley-VCH (1997). 12. J. F. Moulder, W. F. Stickle, P. E. Sobol, and K. D. Bomben, Handbook of X-ray Photoelectron Spectroscopy. Perkin-Elmer Corporation (1992). 13. F. Peter, K. Szot, R. Waser, B. Reichenberg, S. Tiedke, and J. Szade, Applied Physics Letters 85, 2896 (2004). 14. S. V. Kalinin and D. A. Bonnell, Nano Letters 4(42), 555 (2004). 15. S. Piskunov, E. A. Kotomin, and E. Heifets, Microelectronic Engineering 2–4, 472 (2005). 16. H. Sugimura, Y. Ishida, K. Hayashi, O. Takai, and N. Nakagiri, Applied Physics Letters 80, 1459 (2002). 17. J. Halbritter, Applied Physics A 68, 153 (1999). 18. F. Peter, A. Rudiger, R. Dittmann, R. Waser, K. Szot, B. Reichenberg, and K. Prume, Applied Physics Letters 87(8), 082901 (2005). 19. T. Schmitz, K. Prume, B. Reichenberg, A. Roelofs, R. Waser, and S. Tiedke, Journal of the European Ceramic Society 24, 1145 (2004). 20. B. Reichenberg, S. Tiedke, K. Szot, F. Peter, R. Waser, S. Tappe, and T. Schneller, Journal of the European Ceramic Society in press (2005). 21. C. L. Jia, M. Lentzen, and K. Urban, Science 299, 870 (2003). 22. D. A. Muller, N. Nakagawa, A. Ohtomo, J. L. Grazul, and H. Y. Hwang, Nature 430, 657 (2004). 23. J. Mannhart and D. G. Schlom, Nature 430, 620 (2004). 24. C.-L. Jia, M. Lentzen, and K. Urban, Microscopy and Microanalysis 10, 174 (2004). 25. Z. Zhang, W. Sigle, and W. Kurtz, Physical Review B 69(14), 144103 (2004). 26. R. Wang, S. M. Shapiro, and Y. Zhu, Physical Review Letters 80, 2370 (1998). 27. K. Szot, W. Speier, R. Carius, U. Zastrow, and W. Beyer, Physical Review Letters 88, 075508. 1 (2002). 28. C. Rossel, G. I. Meijer, D. Bremaud, and D. Widmer, Journal of Applied Physics 90(6), 2892 (2001). 29. L. A.Bursill, J. Peng, and X. Fan, Ferroelectrics 97, 71 (1989). 30. W. Sigle and Z. Zhang, Philosophical Magazine Letters 83(12), 711 (2003). 31. A. Gruverman, C. Isobe, and M. Tanaka, Mat. Res. Soc. Symposium Proceedings 655, CC8.5 (2001). 32. Nanoscale Phenomena in Ferroelectric Thin Films. Kluwer Academic Publishers (2004). 33. B. Reichenberg, K. Szot, T. Schneller, U. Breuer, S. Tiedke, and R. Waser, Integrated Ferroelectrics 61, 43 (2004). 34. J. Rodriguez Contreras, H. Kohlstedt, A. Petraru, A. Gerber, B. Hermanns, H. Haselier, N. Nagarajan, J. Schubert, U. Poppe, Ch. Buchal, and R. Waser, Journal of Crystal Growth, 277, (2005) p. 210–217. 35. H. Fujisawa, M. Shimizu, T. Horiuchi, T. Shiosaki, and K. Matsushige, Applied Physics Letters 71, 416 (1997). 36. H. Fujisawa, M. Shimizu, H. Niu, T. Shiosaki, T. Horiuchi, and K. Matsushige, Integrated Ferroelectrics 18, 71 (1997). 37. M. Huffman, J. P. Goral, M. M. Al-Jassim, and C. Echer, Journal of Vacuum Science and Technology A 10(4), 1584 (1992). 38. K. F. Etzold, R. A. Roy, K. L. Saenger, and J. J. Cuomo, Ferroelectric Thin Films. (1990).

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39. M. Kim, G. Duscher, N. D. Browning, K. Sohlberg, S. T. Pantelides, and S. J. Pennycook, Physical Review Letters 86, 4056 (2001). 40. H. Saka T. Matsunaga, Philosophical Magazine Letters 80, 597 (2000). 41. D. M. Schaadt, E. T. Yu, V. Vaithyanathan, and D. G. Schlom, J. Vac. Sci. Technol. B 22, 2030 (2004). 42. A. Gruverman, H. Tokumoto, A. S. Prakash, S. Aggarwal, B. Yang, M. Wuttig, R. Ramesh, O. Auciello, and T. Venkatesan, Applied Physics Letters 71, 3492 (1997). 43. R. Waser and M. Klee, Proceedings of the ISIF 1991 (1991). 44. A. Sanjeev and R. Ramesh, Annual Review of Material Science 28, 463 (1998). 45. H. L. Tuller and R. Ramesh, editors, Thin Film Ferroelectric Materials and Devices. (1997). Springer, Boston. 46. R. Waser, editor, Nanoelectronics and Information Technology—Advanced Electronic Materials and Novel Devices. Wiley-VCH (2003). 47. S. Hong, editor, Nanoscale Phenomena in Ferroelectric Thin Films. Kluwer Academic Publishers (2004). 48. A. Kindlein, K.-M. Schindler, Ch. Hagendorf, H. T. Langhammer, H.-P. Abicht, and H. Neddermeyer, Surface Science 532–535, 501 (2003). 49. M. Dawber and J. F. Scott, Applied Physics Letters 76, 1060 (2000). 50. J. F. Scott and M. Dawber, Applied Physics Letters 76, 3801 (2000). 51. A. K. Tagantsev and I. A. Stolichnov, Applied Physics Letters 74, 1326 (1999). 52. E. L.Colla, A. L.Kholkin, D. Taylor, A. K.Tagantsev, K. G.Brooks, and N.Setter, Microelectronic Engineering 29, 145 (1995). 53. S. V. Kalinin and D. A. Bonnell, Physical Review B 70, 235304 (2004). 54. I. Stolichnov, A. K. Tagantsev, Colla, and N. Setter, Applied Physics Letters 73, 1361 (1998). 55. I. Stolichnov, A. Tagantsev, N. Setter, J. S. Cross, and M. Tsukada, Applied Physics Letters 74, 3552 (1999). 56. S. Lenjer, O. F. Schirmer, H. Hesse, and Rh. W. Kool, Physical Review B 66, 165106 (2002). 57. K. Szot and W. Speier, Physical Review B 60, 5909 (1999). 58. F. S. Galasso, Structure, Properties and Preparation of Perovskite-Type Compounds. Pergamon Press, Oxford, England (1969). 59. F. Jona and G. Shirane, Ferroelectric Crystals. Pergamon Press, Oxford, England (1962). 60. P. A. Cox, Transition metal oxides—An introduction to their electronic structure and properties, Clarendon Press, Oxford (1995). 61. A. Gruverman, O. Auciello, and H. Tokumoto, Applied Physics Letters 69(21), 3191 (1996). 62. C. Yoshida, A. Yoshida, and H. Tamura, Applied Physics Letters 75(10), 1449 (1999). 63. Z. Xie, E. Z. Luo, J. B. Xu, I. H. Wilson, H. B. Peng, L. H. Zhao, and B. R. Zhao, Applied Physics Letters 76(14), 1923 (2000). 64. K. Szot, W. Speier, G. Bihmayer, R. Waser, Nature Materials 5, 312 (2006).

III.9 SPM Measurements of Electric Properties of Organic Molecules TAKAO ISHIDA, WATARU MIZUTANI, AND HIROSHI TOKUMOTO

Au: “molecules” ok here?

YASUHISA NAITOH,

In 1994, individual molecules in alkanethiol self-assembled monolayers (SAMs) were imaged using scanning tunneling microscopy (STM). Since this breakthrough, the electric conduction of individual molecules has been estimated using scanning probe methods. In this chapter, we describe methods for evaluating the electric properties of conjugated molecules embedded in alkanethiol SAMs. First, the electrical conduction and barrier height measurements of SAMs and single molecules using STM are described. Here we discuss a method for estimating the molecular resistance based upon analysis of STM cross-sectional profiles. Secondly, the electrical conduction measurements of SAMs using conductive probe AFM (CP-AFM) are described. Finally, we describe related methods that enable applications like molecular devices.

1 Introduction Organic molecules can be synthesized with unique properties that can be used to promote their self-assembly with one another and to specific surfaces. This beneficial property of organic molecules is very attractive for device applications. Recently, molecular scale electronics have attracted much attention [1]. The recent progress of molecular scale electronics have been accelerated by funding in nanotechnology research. For example, high-density molecular memory [2], random access memory [3], and single electron transistors [4,5], are attracting much attention. However, creating molecular devices at a mass production scale level requires understanding the fundamental properties of organic molecules. Here, a brief history of molecular conduction measurements, which began in 1994 from the imaging of individual molecules in alkanethiol SAMs using scanning tunneling microscopy (STM) [6,7], will be presented. Since then, the electric conduction of individual molecules crucial for electronic applications of molecules was widely studied using scanning probe microscopy (SPM) [8–27]. In this chapter, we mainly introduce methods to evaluate the electric properties of conjugated molecules embedded in alkanethiol SAMs using SPM techniques. We also describe related 776

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methods related to molecular devices, i.e., fabrication of nanogap electrodes by simple shadow evaporation and conduction measurements.

2 Measurement of Electrical Properties of SAMs and Single Molecules by STM In 1996, Bumm et al. estimated the conductance of single conjugated molecules embedded in an insulative SAM film using STM [8].They measured the height of the molecules adsorbed on a metal surface with the molecular axis almost vertical to the surface (Figure 1). Similar measurements have been also performed using conjugated molecules, e.g., phenylene oligomers, to form a phase-separated SAM surface made by a fill-in (exchange) technique [8]. It has been found that various sized domains of these conjugated molecules were implanted in the insulating alkanethiol SAMs [12–15]. We attempted to measure the height difference of several kinds of phenylene oligomers with thiol groups in order to understand the molecular structural effects on the electrical properties [15]. We used several kinds of conjugated molecules with two or three aromatic rings to evaluate the effect of the number of aromatic rings. We used conjugated molecules having one to three methylene groups between the sulfur and the aromatic rings to investigate the metal-molecular contact effect, since we expected that the presence of a methylene group affected both the molecular arrangements [28] and electrical conduction. In STM, we evaluated the electrical properties of the conjugated molecules by analyzing the dependence of the measured height of the conjugated molecular domains on their lateral sizes, when these conjugated molecules were embedded into nonanethiol (C9) SAMs by the fill-in technique. The details of the molecular structures used in this study are shown in Figure 2. The measured height of the conjugated molecular domains depended on their lateral sizes, in the case of the conjugated molecules with a methylene group between the sulfur and the phenyl rings, and in the case of TP3, TP1, and BP1 (Figure 3a–c). By analyzing the size

STM Tip

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FIGURE 1. Schematic drawing of conductance measurements using STM. (See also Plate 10 in the Color Plate Section.)

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FIGURE 2. Molecular structures of conjugated molecules used in STM study. Molecular lengths were calculated using the following methods. The lengths of TP, BP, and monophenyl units were about 1.4, 1.0, and 0.52 nm, respectively [15]. When one methylene group was located between the sulfur and conjugated rings, the molecular length of 0.12 nm increased [29] Thus, the molecular lengths of BP1, TP1, and TP3 were expected to be 1.15, 1.52, and 1.76 nm, respectively.

dependence on the height of the conjugated molecular domain, we attempted to estimate the electronic properties of the molecular domains. The obtained single molecular resistances are in the order TP3 > TP1 > C9 ≥ BP1 (cf. Figure 3d–f). However, to correlate the height difference with the resistance using that method, an estimation of tunneling resistance (Rt ) versus Z-displacement value (dR/dz) is required. We assumed the dR/dz value constant and roughly estimated the molecular conduction. We explained quantitatively the change in the conduction of various molecular domains, and concluded that a methylene group is necessary between the sulfur and aromatic rings to increase the vertical conduction of the molecular domains. However, we used another technique to estimate the molecular conduction, because the quantitative analysis was difficult in the case of STM.

3 Electrical Conduction Measurement of SAMs Using Conductive Probe AFM Conductive probe atomic force microscopy (CP-AFM) is a good candidate for direct measurement of electrical conduction of SAMs (Figure 4) [16–27], because the tip directly touches the molecules. For instance, for monolayers, Wold and Frisbie [18–22]measured the I –V curves of alkanethiols and conjugated molecular SAMs systematically using CP-AFM. Their findings indicate that the current increased exponentially with molecular length for both insulating alkanethiol and conjugated molecular SAMs. For current-voltage (I –V ) measurements using CP-AFM, the effects of the contact or load value between the AFM tip and the SAM surface are important. Wold and Frisble also measured the load effect on the conduction and observed that the conduction was dependent on the applied load value, i.e., larger load, higher conduction. After these studies, many research groups adopted CP-AFM to measure the electronic conduction through the monolayer and single molecule. In this present

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FIGURE 3. (a) Relationship between the domain sizes of TP1 in C9 SAM and observed height differences. (b) Same plot of TP3 in C9 SAM. (c) Same plot of BP1 in C9 SAM. Schematic drawing of conjugated molecules embedded into C9 SAMs. (d) TP1 in C9. (e) TP3 in C9. (f) BP1 in C9. Reprinted with permission from [15]. Copyright 2000, American Chemical Society.

chapter, we describe the details of the CP-AFM results mainly based on our data [25,26]. We also discussed the effect of molecular length on electrical conduction. All the conjugated oligophenylene molecules used in this section have one methylene group between the sulfur and aromatic ring, because the presence of a methylene spacer has a significant effect on molecular arrangement as well as on the monolayer STM measurements confirmed that these molecules exhib√ resistance. √ ited ( 3 × 3) R30◦ structures [15]. On the other hand, without the presence

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FIGURE 4. Schematic drawing of conductance measurements by CP-AFM. (See also Plate 11 in the Color Plate Section.)

Conductive Cantilever (Au Pt coated)

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√ √ of a methylene spacer, it was difficult to obtain highly ordered ( 3 × 3) R30◦ structures. For any detailed discussion, a highly ordered and densely packed SAM is better than a disordered or less densely packed one. Thus, in this section, we did not use conjugated molecules without a methylene group. We measured I –V curve ranging from −0.5 to +0.5 V to understand the direct tunneling region. The transport mechanism is expected to be direct tunneling between ±0.5 V (direct tunneling),because Wang et al. [30] have shown that the transport mechanism through alkanethiol SAMs at the lower bias region is direct tunneling by obtaining temperature independent I –V curves [31]. The I –V curves were almost linear in this tunneling region. Figure 5(b) shows the dependence of the tunneling resistances on the molecular length of the conjugated molecular SAMs. The resistances were estimated from the slopes of the I –V curves. The estimated monolayer resistances of the conjugated molecular BM, BP1 and TP1 SAMs were (5.0 ± 0.5) × 105
,

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FIGURE 5. (a) Monolayer resistance dependence on the molecular length of conjugated molecular SAMs with one methylene group. Resistances estimated by currents at +100 mV. (b) Current dependence on the applied load of the conjugated molecular SAMs. All currents measured at +100 mV. Reprinted with permission from [25]. Copyright 2002, American Chemical Society.

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(1.67 ± 0.4) × 106
, and (5.55 ± 0.5) × 107
, respectively. The deviation of the resistances was small and the resistance increased exponentially with an increase in the number of phenyl rings, as follows. The resistance by direct tunneling is likely to exponentially increase with the tunneling length, i.e., molecular length. Thus, the resistance R is described as [18] R = Ro exp (βd),

(1)

where Ro , β, and d are the effective contact resistance, the decay constant of the transconduction, and the molecular length (thickness of monolayer), respectively [18]. The decay constant β includes the information of the total effective barrier height at the tip/molecular/Au tunnel junction. There are two methods to estimate β value: (1) Using the slope of the resistance versus molecular length plot [18–22]. (2) When both the Ro and the SAM thickness are known, the β value can be estimated by only measuring the monolayer resistance [25,26]. In method 2, the β values were estimated by inserting the Ro , resistance and thickness values of each conjugated molecules into Eq. (1). This method requires that we determine the Ro value. Estimating the Ro value from the slope of the conjugated molecular SAMs using existing data seems to be difficult, because the intermolecular interaction strongly affects the total tunneling barrier and the effective barriers at the molecule/Au interfaces of these conjugated molecular SAMs are dependent on the molecular species [16]. This is the reason why we did not use method (1), the slope of the resistance versus molecular length plot to obtain the β value. (When we obtained the β value using this method, the value became 7.7 nm−1 ). We speculate that the Ro may fall in to a universal value of h/2e2 where h is a Planck constant [32,33]. Under some ideal conditions, the contact formed between the AFM tip and the Au surface becomes quite similar to the zero molecular length situation. Recently, in order to estimate the β value, Wold et al. used an experimentally obtained Ro value of 1 × 104
, a value that was close to the inverse of units of quantum conductance units [21]. In addition, Beebe et al. obtained Ro value of 1.65∼1.85 × 104
when using an Au-coated AFM tip [24]. Using method 2, we estimated β values of the BM, BP1, and TP1 SAMs to be 6.1 nm−1 , 4.5 nm −1 , and 5.7 nm −1 , respectively. The lower β values of the phenylene oligomer SAMs are simply explained by the total effective barrier heights of the conjugated Au tip/molecule/Au junction being lower than those of the alkanethiol SAMs. We also measured the load effect on the conduction. Figure 5b shows the current dependence on the applied load of the conjugated molecular SAM. Except for the TP molecules, the measured electronic currents through the monolayer increased with the applied load. However, in the case of TP molecules, we observed the current decreasing at loads between the 1 nN and 14 nN. However, the current of the TP1 SAM began to increase at the loads over 25 nN [25]. It can be assumed that for conjugated molecular SAMs, the intermolecular interaction (e.g., π–π interaction [34]) is likely to contribute to the monolayer electrical conduction [25]. When the load is applied, the AFM tip pushes or penetrates the monolayer, introducing the

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a) STM

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FIGURE 6. (a) STM, (b) AFM topography, (c) AFM current images, and (d) domain size dependence of observed resistance of TP1 molecules embedded into C12 SAM. Images (b) and (c) were taken simultaneously. Current image were taken at +250 mV bias. Reprinted with permission from [25]. Copyright 2002, American Chemical Society.

molecular disordering. This disorder may lower the electrical conduction of the monolayer, i.e., decreased electrical conduction. On the other hand, the reason for the current increase of the TP1 SAM at larger applied loads of 25 to 37.5 nN of the TP1 SAM is likely caused by the decrease in the tunneling distance, including the increase in the contact area and pressure effect, as discussed previously. To estimate the single molecular conduction, fill-in techniques are also utilized for sample preparation. Using this method, Leatherman et al. measured the electrical conduction of carotenoid molecules embedded in alkanethiol SAMs and obtained a single molecular resistance of 4.2 × 1010
[17]. We measured the isolated single molecular resistance of TP1 using conductive AFM [25]. Figure 6 shows the STM, current and topographical images of single TP1 molecules embedded in insulating C12 SAMs. These current and topographical images were taken simultaneously at +250 mV bias. Small protrusions, which we considered to be single or nanoscale domains of embedded TP1 molecules, were observed in the STM image (Fig 6(a)). On the other hand, in the AFM topographical image (Figure 6(b)), such protrusions were not observed, because the thicknesses of the TP1 and C12 SAMs are considered to be almost identical, while the observed height differences in the STM image are more than 0.2 nm [21]. For the TP1

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in C12 SAM, the apparent resistances of the TP domains in the current image (Figure 6(c)) are not uniform and depend on the TP1 domain size. Due to the large tip radius, we could not find the presence of a TP1 domain smaller than 2.0 nm in the current image. The small protrusions with diameters of 2 to 3 nm probably correspond to a single TP1 molecule and appears the lowest in height. Figure 6(d) shows the relationship between the conductive molecular domain size and the observed resistances of TP1 in the C12 SAMs. The single molecular resistance was estimated at 5.4 × 1010
by averaging the observed resistances of small protrusions with diameters of 2 to 3 nm. This resistance value was larger than that of the mono-component TP1 SAMs (5.55 × 107
). The larger single TP1 resistance might be due to the contact problem between the molecule and the tip. Even at 10 nm, the observed resistances were not saturated and they were still larger than mono-component TP1 SAMs, which suggests that the influence of the intermolecular interaction was larger than expected. To obtain lower tunneling resistance, it seems to be necessary to form and measure larger size TP1 domains. In any case, we believe that these size dependence data on the resistance to be evidence that size dependence is mainly due to electronic conditions. We further measured oligo(para-phenylenevinylene) (OPV) molecules, because OPV are a good conductor since such phenyl rings are coplanar around the molecular axis and can increase the conjugation of the π -system, resulting in increased electrical conduction. The single molecular resistance bi (para-phenylenevinylene) (BPV) molecule was estimated at 2.6 × 108
, by averaging the observed resistances of small protrusions with diameters of ca. 2 to 4 nm. The estimated single molecular resistance of BPV was about 100 times lower than the TP1, while the molecular length of BPV was only 0.1 nm shorter than that of TP1. Thus, these resistance data demonstrated that the OPV structure was effective in increasing the electrical conduction of the single molecule. For single molecular conduction measurements using CP-AFM, Cui et al. established a significant method to estimate single molecules embedded in insulating alkanethiol matrices [21]. In their study, Au nanoparticles were attached to the inserted single dithiol molecules. They estimated the single molecular resistance of single octanedithiol to be 8 × 108
[21]. The merit of the presence of Au nanoparticles is that stable contact is formed between the Au nanoparticle and the molecule. However, the above studies were based on the data measured by contact-mode AFM. To reduce the damage to the molecules, tapping mode AFM is expected to be more effective. Otsuka et al. developed a combination of tapping mode-AFM and current imaging tunneling spectroscopy (CITS) using CP-AFM. They called their method “point-contact current-imaging” (PCI) AFM [35]. Azehara et al. attempted to measure the conduction of OPV derivatives (4-4′ Bis(mercaptomethyl)-trans-stilbene BMMS)) [36] embedded in matrix alkanethiol SAMs with a PCI-AFM technique. The conductance peaks presumably involved with BMMS molecules have been found in the conductivity map and the corresponding I –V curves showed fluctuations in the current. From these data, we concluded that the conduction of embedded the BMMS was up to 4.2 G
. For studies using SAM, the influence of tip damage was not discussed.

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PCI-AFM is likely to become a powerful tool to study soft materials on the insulating substrates.

4 Methods Related to Molecular Devices: Fabrication of Nanogap Electrodes and Conduction Measurements Although SPM techniques have an advantage of visualizing the molecules under the probes, they cannot be integrated on a chip. Therefore, another technique is necessary to fabricate electrodes with a gap comparable to the molecular length [37,38]. A variety of techniques for nanogap junction fabrication have already been developed. One of the most popular techniques to fabricate nanogap electrodes is electron beam lithography (EBL) [39–44], which allows focusing electrons to diameters less than 10 nm and thus enables fabrication of structures at the nanometer level. However, the EBL is an expensive and time-consuming process and is not suitable for mass manufacturing of nanogap electrodes. Other techniques for nanogap electrodes fabrication are available, such as electromigration [45], shadow evaporation [46], mechanical break junction [39], and electroplating [47]. Among these techniques, Naitoh et al. [48] demonstrated a high-yield production process to fabricate sub-10-nm co-planar metal-insulator-metal junctions without using EBL. The fabricating procedure contains two photolithography steps followed by shadow evaporation. Figure 7 shows a schematic drawing of the nanogap electrodes fabrication process. Ultrasmall gaps are formed in the crossing region of the two metal layers during the evaporation of the second layer. The sizes of the

Au vapor

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SiO2(400nm)

SiO2(400nm)

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n-Si(Gate)

FIGURE 7. Schematic drawing of the nanogap electrodes fabrication process.

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FIGURE 8. Characterization of the electrodes. (a) Representative SEM image of the G = 20-nm electrodes. (b) A magnified image of the area indicated by the white dashed rectangle in (a). Reprinted with permission from [48]. Copyright 2003, Surface Science Society of Japan.

ultrasmall gap can be adjusted by the height of the first metal layer and the angles of the two evaporations. With this method, metal electrodes with intervals ranging from 5 to 60 nm have been successfully produced, as shown in Figure 8. Organic semiconductor poly(3-hexylthiophene-2,5-diyl) layers were deposited on the electrodes using a special ink-jet technique. The measured resistances of the molecular layer changed clearly with the gap sizes. The yields of the sub-10-nm gap fabrication have been improved to over 80% with the combination of the electromigration. Different kinds of conjugated molecules bridging the nanogap electrodes produced by this technique are currently under investigation [49]. A single electron transistor (SET) device has also been successfully fabricated by covering this type of nanoelectrode with a self-assembled organic multilayer [50].

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Acknowledgments. This work was partly supported by NEDO under the Nanotechnology Materials Program, by MEXT under the NanoProcessing Partnership Program, and by the science and technology research grant program for young researchers with a term from MEXT of Japan (T.I.). We acknowledge M. Horikawa, T. Nakamura, H. Deng, H. Azehara, Y. Kawanishi, and H. Yokoyama (NRI, SYNAF, AIST), M. Nakano (NRI-AIST and JST) for many useful suggestions and their experimental support.

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23. X. D .Cui, A. Primak, J. Tomfohr, O.F. Sankey, A.L. Moore, T.A. Moore, D. Gust, L. A. Nagahara, and S.M. Lindsay, J. Phys.Chem. B 106, 8609 (2002). 24. J. M. Beebe, V. B. Engelkes, L. L.Miller, and C. D. Frisbie, J. Am. Chem. Soc. 124, 11268 (2002). 25. T. Ishida, W. Mizutani, Y. Aya, H. Ogiso, S. Sasaki, and H. Tokumoto, J. Phys. Chem. B 106, 5886 (2002). 26. T. Ishida, T.-T. Liang, H. Azehara, W. Mizutani, K. Miyake, S. Sasaki, and H. Tokumoto, Ann. N. Y. Acad. Sci. 1006, 164 (2003). 27. S. Wakamatsu, U. Akiba, and M. Fujihira, Jpn. J. Appl. Phys. 41, 4998 (2002). 28. Y.-T. Tao, C.-C. Wu, J.-Y. Eu, W.-L. Lin, K.-C. Wu, and C. Chen, Langmuir 13, 4018 (1997). 29. C. D. Bain, E. B. Troughton, Y.-T. Tao, J. Evall, G. M. Whitesides, and R. G. Nuzzo, J. Am. Chem. Soc. 111, 321 (1989). 30. M. A. Ratner, B. Davis, M. Kemp, V. Mujica, A. Roitberg, and S.Yaliraki, Ann. N. Y. Acad. Sci. 852, 22 (1998). 31. W.Y. Wang, T. Lee, and M. A. Reed, Phys. Rev. B 68, 035416 (2003). 32. J. K. Gimzewski, and R. Moller, Phys. Rev. B 36, 1284 (1987). 33. Y. Kuk, and P. J. Silverman, J. Vac. Sci. Technol A8, 290 (1990). 34. A.V. Muehldorf J. Am. Chem. Soc. 110, 6561 (1988). 35. Y. Otsuka, Y. Naitoh, T. Matsumoto, and T. Kawai, Jpn. J. Appl. Phys. 41, L742 (2002). 36. H.Azehara, T.-T. Liang, Y. Naitoh, T. Ishida, and W. Mizutani, Jpn, J. Appl. Phys. 43, 4511 (2004). 37. M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, Science 278, 252 (1997). 38. H. Park, J. Park, A. K. L. Lim, E. H. Anderson, A. P. Alivisatos, and P. L. McEuen, Nature 407, 57 (2000). 39. P. B. Fischer and S. Y. Chou, Appl. Phys. Lett. 62, 2989 (1993). 40. S. Itoua, C. Joachim, B. Rousset, and N. Fabre, Nanotechnology 5, 19 (1994). 41. E. Di Fabrizio, L. Grella, M. Gentili, M. Baciocchi, L. Mastrogiacomo, and M. Morales, Jpn. J. Appl. Phys. 36, L70. (1997) 42. M. A. Guillorn, D. W. Carr, R. C. Tiberio, E. Greenbaum, and M. L. Simpson, J. Vac. Sci. Technol. B 18, 1177 (2000). 43. K. Liu, Ph. Avouris, J. Bucchignano, R. Martel, S. Sun, and J. Michl, Appl. Phys. Lett. 80, 865 (2002). 44. M. S. M. Saifullah, T. Ondarcuhu, D. K. Koltsov, C. Joachim, and M. E. Welland, Nanotechnology 13, 659 (2002). 45. H. Park, A. K. L. Lim, A. P. Alivisatos, J. Park, and P.L. McEuen, Appl. Phys. Lett. 75 301 (1999). 46. G. Philipp, T. Weimann, P. Hinze, M. Burghard, and J.Weis, Microelectron. Eng. 46, 157 (1999). 47. A. F. Morpurgo, C. M. Marcus, and D. B. Robinson, Appl.Phys. Lett. 74, 2084 (1999). 48. Y. Naitoh, K.Tsukagoshi, K.Murata, and W. Mizutani e-J. Surf. Sci. Nanotech. 1, 41 (2003). 49. Y. Naitoh, T.-T Liang H.Azehara, and W. Mizutani Jpn, J. Appl. Phys. 44, L472 (2005). 50. T. Ishida, M. Horikawa, M. Nakano, Y.Naitoh, K.Miyake, and W.Mizutani Jpn, J. Appl. Phys. 44, L465 (2005).

III.10 High-Sensitivity Electric Force Microscopy of Organic Electronic Materials and Devices WILLIAM R. SILVEIRA, ERIK M. MULLER, TSE NGA NG, DAVID H. DUNLAP AND JOHN A. MAROHN

1 Introduction 1.1 Overview Conducting and semiconducting organic materials have long been known [1,2], but recent advances in chemical synthesis [3,4] have enabled organic materials to begin delivering on the promise of mass-produced economical electronic devices. Organic electronic materials are better suited for constructing high-efficiency lightemitting diodes [5–8], solar cells [9,10], and cheap solution-processable thin-film transistors [6,11–18] than are crystalline inorganic semiconductors such as silicon and gallium arsenide. The electronic/optical properties and solubility of organic materials can be tuned independently by chemical synthesis [4]. Since they can be processed and patterned at ambient temperature, organic electronic materials are compatible with flexible large-area substrates [19]. Development of organic electronic devices today proceeds largely by trial and error because a fundamental microscopic understanding of charge injection [20], transport, and trapping in many important organic electronic materials is still lacking. While continuing advances in phenomenological understanding have allowed organic light-emitting diodes to proceed steadily toward commercialization [21], development of compatible organic switching circuit elements such as field-effect transistors has been frustratingly slow. In 2000, Katz and Bao reviewed the physical chemistry of organic field-effect transistors, concluding that [17] “our understanding of aspects of both materials and electronic issues is primitive” and that “the realization of a competitive technology based on organic electronics will require far greater phenomenological insight and control of variables than we now possess.” Since this review was written, our understanding of organic electronic materials has advanced considerably. The last few years of progress have demonstrated that characterization of organic electronic materials by electric force microscopy is a particularly powerful approach to generating new insights into charge injection and trapping. These are two areas in which a basic understanding is absolutely required to make organic field-effect transistors more competitive. To see why, consider the pentacene thin-film transistor sketched in Figure 1.

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HOMO

FIGURE 1. Organic thin-film transistor. Applying a voltage to the gate electrode generates an electric field across the insulator which can either accumulate or deplete charges from the semiconductor-insulator interface. The formation of this charged channel allows current to flow from a source to a drain electrode; the gate voltage switches the channel open or closed. The performance of the transistor depends on charge injection, which is determined by energy-level alignment and is affected by interface dipoles (left box), as well as on charge flow through the polycrystalline pentacene film (right box; 1 × 1 µm image).

The current carried by the transistor is proportional to the mobility of holes in the polycrystalline pentacene near the interface with the underlying dielectric. It is not known whether the mobility is limited by conduction through grain boundaries or by charge traps. For the transistor to switch off reproducibly, the pentacene– dielectric interface must be free of charge traps; this is presently not the case. The chemical nature of these traps is not known and it is therefore not clear how to eliminate them. Even if polycrystalline pentacene were well behaved, we would still have the contacts to consider. Ideally, the transistor conductivity should be dominated by conduction through the accumulation layer in the pentacene. This demands forming a low-resistance contact with the metal source and drain electrodes. For hole injection, this requires aligning the highest occupied molecular orbital of pentacene with the Fermi level of electrons in the metal. It is not known definitively if aligning orbitals at the organic/metal interface is a simple matter of choosing materials or whether energy levels in device-grade films are affected by energetic disorder and/or dipole layers arising from interfacial bonding and electron transfer. It is not clear how much knowledge from the inorganic semiconductor community can be applied to engineer charge injection, or whether new predictive theories must be developed to describe charge injection at the organic/inorganic interface.

Au: Please confirm right running head.

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1.2 Approaches to Microscopic Characterization of Organic Electronic Materials The photophysics and mechanisms of charge conduction in heavily doped disordered bulk polymers such as polyacetylene and polyaniline is rich and well studied [22]. Disordered molecularly doped polymers, in which charge motion occurs via hopping transport, are also quite well studied [1,2], although the origin of the universally observed field-dependent mobility in these materials was only recently explained [23–29]. Unfortunately, very little of this rich cache of knowledge pertains to building and understanding organic thin-film transistors since these devices are ideally made from a highly purified crystalline or semi-crystalline high-mobility material [17]. The present microscopic picture of the organic/metal interface, charge injection, transport, and trapping has been developed primarily via photoelectron spectroscopy [30–32], hole and electron time of flight [2,33], and charge transport measurements [20,21,34,35] which provide information on bulk properties only. This picture is far from complete, however, in part because of the limitations of these bulk characterization techniques. For example, photoelectron spectroscopy cannot be easily applied to polymer and polymer-molecule solid solutions, particularly in working devices. Metal/organic interfaces prepared in ultrahigh vacuum typically exhibit large interface dipoles, yet devices prepared under realistic manufacturing conditions are usually found to have a negligible interface dipole [21]. Electron and hole time-of-flight measurements become challenging in samples with high mobility, because of the short time scales involved, and the technique can only be applied to a test device having a blocking contact. Interpreting charge transport measurements requires a careful disentangling of bulk and contact effects by modeling the transport through devices of different length. Only “bad” contacts, which contribute significantly to the total device resistance, can be studied by transport measurements. In a device with a “good” contact, the device current is space-charge limited and independent of the contact resistance altogether. Given these limitations, it is fair to ask what new information might be obtained by harnessing measurements with higher spatial resolution. Table 1 lists microscopies that have been, or could be, brought to bear to study charge injection, transport, and trapping in device-grade organic electronic materials. Before high-sensitivity vacuum electric force microscopy (EFM) was employed to study organic electronic materials, CP-AFM, NSOM, STM, and electric force microscopy in air had shown that these materials’ properties are heterogeneous at the 10–100-nm length scale. Frisbie et al. have investigated monolayer-thin iodine-doped sexithiophene crystals [36] by conducting probe atomic force microscopy (CP-AFM) [37–40]. They have investigated charge transport across a single-grain boundary, the role of contacts, the temperature dependence of the mobility, and the dependence of the conduction on crystal thickness [36,41–43]. Those thin-film organic materials that fluoresce are amenable to study by nearfield scanning optical microscopy (NSOM) [44], as has been recently reviewed by

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TABLE 1. Candidate microscopies for studying organic thin-film transistors∗ Technique

Abbrev.

Subsurface

Transmission electron microscopy Scanning tunneling microscopy Atomic force microscopy Near-field scanning optical microscopy Conducting-probe atomic force microscopy Scanning capacitance microscopy Scanning single electron transistor Electric force microscopy

TEM STM AFM NSOM CP-AFM SCM S-SET EFM

N N N Y N Y Y Y

Disordered

Charge

N Y Y Y Y Y Y Y

N N N N Y Y Y Y

∗

We briefly evaluate each technique according to its ability to probe subsurface features, to glean signal from disordered organic material, and to observe charge directly.

Buratto [45] and Barbara [46]. Van den Bout et al. [47] have used polarizationresolved NSOM to show that even in cases where a spin-coated thin film of poly(p-pyridylvinylene) appears atomically flat, the polymer exhibits 200-nm domains of molecular orientation. The Buratto group has shown that photoluminescence, photoconductivity, and photo-oxidation depend dramatically on variations in morphology at the 100–500-nm length scale in, for example, poly( pphenylene) [48–50]. Atomic force microscopy and electric force microscopy have been used by Semenikhin et al. to prove local structural inhomogeneity and a nonuniform dopant distribution in conducting polythiophenes [51–53] and by Hasselkam et al. [54] to view potential drops across individual grains in doped polythiophene. Scanning tunneling spectroscopy has been used to measure the exciton binding energy in conjugated polymers and to explore local variations in the single-particle bandgap [55,56]. These microscopic studies clearly demonstrate that doping, conductivity, molecular orientation, and energy-level splittings are heterogeneous in a wide variety of π -conjugated systems. By allowing us to detect charge and potential directly in pristine undoped materials by a noncontact measurement, high-sensitivity vacuum electric force microscopy significantly extends this picture.

1.3 Electric Force Microscopy Electric force microscopy [57,58] has a number of advantages over techniques previously used to study organic electronic materials. EFM measures local capacitance and potential, which are directly relevant to device operation. Trapped charge can also be probed, via the resulting shift in the surface potential [59,60]. Because electrostatic forces are long range, EFM can be used to probe charge trapped below a surface. It has a higher per-charge sensitivity than scanning capacitance microscopy and can follow trapped as well as mobile charge. The single-electron transistor has comparable sensitivity but only operates at cryogenic temperatures.

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A potential disadvantage of EFM is that it requires planar samples, which would seem to preclude studying directly sandwich structures such as organic lightemitting diodes. EFM’s spatial resolution depends on tip shape and distance from the sample. Its typical resolution of 100 nm is much worse than for STM, but more than adequate to disentangle bulk and contact resistances in a working thin-film transistor. If meaningful EFM data is to be collected, care must be taken with lowmobility samples to prevent triboelectric charging during topographic scanning. Achieving the highest possible sensitivity demands using a microscope operating in vacuum. Nevertheless, EFM is extremely powerful. Potential drops can be observed across individual grains [54,59] and at contacts [61–64], allowing one to estimate both the contact resistance and the true mobility in the organic film. Furthermore, the electric force microscope gives local information that cannot be gleaned by any other method. Differentiating the potential measured in a device gives the local lateral electric field. This electric field can be combined with measured current density to give, in samples with well characterized mobility, information about local charge density. The evolution of this charge density with local electric field gives information about orbital lineups at the organic/inorganic interface [65]. In gated samples the locally induced charge density can be estimated from measured local potential, in which case current and local electric field information can be combined to give the local mobility [62,66]. EFM is a noncontact technique; this is important when studying fragile polymer films. It is well suited for variable-temperature work, which enables the elucidation of charge conduction mechanisms and rigorous testing of theories of charge injection and trapping. Finally, EFM is extremely sensitive—single-charge sensitivity has been reported in vacuum at room temperature [67–70]. In this review, we will show that imaging charge and potential in devices and films using high-sensitivity electric force microscopy is a powerful and general way to address the present lack of understanding of fundamental processes in organic electronic materials. The results of recent microscopic studies have been dramatic and surprising, calling into question widely accepted theories of charge injection and trapping in some of the most widely used organic electronic materials. The goal of this chapter is to provide an overview of recent advances in electric force microscopy of organic electronic materials and devices in our laboratory; where relevant, we will to compare our methods and results with others’ recent and prior work. The remainder of this chapter is organized as follows. In section 2 we develop a theory for the cantilever-sample interaction that is applicable to the case of a metal plate, a working two-terminal organic device, and trapped charge in an organic thin-film transistor. In section 3 we briefly describe our custom-built electric force microscope and discuss sensitivity. We apply this instrumentation to study π -electron systems in the four case studies reported in section 4. In these studies we explain how to use the electric force microscope to examine local variations in contact potential and capacitance, probe charge injection and aging in a triarylamine/polystyrene solid solution, and image long-lived charge traps in

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polycrystalline pentacene. We conclude the chapter by discussing future directions in section 5.

2 Theory The simplest electric force microscope measurement involves bringing a metalcoated cantilever near a surface and measuring the mechanical resonance frequency of the cantilever as a function of the voltage applied between the cantilever and the sample surface. Here we apply this measurement to films of organic electronic materials present in co-planar two-terminal devices and field-effect transistors. In this section we derive the free energy, force, and force gradient experienced by the cantilever when studying such organic electronic devices.

2.1 Metal Plates We begin by analyzing the situation sketched in Figure 2(a). A metal-coated cantilever tip having chemical potential µt is brought near a metal sample with chemical potential µs . The sample is grounded and a voltage V is applied to the tip. As a result of the tip-sample chemical potential difference and the applied voltage, a charge Q is transferred from the sample to the tip. The energy to charge the system at constant temperature, the Helmholtz free energy, is given by Q Q2 + (µs − µt ) , (1) 2C e where C is the tip-sample capacitance. The first term is the energy stored in the electric field generated between the tip and the substrate, and the second term is the change in free energy associated with transferring electrons between materials with different chemical potentials. The voltage is conjugate to the charge, and is given by the derivative   ∂A µ Q V = + , (2) = ∂ Q T,z C e A(Q, T ) =

(a)

(b) µt

µt V

V

+Q

+Q Vs = 0 µs

−Q

Vd

µs(x) −Q

FIGURE 2. (a) Cantilever near a metal sample. (b) Cantilever positioned over a two-terminal device.

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William R. Silveira et al.

where µ = µs − µt . When the cantilever is set to vibrate, charge will redistribute between the plates to maintain constant voltage. This is possible if the time constant of the circuit is sufficiently small compared to the period of oscillation. Assuming this to be the case, the force experienced by the cantilever is obtained by differentiating the grand canonical free energy, which we obtain from A by a Legendre transformation:
(V, T ) = A − QV.

(3)

The term −QV accounts for the energy required to move the charge through the battery. In writing
we must eliminate Q as a dependent variable. We do this in the usual way, by using Eq. (2) to write Q as a function of V and using the resulting expression to recast A in terms of V . The result is   1 µ 2
(V, T ) = − C V − . (4) 2 e If the cantilever vibrates slowly enough that the process of moving charge between the metal cantilever tip and the metal substrate may be considered isothermal, then the electrical force on the cantilever is given by the derivative of the grand canonical free energy with respect to the vertical displacement z of the tip,     ∂
1 ∂C µ 2 F =− . (5) V− = ∂z T,V 2 ∂z e For small deflections, the cantilever may be modeled as a one-dimensional harmonic oscillator having a spring constant k0 . Balancing the electrical force F with the Hooke’s law restoring force k0 z, we see that the equilibrium deflection,   µ 2 1 ∂C z= , (6) V− 2k0 ∂z e is a quadratic function of voltage. In addition to displacing the cantilever, the applied voltage will also change the cantilever’s spring constant and thus its resonance frequency. To see this, we expand the capacitance derivative, ∂C/∂z = C ′ + C ′′ z + O(z 2 ), in a series about z = 0. To first order, the electric force is linear in the cantilever displacement,     1 µ 2 1 ′′ µ 2 F ≃ C′ V − + C V− z. (7) 2 e 2 e It follows that the net restoring force, F − k0 z, is linear in z, and may be described by an effective cantilever spring constant,   µ 2 1 ′′ . (8) k = k0 − C V − 2 e

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The mechanical resonance frequency f of the cantilever is determined from the spring constant and the effective mass m of the cantilever using  1 k f = . (9) 2π m In all experiments discussed here, the voltage-induced change in the cantilever spring constant is small compared to k0 . In this limit, the cantilever resonance frequency is given by   f 0 ′′ µ 2 f (V ) ≃ f 0 − . (10) C V− 4k0 e

The cantilever resonance frequency decreases quadratically with voltage, having a maximum at a voltage Vmax = µ/e determined by the difference in the chemical potentials between the sample and the tip. Since f 0 and k0 are known, we can determine C ′′ from the curvature of the frequency-voltage parabola.

2.2 Organic Device with Two Co-Planar Electrodes We use the two-terminal device shown in Figure 2(b) to study metal-to-organic charge injection. Charge is injected from a grounded metal source electrode, flows through an organic film, and is extracted at a metal drain electrode held at a voltage Vd . We want to infer what the electric force microscope measures if placed over such a device. Before we begin, let us briefly consider the distinction between the electrostatic potential, chemical potential, and voltage. The electrochemical potential or voltage in the organic film is µ(x) , (11) e where φ is the electrostatic potential and µ is the local chemical potential, given by 2 $ γ (x)n(x) . (12) µ(x) = µ0 + kT ln n0 Vs (x) = φ(x) −

Here, n is the charge concentration (in units of C/m3 , negative in sign for electrons), γ is the activity coefficient, and µ0 and n 0 are the intrinsic chemical potential and free charge concentration, respectively, in the bulk material. We take one type of charge carrier, electrons, for simplicity. Let us assume here the Maxwell– Boltzmann (infinite dilution) limit, and set γ = 1 accordingly. The current density at any point in the film is proportional to the concentration of free charges and the gradient in the electrochemical potential. In one dimension, eD d Vs n(x) , (13) kT dx where D is the diffusion constant. Equation 13 contains contributions to the current from both drift and diffusion. To see this, substitute Eqs. (11) and (12) into Eq. (13). J=

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William R. Silveira et al.

This yields, after some simplification, dφ dn −D . (14) dx dx Here we have used the Einstein relation, µ = eD/kT , to relate the diffusion constant to the mobility. The first term in Eq. (14) represents the current due to drift of electrons in an applied field E = −dφ/d x, and the second term is the current arising from diffusion of electrons from high concentration to low concentration. The important point is that the current we measure is proportional to the gradient of the electrochemical potential (or voltage), not the electrostatic potential. The Helmholtz free energy associated with charges below the tip is given by J = µn

Q2 Q (15) + (µs (x) − µt ) , 2C e where the local chemical potential µs (x) is position dependent. We have left out the mechanical part of A for simplicity. With the sample under bias, we assert that A=

∂A = V − Vs (x). ∂Q

(16)

The term V is the voltage drop though the external battery, and the term −Vs (x) accounts for the I R drop between the source electrode and a point x in the film. Including both voltages is required to correctly account for the total voltage drop that the charge Q experiences in passing from the tip to a point below the tip in the sample. With this in mind, we construct the grand canonical free energy,
= A − Q(V − Vs (x)), and find, after some simplification,   µt µs (x) 2 C V+ . − Vs (x) −
=− 2 e e Considering Eq. (11), this may be written simply as 2 C µt
=− V+ − φs (x) , 2 e from which it follows that 2 f 0 ′′  µt f ≈ f0 − C V+ − φs (x) . 4k0 e

(17)

(18)

(19)

(20)

Thus, the voltage at which the cantilever frequency is maximum is an indicator of the value of the local electric potential φs (x). This is true in general, whether or not the sample to be measured is under bias. When the drift current is larger than the diffusion current, we can obtain the local charge density directly from φs . Neglecting dn/d x in Eq. (14) gives n(x) ≃

J 1 . eβ D φs′

(21)

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Regions where this approximation is obviously problematic are near materials interfaces, where φs′ can be very large due to the interface dipole, and, moreover, can be either positive or negative. In such a case we must return to the drift-diffusion equation, Eq. (14), which we rewrite as a first-order differential equation for n(x) J dn − eβφs′ n = − . dx D

(22)

If we multiply both sides of Eq. (22) by exp(qβφ) and integrate, we find the solution, n(x) = e

+φ(x)e/kT

J {n(0) − D



x 0

′

e−φ(x )e/kT d x ′ },

(23)

in terms of the relative potential φ(x) ≡ φ(x) − φ(0) . For an ideal current flowing in one dimension with constant cross sectional area, Eq. (23) allows us to determine the charge density from the measured potential φs (x) and current density J .

2.3 Organic Field-Effect Transistor with Trapped Charge Let us now calculate the force that the cantilever experiences in the experiment sketched in Figure 3(a). A thin layer of pentacene sits on top of a dielectric layer above a gate. An amount of charge Q T is transferred to the pentacene, leaving a charge Q 1 on the tip, and a charge Q 2 on the gate, subject to the constraint of charge conservation, Q 1 + Q 2 + Q T = 0. (a) Q1 C1 C2

d1 d2 Q2

cantilever tip vacuum QT = −Q1 − Q2

(24)

(b) cantilever tip radius R

k

charge qi

+Q d

ri hi

dielectric gate

gate − qi −Q

FIGURE 3. Cantilever sample interaction with trapped charge. (a) Parallel-plate model. Charge Q T is trapped at the dielectric-vacuum interface. (b) Point-probe model. In this model, the cantilever interacts with its image charge in the gate, a trapped charge qi , and the trapped charge’s image charge −qi .

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William R. Silveira et al.

For a parallel-plate geometry, the Helmholtz free energy associated with a uniform layer of trapped charge is A=

Q2 Q1 Q2 Q 21 + 2 − µ1 − µ2 , 2C1 2C2 e e

(25)

where µ1 = µtip − µpentacene

µ2 = µgate − µpentacene

(26) (27)

Here C1 is the capacitance between the tip and the pentacene, and C2 is the capacitance of the dielectric between the pentacene and the gate. For simplicity, we have neglected contribution of the pentacene to C1 , assuming that the pentacene thickness is much less than d1 . Considering that the charges Q 1 and Q 2 are not independent, we will be interested in the change of A with respect to the change of one or the other. The difference in charge, Q1 − Q2 , (28) 2 is also a convenient variable because it is directly related to the difference in voltage between the tip and the gate, q=

Vtip − Vgate =

∂A ∂A ∂A − = = V, ∂ Q1 ∂ Q2 ∂q

which is held constant. In terms of q, the Helmholtz free energy is   q2 µ QT Q2 (µ1 + µ2 ) , A= + q
+ + T + 2C e 8C 2e

(29)

(30)

where the quadratic term depends on the equivalent series capacitance,

C1 C2 , (31) C1 + C2 and the term linear in q depends on the difference in chemical potential between the tip and the gate, C=

µ = µtip − µgate , and an additional potential due to the trapped charge,   1 1 QT .


= − 2 C2 C1

Differentiating Eq. (30) with respect to q yields   µ q = C V −
− . e

Subtracting q V from Eq. (30) gives the grand canonical free energy 2  µ QT Q2 1 (µ1 + µ2 ) −
+ T +
=− C V − 2 e 8C 2e

(32)

(33)

(34)

(35)

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which has a maximum at the voltage µ +
. (36) e The force on the cantilever is given by the derivative of
with respect to z;   2  1 ′ µ µ Q2 ∂
′ = C V− −
− C
V −
− + T2 C ′ F =− ∂z 2 e e 8C    2 ′ 2 2 1 µ Q 1 C
= C ′ V − F − + T2 C ′ . (37) − ′ 2 e 2 C 8C V
max =

Completing the square in Eq. (37), we observe that a minimum force occurs at a voltage offset µ + F . (38) e It should be emphasized that the voltage offset for the force is not the same as
, but is related to
through a derivative, VFmin =

F =

1 d (C
) , C ′ dz

When V = VFmin , there remains an additional force on the cantilever, 2  1 C ′
Q2 min F(VF ) = − + T2 C ′ , ′ 2 C 8C

(39)

(40)

which is given by the last two terms in Eq. (37). A nonvanishing F(VFmin ) implies a shift in the equilibrium position and effective spring constant of the cantilever which depends on Q T , but not on V . Here we ignore F(VFmin ) and focus only on the voltage-dependent part of the effective cantilever spring constant, since it is this which determines the curvature and voltage offset of the cantilever frequencyversus-voltage parabola. The change in the spring constant is given by the derivative of Eq. (37),    µ 2 ∂ 1 ′ C V − F − . (41) k = k − k0 = − ∂z 2 e Carrying out the differentiation in Eq. (41), and completing the square, we see that the resulting expression for k is isomorphic to Eq. (37),     µ 2 µ 1 k = − C ′′ V − F − + C ′ ′F V − F − 2 e e  ′ ′ 2  2 µ 1 C F 1 . (42) + = − C ′′ V − k − 2 e 2 C ′′ The maximum spring constant occurs at a voltage, (k) Vmax =

µ + k , e

(43)

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William R. Silveira et al.

however, such that the dependence on trapped charge is neither through
, nor

F , but through the offset

k =

1 d 1 d2 (C ′ F ) = ′′ 2 (C
) . ′′ C dz C dz

(44)

2.4 Nonuniform Distribution of Trapped Charge In our discussion so far, we assumed that the trapped charge is uniformly distributed so that we could easily write down the electrostatic energy for the tip-gate volume, which we have represented as a parallel-plate capacitor. It is instructive to examine the voltage offsets
, F , and k for this geometry in more detail, by writing capacitances explicitly: ǫ0 α , d1 + z ǫ0 α , C2 = d2

C1 =

(45) (46)

where α is the plate area, and d1 + z and d2 are the gaps between tip and sample, and sample and gate, respectively. As illustrated in Figure 3(a), the gap between the tip and the sample depends on the vibrational amplitude z, whereas the gap d2 between the sample and the gate remains constant. Here d2 is scaled by the relative permittivity of the substrate. Substituting Eqs. 45 and 46 in Eqs. (33), (39), and (44), we find voltage offsets QT (d2 − d1 − z) , 2ǫ0 α d2 QT

k = F = −Q T =− . ǫ0 α C2


=

(47) (48)

Thus, the minimum force and maximum spring constant occur at the same voltage, and each is a measure of the total amount of trapped charge. It is useful to note that the free energy is not unique. At constant voltage, the same force may be obtained ˜ =
− λV, where λ is a constant. from the derivative of an alternate free energy
Choosing λ = Q T /2 leads directly to a z-independent voltage offset


˜ = −

QT , C2

(49)

from which Eq. (48) follows immediately. When the distribution of trapped charge is non-uniform, an explicit expression for the Helmholtz free energy can be determined using the method of images. The calculation is straightforward if we neglect the polarizability of the dielectric layer. In such a case it can be shown that the grand canonical free energy has the same form as Eq. (35), but in this case the offset voltage is given by


= −

QT z +
0 , 2ǫ0 α

(50)

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where the constant
0 is a weighted sum of the trapped charges qi over the difference in their vertical separations d1i from the tip and d2i from the gate;
qi   (51) d2i − d1i .


0 = 2ǫ0 α i

Substituting Eq. (50) into Eqs. (39) and (44), we again find that the voltage offsets
qi    

F = k = (52) d2i + d2 + d1 − d1i 2ǫ α 0 i

for the force and spring constant are the same. It can be shown that the equality of

F and k follows from the fact that both 1/C and
(Eq. (50)) are linear in z for the case of a parallel-plate geometry.

2.5 Deviations from the Parallel-Plate Geometry To understand how the voltage offsets F and k change as a function of tip location in an electric force microscope measurement, it is important to consider a case in which the tip is much smaller than the feature size. The problem can be solved exactly in the point-probe limit, in which the tip is taken to be a small metal sphere of radius R which is suspended above the gate electrode at a height d ≫ R, as sketched in Figure 3(b). In this limit, the grand canonical free energy takes the form  2 1 µ
=− C V − −
, (53) 2 e where the capacitance is that of a conducting sphere above a conducting plane, +  2 , R R +O , (54) C ≃ 4πǫ0 R 1 + 2 (d + z) d+z and may be expanded as a power series to first order in R/d. The free energy offset, ⎞ ⎛
qi 1 1 ⎠, ⎝


= (55) − 4π ǫ0 i (h + d + z)2 + r 2 (h − d − z)2 + r 2 i

i

i

i

is the Coulomb potential at the tip due to the trapped charges, located by their cylindrical coordinates (ri , h i ) with respect to an axis through the tip, and their images at (ri , −h i ) in the gate electrode below. We again neglect the polarization of the dielectric. Substituting Eq. (54) into Eqs. (39) and (44), we find that the force offset

F =
− d ′
−

2d 2 ′

R


(56)

and the spring constant offset

k =
− d ′
+ d 2 ′′
+

d 3 ′′

R


(57)

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William R. Silveira et al.

are not necessarily equal. If the distribution of charge is uniform, then ′
=

′′
= 0, and indeed, F = k , as is the case for a parallel-plate capacitor. When the distribution is nonuniform, however, for small enough R, the derivative terms

′
and ′′
in (56) and (57) will be enhanced by the factor d/R (≫1). In such a case, the voltage offsets for the force and spring constant,

F ≃ −2

k ≃

d2 ′

R


d 3 ′′

, R


(58) (59)

will be largely determined by ′
and ′′
, respectively.

3 Instrumentation The case studies described below were carried out using the highly sensitive custom-built electric force microscope shown in Figure 4. This instrument has the following unique combination of abilities: r Operating over a large temperature range, from 4.2 to 340K. This is crucial because essentially all fundamental processes—charge injection, transport, and trapping—are thermally activated in organic electronic materials. r Operating in vacuum. This eliminates degradation concerns associated with our materials reacting with oxygen and water, and increases cantilever sensitivity by 10–20-fold by reducing viscous damping due to air. r Using a fiber-optic interferometer. This allows us to quantitatively measure ˚ (in a 1-Hz measurement cantilever oscillations as small as 10 × 10−3 A

Electrical connections

Coarse approach

Optical fiber

Cantilever Sample scanner 1.2” diameter

FIGURE 4. Left: Microscope head, including electrical connections, coarse approach, and x y-scanner. Right: Vibration isolation, Dewar, vacuum lines, and pump.

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bandwidth) which in turn lets us monitor cantilever frequency shifts as small as 5 parts in 107 . r A large-range piezoelectric scanner. This enables imaging of entire working devices, even at low temperature. A scan range of 5 µm is obtained at 4 K. A coarse positioning mechanism allows locating devices on a large substrate in situ. r A novel mechanism for bringing a cantilever into close contact with a surface in nanometer-sized controllable steps, very reliably, at temperatures ranging from 4.2K to 340K [71]. We now discuss the main components and operating modes of the microscope.

3.1 Positioning: Coarse Approach and Scanning Stage We have developed an inertial coarse approach mechanism that controls the fine positioning of the cantilever using the same piezoelectric stack that drives the cantilever in coarse steps toward or away from the surface [71]. Our design is most similar to that of Renner et al. [72], yet does not require parallel sapphire rails. The translator operates horizontally and vertically in high vacuum from 4 to 340 K. It is reliable, mechanically simple, and easy to control. Remarkably, this compact, rigid design is both nonmagnetic and glueless, which is beneficial for work in strong magnetic fields while holding up under the demanding stresses of temperature cycling. We have successfully incorporated this positioning mechanism into a variable temperature atomic force microscope (AFM) and a magnetic resonance force microscope (MRFM) [73]. We have interfaced our coarse approach mechanism with a scanning stage based on bimorph piezos capable of withstanding cryogenic temperatures [74]. While it is more complex than the commonly used piezotube scanner, the bimorph scanner gives a much larger scan range per unit length of bimorph. Using only a 1/2-inch long bimorph piezo, we can obtain a 5-µm scan range at 4 K.

3.2 Mechanical Design, Vacuum, and Vibration Isolation The microscope head is shown at the left of Figure 4. Only 1.2 inches in diameter and constructed primarily of brass, the microscope and a small copper heat sink hang from a soft bellows and reside in a 1.75-inch copper vacuum space attached to the bottom of a long stainless steel tube. At the top of the stainless steel tube, we have placed fiber-optic and electrical feedthroughs into the vacuum space. The approach of cooling the microscope at the end of a vacuum tube is common among groups who require high magnetic fields, where the magnet is placed in the bottom of the Dewar, surrounding the copper end of the vacuum chamber [75]. We also found this design compatible with initial testing in a helium transfer Dewar. The entire Dewar and vibration isolation system are shown in the right of Figure 4. A winch mechanism was implemented to raise the Dewar to a 2,000-pound plate where it seals against an aluminum interface. The heavy plate rests on four air legs. The turbomolecular vacuum pump, to the right of the vibration isolation stage, is

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FIGURE 5. (a) Interferometer output signal versus laser diode temperature. (b) Interferometer output signal versus time for an over driven cantilever. (c) Thermal motion of a 1N/m cantilever. (d) Power spectrum of the thermal motion of the cantilever.

vibration-isolated from the probe through a concrete block resting in sand followed by a series of flexible vacuum lines attached rigidly to the massive plate.

3.3 Interferometer The electric force microscope uses a fiber-optic interferometer [76–78] to detect the displacement of the cantilever. The wavelength of the laser diode is λ = 1,310-nm, well below the bandgap of most organic semiconductors. The fiber-optic interferometer is compatible with ultrahigh vacuum [79]. In contrast to other detection schemes, such as beam deflection [80] or piezoresistance-based detection [81,82], the fiber-optic interferometer measures displacements quantitatively. Figure 5(a) shows the interferometer output signal versus the temperature of the laser diode. Maximum sensitivity is achieved by tuning the temperature of the laser diode to the linear-response region of the curve [78]. By using rf current injection [83] to eliminate mode-hopping instabilities in the interferometer’s diode laser, the interferometer’s √ noise floor (minimum detectable displacement) can be ˚ extended to ∼10 mA/ Hz at a typical fiber-separation of 50–100 µm. Figure 5(b) shows the interferometer output signal as a function of time for a cantilever whose peak-to-peak amplitude is larger than the linear-response of the

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interferometer (160nm corresponds to a 10% error). In each case the peak-to-peak voltage, Vpp , is the same and can be used to calibrate the cantilever displacement. In the linear response regime, the sensitivity is given by, 2π Vpp /λ, where λ is the laser wavelength. The interferometer output versus time for a cantilever undergoing only random thermomechanical motion is shown in Figure 5(c). The corresponding averaged power spectrum is shown in Figure 5(d). The area under this power spectrum, equal to k B T /k, can be used to determine the cantilever spring constant if the cantilever’s temperature is known [84].

3.4 Atomic Force Microscope Operation The microscope employs custom-built feedback control electronics for operation in contact and intermittent contact mode imaging. The circuitry is very similar to the proportional-integral control electronics used in scanning tunneling microscopy. For intermittent contact mode, we drive the cantilever below resonance with a small piezo at the cantilever base, resulting in a peak-to-peak amplitude of 100 nm. We approach the surface until the amplitude decreases to approximately 90 nm, at which time the feedback loop is turned on. A spring constant of 1 N/m or higher is sufficient to avoid cantilever snap-in during imaging, which occurs when the van der Waals force gradient overcomes the spring constant. For contactmode imaging, we prefer a much softer cantilever, with a spring constant of 0.02– 0.1 N/m, to avoid damaging the surface. We image at constant force with less than 1 nN of force between the tip and sample.

3.5 Variable Temperature Operation To achieve low temperatures, the entire microscope and sample are slowly cooled using helium as an exchange gas. The exchange gas is introduced at the top of the stainless tube through a valve while the copper end of the probe, which houses the microscope, is immersed in cryogen. Once thermal equilibrium is achieved, the exchange gas is evacuated with a turbomolecular pump until a high vacuum is achieved. A series of baffles and a heat sink are used to slow heat transfer into the microscope. We have also been able to operate the experiment at higher temperatures by submersing the copper end of the probe in heated water. Because the microscope is suspended from a soft bellows, we do not find that vibrations arising from the cryogen affect our experiment.

3.6 Measuring Cantilever Frequency Monitoring the resonance frequency of the cantilever, we are able to obtain the force gradient between the sharp tip and the surface using f 1 ∂F ≈ − , f0 2k ∂z

(60)

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where  f is the frequency shift about the natural resonance, f 0 ; and z is the tipsurface coordinate. The cantilever is made the resonant element in a self-oscillating positive feedback loop by driving a piezo at the base of the cantilever with a copy of the interferometer displacement signal that has been phase shifted by 90◦ [85]. A commercial frequency counter is used to record the cantilever frequency.

3.7 Sensitivity Working in ambient conditions severely limits force and force gradient sensitivity. Using a fiber-optic interferometer to detect the cantilever motion, the noise level in our experiment is limited by the thermally induced (Brownian motion) fluctuations in position, which are set by the cantilever parameters and the temperature. At a well defined temperature T , we can obtain the spring constant k, the quality factor Q, and resonance frequency f 0 from a power spectrum of cantilever thermal motion (Figure 5(d)). This allows us to quantify force and force gradient sensitivities. The minimum detectable force, Fmin , is given by  2kkB T B , (61) Fmin = π Q f0 where F is the force between the cantilever and the surface and B is the measure′ ment bandwidth. The minimum detectable force gradient, Fmin , is given by  kkB T B ′ Fmin = , (62) 2 π Q f 0 z rms 2 where z rms is the root mean square displacement of the driven oscillator [85]. The sensitivities reported in Table 2 demonstrate the great advantage of operating a scanned probe microscope in high vacuum (1 × 10−6 mbar). The quality factor, Q, which is proportional to the oscillator’s displacement in response to an applied force, increases dramatically from Q ∼ 102 to Q ∼ 104 . The frequency noise with

TABLE 2. Comparison of typical room temperature sensitivities at ambient pressure and in high vacuum obtained in a B = 10 Hz measurement bandwidth∗ Parameter

Units

P = 1, 000 mbar

P = 10−6 mbar

Q Fmin ′ Fmin

— 10−15 N 10−6 N/m

50–150 100 7

10,000–20,000 8 0.6

∗ The values for the quality factor, Q, the minimum detectable ′ , are force, Fmin , and minimum detectable force gradient, Fmin common for the titanium/platinum-coated commercial cantilever used here. These cantilevers have a resonance frequency of f 0 = ′ was 24–26 kHz and a spring constant of k = 1–2 N/m. Here Fmin obtained assuming z rms = 10 nm.

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B = 10Hz and a drive of z rms = 10 nm is 14 mHz, within a factor of 1.2 of the thermal limit. The force and force gradient sensitivities are improved by a factor of 10–20 at room temperature. Sensitivity improves further as the temperature is decreased and Q increases, according to Eqs. 61 and 62. Two electrons spaced 50 nm apart make a force of F = 9 × 10−14 N and a force gradient of F ′ = 3.7 × 10−6 N/m. Table 2 indicates that the electrostatic interaction between two such electrons is already detectable using a commercial cantilever at room temperature, if operated in vacuum.

4 Case Studies 4.1 Mapping Potential and Capacitance This section describes procedures common to the next three case studies. We show how the cantilever frequency is used to measure the local potential and the capacitance derivative and how images of potential are created. We study planar interdigitated-electrode devices, which significantly decreases the time required to locate a device channel in situ and allows us to study variability across different sections of a device gap without having to remount a sample. After depositing the organic film onto the device substrate by solution casting (in air) or thermal evaporation (in vacuum), we measure the device’s current-voltage characteristics in high vacuum with a commercial probe station. The device is then transported to the electric force microscope. The microscope’s vacuum space is pumped to a base pressure of 10−6 mbar. For EFM and atomic force microscope measurements, we employ a titanium/platinum-coated cantilever (model NSC21, MikroMasch) having a typical resonance frequency f 0 = 24–26 kHz, a spring constant k0 = 1N/m, and a quality factor Q ∼ 104 in vacuum. Depending on the device, it may be necessary to locate a source-drain channel. Instead of imaging the topography of the surface until a channel is found, we apply a small potential to the electrodes or the tip. This creates a large force gradient between the metal electrodes and the tip that makes the electrodes easy to “see” in a cantilever frequency image. The electrodes stand out even when the tip is up to 500 nm above the sample surface, making inertial repositioning using the x y sample scanner straightforward. When studying organic electronic films and devices, it often happens that unwanted particles or static charge appear in the image, so easy coarse sample positioning in situ is an important capability. Once the device is positioned below the tip, the topography is usually obtained by intermittent contact mode imaging. The sample surface is located by recording a cantilever displacement versus distance curve and finding the “snap-in” distance at which the cantilever spring constant is overcome by the van der Waals force gradient. During this process, the height of the tip is measured using a second fiberoptic interferometer. To correct for sample tilt, we control the tip height so that it lies in a plane above the surface during electric force microscope scans. This is

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0 −2 −4 −6 −8 −10

0

(b)

−40 −80 −120 −1.0 −0.5 0.0 0.5 1.0 Vs [V]

220 200 180 160 330 320 310 300 290 280

(c)

(d) 0.0

0.5

1.0

1.5

FIGURE 6. (a) Force gradient image of a 50% weight TPD-PC film on epitaxially grown gold. (b) Quadratic response of the cantilever resonance frequency with applied surface potential. (c) The potential, φ, derived from acquiring the frequency as a function of applied potential to the underlying gold along the linescan shown in image (a). (d) The capacitance derivative, ∂ 2 C/∂z 2 , along the linescan shown in image (a).

accomplished by acquiring force-distance curves at selected points near the edges of the image and then using this information to level the scan by adjusting the tip height in real time while scanning. We quantify the local potential, φ, and the capacitance derivative, ∂ 2 C/∂z 2 , between the metallic probe and the sample by measuring the cantilever frequency as a function of either the tip or sample potential along a line. The tip is typically grounded. When scanning over films deposited on metal, a potential is applied to the underlying metal; when scanning devices, the tip potential is referenced to either the source or drain electrode. We have studied molecularly doped polymer films of TPD, N,N′ -diphenyl-N-N′ bis(3-methylphenyl)-(1,1′ -biphenyl)-4,4′ -diamine, dissolved in polystyrene (PS) or polycarbonate (PC) using high-sensitivity electric force microscopy. Figure 6(a) is a force-gradient image of a 50% weight TPD-PS film on an epitaxially grown gold substrate. This 2 × 2-µm image, acquired at a tip height of 50 nm with an applied potential of 1.5 V to the underlying gold film (tip is ground), shows a change in the electrostatic force gradient on a 100–200-nm length scale. However, by imaging the cantilever frequency at just one applied voltage we cannot distinguish whether the variation arises from local variations in the potential, changes in tipsample capacitance, or both. Figure 6(b) shows the cantilever frequency, at a selected point in the film, as a function of the voltage applied to the gold film. From this data, using Eq. (20), we can extract φ and ∂ 2 C/∂z 2 . Figure (6)(c), and Figure 6(d) show the change in φ and ∂ 2 C/∂z 2 , respectively, along the line in Figure 6(a). Here, the primary contribution to the force gradient is φ. We find that ∂ 2 C/∂z 2 exhibits only a small variation, shown to arise from a small 1–2-nm, drift in tip-sample height during imaging. This open-loop approach to acquiring surface potential and capacitance information is different from standard Kelvin probe techniques since we do not modulate

2.0

III.10. High-Sensitivity Electric Force Microscopy

2 µm × 2 µm [nm]

(a)

20 15 10 5 0 2 µm × 2 µm ∆ f / f0 (d) [10−6] 0 −10 −20 −30 −40 Vs = −1.0 V

1 µm × 1 µm [nm]

(b)

1.0 0.5 0.0 −0.5 −1.0

2 µm × 2 µm ∆ f / f0 (c) V = +1.0V s [10−6] 0 −2 −4 −6 −8

2 µm × 2 µm ∆f / f0 (e) [10−6] 40 20 0 −20 −40

809

Vs = −1.0 V

1 µm × 1 µm ∆f / f0 (f ) [10−6] 40 20 0 −20 −40

Vs = +1.0 V

FIGURE 7. (a) Topography of a test grating with 25 nm steps, acquired by contact mode imaging. (b) Topography of a 100 nm polycarbonate film on polycrystalline gold, acquired by intermittent contact mode imaging. (c) A larger force gradient image of the same area shown in (b), illustrating the deposition of charge on polycarbonate after intermittent contact mode imaging. (d) Force gradient image of a 100 nm film of 5% TPD-PC on polycrystalline gold. (e) Force gradient image of the same area shown in (d) after charge has been deposited by the tip. (f) Force gradient image of the surface charge in (e), but imaged under opposite bias, which reverses the image contrast.

the applied voltage and do not rely on a feedback circuit to continuously null the potential difference between the tip and surface. Although imaging speed is reduced with our approach, the local potential and tip-sample capacitance derivative are obtained in a single linescan. Figure 7(a) shows a contact-mode image of a calibration grating. We typically use much softer cantilevers, with spring constants of 0.1–0.01 N/m, for contactmode imaging. The calibration grating is used to determine the range of the sample scanner. By operating in intermittent contact mode we can image much softer polymers nondestructively, as shown by the topography of a 100 nm polycarbonate film on gold (Figure 7(b)). However, even while imaging in intermittent contact mode, charge can be triboelectrically transferred from the tip to the polymer surface. This is apparent in the electrostatic force gradient image of Figure 7(c). Only the lower left quadrant of Figure 7(c) has been imaged topographically in intermittent contact mode and consequently exhibits a large surface potential variation. The surrounding area is untouched and shows little variation in electrostatic force gradient. Whenever a low-mobility film is studied, therefore, the danger of triboelectric charging exists. Figure 7(d) shows a 100 nm, 5% weight TPD-PS film on gold. We

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see a small variation in the force gradient, but upon touching the surface during a force-distance measurement, we observe a bright spot in the force gradient image, shown in Figure 7(e). This image was was acquired while applying a potential of −1.0 V to the underlying gold. The surface charge is positive, since it decreases the force gradient in front of a negatively biased gold electrode. Figure 7(f) is a smaller force gradient image of the same charged area, but acquired under an applied potential of +1.0 V to the gold film. Note the surface charge appears as a dark spot in front of a positively charged gold electrode, confirming that the triboelectrically deposited charge was positive. The more insulating the film, the more challenging it is not to triboelectrically charge the surface and induce local contact potential variations. Interestingly, the 60–100-mV peak-to-peak variations occurring on a 100– 200-nm length scale in Figure 6(a) are uncorrelated with surface topography, which is essentially flat at the nanometer length scale. This surprisingly large surface potential variation consistently appears under a variety of chemical conditions (the host polymer being polystyrene or polycarbonate, dipole doping, conductive and insulating substrates) and physical conditions (room and low temperature). Explaining this effect in terms of interface dipoles or correlated energetic disorder [23–29] has been challenging and will be the topic of an upcoming paper.

4.2 Charge Injection in a Triarylamine In this case study, we employ a classic molecularly doped polymer to help elucidate, microscopically, how charge is injected from a metal into a disordered organic system. Our approach has enabled— r The microscopic observation of the transition from ohmic conduction to the space-charge limited conduction (SCLC) mechanism. r The probing of interface energetics at a “good” contact. This information cannot be obtained by bulk current-voltage characterization. r The measurement of the local charge density at the organic/metal interface as a function of electric field, which can be used to test models of charge injection. The following discussion parallels our previously published investigation [65] on a similar device. We have chosen to investigate one of the most commonly used triarylamines, N,N′ -diphenyl-N,N′ -bis(3-methylphyenyl)-(1,1′ biphenyl)-4,4′ diamine (TPD). This small molecule is dispersed into a host polymer, polystyrene (PS), resulting in an amorphous solid solution. The structure of TPD and the host polymer are shown in Figure 8(a). The accepted description of charge transport in molecularly doped polymers is the correlated disorder model [23–29]. The transport of injected holes occurs by hopping between the highest occupied molecular orbitals on adjacent molecules. Electrostatic interactions with the permanent dipole and quadrupole moments of distant molecules allow for a large number of independent contributions to the energy of an ionized molecule. By the central limit theorem, this leads to an

III.10. High-Sensitivity Electric Force Microscopy (b)

(a)

(c) φt

N

811

[nm] 60

N

40

w

5 µm

20

Vsd t

0

[nm]

CH2 CH

L

60 30 0

FIGURE 8. (a) Structures of the triarylamine, TPD, and the host polymer, PS. (b) Planar TPDPS device and electrical convention for scanning potentiometry. (c) Topography across the 5-µm source-drain gap in an interdigitated gold electrode device.

approximately Gaussian density of site energies, with a width σ between 50 and 100 mV in typical molecularly doped polymers. These same long-range interactions also give rise to spatial correlations in the energy landscape; distant multipoles will influence the energy of a charge on two adjacent dopant molecules in nearly the same manner. This correlated disorder is the central feature that allows this model correctly to explain the Poole–Frenkel dependence of the mobility on electric field seen in molecularly doped polymers. Because their charge-transport properties are so well understood, molecularly doped polymers like TPD-PS now serve as a proving ground for theories of metal/organic charge injection [20,86–93]. The electric force microscope data reported here provides a particularly stringent test of charge injection theories. To make our TPD-PS device, interdigitated source and drain electrodes are patterned onto a quartz substrate by standard photolithographic techniques and then TPD-PS is spin-coated from solution onto the substrate. The source and drain electrodes are spaced L = 5 µm apart and have a total length of w = 201 mm. The polycrystalline gold electrodes, t = 50 nm in height, are electron-beam evaporated onto a 5 nm adhesion layer of chromium. The experimental configuration of the potential applied to the source electrode, Vsd , and the tip potential, φt , is illustrated in Figure 8(b). The resulting polymer film coats the electrodes and the source-drain electrodes conformally, as can be seen in the topographical image in Figure 8(c). The film has a thickness of 100 nm and a surface roughness less than 1 nm rms. The electrical characteristics of the device show an evolution from ohmic conduction at low voltages, with the current proportional to the applied potential (I
∝ V ), to space-charge limited current at high voltages, with the current proportional to the square of the applied potential (ISCL ∝ V 2 ) Figure 9(a). At low voltages we expect an ohmic current density I
= µ0 eN0 V

wt , L

(63)

(a)

William R. Silveira et al.

10-9 Isd [A]

(b) 50

10-8

40

E(x) φ(x)

10-10

Vsd = 50 V

Vsd = 1 V

10-11

[V]

812

30 20

E(x)

10

10-12

φ(x) 0.1

2

4 6 8

1

2

4 6 8

10

2

0

4

2

Vsd [V]

4

6

8

x [µm]

FIGURE 9. (a) Current-voltage characteristics of the TPD-PS thin-film with normalized potential and electric fields at 1 V and 50 V (insets). (b) Evolution of the potential illustrating the transition from ohmic to space-charge limited current (SCLC).

where N0 is the density of intrinsic free carriers and µ0 is the zero field mobility. In writing Eq. (63), we neglect the field dependence of the mobility. This is appropriate at low voltage. When the voltage is high enough so that the total injected charge exceeds the total intrinsic (compensated) charge, then the space-charge electric field is sufficient to alter the voltage dependence of the current. In the space-charge limit the current is often given by the modified Mott–Gurney equation [94] ISCL =

√ wt 9 µ0 ǫ V 2 e0.89βµ V /L 3 , 8 L

(64)

where βµ accounts for the Poole–Frenkel field dependence of the mobility in TPDPS [95], µ0 is the extrapolated zero-field mobility, and ǫ ≃ 3ǫ0 is the TPD-PS dielectric constant. Equation (64) is valid strictly only for a parallel-plate device. Grinberg et al. [96] have explored the space-charge limited current in devices with coplanar electrodes. In the limit when t ≪ L, which is the case here, ISCL = 0.57 µ0 ǫ V 2 eβµ

√

V /L

w L2

(65)

Above 1V, both Eq. (63), appropriately modified to account for the field dependence of the mobility, and Eq. (64) (or Eq. (65)) all fit the current equally well. We simply cannot distinguish ohmic conduction from space-charge limited conduction based solely on curve fitting the current-voltage data. Remarkably, we can observe the onset of space-charge limited conduction directly using electric force microscopy. At low voltage, the potential drops linearly between the injecting and extracting electrodes (Figure 9(a), upper inset). The lateral electric field, calculated by differentiating the potential, is uniform and symmetric within the device gap at low voltages, as expected for ohmic conduction. At higher voltages the electric field becomes non-uniform, indicating a buildup of positive space-charge (Figure 9(a), lower inset).

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TABLE 3. Properties of TPD-PS and the TPD-PS/Au interface inferred from electric force microscopy and current-voltage measurements∗ Reference

JSCL

[65] This work This work

Eq. (64) Eq. (64) Eq. (65)

µ0 (m2 V−1 s−1 )

βµ ((m/V)1/2 )

N0 (m−3 )

ε F − Ev (mV)

φB (mV)

βs ((m/V)1/2 )

2 × 10−9 1.1 × 10−10 2.2 × 10−12

0.6 × 10−3 1.2 × 10−3 1.1 × 10−3

2.8 × 1020 1.5 × 1020 7.7 × 1021

540 560 455

370 366 270

2.2 × 10−3 4.3 × 10−3 4.4 × 10−3

∗

Here ε F is the chemical potential in the bulk of the film and E v is an abbreviation for E HOMO . The injection barrier φ B and the parameter βs accounts for the electric field dependence of the barrier lowering. The relative error in µ0 and N0 is ±10%, the error in the estimate of ε F − E v and φ B is ±10 mV, and the error in βµ and βs is ±0.1 × 10−3 (m/V)1/2 .

We can also use electric force microscopy to determine if the contact is “good” or “bad.” A bad contact has a resistance higher than that of the bulk of the device. In a device with a bad contact more of the applied voltage is dropped at the contact than in the bulk. The EFM measures the local potential however, not the local voltage. Nevertheless, at high electric fields where diffusion currents can be neglected, we expect the difference between the voltage drop and the potential drop to be small. While this assumption deserves further attention, we will tacitly equate measured potential with voltage in the analyses that follow. At all applied voltages there is no discernable potential drop at the contacts in our TPD-PS device. This supports the common assumption that ohmic conduction is the appropriate model at low voltage and space-charge conduction is the appropriate description at high voltage. However, this should not be automatically assumed with different materials, or with TPD-PS/Au at higher temperatures; bad contacts may show nonlinear current-voltage characteristics and, even with a good contact, the exponential rise in current due to the electric field dependence of the mobility can easily make it impossible to distinguish between ohmic or spacecharge limited conduction mechanisms simply by examining the current-voltage curve. The current at high voltage is used to determine µ0 and βµ . Then, with µ0 known, the low-voltage current is used to determine N0 . The first row of Table 3 shows the properties of the TPD-PS film of (65), where Eq. (64) was used to infer µ0 and βµ . The second and third rows of Table 3 shows the properties of the film studied here, where we have used Eq. (64) and Eq. (65), respectively, to analyze the high-voltage current. Comparing rows two and three, we see that using the more relevant Eq. (65) instead of Eq. (64) returns a much lower estimated mobility and a much higher estimated background charge. The TPD-PS mobility in our device is approximately fifty times lower than the value of 2 × 10−9 m2 /Vs found by Yuh et al. [95]. It is reasonable to expect thin-film mobility to depend on sample preparation details, since spin casting is a non-equilibrium process and since mobility depends on energetic disorder which is extremely sensitive to molecular packing. An increase in energetic disorder should also increase βµ , which is observed here. Our device is prepared on quartz, which

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6

E(x) [10 V/m]

(a)

(b)

(c)

0

1.0

-4

0.8 0.6

-8

0.4 -12

0.2 0.0 2

4

6

8

0

10 20 30 40 50 Vsd [V]

FIGURE 10. (a) Electric field derived from the potential. (b) Schematics of charge density in the extracting electrode, bulk organic, and injecting electrode. The voltage increases going from the bottom diagram to the top diagram. (c) Degree of space-charge-limited current.

may be an additional source of energetic disorder [97,98]. Both the decrease in µ0 and the increase in βµ compared to Yuh et al. can be quantitatively explained using Eq. (16) in [25], if we let σ increase from 100 mV to approximately 250 mV. Let us consider the measured electric field in some detail. The lateral electric field, Figure 10(a), is obtained from the potential using E(x) = −dφ/d x. The constant slope of E in the bulk implies a uniform charge density. We currently attribute this discrepancy with the standard Mott–Gurney prediction to deviations from the idealized one-dimensional conduction between two parallel-plate electrodes. We use the behavior of the electric field at the interface to quantify the extent to which the current is space-charge limited. Figure 10(b) qualitatively shows what is expected during the transition from ohmic to space-charge limited conduction. Initially, conduction occurs via the background charge carriers and the bulk is neutral. As the injected charge increases, a positive space-charge is formed. A quantitative measure of the degree to which SCLC dominates transport is η = (E L − E 0 )/E L , with E 0 and E L the electric field at the injecting and extracting electrodes, respectively. As defined, η = 0 for purely ohmic currents and η = 1 when the current is space-charge limited. Figure 10(c) shows η as a function of Vsd . A great advantage of EFM is the ability to measure electric fields microscopically. By combining the current density with the local electric field, we can infer the mobility-charge density product using µρ = J/E. Examining µρ as a function of electric field allows √ us to test models of charge injection. In Figure 11(a) we plot ln (µρ) versus E at positions near the injecting and extracting electrodes. The observed exponential increase of µρ with electric field cannot be explained by considering only the field dependence of the mobility µ. If, however, the charge density ρ at the injecting electrode is increasing due to a Schottky-effect lowering

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(a)

815

(b) TPD-PS

Injecting electrode Extracting electrode

−14 −16 −18

Au

EHOMO

−20

Schottky Emtage & O’Dwyer

−22

0

100 mV

455 mV

270 mV

1000 2000 3000 4000 E1/2 [V/m]1/2

FIGURE 11. (a) Interfacial charge density as a function of electric field. (b) Energy level diagram derived from current and electric force microscopy measurements.

of the injection barrier by the field, then we would expect the data at the injecting electrode in Figure 11(a) to follow a line. This is exactly what is seen (dotted line). The slope of the line is βµ + βs , where βs = 0.85 × 10−3 (m/V)1/2 accounts for the electric field dependence of the barrier lowering. From the intercept of the line, µ0 ρ(0), we can estimate the injection barrier φ B from the density of charges at the metal/organic interface, ρ(0) = eNTPD exp (−φ B /k B T ), with NTPD = 2.66 × 1026 m−3 the concentration of TPD molecules. Taking µ0 = 2.2 × 10−12 m2 V−1 s−1 , we find φ B = 270 mV, which is reasonable. The Schottky analysis is valid only at high fields, however, and assumes that equilibrium is reached via electron transfer from the metal to the empty HOMO states of the organic. This assumption does not hold for our sample, as can be shown. Although the chemical identity, concentration, and energy levels of the acceptor states giving rise to the bulk free carriers are not known, we can use Fermi–Dirac statistics to determine the chemical potential ε F in the bulk TPD-PS from the measured density N0 of bulk free carriers:  +∞ exp (−ε2 /2σ 2 ) e NTPD dε. (66) N0 = √ 2π σ 2 −∞ 1 + exp ((ε F − εHOMO )/(k B T )) Assuming a width for the HOMO Gaussian density of orbitals of σ = 100 mV, we calculate ε F − E HOMO = 455 mV. For σ = 250 mV, we find ε F − E HOMO = 1,020 mV. Both estimates are consistent with the material being a p-type semiconductor. By combining this information with the estimated injection barrier, we have constructed the energy-level diagram of Figure 11(b), drawn for σ = 100 mV. We can conclude from this energy-level diagram that equilibrium is reached between TPD and Au by a transfer of electrons that results in the accumulation, not depletion, of holes near the metal/organic interface. (This conclusion holds for σ = 250 mV

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as well.) In this situation, the diffusion-limited thermionic emission theory of Emtage and O’Dwyer [99] is the most appropriate description of charge injection, although it does not account for energetic disorder at the organic/metal interface. Their theory predicts [100] e NTPD e−φ B /k B T µ0 eβµ µρ = √ √ βs E K 1 (βs E)

√

E

,

(67)

where βs = (q 3 /16πǫ(kT )2 )1/2 and K 1 is a modified Bessel function of the second kind. The fit to this theory, with the injection barrier as the only free parameter, is quite poor (data not shown). However, better agreement is achieved if we allow the parameter βs describing the electric field dependence of the barrier lowering to vary. The solid-line fit of µρ at the injection electrode to Eq. (67) gives φ B = 270 mV and βs = 4.4 ± 0.1 × 10−3 (m/V)1/2 , much larger than the 0.85 × 10−3 (m/V)1/2 expected from diffusion-limited thermionic emission theory. It is unlikely that βs is larger than expected simply because we have underestimated the local electric field at the organic–metal interface with our microscope. While the electric field is known to diverge near an ideal thin, planar electrode [101], the divergence is relatively gradual in the lateral dimension. We do not observe an enhanced electric field, however, at any voltage, within 100 nm of either electrode. Perhaps this is because the organic film is thicker than the planar electrodes and covers them completely, which could alter the expected field. The divergence could also well be mitigated by space-charge at the organic–metal interface. Such a space-charge field must be present, even at zero applied source-drain voltage, to equilibrate the chemical potential of the organic and the metal across the interface. That the βs found here is larger, by a factor of two, than that found in our previous work [65] on an essentially identical device suggests that the large βs is due to the material and is not solely a geometric property. An enhanced βs has been observed in Monte Carlo simulations of charge injection incorporating energetic disorder [87] and has been suggested by Burin and Ratner [102]. Our data suggests that it may be critical to account for energetic disorder when developing a microscopic model of charge injection. B¨urgi et al. [62] have used EFM to study contact resistance versus gate voltage and temperature in a polythiophene field-effect transistor. They also call into question widely used theories of charge injection; their approach to using EFM to study working devices is complementary to ours. B¨urgi et al. make use of the fact that polythiophene forms a field-effect transistor with a high on-off ratio. This allows them to control the charge density in their sample via the voltage applied to an underlying gate electrode. They infer the local mobility using µ = J/ρ E, where J is the measured current density, assumed homogeneous, E is the local electric field measured by differentiating the local potential, and ρ is the charge density calculated from the local voltage relative to the gate voltage. This approach is appropriate because the electric field and charge density dependence of the mobility in polythiophene is not well understood. In a low-mobility material like TPD-PS, forming

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(b)

(a) 2

2

1

1

0

0 0

4

8

0

4

8

FIGURE 12. Measured potential profiles across the source-drain gap in two TPD-PS devices. (a) The current through a device operating at room temperature is limited by the resistance of the TPD-PS film; no potential drops are seen at the contacts. (b) In a device operated at elevated temperature the current is limited by the resistance of the TPD-PS/Au contacts, as suggested by the potential drops apparent at the electrodes. In both devices, the injecting gold electrode is on the right and the extracting gold electrode is on the left.

a field-effect transistor is problematic, however [97,98]. Fortunately, we can calculate µ from the measured electric field and βµ using a functional form for µ(E) well-known from time-of-flight studies. This allows us to infer the local charge density from the measured J and E using ρ = J/µE.

4.3 Aging of a Metal Organic Contact In section 4.2 we concluded that the resistance of our TPD-PS film was set by the resistance of the bulk and not by the resistance of the TPD-PS/Au contact because all of the potential was dropped in the bulk of the film (Figure 12(a)). Bulk-limited conduction is achieved when the charge density available at the organic/metal interface for injection, ρ(0), exceeds the density of bulk intrinsic carriers in the film, N0 . We further showed, by calculating the lateral electric field, that the bulk current was carried by thermally ionized carriers at low voltage and by injected space-charge at high voltage. When ρ(0) < N0 , the current through the film is contact-limited. A potential profile for a contact-limited device is shown in Figure 12(b). In this device most of the potential is dropped near the electrodes instead of in the bulk of the film. In this section we show how electric force microscopy can be used to follow the degradation of a TPD-PS/Au contact. We identify two degradation mechanisms. Crystallization of TPD and operation at an elevated temperature both result in a film whose current becomes contact-limited over time even though it was bulk-limited initially. We find that crystallization of TPD in polystyrene proceeds spontaneously if the TPD-PS film is stored in air for a few days. This can be seen by comparing the topography image of Figure 13(a) to a topographic image acquired immediately after the film was cast, Figure 8(c). Crystallization of TPD from pure amorphous

(a) [nm] 60 40 20 0

William R. Silveira et al. (b)

(c) 1.0

0 E(x) [106 V/m]

818

0.5 0.0 −0.5

−4 −8 −12

0

4

8

0

4

8

FIGURE 13. A crystallized TPD-PS film in a two-terminal device with coplanar gold source and grain electrodes. (a) Topography, from intermittent contact-mode AFM. (b) Potential profile at Vsd = 2 V (closed circles), Vsd = −2 V (inset), and Vsd = 40 V (open circles). The potential profiles have been normalized for purposes of comparison. (c) Lateral electric field profile at Vsd = 40 V.

films [103–105] and solid solutions with polycarbonate [106,107] is well established. As TPD crystallizes out of polystyrene, the resistance of the TPD-PS/Au contact increases. The potential drops at the source and drain contacts are comparable at low voltage (Figure 13(b)) and remain symmetric when the applied voltage is reversed (Figure 13(b), inset). At high voltage, a slight potential drop is still evident at the injecting electrode. Nevertheless, the injecting contact has become “good” enough at high voltage to begin delivering space-charge, as evidenced by the nonconstant electric field profile inside the bulk of the film (Figure 13(c)). Qualitatively, the TPD-PS/Au contact in the TPD-crystallized device evolves from “bad” to “good” as the applied voltage is increased and the interfacial electric field rises. A second mechanism of contact degradation can be initiated by operating the device at an elevated temperature, T = 330 K. No topographic evidence of crystallization is evident at short times in vacuum at this temperature (data not shown). The current through the film again becomes contact-limited, but now the potential at low voltage is dropped asymmetrically, primarily at the right (injecting) electrode (Figure 14(a), (c)). Upon reversing the applied voltage, we expect the large potential drop to appear instead at the left electrode. This is not seen (Figure 14(a), inset), suggesting that the right-side electrode has been damaged. At high applied voltage, no potential drop is evident at the injecting electrode. In contrast to the previous case, the damaged electrode cannot supply the film’s space-charge limited current at high voltage, as evidenced by the comparatively constant electric field profile seen in the bulk of the device in Figure 14(b). In each of these two cases, the current evolves from being bulk-limited to being contact-limited. In the case of the crystallized sample, we do see evidence of spacecharge, and can therefore fit the current density observed at high voltage to Eq. (65) to extract µ0 (and β). Having estimated µ0 , we fit the current density at low voltage

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FIGURE 14. TPD-PS film after operating at T = 330 K. (a) Potential profile at Vsd = 2 V (closed circles), Vsd = −2 V (inset), and Vsd = 40 V (open circles). The potential profiles have again been normalized for purposes of comparison. (b) Lateral electric field profile at Vsd = 40 V. (c) Electric force microscope image. Note the “stripe” of shifted potential near the right (injecting) gold electrode.

to Eq. (63), accounting for the potential drop at the contacts, to obtain N0 . Table 4 compares µ0 and N0 before and after crystallization. We find that µ0 decreases upon crystallization, presumably because the mean distance required to hop between TPD molecules has increased. We find that the concentration of bulk intrinsic charge is not dramatically affected by crystallization. We can therefore conclude that the current has become contact-limited because ρ(0) has decreased and not because N0 has increased—the contact has degraded. Crystallization of TPD could either raise the injection barrier or decrease the density of states available for injection by, for example, reducing the energetic disorder present in the film. In the future, variable temperature measurements will allow us to distinguish between these two possibilities. Contact-limited behavior is seen also in the high-temperature case, but the mechanism must be quite different. The combination of increasing temperature and running current through the device causes irreversible damage which is confined primarily to the injecting electrode. It is plausible that the damage is due to a chemical reaction, which would presumably alter the injection barrier by creating interface dipoles, at least at high voltage where space-charge is concentrated at the injecting electrode. Alternatively, operating at elevated temperature could affect the injection barrier by facilitating rearrangement of interface dipoles already present. By making detailed measurements of contact resistance as a function of current and electric field is should be possible to distinguish between these two possible mechanisms. TABLE 4. Comparison of the zero-field hole mobility µ0 and the density of intrinsic carriers N0 before and after TPD crystallization N0 Before crystallization After crystallization

1 × 1021

1 × 1021

µ0 m−3

m−3

3.2 × 10−11 m2 /Vs 1.4 × 10−12 m2 /Vs

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Short lifetimes of organic light-emitting diodes is a major problem in organic electronics. Crystallization of pure TPD at room temperature has long been associated with a loss of electroluminescence efficiency in light emitting diodes [103,104]. At elevated temperatures (near the glass transition temperature in neat TPD films), the loss of luminescence efficiency has been correlated with increased roughness, again suggesting crystallization, which was assumed to cause poor injection [105]. In this section we have used electric force microscopy to show that crystallization and elevated temperature lead to two distinct types of failure. Crystallization leads to both a decreased bulk mobility and a poor contact at both electrodes while elevated temperature leads to asymmetric damage at the injecting electrode.

4.4 Charge Trapping in Pentacene Besides the molecularly doped polymer systems discussed in the previous section, small molecules constitute another broad class of organic materials used in devices. Pentacene, one of the highest mobility small molecule organics, forms a polycrystalline thin-film when thermally deposited. The comparatively high mobility of pentacene and its ability to be deposited on flexible substrates at low temperature [108,109] make it an attractive alternative to amorphous silicon in lowcost large-area electronics applications. However, polycrystalline pentacene films exhibit a number of problematic behaviors usually attributed to charge traps. For example, threshold voltage shifts have been explained as due to a slow structural change in the film which creates deep localized states near the interface [110]. The dependence of the mobility on gate voltage, [18,108,110–113], temperature [110], and degree of unintentional doping [112] is usually modeled in terms of the filling of traps. The traps may [112–114] or may not [108,110,111] be explicitly associated with grain boundaries, depending on the model. The presumed increase in charge traps at smaller pentacene grains near the electrodes has been used to rationalize the apparently lower mobility in bottom contact devices [18]. Here we use electric force microscopy to directly observe and image trapped charge in a pentacene thin-film transistor. The trapped charge is found to be inhomogeneously distributed throughout the pentacene film and not confined to the grain boundaries, as is generally assumed. Previous EFM studies on pentacene focused on understanding contact resistance by mapping the local potential of an operating thin-film transistor. The quality of the contact was studied by comparing top versus bottom contacts [63] and by comparing different electrode metals [61]. By contrast, we are using EFM to study charge trapping microscopically in the bulk, far away from the contacts. Bottom-contact pentacene transistors were fabricated with source and drain electrodes recessed into the gate oxide (Figure 15(a)). Device substrates were fabricated beginning with a heavily p-doped Si wafer (0.001–0.003
cm; 100 orientation). A 325-nm-thick thermal oxide was grown as a gate dielectric. Source and drain electrodes were defined using standard optical photolithography. Prior to evaporating 5 nm of Cr and 70 nm of Au as the source and drain electrodes, shallow

III.10. High-Sensitivity Electric Force Microscopy

(b) 10nm

Vtip SiO2

325nm

ISD [mA]

(a)

821

++

n Si

VG

VSD [V]

FIGURE 15. Pentacene thin-film transistor. (a) Diagram of the device substrate (L = 6.5 µm and W = 20.1 cm). The blow-out shows the small height difference between the SiO2 and the electrodes. A metal coated cantilever used for the imaging is also shown. (b) Currentvoltage characteristics. Here VG ranges from 0 V to −50 V in 5 V steps.

trenches (60 nm) were etched in the SiO2 to recess the electrodes. Interpretation of electric force microscope images is simplified by having the electrodes at the same height as the oxide. The transistor current-voltage characteristics can be seen in Figure 15(b), with a threshold voltage of VT ≈ −10 V and a mobility, calculated in the saturation regime, of µsat = 2 × 10−6 m2 /Vs. These values are typical of a bottom contact device prepared by evaporative deposition onto an untreated SiO2 substrate [115]. The presence of trapped charge in the devices causes a change in the local contact potential. During electric force microscope experiments, the sample is at room temperature and in the dark. Because the response time of the cantilever amplitude is quite long in vacuum (seconds), we track the cantilever resonance frequency which responds instantaneously to changes in local contact potential according to Eq. (20). Recall that the cantilever frequency depends on the voltage applied to the cantilever, V , on the electrical potential difference between the tip and the sample, φ, and on C ′′ = ∂ 2 C/∂z 2 , the second derivative of the tip-sample capacitance with respect to the tip-sample separation z. We detect trapped charge by its effect on the electrical potential, according to Eq. (48). Trapped charge at the pentacene/SiO2 interface will shift the potential difference by an amount φtrap ≈

σd κǫ0

(68)

where σ is the planar charge trap density, d and κ are the thickness and dielectric constant of the SiO2 , respectively, and ǫ0 is the permittivity of free space. Traps are filled at the pentacene/SiO2 interface by grounding the source and drain electrodes and applying a negative voltage to the gate electrode, as sketched in the second energy level diagram of Figure 16(a). The threshold voltage is the gate voltage below which charge begins to accumulate at the pentacene/SiO2 interface, making the pentacene highly conductive. Above the threshold voltage, the pentacene behaves like an insulator. To observe

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(a) EC

VG

VG VT . When VG is negative and below the threshold voltage (VT ≈ −8 V), however, charge accumulates at the pentacene/SiO2 interface and shields the tip from the gate, resulting in φ ≈ 0. It is interesting to note that in Figure 16(b) we are measuring the transistor threshold voltage locally. Because of this shielding, φ is therefore insensitive to charge traps when VG < VT . Figure 17(a) shows a frequency image of pentacene taken with VG = 0 V, where no traps are present, and with VG = −50 V , where the trap concentration should be large. The images are virtually identical. The contrast seen in the images comes exclusively from topography-related variations C ′′ . For comparison, an atomic force microscope image of the sample is shown in Figure 17(b). Traps can however be imaged by following the approach suggested by Figure 16(a). After charging the traps by setting the gate voltage negative for 30 s, we return the gate voltage to zero before imaging. The free carriers quickly leave the channel, but the trapped charge remains in the device long enough to

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Topography

FIGURE 17. (a) EFM images of polycrystalline pentacene in a thin-film transistor at decreasing gate voltages, (b) topography of region used in (c), and (c) pentacene EFM images at decreasing charging voltages. The transistor length is 6.5 µm.

image with the electric force microscope. These charges are not in equilibrium and slowly leave the device. Images of the cantilever frequency as a function of the charging voltage Vcharging are shown in Figure 17(c). In contrast to Figure 17(a), a dramatic evolution in the frequency variation is observed in this series of images. The image contrast in Figure 17(c) arises predominantly from variations in contact potential, which we determine by measuring φ and C ′′ along a representative line in the transistor gap. Approximately 85% of the variation in  f is due to changes in contact potential. We can therefore treat C ′′ as constant and use Eq. (68) to calculate the local contact potential φ from the measured cantilever frequency. We attribute the variation in φ as due to long lived traps, since the observed variation in φ across the transistor gap is (1) less than 50 mV before the gate voltage is increased above the threshold voltage, (2) increases with Vcharging , and (3) disappears after approximately 24 hours. The central result of this case study is Figure 17(c). The trap distribution at higher charging voltages shows that the traps are clearly not homogeneously distributed in space; large variations in trap concentration are seen on a length scale of ≥300 nm. The trap density can be calculated quantitatively using Eq. (20) and Eq. (68), the known k, κ, d, and Vtip , and the measured  f , f 0 , and C ′′ . The mean trap density

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at Vcharging = −30 V is 1.6 × 1011 holes/cm2 , or about one hole per 2.5 × 103 pentacene molecules (assuming that the accumulation layer is one monolayer thick). Using an effective tip diameter of approximately 300 nm (the apparent EFM imaging resolution as estimated by the smallest feature seen in Figs. 17(b)), we calculate that we can detect the contact potential shift due to as few as ∼ 3 trapped holes underneath the cantilever tip. Our findings can be used to eliminate a number of proposed trap candidates. First, we note that trapping at grain boundaries near within the first few monolayers is not necessarily inconsistent with our data, since these grain boundaries do not necessarily correspond to the grain boundaries seen by AFM topography [63]. However, since the observed charge traps do not appear to follow the shape expected of grain boundaries, it is extremely unlikely that trapping occurs at grain boundaries in the first few monolayers. Future electric force microscope studies on transistors consisting of only a few monolayers will allow us to establish a direct connection, if it exists, between grain boundaries and charge traps. Previous studies by Knipp et al. have shown that roughness of a silicon nitride dielectric has an effect on the trap depth, which suggests that trap energies are influenced by perturbations in pentacene energetics arising from the dielectric [110]. This is unlikely to be the cause of trapping in our case because the length scale associated with the charge trap domains in Figure 17(c) is much larger than the length scales of either the pentacene topography of the SiO2 topography (data not shown). Establishing a direct connection between the local chemical structure at the pentacene/dielectric interface and charge trap energies will be difficult since no analytical tools exists to study a buried solid–solid interface. In conclusion, we find that charge traps in polycrystalline pentacene are distributed inhomogeneously but do not appear to be associated with grain boundaries. Charge traps are imaged directly using frequency-shift electric force microscopy which is quite general, requiring no assumptions about charge transport in either the bulk or at the contacts. The traps imaged in this experiment are those which fill quickly (20 min). The trap densities calculated in this experiment are comparable to those calculated by others [110], suggesting that we are indeed imaging a majority of the charge traps.

5 Conclusions In this chapter we have presented case studies showing how high-sensitivity electric force microscopy can be used to examine organic electronic devices. In these samples, we have used electric force microscopy to make the following observations: 1. Observe local variations in potential and capacitance. 2. Observe the transition from ohmic to space-charge limited current. 3. Follow the evolution of charge density at the organic/metal interface as a function of local electric field, by combining EFM data with current-voltage

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measurements. We thereby infer injection barriers, the degree of band bending, and the mechanism of band alignment at the interface. 4. Hint at contact degradation mechanisms. 5. Quantify and image long-lived charge traps. By describing our custom instrumentation and presenting the foundations of a rigorous theory for our electric force microscope measurements, we have emphasized in this chapter the quantitative aspects of electric force microscopy. We should also stress that that EFM measurements yield extremely informative qualitative information too. For example, before performing a detailed analysis, from the shape of the potential drop in our TPD-PS device we can infer that the contact is supplying a space-charge limited current to the film. Even before we had quantified the density of charge traps in polycrystalline pentacene, from the EFM image we could already conclude that long-lived traps are not isolated at the grain boundaries as widely supposed. Future studies of organic electronic materials would benefit greatly from a better theoretic understanding of electric force microscope measurements. The capacitance profiles of Figure 9 clearly evolve as space-charge is injected into the device. With a suitable theory, this local capacitance data could give additional important information about mobile charge density or perhaps the density of states. In organic electronic materials, we often make the distinction between mobile charge and trapped charge. In reality, charges hopping in energetically disordered materials encompass a broad distribution of timescales. Deriving the voltage-dependent cantilever resonance frequency is this general case is a challenge. In the theory section of this chapter we have attempted to derive rigorously the force and force gradient experienced by a cantilever in a EFM experiment, starting from a Helmholtz free energy. We have discovered cases in which the expressions widely used in EFM to estimate trapped charge are recovered only by approximation. This observation deserves further attention. This chapter has highlighted work done in our laboratory using a custom-built electric force microscope operating in vacuum. A commercial vacuum electric force microscope capable of carrying out many of these experiments has recently become available. Operating with the cantilever in vacuum is important because it increases sensitivity by 10–20-fold. Operating with the cantilever in vacuum is thus required if one wants to differentiate the potential to obtain the lateral electric field (observations 2 and 3) and to see potential variations smaller than k B T /e (observation 1). Electric force microscopy has exposed two features of charge injection that are hard to understand using available analytic theories. The first is that the activation energy for injection through a resistive contact is much smaller than expected from the Schottky barrier and the activation energy of the mobility [62]. The second is that the charge density at the metal/organic interface in a good contact rises much faster with electric field than expected [65]. Disagreement with theory is not unreasonable, since (most [102]) available analytic theories of injection neglect the correlated energetic disorder known to be present in molecularly doped

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polymers like TPD-PS and expected to be present in semiconducting polymers like polythiophene. Repeating our approach [65] to characterizing charge injection at a good contact as a function of temperature should help resolve these charge injection puzzles. Veres et al. have shown that, by working with a low dielectric constant gate material, it is possible to fabricate field-effect transistors even in low mobility materials like TPD-PS [97,98]. This is exciting because it means that the approach of B¨urgi et al. [62,66] can also be used to study injection in molecularly doped polymers where the mobility is well understood and energetic disorder has been characterized by time of flight transport measurements. Electric force microscopy has also provided the first direct images of long-lived traps in an organic electronic material [59,60]—information not accessible via a bulk measurement technique. These images have led us to question whether grain boundaries are the locus of long-lived charge traps in polycrystalline pentacene, as is widely assumed [60]. Further studies show promise for extracting a better understanding of the trapping spatial and energetic distributions. While these experiments relied on charge traps de-trapping on a timescale that was long compared to the image acquisition time, it should be possible to extend charge-trap studies to short lived traps by measuring the cantilever frequency versus time point by point. With suitably fast feedback electronics, small cantilever frequency shifts can be followed on a millisecond timescale. The expected large frequency shifts due to trapped charge may, however, make this experiment challenging. Following fast traps may require considerable creativity. Nevertheless, it should be possible to explore trap energetics and kinetics with single charge sensitivity [67] by working with monolayer pentacene transistors and by operating the tip at closer distances. In closing, let us emphasize that using electric force microscopy to view organic electronic materials has revealed new phenomena; two examples discussed here are non-grain-boundary charge trapping in pentacene and the large inhomogeneous contact potential observed in TPD-PS films. These two phenomena were completely unexpected; that they were observed in well-known materials makes them all the more surprising. Recent work therefore suggests that EFM will continue to generate new qualitative and quantitative insights into the workings of organic electronic materials and devices.

Acknowledgments. We would like to thank Andronique Ioannidis, Martin Abkowitz, George Malliaras, and particularly J. Campbell Scott for useful discussions. We thank Showey Yazdanian for a careful reading of the manuscript. W.R.S. gratefully acknowledges an American Chemical Society summer fellowship funded by the Eastman Chemical Company. This work was supported by the National Science Foundation (Career Award DMR-0134956), the National Institutes of Health (Grant 1R01GM070012-01), and Cornell University. Additional support was provided by the Cornell Center for Nanoscale Systems, which is funded by the Nanoscale Science and Engineering Initiative of the National

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Science Foundation (EEC-0117770) and the New York State Office of Science, Technology and Academic Research under (NYSTAR Contract C020071). A portion of this work was conducted using the facilities of the Cornell Center for Materials Research (CCMR), with support from the National Science Foundation Materials Research Science and Engineering Centers (MRSEC) program (DMR-0079992), and the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation under grant ECS 03-35765.

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IV Electrical Nanofabrication

IV.1 Electrical SPM-Based Nanofabrication Techniques NICOLA NAUJOKS, PATRICK MESQUIDA, AND ANDREAS STEMMER

Scanning probe microscopes (SPM) have been envisaged and applied from the beginning as tools both to image surfaces with unprecedented resolution and to interact with surfaces like an extension of the operator’s fingertips. The prototype for electrical SPM certainly was the scanning tunneling microscope (STM). For the purpose of this chapter we do not consider mechanical nano-machining, i.e., scratching with the tunneling-tip, as a form of electrical SPM, despite the mechanical contact between tip and specimen surface being induced by low tunneling voltages and high current set-points. Applying a voltage of a few 10 V to the tip, McCord and Pease [1] succeeded in writing lines of contamination on bare silicon that protected the substrate during the subsequent etch. Line widths below 50 nm were achieved. Contamination lines were already observed before on metallic glass [2]. Later, Okawa and Aono [3] were able to induce the formation of polymeric nanowires on a graphite substrate covered by a monolayer of a diacetylene compound by applying voltage pulses to the STM tip. Positioning single xenon atoms on a nickel (110) surface at cryogenic temperatures, as demonstrated by Eigler [4], or removing a single atom from a MoS2 crystal to create, according to the Guinness World Records book, the smallest hole in the world, as shown by Heckl, mark the ultimate forms of nanofabrication possible with the STM. So far, however, most application- or device-directed nanofabrication by SPM takes place on a scale of molecules to several dozen nanometers. Electrochemical patterning constitutes a particularly important class of electrical SPM-based nanofabrication techniques (for a recent overview see, e.g., [5]). Starting from localized electrochemistry using an STM tip operated in tunneling or field emission mode, the concept was later transferred to atomic force microscopy (AFM) and subsequently expanded to electrochemical dip-pen lithography. AFMbased techniques offer the clear advantage over STM-based ones that an interaction mechanism independent of the nanofabrication process can be used for controlling the proximity of the probe. This feature is particularly useful for patterning semiconductor materials, for example, to confine electrons to quantum structures that are drawn via local oxidation ([6] and references therein). Conductive AFM probes also find application in structuring conductive polymers via voltage pulses [7]. Similarly, conductive AFM probes allow one to write and trap electric charges 833

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into oxide and polymer layers that may serve as bits for data storage [8] or aid in xerography-like nanofabrication [9]. SPM-based nanolithography is inherently slow. Feedback circuits employing modern model-based control methods allow one to increase the maximum scan speed significantly compared with conventional proportional-integral controllers [10]. Probe arrays that are individually addressable like the “millipede” [11] allow for higher throughput due to parallel processing, albeit at the cost of a much more complex feedback system if each probe needs to be controlled individually. Speedwise, even large probe arrays cannot compete with masks or stamps [12]. However, many of the currently available SPM-based nanofabrication techniques are still at an explorative stage where speed is not so critical yet. Furthermore, the decisive advantage of SPM-based techniques is the possibility to observe and process with the same probe, therefore providing an ideal tool for site-directed nanofabrication. In the following chapters we focus on SPM-based nanostructuring-techniques relying on electrochemical reactions taking place in a solution bath or being confined to a liquid capillary between probe and specimen (section 1), charge-writing into polymer and oxide electret layers (section 2), and on the electrostatically driven, parallel deposition of nanoparticles and molecules onto such charge patterns (section 3). SPM-based oxidation, nanofabrication on silicon in UHV, as well as patterning of ferroelectrics and self-assembled monolayers are covered separately in this volume.

1 Electrochemically Induced Surface Modifications 1.1 Material Deposition via Electrochemical Processes Many SPM-based fabrication processes occur at the solid–liquid interface, where local electrochemical synthesis leads to spatially confined material deposition on a solid substrate. Reactions either occur in a liquid electrolyte, or in a water meniscus that evolves while working in air and serves as a nanoelectrochemical cell when a bias is applied between a conductive SPM tip and the substrate. Controlled deposition of material has been achieved with various kinds of setups: AFM, (electrochemical) STM, and with scanning electrochemical microscope (SECM). Experiments conducted with an SECM applying an ultramicroelectrode (UME) will be presented in a separate section. 1.1.1 AFM/STM-Guided Processes Although most workers have concentrated on depositing metallic nanostructures [13–20], considerable effort has been put into fabricating structures of conductive polymers [21–24] and magnetic dots [25,26]. Penner et al. were among the first to deposit metal clusters onto graphite, where bias-induced pits in the graphite served as nucleation sites [27]. Other prominent examples include the deposition of silver structures in Nafion films [15], and the local deposition of copper either by transferring the metal from an STM tip to a gold substrate by mechanical

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FIGURE 1. AFM contactmode deflection images of electrochemically induced Ag nano-features on RbAg4 I5 . Positive (a,c) and negative (b) features generated by 200 mV. Reprinted with permission from [28]. Copyright 2004, American Institute of Physics.

contact in a “jump-to-contact” manner [13], or by first inducing surface defects in the passivation layer of an immersed copper electrode with an AFM tip [14]. By applying ultrashort voltage pulses (10 to 1000 ns), Kirchner et al. achieved a significant increase in resolution in electrochemical STM-based nanostructuring [19]. Nanosecond voltage pulses cause the electrochemical reactions to be confined to the tunneling region. Recently, Lee et al. [28] presented a method for solid-state electrochemical patterning on a solid ionic conductor: Ag patterns are generated locally on the surface of the ionic conductor, by applying a short voltage bias between a silver coated AFM tip and an Ag counter electrode at the backside of the ion conductor. Silver ions, produced by Ag oxidation, then migrate through the conductor. Figure 1 shows positive and negative features fabricated in ambient conditions. The authors attribute the formation of negative features like those shown in Figure 1(b) to mechanical knock-off that occurs while scanning already deposited Ag clusters. Not only the deposition of pure metallic nanostructures, but also the local formation of several alloys was shown to be feasible with an electrochemical STM [20]. Localized alloy formation was achieved by scanning an STM tip very closely above a substrate, which was covered by an underpotentially deposited (UPD) metal adlayer. Figure 2 shows an example of a Cu nanostructure formed on a Au(111) surface immersed in a Cu2+ electrolyte. Working at a potential where the UPD layer was completed, both the surface of the electrode as well as the STM tip were covered with a monolayer of copper. Alloy formation is assumed to be induced by atomic place exchange, in particular due to the incorporation of UPD atoms into the substrate surface. As mentioned above, a considerable amount of research concentrates on investigating the fabrication of patterns of conductive polymers by SPM. One of the earlier examples is the work of Yang et al. who used an electrochemical STM to deposit polypyrrole onto gold from a monomer containing solution [23]. They achieved an excellent resolution and reproducibility, and showed that, by applying an opposite potential, the structures could be removed. A recent approach dealing with the deposition of conducting polymers is based on a completely different principle. Namely, electrochemical oxidative nanolithography is used to locally

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FIGURE 2. Tip-induced nanostructuring of Au(111) in 0.05 M H2 SO4 + 4 × 10−4 M CuSO4 . Manufacturing conditions: E s = +10 mV vs. Cu/Cu2+ , Ubias = 1.5 mV, It = 60 nA, scan rate = 8 Hz, scanned area 160 × 10 nm. Imaging conditions: E s = +10 mV vs. Cu/Cu2+ , Ubias : 20 mV, It = 1 nA. Scale bar: 50 nm. Reprinted with permission from [20]. Copyright 2003, Elsevier.

convert an insulating precursor polymer on a solid substrate into a conductive polymer via solid-state oxidative cross-linking [24]. Figure 3 shows conductive polymer lines fabricated in solution by applying voltage to a conductive AFM tip, resulting in a conductive polymer pattern embedded in an insulating background. Patterning can be conducted at remarkably high writing speeds reaching up to a few µm/s, and is widely substrate independent. 1.1.2 SECM-Based Deposition SECM-based fabrication relies on a UME that is scanning over a surface, thereby creating electrochemical reaction products that diffuse toward the surface and induce local reactions like material deposition or etching. For a detailed review on SECM and its applications in nanopatterning, the reader is referred to Ref. [29].

FIGURE 3. Height (a) and phase (b) image of conductive polymer nanolines written at 15 µm/s (1) and 10 µm/s (2) via tapping mode writing. Performed in 0.1 M TBAP/PC at 1.4 V (vs. SHE) using Au-coated SiN4 AFM tips. Reprinted with permission from [24]. Copyright 2004, The American Chemical Society.

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FIGURE 4. A 350-µm long silver strip on a gold covered substrate. A 10-µm platinum tip electrode was moved along a line at a speed of 1 µm/s and a distance of 15 µm. Tip potential: +1,484 mV vs. NHE, sample potential +410 mV. The width is found to be 10 µm, the same as the active tip diameter. Reprinted with permission from [30]. Copyright 1999, The Electrochemical Society, Inc.

Here, we will discuss fabrication methods that are based on the so-called feedback mode, where a mediator shuttles between the UME and the substrate inducing the desired reaction. The lateral resolution typically is in the range of µm (>10 µm), due to the structure size’s being mainly determined by the size of the UME, its distance to the substrate surface, and, furthermore, by the diffusion lengths of the reactive species. To date, research has been primarily concentrated on the deposition of metals [30,31] and polymers [32–34]; though there have been efforts to deposit magnetic structures, like cobalt onto gold [35] or to investigate writing-reading-erasing processes on tungsten oxide [36], to name a few examples. Borgwarth et al. reported on increasing the resolution by a process called the chemical lens, which results in structure sizes even below half the UME diameter [30]. To this end, a scavenger is introduced into the electrolyte solution to react with the tip-generated species, stopping the reaction in the outer part of the diffusion field. Figure 4 shows a resulting silver line deposited on gold. The silver ions in solution were complexed by ammonia, avoiding initial deposition of silver on the substrate. In proximity of the tip, the complex formation equilibrium is shifted to a higher concentration of free silver ion. The ammonia also acts as the scavenger by recomplexing excess ions. One example of polyaniline deposition from a monomer solution onto a gold substrate is shown in Figure 5 [33]. Deposition was achieved on gold and platinum, as well as on carbon surfaces, and is driven by a microreagent mode, in which a local increase in pH at the tip induces the reaction. Another method of local polymerization was developed by Borgwarth et al. [32]: Thiophene monomer is polymerized onto an oxidizing manganese dioxide surface. Tip-generated protons locally activate the surface, inducing the oxidation process to produce polythiophene from its monomer (Figure 6).

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FIGURE 5. (a) A light microscope image of a polyaniline pattern deposited on a Au substrate using a 10-µm Pt tip electrode. (b) is a magnification of part of (a). Deposition conditions: substrate potential is 600 mV; tip potential is –1,400 mV; tip-substrate separation is about 1 µm; and the tip scan speed is 0.5 µm/s. Reprinted with permission from [33]. Copyright 1997, The Electrochemical Society, Inc.

1.1.3 Electrochemical Dip-Pen Nanolithography A further approach to transporting material to defined locations on a sample surface in a direct-write manner relies on using an AFM tip as a dip-pen—so-called electrochemical dip-pen nanolithography (E-DPN). The ink is transported to the substrate via a water meniscus evolving while working in air. Unlike the conventional DPN processes, in E-DPN the water meniscus is also used as a nano-electrochemical cell in which the redox-active species, the “ink,” is electrochemically activated by a bias potential applied to the tip, and deposited on the surface. Li et al. reported on the first application of this method [37]. Platinum lines have been drawn on silicon via a reduction of the corresponding metal salt in the meniscus at the AFM tip. E-DPN was soon been extended to write organic structures, especially conductive polymers. Maynor et al. fabricated polythiophene nanostructures on semiconducting and insulating surfaces by in situ oxidative polymerization of the monomer [38]. The monomer has been delivered to the water meniscus by first coating it onto the AFM tip. Agarwal et al. achieved local immobilization of histidine-modified proteins on metallic nickel surfaces by E-DPN utilizing the natural nickel-histidine bond [39]. The process is based on local electrochemical ionization of the nickel surface by applying a negative bias to the AFM tip. Histidine-tagged molecules are delivered through the water meniscus and attach to the ionized nickel (Figure 7 (a)).

FIGURE 6. Polytiophene on manganese dioxide. Tip = 10 µm Pt. Galvanostatic process, I = 20 nA; scan rate = 0.8 µm/s at a distance of 8 µm from the surface; pattern width 20 µm. Reprinted with permission from [32]. Copyright 2001, The American Chemical Society.

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FIGURE 7. (a) A thin array of globules of TlpA-8, a truncated mutant of TlpA, deposited on nickel via E-DPN. Reprinted with permission from [39]. Copyright 2003, The American Chemical Society. (b) AFM image of a GaN nanodevice that was modified in situ using E-DPN. The first modification (upper right) was performed at 10 V, 40% humidity, 50 s dwell time. The second modification (lower left) was performed at 10 V, 40% humidity, 30 s dwell time. Reprinted with permission from [40]. Copyright 2004, The American Chemical Society.

Besides the ability to write metallic or organic nanowires, a recent publication from Maynor et al. shows the possibility o using E-DPN for the fabrication of nanoscale hereostructures [40]. Figure 7(b) shows a GaN nanowire which has been locally changed into a gallium oxide heterostructure.

1.2 Local Surface Etching All SPM devices described above not only have found applications in local material deposition, but have also proven useful for material dissolution, especially as a tool for a one-step etching process in nanofabrication, rendering standard lithography and masks unnecessary. Soon after observing semiconductor surfaces to be modified while recording STM images in liquid environments, Nagahara et al. published a technique for controlled semiconductor etching under diluted HF solutions [41]. Feature formation was attributed to a field-induced oxide growth followed by chemical etching of the oxide. Since then, localized etching in liquids by SPM techniques has been studied for a variety of materials, ranging from local dissolution of metals [19,42–47] and semiconductors [41,48–50], to the structuring of graphite [51]. As an example, Chen et al. reported on the local corrosion of Al in a contact mode-AFM setup, and proposed the selective etching to be induced by dissipated energy from tip-sample frictional forces [46]. A systematic study on spatially confined copper dissolution by an STM tip has been presented by Kolb and coworkers [42]. They fabricated lines through repeated scanning at a positive tip potential (Figure 8). Transfer of electrons from the Cu directly into empty states of the tip was suggested as reaction mechanism for the local dissolution.

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(b) (c)

A

A

B

z/nm

30

B

20 10 0

0

100

200

y/nm

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FIGURE 8. (a) STM image of a Cu(111) surface in a Cu2+ containing sulfuric acid solution. (b) Same area as in image (a), but after the tip had been repetitively scanned in the xdirection over 100 nm for 1 min with IT = 2 nA at E tip = + 20 mV vs. Cu/Cu2+ and E sample = −60 mV (A) or −30 mV (B). Scale bars: 100 nm. (c) Cross section along the vertical line shown in (b). Reprinted with permission from [42]. Copyright 2000, Elsevier.

Local dissolution of metals and silicon has also been conducted by means of SECM-based methods [48,50]. Figure 9(a) shows an example of an etched pattern in silicon [48]. Etching has been accomplished by locally electrogenerating a strong oxidant, bromine, at an UME, which was scanning over the silicon wafer in close proximity. The formation of holes on surfaces using an SPM not only has been studied in UHV or liquids, but also in different gas atmospheres that served as chemical reaction environment. For instance, Lebreton et al. studied the STM-induced

FIGURE 9. (a) “HU” microwriting etching patterns obtained as a result of scanning (0.1 µm/s) a 10 µm Pt microelectrode across an n-type Si(111) wafer in a solution consisting of 5 mmol/L HBr, 1 mol/L H2 SO4 , and 1 mol/L HF. Reprinted with permission from [48]. Copyright 1995, The Royal Society of Chemistry. (b) On an atomically flat gold surface, the legend “NANO” is written by applying successive voltage pulses across the tunneling gap. The letters are about 30 nm tall and 25 nm wide and are made up of lines of 5 nm width and 0.24 nm depth. In average each letter represents 5,000 missing gold atoms. Reprinted with permission from [47]. Copyright 1998, Springer-Verlag GmbH. (See also Plate 12 in the Color Plate Section.)

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formation of nanoholes on gold surfaces in different atmospheres [47], where water or ethanol vapor, together with positive bias applied to the sample, lead to hole formation (Figure 9 (b)). The hole formation is suggested to be induced by bias-induced anodic oxidation of the gold surface occurring in the adsorbed liquid layer and following place exchange mechanisms.

1.3 Electrically Assisted Local Modification of Surfaces Considerable effort has been made in extending the field of SPM-based fabrication techniques to field emission lithography, where a low-energy electron beam, emitted from a conductive tip, induces local surface modifications. First experiments in this direction concentrated on writing patterns into “classical” polymeric resists on silicon substrates. In an early work, Majumdar et al. demonstrated the modification of PMMA films with a conductive AFM tip [52], resulting in negative as well as positive resist patterning. The use of the AFM instead of the STM provides the possibility of imaging the surface without any chemical modifications during scanning. Other examples of classical resist structuring include AFM-based patterning using siloxene, commonly known as spin-on glass [53], or STM-based lithography on a conductive layer on top of a resist [54]. Juhl et al. presented a different nanolithography approach [55]. By means of a process called z-lift electrostatic lithography, nanoscale features are created on a polystyrene film by applying a voltage pulse between tip and substrate, and, at the same time, controlling the height of the cantilever (Figure 10). Local polymer reshaping is proposed to occur due to local Joule heating between the conductive AFM tip and the substrate, followed by electrostatic attraction of the softened polymer to the tip. Since the features proved to be erasable, chemical modification of the polymer during feature formation is not likely to occur. Another method of local polymer modification was developed by Aono et al., who used a biased STM tip to induce and guide chain polymerization, resulting in polydiacetylene nanowires [3]. Figure 11 shows the process of creating three

FIGURE 10. AFM image of an array of dots patterned on a 25-nm-thick 110 k Mw PS film where the initial voltage ramp is held constant at 0.025 s, every row denotes a voltage increase (−25 to −30), and every column denotes an increase in the z-lift value (−30, −20, 0, +20, +40, +60, +80, +100, +200, and +300). Reprinted with permission from [55]. Copyright 2004, American Institute of Physics.

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FIGURE 11. Scanning tunneling microscope (STM) images and diagrams showing the process of controlling the initiation and termination of linear chain polymerization with an STM tip. STM images were obtained in air at room temperature in constant-current mode. Reprinted with permission from [3]. Copyright 2001, Nature Publishing Group. (See also Plate 13 in the Color Plate Section.)

nanowires on graphite. Before initiating the polymerization, artificial defects are created in the molecular layer. The subsequently induced chain polymerization terminates at these defects. Recently, Li et al. presented a method to create nano-sized patterns in perovskite manganite thin films [56] using an ambient AFM, suggesting applications such as the fabrication of spintronic nano-devices. The patterns, obtained under negative sample bias, exhibited different mechanical, electrical, and, possibly, magnetic properties compared to unpatterned regions, while the extraordinary physical properties remained unchanged. These patterns can also be transferred into grooves by wet etching due to the high etching selectivity (Figure 12). Conductive-probe AFM has also been implemented for local solid-state modifications of molecular conductive materials [57]. Nanometer-scale insulating regions were created on conducting single crystals via locally confined electrochemical reactions, occurring in the nanocell and comprising by the water meniscus between tip and sample. FIGURE 12. Topography of a patterned La0.8 Ba0.2 MnO3 surface (with a Pt-coated tip under a sample bias of −10 V) before (a) and after (b) wet etching. Reprinted with permission from [56]. Copyright 2005, IOP.

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FIGURE 13. Charge-writing process: A voltage UCW is applied between a conductive SPM tip and a back-electrode while the tip is in mechanical contact with the sample (left). The sample consists of a thin, dielectric layer (electret) on top of the back-electrode. Positive or negative charges are transferred by a small current ICW into the dielectric film depending on sign and magnitude of UCW . Geometrically defined charge patterns can be written using the lateral scan function of the SPM. The charge patterns are detected in non-contact mode at lift-height h by recording electrostatic forces F between tip and sample (right). A detection voltage UD is applied to the tip in electric force mode.

2 Scanning Probe Microscopy-Based Charge Writing Shortly after the invention of scanning probe microscopy (SPM) in the 1980s, it was utilized to perform charge-writing (SPM-CW) on the nanometer scale on dielectric materials. With this method, positive (holes) or negative (electrons) charges are injected into or deposited on the surface of a dielectric by applying a bias voltage to a conductive SPM tip in close proximity or contact with the sample. Charge carriers are trapped in the sample and kept spatially localized for a certain time. The general principle is shown in Figure 13. One of the main motivations for performing SPM-CW was the potential applicability to high-density data storage using charge “dots” as data bits. Encoding digital information in electrostatic instead of magnetic form seemed promising due to the small size of the charge patterns. On poly(methyl methacrylate) (PMMA), for example, 70-nm-diameter charge dots could be created [58]. There is no a priori physical restriction of the size of the charge patterns. This is different from magnetic recording-techniques, where the finite size of magnetic domains or the superparamagnetic effect limit the resolution. In principle, the smallest charge pattern would be generated by a single elementary charge at a fixed position. However, factors such as diffusion and recombination of charge carriers leading to decay of the charge patterns limit the applicability of this approach. A newer application, which has been increasingly reported in the literature in the last five to six years, is the use of nanoscale charge patterns as local attachment sites for nanoparticles or molecules [59–68]. Because of the analogy to the workingprinciple of photocopiers and laser printers, it is often referred to by the term microor nano-xerography. This application of SPM-CW is described in more detail in the next chapter.

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2.1 Methodical Aspects SPM-CW has to be performed with materials that can trap charges for a sufficiently long time, that is electrets. Electrets are dielectric materials, which exhibit a quasi-permanent, electric charge, for at least the time of the experiment [69]. This very general definition includes “real”-charge electrets, in which surface or space charges occupy trapping-sites, as well as piezo- or ferroelectric materials, although in practice the latter often are not referred to as electrets but are considered separately. In general, dielectrics are characterized by a large bandgap of more than 4 eV, which leads to a very small conductivity at ambient temperature [69]. In the case of electrets, defects in the crystalline structure such as impurities or interfaces offer trapping-sites for holes or electrons within the bandgap [69]. In this chapter we will only discuss real-charge electrets. As the tips must be conductive, full-metal, metal-coated, or highly doped semiconductor tips are used for SPM-CW. Examples are etched STM tips made of W- or Ni-wires or metal-coated (Au, Pt, PtIr, TiPt, Co) AFM tips. Doped Si tips with a resistivity of the order of 0.001
·cm are sometimes considered better than metal-coated tips because the latter can show abrasion of the metal layer during SPM-CW. An additional metal-coating also increases the tip radius. Besides pure charge transfer and trapping, unwanted effects may occur, which are often difficult to control and separate from the charge-writing process. For example, material can be transferred between tip and sample due to the current and topographic or chemical modifications can be induced when applying a voltage, as discussed in section 1. In an ideal case, the process consists exclusively of the creation of net surface or space charge areas of the sample. SPM-CW has been applied to thin-film electrets of a thickness ranging from a few nanometers to several hundred micrometers. Typical materials are polymer layers or oxides. If the tip is in direct mechanical contact with the surface, true contact-charging occurs, whereas a corona discharge can occur if the tip is held at some distance (several 100 nm) from the surface. Because of this short distance between tip and surface or back-electrode the electric field is often very high even at low bias voltage and the breakdown field strength of the electret can easily be reached. The quantity of charge transferred does not only depend on the material properties of the electret, i.e., the number, location, and energy levels of the trapping sites, but also on parameters such as the applied voltage, its polarity, the film thickness, the pretreatment of the electret, etc. SPM-CW has the advantage that in situ studies can be carried out conveniently by performing the charge injection and the subsequent charge pattern-imaging using the same tip and instrument. Electric force microscopy and its variants such as Kelvin-probe force microscopy (KFM) are used to image and quantify the charge patterns [70,71]. An important, common characteristic of these methods is that the spatial, electrical resolution is considerably lower than the topographical one. This is due to the long-range of electrostatic forces and the large interaction area caused by the finite geometry of the tip [72]. In practice, the best resolution with standard SPM-tips is in the range of 50–100 nm. STM-based imaging methods,

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which record currents instead of electrostatic forces, achieve a higher resolution but STM is difficult to perform on insulating surfaces and the interpretation of the data is not straightforward [73].

2.2 Polymeric Materials Polymers were among the first materials investigated by SPM-CW, mainly because they are known to exhibit very good charge storage properties [69] and because thin-films can easily be produced by spin-coating or gas phase deposition methods. The first example was PMMA, which is commonly used as resist in electron beam lithography and which can be spin-coated to form very thin ( εs the particles are attracted toward the increasing field and vice versa.

an electric field, E (Figure 16). Firstly, the Coulomb force FCoul = q E

(1)

which acts on a particle carrying a net charge, q, being attracted by an oppositely charged (or repelled from an equally charged) surface. Secondly, the dielectric force π ε p − εs FDiel = d 3 ε 0 εs ∇ E 2 (2) 4 ε p + εs

which acts on a particle of diameter d, if the electric field in the vicinity of the charge pattern is inhomogeneous, ∇ E 2 = 0, and if the dielectric constants of particle, εp , and solvent, εs , are different (ε0 is the vacuum dielectric constant) [101]. Both interactions usually occur simultaneously and the resulting attraction or repulsion depends on the relative magnitudes of these two contributions. Charging of dispersed particles is caused by different processes, such as selective adsorption of ions on the particle surface, ionization and deprotonation of surface groups, or transfer of electrons between particle and solvent, i.e., frictioncharging. In aqueous solvents, the first two processes are usually dominant and the properties of aqueous colloidal solutions can be described by the DerjaguinLandau-Verwey-Overbeek (DLVO) theory. Particle-charging in nonpolar solvents, such as perfluorinated oils, is less understood and the DLVO theory is difficult to apply [102]. However, the rule of Coehn describes the charging of dielectrics and states that a dielectric material with a high dielectric constant is charged positively when brought into contact with a dielectric material of a low dielectric constant, which in turn is charged negatively [103]. Under this assumption, e.g., silica particles suspended in FC77 are positively charged because ε Si O2 = 3.7 > ε FC77 = 1.86. Micrometer-sized particles are often available as dry powders, whereas smaller nanoparticles are usually suspended in liquids and biomolecules are dissolved in aqueous buffer solutions. For dispersion of the various particles/molecules in FC77, two different methods are used. Powder particles (>1 µm) are

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FIGURE 17. Wet-dispersion: An aqueous suspension of colloidal nanoparticles or molecules is added to a water-immiscible oil. Ultrasonication provides the energy to increase the water-oil interface and creates an emulsion of small water droplets, which contain the solid phase, in the nonpolar oil. The water droplets are attracted electrostatically to the immersed, electrified sample and deliver the solid phase to the surface.

dry-dispersed directly into the non-polar liquid by ultrasonication (US). Smaller particles/molecules available as aqueous suspension/solution are wet-dispersed by adding the suspension/solution to FC77 at a volume-to-volume ratio of typically 1–100 µl solution with a few ml FC77 and applying ultrasound (US) for a few seconds. This results in a water-in-oil emulsion, where the water droplets contain the solid phase or the molecules (Figure 17). Both methods do not generate thermodynamically stable dispersions, however, this is not necessary for particle attachment to charge patterns as the process usually takes place within a few minutes. In both, the dry- and wet-dispersion case, a net charge of the particles/droplets can occur, which may be explained by friction-charging or clustering and orientation of ions at the interface between the dispersed phase and the solvent [103,104].

3.2 Results and Discussion Particle attachment by SPM-CW has first been demonstrated with wet-dispersed, 290-nm-diameter silica beads on charge patterns written on a thin FC-film [62]. The beads attached only to negative charge patterns whereas positively charged areas remained nearly free of particles, which indicates a dominant Coulomb-attraction between positively charged water droplets containing the beads and the negative pattern (Figure 18(c)). With wet-dispersed 50-nm-diameter silica beads, a lateral deposition accuracy of about 1 µm could be achieved using the same procedure [62]. The method was later extended to metal particles and biomolecules. Wetdispersed commercial Au nanoparticles of 20 nm diameter were attached to charge patterns with a lateral accuracy of ca. 500 nm (Figure 18(d)) [59]. Ultrasonicating a solution of the fluorescently labeled protein avidin into FC77 was used to produce patterns of avidin on FC-films demonstrating the versatility and the wide applicability of the method [60]. In both cases the suspended material only attached to negative patterns. Specific biomolecular recognition, an important prerequisite for the development of biosensor-arrays, was demonstrated using the avidin-biotin interaction

Au: “Solution” correct? Au: “Ultraround” correct.

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(d)

FIGURE 18. (a–c) Silica particle attachment: negative (a) and positive (b) charge pattern on a FC-film; 290-nm-diameter wet-dispersed silica beads are attached to the negative charge pattern (c); (a) and (b) are images of the surface potential prior to immersion of the sample; (c) is an optical microscopy image after attachment; scale bars: 10 µm. Reprinted with permission from [62]. Copyright 2001, John Wiley and Sons Ltd. (d) Au particle attachment: Wet-dispersed 20-nm-diameter Au nanoparticles attached on negative charge lines on a FC film. AFM topography image; scale bar: 5 µm. Reprinted with permission from [59]. Copyright 2002, Elsevier.

[61]. A solution of biotin-modified anti-mouse immunoglobulin G (IgG) was emulsified into FC77 and a charge-patterned 150-nm-thick PMMA-electret was exposed to the emulsion resulting in selective attachment of biotin-IgG on positive charge patterns. After rinsing and drying, the sample was re-immersed into an aqueous solution of fluorescently labeled avidin, which selectively attached to the predeposited biotin-IgG patterns. Fluorescence microscopy confirms the specificity of the avidin attachment (Figure 19). The attraction of particles and/or droplets to the charge patterns is characterized by a delicate balance of dielectric and Coulomb forces, which depend on the nature of the particles, the solvent, the electret material and the geometry of the charge pattern. The influence of different electrets has been demonstrated by comparing the attachment of wet-dispersed nanoparticles on charge-patterned FCand PMMA-films [63]. On FC-films the particles attached selectively on negative charge patterns whereas positive charge patterns repelled the water droplets containing the particles, indicating a predominant Coulomb-type interaction, FCoul . However, on PMMA-films the same particles attached on patterns of both polarities and showed an enhanced decoration of the edges of large patterns, which indicates a predominant dielectric-type interaction, FDiel . The difference between the two

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FIGURE 19. Specific avidin attachment: Fluorescently labeled avidin selectively attached to a previously deposited pattern of biotin-IgG. Optical microscopy image. Scale bars: 20 µm. Reprinted with permission from [61]. Copyright 2004, Elsevier.

electrets may be explained by a positive background surface charge of PMMA in contact with the FC77-solvent, which results in a shift of the force balance to the dielectric contribution [63]. Similar electrostatically driven attachment of colloidal particles using non-SPMbased methods for creating the charge patterns has been performed by several other groups in recent years. Fudouzi and coworkers deposited micrometer-sized silica particles from a fluorocarbon solvent to charge patterns created by electronand ion-beam-drawing in ceramic substrates [64,65]. As early as 1976, Feder ha reported the attachment of carbon-black particles to electron-beam-charged patterns in TeflonTM -foils with a resolution of about 20 µm [105]. Jacobs and Whitesides created charge patterns in PMMA with ca. 150-nm resolution using metal-coated silicone-stamps and attached metal or dielectric particles of different sizes to the patterns [12]. Using 80-nm-diameter carbon particles suspended in a fluorocarbon liquid a positional accuracy of about 800 nm of the attached particles was reported [66]. Silver nanoparticles were attached by the same process resulting in a spatial accuracy of about 500 nm [67]. Nanoparticles could also be attached directly after creation from the gas phase [68]. Conductive stamps have the advantage of allowing the parallel fabrication of an extended and complex charge pattern in one step. Serial methods, on the other hand, are necessary if different particles have to be attached at different locations, e.g., for biosensor-arrays. Using emulsified water droplets as transporters is attractive because, in principle, any kind of water-soluble solid particle or macromolecule can thereby be attached to charge patterns, which makes the method very flexible and widely applicable. Furthermore, a wide variety of different electret materials can be used for SPM-CW, as seen in the previous chapter. Anchoring and positioning biomolecules such as, e.g., proteins or oligonucleotides on a surface could be used for the fabrication of biosensors, whereas nanoparticles are generally considered as building-blocks for future (quantum-based) nanodevices. Positional control adds an important, additional degree of freedom in designing and developing such devices.

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73. S. P. Wilks, T. G. G. Maffeis, G. T. Owen, K. S. Teng, M. W. Penny, H. Ferkel, J. Vac. Sci. Technol. B 22 (4), 1995 (2004). 74. J. E. Stern, B. D. Terris, H. J. Mamin, D. Rugar, Appl. Phys. Lett. 53 (26), 2717 (1988). 75. B. D. Terris, J. E. Stern, D. Rugar, H. J. Mamin, J. Vac. Sci. Technol. B 8 (1), 374 (1990). 76. N. Umeda, K. Makino, T. Takahashi, A. Takayanagi, J. Vac. Sci. Technol. B 12 (3), 1600 (1994). 77. P. Mesquida, H. F. Knapp, A. Stemmer, Surf. Interface Anal. 33, 159 (2002). 78. P. Mesquida, Ph.D. thesis, ETH Zurich, 2002, (http://e-collection.ethbib.ethz.ch/ show?type=diss&nr=14854). 79. W. Olthuis, P. Bergveld, IEEE Trans. El. Insul. 27 (4), 691 (1992). 80. S. Morita, Y. Sugawara, Y. Fukano, Jpn. J. Appl. Phys. 32 (Pt.1, No.6B), 2983 (1993). 81. S. Morita, Y. Sugawara, Y. Fukano, T. Uchihashi, T. Okusako, A. Chayahara, Y. Yamanishi, T. Oasa, Jpn. J. Appl. Phys. 32 (Pt.2, No.12B), L1852 (1993). 82. Y. Fukano, T. Uchihashi, T. Okusako, A. Chayahara, Y. Sugawara, Y. Yamanishi, T. Oasa, S. Morita, Jpn. J. Appl. Phys. 33 (Pt.1, No.12A), 6739 (1994). 83. Y. Sugawara, Y. Fukano, T. Uchihashi, T. Okusako, S. Morita, Y. Yamanishi, T. Oasa, T. Okada, J. Vac. Sci. Technol. B 12 (3), 1627 (1994). 84. Y. Fukano, Y. Sugawara, T. Uchihashi, T. Okusako, S. Morita, Y. Yamanishi, T. Oasa, Jpn. J. Appl. Phys. 35 (Pt.1, No.4A), 2394 (1996). 85. T. Uchihashi, T. Okusako, Y. Sugawara, Y. Yamanishi, T. Oasa, S. Morita, Jpn. J. Appl. Phys. 33 (Pt.2, No.8A), L1128 (1994). 86. E. T. Enikov, A. Palaria, Nanotechnology 15, 1211 (2004). 87. T. Uchihashi, A. Nakano, T. Ida, Y. Andoh, R. Kaneko, Y. Sugawara, S. Morita, Jpn. J. Appl. Phys. 36 (Pt.1, No.6A), 3755 (1997). 88. H. Amjadi, C.-P. Franz, J. Electrostatics 50, 265 (2001). 89. R. C. Barrett, C. F. Quate, J. Appl. Phys. 70 (5), 2725 (1991). 90. B. D. Terris, R. C. Barrett, IEEE Trans. Electron Devices 42 (5), 944 (1995). 91. I. Fujiwara, S. Kojima, J. Seto, Jpn. J. Appl. Phys. 35 (Pt.1, No.5A), 2764 (1996). 92. S. D. Tzeng, C. L. Wu, Y. C. You, T. T. Chen, S. Gwo, H. Tokumoto, Appl. Phys. Lett. 81 (26), 5042 (2002). 93. T. Uchihashi, T. Okusako, T. Tsuyuguchi, Y. Sugawara, M. Igarashi, R. Kaneko, S. Morita, Jpn. J. Appl. Phys. 33 (Pt.1, No.9B), 5573 (1994). 94. J. T. Jones, P. M. Bridger, O. J. Marsh, T. C. McGill, Appl. Phys. Lett. 75 (9), 1326 (1999). 95. J. Lambert, M. Saint-Jean, C. Guthmann, J. Appl. Phys. 96 (12), 7361 (2004). 96. N. Gemma, H. Hieda, K. Tanaka, S. Egusa, Jpn. J. Appl. Phys. 34 (Pt.2, No.7A), L859 (1995). 97. E. A. Boer, M. L. Brongersma, H. A. Atwater, R. C. Flagan, L. D. Bell, Appl. Phys. Lett. 79 (6), 791 (2001). 98. E. A. Boer, L. D. Bell, M. L. Brongersma, H. A. Atwater, J. Appl. Phys. 90 (6), 2764 (2001). 99. T. G. G. Maffeis, G. T. Owen, M. Penny, H. S. Ferkel, S. P. Wilks, Appl. Surf. Sci. 234, 2 (2004). 100. J. Mort, The anatomy of Xerography: Its Invention and Evolution (Mc-Farland, London, 1989). 101. T. B. Jones, Electromechanics of particles (Cambridge Univ. Press, New York, 1995).

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102. I. D. Morrison, S. Ross, Colloidal Dispersions: Suspensions, Emulsions, and Foams (John Wiley & Sons Inc, Weinheim, 2002). 103. A. Coehn, U. Raydt, Ann. Phys. 30 (4.Folge) 777 (1909). 104. K. G. Marinova, R. G. Alargova, N. D. Denkov, O. D. Velev, D. N. Petsev, I. B. Ivanov, R. P. Borwankar, Langmuir 12, 2045 (1996). 105. J. Feder, J. Appl. Phys. 47 (5), 1741 (1976).

IV.2 Fundamental Science and Lithographic Applications of Scanning Probe Oxidation J. A. DAGATA

Local oxidation of metal, semiconductor, and insulating surfaces by a scanning probe microscope (SPM) is a promising approach for nanoelectronics device prototyping. Voltage applied between a conductive SPM tip and (positively biased) substrate, results in the formation of a highly non-uniform electric field. The electric field attracts a stable water meniscus to the tip-sample junction, creates oxyanions from water molecules, and transports these oxyanions through the growing oxide film. This leads to oxidation of the substrate on a scale determined by the dimensions of the water meniscus. Experimental studies have shown that almost every material oxidizes under the extremely high electric-field conditions at the tip-substrate junction, including some noble metals, diamond, and nitrides of silicon, titanium, and zirconium. This chapter organizes fundamental relationships between oxide volume growth, current flow during exposure, and the resulting electrical and structural properties of the oxide. The underlying transport and reaction kinetics within the electrochemical nanocell is presented in a self-consistent manner in terms of dispersive kinetic theory through time-dependent rate constants. Key signatures of scanning probe oxidation, extreme simplicity and flexibility, become apparent when local oxidation is combined with standard device processing techniques. Nanodevices fabricated using this method include superconducting quantum interference devices, single-electron tunneling transistors, and antidote lattices in a wide variety of materials, such as titanium, Nb/NbN, GaAs/AlGaAs 2-D electron gas, SrTiO3 , and SiGe thin films. Examples of some of these devices will be reviewed in terms of the kinetic and materials insights revealed by fundamental studies.

1 Basic Principles 1.1 Low-Temperature and Anodic Oxidation Local oxidation using scanning probe microscopy (SPM) is a convenient technique for the fabrication of nanometer-scale structures [1]. Independent demonstrations of functional nanoelectronic devices fabricated by SPM oxidation during 858

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1994–1995 by the groups of Quate, Snow, and Matsumoto [2–4] focused attention on the need for establishing a detailed kinetic understanding of the self-limiting nature of SPM oxide growth, especially with respect to silicon. Work by Gordon, Teuschler, Stievenard, Avouris, and others provided an important foundation for this development [5–8]. Kinetic information from experiment was derived from measurements of oxide volume, current, and residual charge incorporated into the oxide film and at interfaces. Early local oxidation kinetics studies relied primarily on height measurements, which were convenient to obtain from SPM topographs. Later on, selective oxide etching and cross-sectional transmission electron microscopy (XTEM) were included in order to estimate the density of the oxide with respect to high-quality thermally grown silicon oxide. While these approaches have provided significant guidance through the years, inconsistencies have emerged which beg for clarification. For example, if SPM oxidation of silicon conforms to anodic oxidation, then why is there little or no difference in the apparent silicon oxide growth rate of p-type vs. n-type silicon, given that the hole concentration at the silicon–oxide interface is in accumulation and inversion, respectively? As we demonstrate in this chapter, self-consistent interpretation requires knowledge of more than simply a growth rate since the self-limiting oxide growth rate appears to be largely independent of the substrate material. Initial interpretations of SPM oxidation kinetics made contact with principles from low-temperature oxidation, mainly, the Cabrera–Mott theory, and principles from anodic oxidation theory. Teuschler et al. identified power-of-time law behavior of oxide growth [6]. At the time, this empirical observation was not connected to a physical model that could account for this asymptotic behavior and, for quite some time there was little subsequent progress. Now we know that power-of-time laws are associated with charge trapping concepts; this unifying principle is a key theme of this chapter. The first direct observations of local charge trapping within oxide features by electric force microscopy suggested the role of space charge in the underlying kinetics [9]. Such notions have a long history: In fact, kinetic influence of a nonuniform distribution of charge traps within a growing oxide film was recognized long ago by Uhlig in deriving the direct-log form [10]. More recent consideration of low-temperature oxidation principles appears in the work of Fehlner and Mott [11]. Fromhold has given a comprehensive treatment of steady-state space charge effects in anodic film formation [12]. These treatments have proved essential guides to our thinking about SPM oxidation kinetics. The linkage between space charge and power-oftime laws made shortly afterward, in two complementary, and near simultaneous, articles on space charge-based kinetic models, the first by my colleagues [13] and another by Dubois and Bubendorff [14]. In [13], time-dependent rate constants, ki = ko · t γ , with γ < 1, from the study of dispersive kinetics in condensed systems were used to account for the transition from an initially high oxide growth rate at short exposure time, t ≪ 1 s, to selflimiting growth at long exposure time, t ≫ 1 s. Dubois focused on a microscopic

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model of energy-barrier lowering by charge trapping/detrapping processes derived from earlier work of Wolters and van Zuynhoven [15].

1.2 Dispersive Kinetics Power-of-time oxide growth models can be cast into a more general and comprehensive form provided by the language of dispersive kinetics developed by Plonka [16]. However, kinetic results for the group 4 metals and their nitrides, i.e., TiNx , ZrNx , HfNx , 0 ≤ x ≤ 2 [17–19] challenge the “universality” of the foregoing interpretation developed primarily from the analysis of oxide growth on crystalline silicon substrates. In particular, behavior of ZrNx which is found to exhibit super-diffusional characteristics requires us to adopt the more generalized approach afforded by the use of fractional reaction-diffusion equations. In this chapter, the generalization from subdiffusional oxide growth, γ < 1 , for the case of crystalline silicon and its relationship to the models presented in [13,14], indicating how the underlying assumptions and conclusions overlap and how they differ when viewed from the perspective of the fractional kinetics. Analysis of superdiffusional growth, γ > 1, for amorphous ZrNx (0 < x < 2) thin films show that γ is a sensitive function of the nitrogen content of the system, increasing continuously from γ ≈ 1 for the pure metal then saturating near the ballistic limit, γ ≈ 2, with high nitrogen content. We end with a considerably more exact linkage between the non-Gaussian propagation of the oxidation wave front through the substrate and what it says about the initial defect production. In short, power-oftime laws, t γ , with γ = 1, arrive at through an entirely empirical process long ago by Teuschler reflect the persistent memory of this initial defect production.

2 The Electrochemical Nanocell 2.1 Role of the Meniscus The unique geometry of the electrochemical nanocell provides features that allow local control of the nanoscale oxidation process: The elecric field E field attracts a stable water meniscus to the tip-sample junction, creates oxyanions from water molecules, and transports these oxyanions through the growing oxide film. This leads to oxidation of the substrate on a scale determined by the dimensions of the water meniscus. Dimensions of the equilibrium water meniscus for a given voltage, tip-substrate separation, and relative humidity may be calculated, as shown in Figure 1. Since the contact lines associated with the substrate and meniscus and the tip and meniscus can change with the length of exposure, these boundaries are free to move due to ionic interactions at the interfaces. Various methods that employ pulsed voltage and/or oscillating probe tips, i.e., dynamic mode oxidation, have been proposed to limit lateral spreading of the oxide wave front. In the latter case changes in the cantilever oscillation amplitude due to voltage and meniscus formation may be observed directly.

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861

0.5

A (pA)

0.4 0.3 0.2 0.1 0

30

40

(a)

50 60 50 60 % RH

70

80

SPM tip rtip

φ

ntact line contact

rrκ h(%RH)

depletion region silicon

(b)

ro d = 2.ro + R(%RH, V)

FIGURE 1. (a) Empirical (◦) and calculated (−) values of the parameter A; (b) Definition of terms used to calculate the A parameter.

A methodology for determining average SPM oxide density has been described previously. AFM/etching measurements show that the average density of SPM oxide is lower than that of thermal oxide [20]. In this approach, the “as-written” height of an SPM oxide feature, h, and the depth, d, of the subsequently HF-etched feature is measured in order to estimate the volume ratio of SiOx produced relative to that of the silicon consumed. The volume expansion ratio, v ∗ , is obtained by equating moles of silicon consumed and the number of moles of oxide produced, or Vsi /vsi = Vsio2 /vsio2 . This equation may be rearranged using v ∗ = vsio2 /vsi to d = X/v ∗ = (h + d)/v ∗ , since Vsi = A · d and V sio2 = A · X, where it is assumed that the regions share a common interfacial area, A. The average oxide density is inversely proportional to h/d = v ∗ − 1. Figure 2 is a plot of AFM/etching data versus voltage, for SPM-oxide feature height (h), depth (d), total thickness [X t = (h + d)], and h/d ratio. Oxidation was

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J. A. Dagata 9

X, thickness

X,h,d (nm ); h/d

8 7 6

h, height

5 4

d, depth

3

xo = 0

2

h/d ratio

1 0 0

2

4 6 voltage (V)

8

10

FIGURE 2. Dependence of the h/d ratio on the applied voltage as measured by AFM/etching for SMP oxide on a p-type silicon substrate.

h/d, h(nm), Xt(nm)

performed at voltages of VDC = 6, 8, 10 V with a pulse time of 100 s using a p-type silicon substrate. Since any initial surface oxide is etched away, only a net SPM oxide thickness, X = X t − X o , is determined, where X t is the total oxide thickness and X o is initial oxide thickness. There is a smooth extrapolation of X, h, and d to zero as the applied voltage is decreased. This makes it a simple matter to obtain h and d values needed to estimate density. The h/d ratio is ≈1.6, given by the dashed line in the figure, a typical result for AFM/etching studies of p-type silicon. Figure 3 is a plot of XTEM data for X t , h, and h/d measured from SPM oxide features produced on n- and p-type silicon substrates. Oxides were produced with voltages, VDC , of 5 and 10 V. For each voltage, two data points corresponding to scan speeds of 5 and 500 nm/s are drawn. [For simplicity only a single line is used to

n-Si(001)

9 8 7 6 5 4 3 2

Thickness: Xt Height :h Density-1 : h/d

1

0

(a (a)

2

4

6

Pulse Voltage [V]

8

Thickness: Xt Height :h Density-1 : h/d

X0=1nm

1

h/d=1.2

0

p-Si(001)

9 8 7 6 5 4 3 2 10

0

0

(b)

2

4

6

8

10

Pulse Voltage [V]

FIGURE 3. Voltage dependence of the thickness, height, and h/d ratio of SPM oxide features as measured by XTEM on (a) an n-type silicon substrate and (b) a p-type silicon substrate.

IV.2. Fundamental Science and Lithographic Applications of SPO

Pulse-time dependenc dependence

Voltage dependence 2.5

5 nm/s

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863

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(a)

2

4

6

Pulse Voltage [V]

8

10

0

(b)

100

200

300 400

500

Scan Speed [nm/s]

FIGURE 4. Dependence of the h/d ratio on (a) the applied voltage and (b) pulse time as measured by XTEM for SPM oxide produced on n- and p-type silicon substrates.

represent the trends seen in these averaged experimental values.] Thickness, height, and depth evidently increase with voltage for SPM oxide produced on both n- and p-type substrates, similar to the trend for the AFM/etching data (Figure 2). There is a systematic difference between data presented in Figure 2 and that presented in Figure 3. In the XTEM data X t extrapolates to X o ≈ 1.0 nm, the chemical oxide thickness, h extrapolates to 0 nm, and h/d extrapolates to the chemical oxide value of ≈1.26, at 0 V similar to thermal oxide. The slope of XTEM data for n-type oxide is greater than the slope of p-type oxide data in Figure 3. For example, a 10 V pulse on n-type yields X t ≈ 6–8 nm, which is significantly greater than for an identical pulse on p-type for which X t ≈ 4–5 nm. A comparison of these values with AFM/etching data in Figure 2 indicates thickness values for the p-type data are lower than expected. To reinforce this point, we took a closer look at the density variation (the h/d ratio) obtained by XTEM under different exposure conditions (applied voltage and scan speed) for n- and p-type substrates in Figure 4. Not only is the exposure sensitivity (the slope of the h/d ratio) greater for n-type than for p-type, their magnitude is consistently greater as well. AFM/etching experiments yield h/d values of 1.6 to 1.7 for p-type oxide, yet XTEM values for the h/d ratio of p-type substrates are between 1.3 and 1.5. These unexpectedly low XTEM h/d ratios for p-type oxide are consistent with our previous XTEM study21 , which estimated the p-type h/d ratio to be ≈ 1.2. By comparison, XTEM and AFM/etching h/d ratios for n-type oxide are identical. Modification of the SPM oxide during XTEM sample preparation is a likely cause of inconsistent AFM/etching and XTEM density measurement results. In this section we investigate two elements of XTEM preparation capable of modifying the SPM oxide density by relieving internal oxide stress or by imposing external stress on an SPM oxide feature. These are capping layer deposition and annealing.

864

J. A. Dagata PS capping layer (deposited at 600oC ) PS capping layer

Cr capping layer (deposited at RT) Cr capping layer

SPM oxide

SPM oxide

p-Si (001)

p-Si (001)

dislocation

(a)

(b)

FIGURE 5. High-resolution XTEM micrography of SPM oxide formed on a p-Si (100) substrate for a sample prepared using (a) a polysilicon (PS) capping layer deposited at 600◦ C, and (b) a chromium (Cr) capping layre deposited ar room temperature (RT). Arrows indicate the location of the Si/SiOx interface and the oxide-capping layer interface. Arrow also indetify a dislocation loop in the silicon lattice.

Figure 5 compares HR XTEM micrographs of SPM oxide features on p-type silicon prepared using a poly silicon (PS) or, alternately, chromium (Cr) capping layer. The Cr-capped sample, with the capping layer deposited at room temperature during XTEM sample preparation, exhibits numerous shallow dislocations below the SPM oxide feature, one of which is marked by arrows on the right-hand side panel. The interface of the PS-capped sample, with the capping layer deposited at a substrate temperature of 600◦ C, exhibits no evidence of dislocations at all, as shown on the left-hand side panel. Dislocations are not associated with chemical oxide on samples prepared by either capping method. This is direct evidence that significant numbers of defects are produced—not only within the SPM oxide but within the substrate lattice as well—during SPM oxidation. Dislocation networks located several nanometers below SPM oxide are hardly surprising, given the fact that the process occurs at low-temperature under extremely high electric field conditions. As Fromhold [12] has emphasized, these conditions generate high interfacial defect densities within the film as the oxide grows, and the impact of these defects on the kinetics and mechanism of SPM oxidation cannot be dismissed. Dislocations arise either as a result of electronic processes, hot-hole injection, for example, or may be related to ionic mechanisms such as Frenkel pair-type generation mechanisms (e.g., [12], Appendix D). Experiments are currently underway to clarify

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these details. However these defects may be created during the oxidation pulse, they generally appear to be positively charged, as we have shown by SMM surface potential imaging of individual oxide features [13]. For practical use of SPM oxidation of silicon, an annealing step is strongly recommended for repairing such SPM oxidation-induced damage in the substrate lattice. The fact that the average SPM oxide density is not a single, fixed value but varies with exposure conditions must be integrated into our current understanding of the SPM oxidation process. At the microscopic level, this variation reflects degrees “openness” of the resulting silica network imposed by exposure conditions. The role of space charge in oxidation kinetics was explored long ago by Uhlig [10] and more recently by Wolters [15]. Uhlig’s “direct-log” model, in particular, offers a physical description that accounts for all experimentally observed aspects of SPM oxidation. The underlying mechanism explicitly invokes electronic, as well as ionic, concentration gradients, which are necessary for explaining the dependence of SPM oxide growth on substrate doping. The Uhlig model also predicts that space charge buildup generates non-uniform distributions of defects within SPM oxide film. Interfacial defects incorporated into the growing oxide film thus determine the final dimensional, structural, and electrical properties of SPM oxides. For the particular case of silicon, it is quite well known that positively charged interfacial defects are generated under a variety of conditions. These positively charged defects deplete the silicon substrate of holes needed for anodic oxidation within the central tip-substrate region, leading to self-limiting vertical growth and to the promotion of lateral oxide growth. Apparent inconsistencies between the kinetic models of Stievenard [7] and Avouris [8] and our own space charge model disappear altogether when viewed through this model. For example, Uhlig attributes a thickness-dependent change in activation energy to space charge, rather than stress, as we have suggested on the basis of scanning Maxwell-stress microscopy (SMM) results. It is this (linear) thickness dependence that accounts for the ‘direct-log’ form of the rate law for SPM oxide growth, which Avouris first proposed. In addition, the model provides a physical basis for Stievenard’s cutoff field, E L = V /h L , where V is the applied voltage and h L is an oxide thickness. (The required thickness dependence of the cutoff field given by Stievenard is contrary to experiment. See Figure 7 of [7].) In the Uhlig model, the cutoff field is simply the potential at which space charge within the oxide becomes equal in magnitude (and opposite in sign) to an externally applied field. As Uhlig has indicated, this point represents a transition from a faster to a slower oxide growth mode, a feature readily observed for SPM oxidation kinetics. A second important consideration for establishing how the water meniscus may play a role in ionic conduction between the probe tip and the substrate during oxidation arises from analysis of voltage-induced bending of the SPM cantilever to which the probe tip is attached. The bending geometry is illustrated in Figure 6. A comparison of experimental and calculated force versus distance and current vs. distance curves for two different humidity values, 40–45% RH and 65–70% RH, are shown in Figure 7. Higher humidity decreases cantilever bending and suppresses current flow through the tip-substrate junction because production of

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J. A. Dagata z=g -l ∆ l

g

FIGURE 6. Definition of variables describing an SPM (a) cantilever and (b) tip.

z z-∆

(a) φ l r tip

l eff

z-∆

(b)

mobile ions on the separated water films results in screening the maximum ionic charge, thus lowering tip-substrate capacitance. By recording simultaneously a force versus distance curve with an applied voltage and measuring the total current flow through the tip-substrate junction, it is possible to resolve the electronic and ionic components of the current. Current versus distance curves obtained at low and high humidity, Figure 7(b), reveal that the time decay of the current transient differs by more than an order of magnitude due to this effect.

2.2 Role of Space Charge Steady-state electrochemical, i.e., anodic, oxidation concepts [10–12] alone do not adequately describe essential features of SPM oxidation: First, ionic transport during local oxidation is a transient, not steady-state process, as seen in Figure 7. Oxide growth self-limits at a thickness of a few nanometers, not the micrometer thickness usually associated with traditional anodic processes. Self-limited growth, more formally dispersive kinetics, is a consequence of the build up of space charge within the oxide film [13,14]. This explicit time dependence is the reason that direct analysis of current flow during oxidation, not just oxide thickness measurement, is necessary for a more complete understanding of the oxidation process. Second, distinguishing between anionic and cationic transport, which may be valid for steady-state anodic conditions, is not meaningful for the transient growth phase. In particular, transport is dominated by initial generation of electrically charged defects, related to the presence of water in the system. This transforms

IV.2. Fundamental Science and Lithographic Applications of SPO 2 1

deflection (nm)

FIGURE 7. (a) Cantilever bending as a fucntion of zpiezo elongation at V = 15 V and 40–45 and 65–70 %RH. (b) Current as a function of time for the two curves shown in (a).

867

65-70 %RH 65-70 %RH

0 -1

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0

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0 0.1 0-0.1 0.1 -0.1

(b)

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time (s)

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silicon oxidation from inverse log-of-time kinetics—anion transport—into direct log-of-time—trapping/detrapping—growth kinetics. Avouris et al. [8] have shown that SPM oxidation is indeed governed by direct-log kinetics, and our previous studies demonstrate that SPM oxide density is lower than that of thermal oxide and contains significant electrical charge. Both kinetic and structural results indicate that conclusions about transport and oxide growth that may be valid at low electric field conditions no longer apply at the extremely high fields obtained under SPM oxidation conditions. Third, traditional anodic oxidation theory relies on a one-dimensional growth model in which oxide thickness is the sole dimensional parameter in the problem. Local oxidation, on the other hand, is inherently three-dimensional in the sense that the contact area, A, defined by the meniscus contact line at the tip-substrate junction, is not fixed, but is a function of the highly nonuniform, externally applied E field as well as the internal space charge of ions and electrons at the meniscusoxide boundary. Sensitive lateral control of oxide dimensions has been shown to be possible with finite tip-sample distances by noncontact SPM oxidation [22,23]. Fourth, practically all materials can be oxidized by the SPM oxidation technique. In almost every case for which sufficient kinetic data exists for SPM oxidation

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of metal, semiconductor, and insulating films and substrates, a universal growth behavior obtained. This universal behavior, in the language of dispersive kinetics, arises because increasing disorder in the system, rather than underlying chemical reaction rates, determines ionic transport rates. Silicon represents a model system for SPM oxidation because the SiO2 /Si interface is the most thoroughly investigated material system that exists. This is due to its crucial role in microelectronics. Knowledge about the interactions of oxygen, hydrogen, and water and their defects at this interface allows us to understand how charged-defect production during oxide growth plays an essential role in the self-limiting growth behavior and line width control of nanostructural features. Comprehensive experiment and analysis of the electrical current passing through the tip-substrate junction during oxidation of silicon by scanning probe microscopy has been presented recently. Analysis of experimental results under dc-bias conditions resolves the role of electronic and ionic contributions, especially for the initial stages of the reaction, determines the effective contact area of the tip—substrate junction, and unifies the roles of space charge and meniscus formation. Principal requirements of this analysis are (1) distinguishing the contributions of ionic from those of electronic transport mechanisms in determining the total electrical current through the tip-substrate junction, and (2) identifying the effective tip-substrate contact area through which the total measured current passes. The data sets that we employ in this analysis were obtained using complementary techniques and instrumentation described elsewhere [24,25]. Key parameters of current measurements, which will be discussed first, are the applied bias voltage, V ; the exposure time, t; and the percent relative humidity, % RH. By fitting simultaneous current and oxide volume growth data as a function of these parameters, as shown in Figure 8, the role of humidity and voltage in establishing the contact

58 58 56

58 58

54 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0

56 54 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2

fitting

Imax (pA)

Imax (pA)

experiment

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S7 8 S6 S5 7 voltage (V)

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S7

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voltage (V)

(b)

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7

S5

S4

6

S3

S2

5

1 40

50 %RH

FIGURE 8. Surface plot of the maximum total current, Imax , recorded at the onset of scanning probe oxidation (t = 0 s) as a function of applied voltage and relative humidity. (a) Experimental data from Figure 2 of Ref. 13; (b) Fit of the data to Imax (%R H, V ) = A(%R H ) · eβV .

IV.2. Fundamental Science and Lithographic Applications of SPO 1500

1500

1

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1 1 1 11 10 90 80 70 60 50 40 30 20 100 0

fitting

1400

experiment

13 00

diameter di eter (nm)

diameter (nm))

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8

7

voltage (V)

(b)

6

5

1

S8

S4

9

0 10

S3

1 00 0

S9

S7 S6 S5

2 00

S11 S10 10

S11 S10 S9 S8

0

S2

400 300

869

1

2 40

4 350

6 5 60

7

70

%RH

FIGURE 9. Surface plot of the oxide-dot diameter maximum recorded as a function of applied voltage and relative humidity after 10 seconds of scanning probe oxidation exposure. (a) Experimental data from Figure 5 of Ref 13; (b) Fit of the data to d (t) = 2 · r0 + 4.5V · ln(t/τ + 1) + A(%RH ) · [V 2 · t 0.5 + a · (V /t ox )2 · exp(−b · tox /V )].

area of the tip with the substrate can be determined. We are interested in the maximum current at the onset of the voltage pulse, Imax (V, t = 0 s, % RH) and in the regime in which self-limiting growth conditions are reached, I (V, t = 10 s, % RH). We demonstrate that local oxidation is governed by a constant charge density within the tip-substrate contact area. This result applies over a range of voltages, from 5 to 10 V, and humidity values from 40 to 70 %RH explored in this study. SPM oxidation is governed by a maximum charge density generated by electronic species within the junction at the onset of the oxidation process. Excess charge is channeled into lateral diffusion, keeping the charge density within the reaction zone constant, and reducing the aspect ratio of the resulting oxide features. The consequence of this is seen in Figure 9, which is a plot of the oxide dot diameter as a function of both voltage and %RH. Correspondence between current and diameter in Figs. 8 and 9 strongly suggests that diffusion is driven by the accumulation of charge. A uniform charge density implies that SPM oxides contain a fixed defect concentration, in accordance with the space-charge model. The effective (electrical) thickness of SPM oxides determined by these defects is investigated by Fowler– Nordheim analysis (Figure 10). We conclude that most of the electrical current involved in high-voltage SPM oxidation of Si is electronic, arising from direct tunneling at low voltage and Fowler–Nordheim tunneling at higher voltages, and does not actually induce surface oxide growth. We also show that the onset of Fowler–Nordheim electronic tunneling provides electrical current that only serves to enhance lateral diffusion that leads to the well-known broadening of local oxide features (Figure 9.) A further connection between current flow and lateral diffusion can be seen in Figure 11. Figure 11(a) shows an approach curve with two current spikes which coincide with deflection of the cantilever due initially to the formation of the water

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J/V2 ( pA⋅⋅ nm-2 ⋅ V-2 )

10

1 0.05 0.

0. 0.1

0.15 .1

0.2

Jmax

0.

0.1 1

0.01

0.001 1

J10 s 0.0001

0.05 fractional contribution to Jmax

(a)

1.2

0.1

0.15 0.2 voltage-1 (V-1) v

0.25

direct tunneling Fowler-Nordheim

0.8

0.4

0 0

(b)

4

8

12

voltage (V)

FIGURE 10. (a)Fowler-Nordheim (FN) plots of the maximum current density Jmax (t = 0 s) and J (t = 10 s). (b) Fractional contribution of direct tunneling and FN terms to Jmax extracted from the dashed-line fit shown in panel a). Points in b) reflect averaged experimental data and are not required to sum to unity; the line fits, however, do.

meniscus, ∼2 pA, followed by a much larger current, ∼12 pA, flowing once direct contact between the tip and substrate occurs. Although current flow under these two situations is quite different, Figure 11(b) indicates that the resulting oxide volume produced for a given voltage and humidity is quite similar. This indicates that electronic current is the dominant component of the total current during contact mode oxidation and that it contributes little or nothing to oxide growth.

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FIGURE 11. (a) Simultaneous force vs. distance and current vs. distance (SFCD) curves for V = 18 V, 65–70 %RH, K = 4.21 N/m, scan rate = 60 nm/s. (b) Four SPM oxide features produced during SFCD experiments at 13.5 V and 18 V which accessed either noncontact or contact positions.

2.3 Oxide Growth Kinetics of Silicon and Other Materials In traditional developments of chemical kinetics, chemically reactive species are in motion, interacting with other reactive species and equilibrating by collisions with the solute. The system is assumed to be sufficiently dilute so that the concentration of all reactive species are unaffected by the existence of any other species. Fick’s laws are invoked to describe the situation. It is also usually assumed in developing these concepts that the concentration gradient (not the concentration) remains in a steady-state at some location in space [26]. This is valid if the reaction rate is much slower than the diffusion rate, or if the rate constant, k ≪ 4πρD, where ρ is a radius of reaction and D is a diffusion constant. This allows solution of the set of reaction rate laws, assuming first-order processes with constant rate constants [27]. This represents a set of linear differential equations that can be solved—integrated—algebraically. In order to describe SPM oxidation, we must relax some of these restrictions: First, the oxide thickness in which ions are transported by the external electric field increases with time. Initial defect creation, referred to as maximum charge density in our recent work [24], arises as follows: Before the voltage pulse (t < 0), the SPM tip-substrate junction resembles a metal-insulator-semiconductor (MIS) diode, for the case of silicon, say. Its I-V characteristics should obey the diode equation, I (V ) = Io e V/q K T . However, since water, with a high dielectric constant (∈ = 80), forms a meniscus about the junction, electrical breakdown of the water, governed by E bd ∼ ∈−1/2 , limits the current. The maximum current achieved with a given voltage is Imax = Io e V/V th , where the threshold voltage, Vth = E th · tox , is a

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constant that can be expressed in terms of a field and initial thickness of oxide. The initial oxide thickness, tox , is analogous to the charge separation proposed in the Cabrera–Mott theory. It is essential to realize that this initial defect creation does not occur instantaneously at t = 0. In fact, early on Snow and Campbell [28] defined a variable they called a threshold exposure time, τ th , and determined an upper limit of 10−5 seconds for it. It is the exposure time required to form an observable oxide volume given by V = tox · A, where A is the contact area between tip and substrate and tox = 0.3 nm. In Figure 3 of [24a] we obtain a value of tox = 0.28 nm directly from current measurements. This value represents a single layer within the silicon lattice. The τ th < 10−5 s threshold represents a system initialization period that determines the subsequent evolution of the oxidation process; i.e., it establishes the initial defect number, n o (+/−), which depends, of course, on voltage, humidity, tip geometry, surface states of the tip and substrate, and electron/hole fluence. A second consideration regarding chemical kinetic assumptions is that electric field-enhanced diffusion and reaction take place within a solid phase at high concentrations of ionic reactants and oxide. Space charge effects have been identified already [9–15]. Oxide growth requires evaporation (to use Uhlig’s term) of positive ions into the oxide at the oxide-substrate interface and injection of oxyanions into the oxide at the water–oxide interface. One of these steps will be “rate-limiting” in the sense that the condition of constant and balanced concentration gradients for both species, ki ≪ 4πρDi , is not obtained. Dubois and Bubbendorff [14] considered the space charge problem from previous work by Wolters and Zegers-van Duynhoven [15]. The Wolters model considers a steady-state solution to ionic transport through a microscopic charge trapping/detrapping model. The key point is that the volume available for additional ions to cross the interface and enter the oxide is successively reduced with increasing exposure time. Wolters developed a volume reduction factor for the diminishing probability of ion injection or evaporation in terms of continued fractions, a standard method for describing the buildup of interacting elements in a system. A consequence of this is the “distribution of reactant reactivities” [16] leading to time-dependent rate constants k(t) = k · t γ used empirically in [13e] to obtain power-of-time growth laws. The oxide growth model for silicon presented in [13e] was purely empirical; its construction is based on two assumptions—coupled kinetic pathways [27,29] and time-dependent rate constants [16]. That model, based on the Alberty–Miller equations, considers a “direct” reaction represented by A → C, with a first-order rate constant k4 , and an “indirect” one, A → B → C, with successive rate constants k1 and k3 . (Numbering of rate constants follows the scheme given in [29].) Initial conditions are that A(t = 0) = [Ao ] = n o (+/−)/(tox · A), and B(t = 0) = C(t = 0) = 0. An example of this empirical approach is presented in Figure 12. Figure 12(a) illustrates the Alberty–Miller integrated rate equations for the time dependence of species A(t), B(t), and C(t) using the rate constants, ki , and gamma, γ , values obtained for SPM oxidation of silicon. Fitting experimental kinetic data for silicon, expressed in terms of the oxide volume, C(t), yields parameter values of k1 = 4.5 s−1 , k3 = 4.7 · 10−4 s−1 , k4 = 2.4 · 10−3 s−1 , and γ = 0.6. Experimental data points and a curve fit generated by Monte Carlo annealing that generated these

IV.2. Fundamental Science and Lithographic Applications of SPO

1. 0

A

1e+5

C

γ = 0.6

B* volume l ( nm 3 )

0. 8

concentration

B

873

0. 6 0. 4 0. 2

1e+4

0. 0 0. 01

10

10000

tim (s) time

1e+3 0.001

(a)

(b)

0.01

0.1

1

10

ti time (s)

FIGURE 12. (a) Alberty-Miller integrated rate equations for the time dependence of species A(t), B(t), and C(t) using the rate constants, ki , and gamma, γ , values obtained for SPM oxidation of silicon. Fitting experimental kinetic data for silicon, expressed in terms of the oxide volume, C(t), yields parameter values of k1 = 4.5 s−1 , k3 = 4.7 · 10−4 s−1 , K4 = 2.4 · 10−3 s−1 , and γ = 0.6. (b) Experimental data points and a curve fit generated by Monte Carlo annealing that generated these parameters. Data represents SPM oxidation by contact mode with an applied bias voltage of 20 V, and 65% RH for a hydrogen-terminated n-type silicon substrate. The point B ∗ represents the space-charge limit when no further ions can be injected into the oxide for a given applied voltage.

parameters are plotted in Figure 1(b). Data represents SPM oxidation by contact mode with an applied bias voltage of 20 V, and 65 % RH for a hydrogen-terminated n-type silicon substrate. The point B ∗ represents the space-charge limit when no further ions can be injected into the oxide for a given applied voltage. For t > 0 with voltage applied, injection of OH− ions into and evaporation of Si+ ions into the defected junction region leads to growth of an increasingly charged silica network. According to the space charge picture, ion injection proceeds until the internal electric field cancels the external driving field. At this point the intermediate species B reaches its maximum value denoted B ∗ . Evidently, B ∗ is voltage dependent. As also noted by Uhlig, B ∗ must represent a nonuniform charge distribution within the oxide and interface. Relaxation, or reorganization, of this charge distribution, species C, implies that the resulting silicon oxide network may not relax completely to SiO2 , but that defects are “frozen in” at room temperature. Time dependence of species A, B, and C should tell us the extent to which the system attains equilibrium within the finite time of our experiments. As shown in [13(e)], the parameter for SPM oxidation is given by γ = 0.2 (for a linear dimension of the oxide such as height). A fitting of experimental data is shown in Figure 12 for the oxide volume of silicon, where now γ = 0.6. or (0.2)1/3 . Figure 12(a) readily shows that the buildup of charged defects, B, reaches a maximum, B ∗ , after which transition to slow growth sets in. The subsequent conversion of these defects to oxide cannot occur on reasonable time scale so

J. A. Dagata

A A

1.0

B B

1e 1e+7

0.8 concentration

C C

0.6

B B**

a(t)

volume (nm3)

874

b(t) cc(t) (t)

0.4

o x id e,, 66sccm oxide sc cm

0.2 0.0 0.01

(a)

0.1

1 10 time (s)

100

1.9 γ = 1.9

1e 1e+6

1000

(b)

10

time (s)

100

FIGURE 13. (a) SPM oxidation model for zirconium nitride based on Alberty-Miller integrated rate equations. The three curves are as described in the previous figure. (b) Fitting of experimental kinetic data for oxide volume, C(t), as a function of exposure time are 0.029 s−1 , 1.5 · 10−4 s−1 , and 1.0 · 10−3 s−1 and γ = 1.9. The rate constants ki represent an optimized set for the complete set of ZrN samples over 0–10 standard cubic centimeters per minute of nitrogen. Exposure conditions were contact mode, 41 V and 35 %RH.

self-limiting growth is reached. It was thought previously that such self-limiting behavior was the only one obtained for all SPM oxidation. If SPM oxidation were purely diffusive, γ < 1, there would be no need to discuss fractional kinetics.

2.4 Variation of Charge and Density Within SPM Oxides Recent kinetic results for the group 4 metals and their nitrides, i.e., TiNx , ZrNx , HfNx , 0 ≤ x ≤ 2, [17–19,35] challenge the “universality” of a purely dispersive interpretation, developed primarily from the analysis of oxide growth on crystalline silicon substrates. A gamma value of γ < 1 indicates that silicon oxidation is sub-diffusive in the sense that randomizing interactions occur on a time scale comparable to or less than charged-defect-producing reactions. The system is dispersive in the sense that the relaxation of the system into SiOx, or C(t), is described by a distribution of decay times rather than a single one. It is the build up of charged defects that are responsible for this time-dependent distribution. Figure 13 illustrates SPM oxidation of a material system that does not conform to the dispersive kinetics of the silicon model. Kinetic analysis based on the Alberty– Miller scheme has been applied to a series of amorphous ZrNx (0 < x < 2) thin films [35]. The resulting exponent γ is a sensitive function of the nitrogen content of the system, increasing continuously from γ ≈ 1 for the pure metal and saturating near the ballistic limit, γ ≈ 2, with high nitrogen content. Figure 13(a) presents an SPM oxidation model for zirconium nitride based on the Alberty–Miller integrated rate equations. The three curves are as described in the previous figure. Fitting of

IV.2. Fundamental Science and Lithographic Applications of SPO

875

experimental kinetic data for oxide volume, C(t), as a function of exposure time yields 0.029 s−1 , 1.5 · 10−4 s−1 , and 1.0 · 10−3 s−1 and γ = 1.9. The rate constants ki represent an optimized set for the complete set of ZrN samples over a wide range of nitrogen content, from 0 to 10 SCCM. Data points shown in Figure 13(b) are averaged for several 41 V oxidation sequences at 35% RH. The sample is a ZrN film that was sputtered with a 6-standard cubic centimeter per second (sccm) N2 flow rate. This model can be mapped onto a fractional-order vector space representation [32]. The advantage is two ad hoc assumptions become elements of a single selfconsistent description that provides a theoretical interpretation to experimentally determined parameters. The buildup of interacting elements in a complex system can be handled by the Laplace transform method [30] expressed in the language of fractional integral operators [31–34]. The origin of fractional kinetics can be found in the development of continuous time random walks. Such statistics define broad spatial jumps or waiting time distributions leading to non-Gaussian propagators and non-Markovian time evolution of the system [32,33]. The asymptotic short and long-time behavior of these processes is of primary interest since the generalization of Gaussian diffusion processes can be directly associated with the fractional order of the integral/derivative operator, γ , and the mean square displacement becomes simply x(t)2  = t γ [30,33]. Thus we arrive at power-law dependence for SPM oxidation processes and conclude that the special characteristics of a specific reaction-diffusion system can be parameterized by γ , and assigned to the order of fractional derivative. Within this interpretation, super-diffusive growth conditions imply that spatial jumps greater than a single lattice spacing occur with increasing frequency. The noncrystalline nature of the film plays some role, but it is the presence of nitrogen that is the more important factor. Oxygen displacement of nitrogen is energetically favorable and its recombination with hydrogen ions within the oxide film may reduce the build up of space charge.

3 Applications 3.1 Nanoelectronic Devices Nanodevices fabricated using SPM oxidation include superconducting quantum interference devices, single-electron tunneling transistors, and antidote lattices in a wide variety of materials, such as titanium, Nb/NbN, GaAs/AlGaAs 2-D electron gas, SrTiO3 , and SiGe thin films [36–57]. Other chapters in this book review these applications in more detail, so here I focus on some materials issues that may be a consequence of space charge. Devices fabricated by remotely patterning a 2D electron gas system represent an approach that has been reproduced successfully in several laboratories. Remote patterning is advantageous since material defects, especially localized charge traps, produced during the SPM oxidation process remain isolated from the delicate

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electron-gas structure. Evidently, remote patterning is sufficient to disrupt the local continuity of the electron gas, yet the charge traps are far enough away to be screened effectively. The alternative is direct oxide patterning with or without subsequent etching of metal or semiconducting structures. This is required in the case of other materials systems. Here charged defects coexist with a critically dimensioned nanostructure. Controlling the number and types of defects at the atomic scale is inconsistent with the high-field conditions that I have described above. As my colleagues and I have shown, annealing of SPM oxide in the case of silicon offers a promising solution [13(b)]. Moreover, annealing temperatures that increase oxide density and reduce oxide charge are consistent with standard silicon device processing.

3.2 Other Applications SPM oxidation is finding application as a nanolithography method in other areas. It is being used to fabricate nano-resonators in a CMOS-integrated microbalance in order to detect single or a few atoms [58]. Also, fabrication of photonic devices and structures, such as waveguides are being investigated [59–62]. Aside from fabricating nanostructures, an increasingly relevant application of SPM oxidation is its use as a probe of materials properties, in other words, as an additional instrument for materials characterization. Refractory metals [52–66], diamond [67,68], and organic layers [69,70] are being actively pursued.

4 Summary A physical interpretation of SPM oxidation kinetics is constructed. The present model is a generalization of an earlier one based on coupled first-order reaction rates, first derived by Alberty and Miller. This revision was made necessary by oxidation experiments in which the substrates were zirconium nitride thin films. In contrast to the dispersive kinetics that describe the oxidation of crystalline silicon substrates, i.e., γ < 1, amorphous zirconium nitride films were shown to exhibit superdiffusive behavior, i.e., γ > 1. This range of behavior focuses our attention on the non-Gaussian propagation of the oxidation wave front through the substrate and what it says about the initial defect production and reactions taking place within the growing oxide film. In short, power-of-time laws, t γ , with γ = 1, arrived at through an entirely empirical process long ago by Teuschler, reflect the persistent memory of this initial defect production.

Acknowledgments. I would like to acknowledge the many contributions of H. Yokoyama and H. Kuramochi (AIST, Japan), F. P´erez-Murano (CNM-IMB, Spain), R. D. Ramsier, N. Farkas, and J. R. Comer (University of Akron) in making the work described in this chapter possible.

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57. S. Sasa, S. Yodogawa, A. Ohya, and M. Inoue, Jap. J. Appl. Phys. 40, 2026 (2001); V. Bouchiat, M. Faucher, C. Thirion et al., Appl. Phys. Lett. 79, 123 (2001). 58. G.Abadal, Z. J. Davis, A. Boisen, F. P´erez-Murano, X. Borris´e, and N. Barniol, Probe Microscopy 2, 121 (2001); Z. J. Davis, G. Abadal, B. Helbo, O. Hansen, F. Campabadal, F. P´erez-Murano, J. Esteve, E. Figueras, R. Ruiz, N. Barniol, and A. Boisen, Transducers’01 Conference Technical Digest, p. 72 (2001). 59. T. Onuki, T. Tokizaki, Y. Watanabe, T. Tsuchiya, and T. Tani, Appl. Phys. Lett. 80, 4629 (2002). 60. C. F. Chen, S. D. Tzeng, H. Y. Chen, and S. Gwo, Optics Lett. 30, 652 (2005). 61. Y. Takemura, J. Shirakashi, Adv. Eng. Mat. 7, 170 (2005). 62. H. Kuramochi, T. Tokizaki, T. Onuki, J. Obayashi, M. Mizuguchi, F. Takano, H. Oshima, T. Manago, H. Akinaga, and H. Yokoyama, Surf. Sci. 566, 349 (2004). 63. M. Hirooka, H. Tanaka, R. Li, and T. Kawai, Appl. Phys. Lett. 85, 1811 (2004). 64. R. W. Li, T. Kanki, H. A. Tohyama, J. Zhang, H. Tanaka, A. Takagi, T. Matsumoto, and T. Kawai, J. Appl. Phys. 95, 7091 (2004). 65. N. Farkas, J. R. Comer, G. Zhang, E. A. Evans, R. D. Ramsier, S. Wight, and J. A. Dagata, Appl. Phys. Lett. 85 5691 (2004). 66. N. Farkas, G. Zhang, K. M. Donnelly, E. A. Evans, R. D. Ramsier, and J. A. Dagata, Thin Solid Films 447, 468 (2004). 67. V. D. Frolov, V. I. Konov, S. M. Pimenov, and V. I. Kuzkin, Diamond and related materials 13, 2160 (2004). 68. C. Manfredotti, E. Vittone, C. Paolini, A. Lo Guidice, P. Olivero, R. Barrett, and V. Rigato, Surf. Eng. 19, 441 (2003); M. Tachiki, Y. Kaibara, Y. Sumikawa, M. Shigano, T. Banno, K. S. Song, H. Umezawa, and H. Karada, Physica status solidi A 199, 39 (2003). 69. H. Sugimura, Jap. J. Appl. Phys. 43, 4477 (2004). 70. S. M. Kim and H. Lee, JVST B 21, 2398 (2003).

IV.3 UHV-STM Nanofabrication on Silicon PETER M. ALBRECHT, LAURA B. RUPPALT, AND JOSEPH W. LYDING

The ultrahigh vacuum scanning tunneling microscope (UHV-STM) offers intriguing opportunities to explore the integration of novel nanotechnologies with existing semiconductor platforms. This chapter describes the development of the atomic-resolution hydrogen resist technique and its application to the templated self-assembly of molecular systems on silicon. The observation of a giant isotope effect in STM hydrogen desorption experiments has led to the use of deuterium to retard hot-carrier degradation in CMOS transistor technology. We have also explored the integration of carbon nanotubes with silicon and the III-V compound semiconductors. This has been facilitated by the development of the dry contact transfer (DCT) technique that enables atomically clean nanotube/substrate systems to be achieved, even for highly reactive surfaces like atomically clean silicon.

1 Background and Motivation The creation of hybrid nanoelectronic systems that integrate molecular and/or carbon nanotube electronics and photonics with silicon or compound semiconductor platforms is a key objective for the information technology era beyond the foreseeable end of the semiconductor roadmap [1]. This approach would leverage the vast infrastructure already developed for existing technologies. Though appealing, the successful integration of any new nanotechnology will depend in large part on the microscopic interactions between the constituents of the hybrid system. For example, single-walled carbon nanotubes (SWNTs) show considerable promise for high-performance nanoscale transistors [2]; however, forming good ohmic contacts to nanotubes is still a major issue. Though empirically determined processes can and are being developed to solve the contact problem, these can be nicely augmented by an atomic-level understanding of the interface between a nanotube and its substrate. Our primary goal is to explore at the atomic level the integration of new nanotechnologies with existing semiconductor platforms. We have found that the ultrahigh vacuum scanning tunneling microscope (UHV-STM) is well suited to this 880

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task. This chapter describes several avenues that we have taken in this direction. One of these has been the development of the hydrogen resist method for modifying Si(100) surfaces with atomic precision. These modified surfaces can then serve as templates for molecular self-assembly and other local modifications that take advantage of the chemical contrast between clean and hydrogen-passivated silicon. We have also explored the integration of carbon nanotubes with silicon and the III-V compound semiconductors. A key advance has been the development of the dry contact transfer (DCT) technique that enables atomically clean nanotube/substrate systems to be achieved, even for highly reactive surfaces like atomically clean silicon. This has enabled us to study effects such as the orientational dependence of the interaction of a single-walled carbon nanotube with the substrate. This, and other atomic-scale issues, will be of critical importance as nanotube/semiconductor hybrid systems are considered for large-scale nanoelectronic technologies. Focusing atomic-level studies on current key technological platforms also opens the possibility for new discoveries that have current technological application. Our key example of this is the observation of the giant deuterium isotope effect on silicon surfaces, which was then found to translate directly into a dramatic reduction of hot-carrier degradation effects in current silicon CMOS transistor technology. The remainder of this chapter is organized as follows: first we present our UHV-STM technology and the development of the hydrogen resist technique for atomic-scale lithography on Si(100). This is followed by a section on templated self-assembly which utilizes the lithographic patterns for selective chemical modification of the surface. Next, we describe the giant deuterium isotope effect which was discovered in STM studies of hydrogen desorption from Si(100). This provided the basis for the idea of using deuterium to retard hot-carrier degradation effects in current silicon CMOS transistor technology. The remainder of this chapter describes recent work on the integration of SWNTs with silicon and the III-V compound semiconductors. A key distinction between these surfaces and those that have been used in previous STM studies of carbon nanotubes (e.g., gold [3,4] and graphite [5]) is their incompatibility with the ambient-based nanotube deposition schemes. To preserve the atomic cleanliness of the nanotube/semiconductor system we have developed a new in situ DCT method which is generally extensible to integrating a wide range of nanostructures with a wide range of surfaces.

2 UHV-STM and the Hydrogen Resist Technique 2.1 UHV-STM Although STM is considered to be a relatively mature technique, there are several key instrumental issues that deserve close attention and are generally not available in most UHV-STMs. These are very low thermal drift and three-dimensional coarse

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positioning. While operating at low temperatures can minimize thermal drift and enhance electronic resolution, it can also place restrictions on the sample, such as the use of degenerately doped semiconductors. Combined with the desire to evaluate the potential room temperature operation of new nanotechnologies, this creates the need for a STM that can operate with low thermal drift at room temperature. Figure 1 shows a computer-aided design (CAD) rendering of our homebuilt ˚ at room temperature [6]. UHV-STM, which features a low thermal drift of 2 A/h The key feature of this STM is the use of concentric piezoelectric tubes, one to scan the tip and the other to inertially translate the sample holder. To zero order, temperature changes do not affect the relative positioning of the tip and sample. The use of low thermal expansion materials like quartz and invar complement this geometrical symmetry. We routinely use this instrument to perform multi-hour spectroscopy runs over sample regions tens to hundreds of square nanometers in area. Another feature of this instrument is its inertial tip translator [7]. The tip holder is clamped by a spring-loaded mechanism against a sapphire plate that is moved by the scanning piezo tube. A discontinuous voltage applied to either the x- or y-axis of the tube causes the tip holder to slip inertially against the sapphire disk. The clamping force is too great for this to occur under any normal scanning conditions. This capability enables the tip to be translated in two dimensions anywhere within a 3-mm-diameter circle. This STM design has been modified for operation in a vertical orientation [8] and for operation at cryogenic temperatures in UHV [9,10].

2.2 Hydrogen Resist Technique STM lithography on hydrogen-passivated Si(100) surfaces was first demonstrated by Dagata et al. [11] using an ambient STM to break down the wet passivated surface, forming a local oxide. Becker et al. [12] observed and quantified hydrogen desorption in UHV-STM experiments on a wet-passivated Si(111)-1 × 1:H surface. Motivated by these early accomplishments, we developed an all-UHV approach for patterning the Si(100)-2 × 1:H surface down to the atomic level [13]. We chose

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the Si(100) surface both because of its technological relevance and due to the fact that its 2 × 1 surface reconstruction is unaffected by hydrogen passivation. In contrast, the Si(111)-1 × 1:H surface reverts to a 2 × 1 reconstruction upon hydrogen removal. Furthermore, the Si(111)-2 × 1 surface accommodates three equivalent domains rotated 120◦ relative to each other and exhibiting disordered domain boundaries. Although hydrogen-passivated Si(100) surfaces are readily prepared by wet chemical techniques, considerable chemical contamination and incomplete formation of the bulk (1 × 1) dihydride surface termination is observed. These issues can be circumvented by using an all-UHV hydrogen passivation method that exposes an atomically clean Si(100) surface to atomic hydrogen. By doing so at an elevated temperature (∼377◦ C) it is possible to produce an ideally terminated Si(100)-2 × 1:H monohydride surface in which no Si-Si bonds are broken and only the surface dangling bonds are passivated with hydrogen [14]. A typical sample preparation sequence is now described. Following a standard RCA cleaning procedure, n- or p-type Si(100) samples are mounted on the UHV-STM sample holder and degassed in UHV at ∼600◦ C overnight. The atomically clean Si(100)-2 × 1 surface is then prepared by flashing the sample to a high temperature, typically using several short (∼30 s) flashes to 1,200◦ C while maintaining a background pressure less than 2 × 10−10 Torr. The sample is stabilized at 377◦ C and subsequently exposed to atomic hydrogen, which is produced by cracking molecular hydrogen on a hot (1,500◦ C) tungsten filament located 5–10 cm from the sample. A background H2 pressure of 2 × 10−6 Torr and a dosing time of 10 min guarantees complete passivation of the surface. Figure 2 shows a STM image of the resultant Si(100)-2 × 1:H surface. The uniform passivation across multiple terraces is quite evident. It is also interesting to note that the passivation removes surface states making it easier to observe subtle electronic effects. One example of this has been our ability to create 3D maps of sub-surface dopants for both n-type and p-type samples [15,16]. In the hydrogen resist technique, patterning is achieved by using the STM selectively to desorb portions of the hydrogen monolayer. Examples of this are shown in Figure 3. Several key facts about this technique became evident in the first experiments [13]. First, patterning could be achieved down to the atomic

FIGURE 2. 30 × 30 nm2 UHV-STM image of an atomic hydrogen passivated Si(100)-2 × 1:H surface.

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FIGURE 3. STM depassivation of hydrogen from the Si(100)-2 × 1:H surface. (a) 6 × 6nm2 image showing the boundary between clean (left) and H-passivated (right) silicon. (b) 48 × 48-nm2 area showing 1-nm-wide lines and single atoms of patterned clean Si. (c) 22 × 22 nm2 area showing a 5 × 5 array of individual Si dangling bonds created using the feedback-controlled lithography (FCL) technique.

resolution limit (Figure 3(b)). Second, two H-desorption regimes were evident— one at higher voltages in which hydrogen desorption depends only on electron dose and another at lower voltages in which desorption only occurs at higher currents irrespective of the dose. This behavior was further quantified in a subsequent study [17]. The higher-voltage (>5 V), dose-dependent regime corresponds to single-electron excitation of the Si-H bonding-to-antibonding transition (∼6.5 eV). At low voltages, in the current-dependent desorption regime, STM electrons have insufficient energy to excite the bonding-to-antibonding transition. Instead, they excite a Si-H vibrational mode, and, due to its long vibrational lifetime (∼10 ns), additional excitations can occur before the vibrational energy is quenched to the lattice. Thus, if the excitation rate (current dependent) exceeds the quenching rate desorption will eventually occur from a hot ground state. This vibrational heating mechanism was first proposed by Avouris [18] and used to model the data in the STM experiments. The enhanced patterning resolution in the vibrational heating regime is due to the fact that the STM is operating in the tunneling regime rather than in field emission, as is the case for higher voltages, e.g., greater than 5 V. Although atomic patterning resolution can be achieved in the vibrational heating regime, the patterning can be a bit sporadic due to fluctuations in current density associated with temporal changes in the tip during patterning. To account for this, and thus achieve atomically precise control over the patterning, we developed a method termed feedback-controlled lithography (FCL) [19]. In FCL a hydrogen desorption event is detected, e.g., by the jump in the tunneling current associated with the increased density of states of clean Si, and used as a trigger to prevent further patterning. Figure 3 (c) illustrates a 5 × 5 array of individual Si dangling bonds created using FCL. In that particular experiment, the time required to desorb each H atom varied by over two orders of magnitude over the 5 × 5 array due to a highly unstable tip [20].

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3 Templated Self-Assembly The patterns of clean silicon produced by the hydrogen resist technique are ideal templates for performing selective chemical reaction studies on the silicon surface. Examples include selective oxidation [13,21], nitridation [22], and metallization [23]. Templated self-assembly also presents multiple opportunities for exploring molecular electronics through the integration of molecular arrays with silicon. Figure 4(a,b) demonstrates a step in this direction by showing the selective chemisorption of norbornadiene molecules onto a square area of patterned clean Si [24]. By using FCL to create individual molecular binding sites it is possible to observe more subtle effects between molecules and the silicon substrate. An example of this is shown in Figure 4(c,d), in which copper phthalocyanine (CuPc) molecules are allowed to interact with a ‘V-shaped’ pattern of dangling bonds

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[19]. Following a low CuPc dose the dangling bond sites labeled 1, 2, and 3 in Figure 4(c) are now occupied by CuPc molecules in Figure 4(d). Site 4 remains unreacted. Site 5 appears to have disappeared in Figure 4(d) and a new site, 5′ , has appeared. This is consistent with a CuPc molecule adsorbing at the original site 5 location, transporting along its dimer row and then desorbing at a dimer vacancy, leaving a dangling bond there. Transport along the dimer row involves hydrogen exchange, which eliminates the original site 5 dangling bond. A similar process occurs for site 6; however, the CuPc molecule remains on the surface (outside of the Figure 4(d) image area) following transport along the dimer row. We believe that tip-molecule interaction forces promoted the molecular transport associated with sites 5 and 6. The rationale behind the V-shaped pattern was to systematically control intermolecular spacings and hence intermolecular interactions. Evidence for such an interaction is seen as sites 7 and 8 in Figure 4(d) have now become a new unified entity. The development of the UHV-STM hydrogen resist technique has opened a new field of molecular electronics exploration on silicon. Recent work using FCL coupled with templated molecular self-assembly has led for example to the observation of single-molecule negative differential resistance [25] and the ability to create more complex molecular structures by patterning molecular blocking moieties to control the natural chain growth of styrene molecules along Si dimer rows [26].

4 Deuterium Following a suggestion by Avouris [27], the STM desorption experiments were repeated using deuterated Si(100) surfaces. A giant isotope effect was observed (Figure 5(a)) in which deuterium was about two orders of magnitude more difficult to desorb than hydrogen in the direct desorption regime and essentially impossible to desorb in the vibrational heating regime [28]. The behavior in the direct desorption regime was modeled by Avouris et al. [29] in terms of the MenzelGomer-Redhead (MGR) effect [30], which describes the mass-dependent escape of the excited species from the antibonding potential. Deuterium, due to its heavier mass, moves more slowly away from the stable bonding position and therefore more readily falls back into the bonding potential well, reforming the bond and stalling desorption. This effect is unusually pronounced due to the large isotope mass ratio (2). The large isotope effect observed in the STM experiments served as background for the idea by Lyding and Hess [31] of using deuterium to harden CMOS transistors against hot-carrier degradation effects. In an Si field-effect transistor (FET), electrons or holes flow along the oxide-silicon interface from source to drain. This interface has a large number of Si dangling-bond defects (∼1012 /cm2 ) due to the natural structural mismatch between oxide and silicon. By passivating these defects with hydrogen [32], their deleterious electronic effects can be avoided and high-speed transistor operation is possible. However, over time these defects begin

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to reappear as energetic carriers interact with the oxide-silicon interface. A variety of mechanisms have been proposed to explain this degradation process [33]. These fall generally into two categories: hot-carrier injection into the oxide and hot carriers that remain in the Si channel and interact with the interface, thereby directly stimulating the desorption of the passivating hydrogen. By analogy to the STMobserved isotope effect, the latter mechanism suggests that replacing hydrogen with deuterium at the oxide-silicon interface could enhance hot-carrier transistor lifetimes. Testing this hypothesis showed that replacing a standard hydrogen anneal with a deuterium anneal increased transistor hot-carrier lifetimes by factors of 10 to 50 ([31]). This result implied that the direct interaction of channel hot carriers with the oxide-silicon interface is the dominant degradation mechanism under normal stressing conditions. This was further elucidated in a sequence of experiments that used the isotope effect as a probe of the interface degradation mechanisms [34]. A practical issue that arose in these experiments is the effective incorporation of deuterium due to the ubiquitous presence of background hydrogen in Si integrated circuit chips and the presence of diffusion barriers such as multiple metal and dielectric layers above the device layer in a typical chip. We found that this issue could be effectively addressed by using high-pressure anneals to increase the deuterium incorporation, as shown in Figure 5(b) [35]. It is important to note that processing at higher pressures enabled the same magnitude of lifetime improvement with shorter annealing times. Accordingly, for a given pressure the magnitude of improvement increased with the annealing time. In parallel with the transistor lifetime studies, we extended the STM studies of the isotope effect. In particular, using a cryogenic UHV-STM [9] it was possible to desorb deuterium in the vibrational heating regime [36]. The reduced phonon

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population at low temperature reduces the vibrational quenching to the lattice, thus enabling STM desorption of deuterium at high tunneling currents (∼10 nA). The key result was a dramatic increase in the isotope effect compared to that observed in the direct desorption regime. A plausible explanation for this, advanced by Van de Walle and Jackson [37], is the coincidence of the vibrational frequency of the Si-D bending mode (460 cm−1 ) with the bulk transverse optical phonon at the X point in silicon (463 cm−1 ). At 650 cm−1 the Si-H mode is highly mismatched and therefore has a much longer lifetime. The translation of the deuterium isotope effect from a basic surface science observation to a practical application in today’s chip technology was an unanticipated outcome of this research. The tools and techniques of nanoscience and nanotechnology have evolved to the extent that they enable a new look at old problems. In sections 5–7, we describe an approach to studying the integration of carbon nanotubes with silicon and the III-V compound semiconductors. Again, a key aspect of this work is that of control and understanding at the atomic level.

5 Integration of Carbon Nanotubes with Silicon 5.1 Motivation for Hybrid Nanotube/Silicon Systems Since the experimental observation of single-walled carbon nanotubes (SWNTs) in 1993 [38,39], an intense effort has been underway to elucidate the fundamental electrical, optical, mechanical, and thermal properties of these nearly onedimensional graphitic cylinders [40,41]. Critical applications for SWNTs include high-performance field-effect transistors (FETs) [42,43], infrared optical emitters [44], and tunable electromechanical oscillators [45]. Moreover, SWNTs are leading candidates to serve as building blocks in a future nanoelectronic technology [46]. Considering the multibillion-dollar global infrastructure dedicated to the design and manufacture of silicon-based microelectronics, it would be highly advantageous to smoothly integrate carbon nanotube functionality with the silicon paradigm rather than attempt to supplant the latter entirely. In this light, Tseng et al. [47] connected SWNT FETs to Si metal-oxide-semiconductor (MOS) FETs fabricated on the same substrate to create a monolithic integrated circuit. In addition, Tzolov et al. [48] demonstrated electronic transport in a SWNT-Si heterojunction array. Akturk et al. [49] have simulated a hybrid SWNT-Si switching device realized by embedding an array of semiconducting SWNTs in the channel of a MOSFET. Using ab initio density functional theory, Orellana et al. [50] have studied the adsorption of a (6,6) metallic SWNT on the Si(100) surface and implications to nanoscale contacts and interconnects. The aforementioned research serves to motivate an atomic-scale experimental study of the electrical and mechanical properties of SWNTs integrated with Si. Ultrahigh vacuum scanning tunneling microscopy (UHV-STM) represents one viable route to achieving an atomistic understanding of the physical properties of both metallic and semiconducting SWNTs directly interfaced with a silicon surface.

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5.2 Scanning Tunneling Microscopy of Carbon Nanotubes Along with exquisite atomically resolved images of SWNTs, UHV-STM verified the predicted sensitivity of the electronic properties of the SWNT to its geometrical structure. Specifically, UHV-STM measurements by Wild¨oer et al. [3] and Odom et al. [4] independently verified that subtle fluctuations in the diameter or the chiral angle of a SWNT could elicit a transition from metallic to semiconducting behavior. The SWNTs probed in these studies were supported by Au(111), a noble metallic surface compatible with ambient processing. However, the electrical and structural properties of SWNTs in contact with semiconducting substrates having greater technological relevance (e.g., Si(100)) remained an open question. Avouris et al. [51] measured the tunneling current-voltage spectrum corresponding to an individual SWNT deposited onto Si(100)-2 × 1:H. The SWNT on the H-passivated Si(100) surface appeared more lightly p-doped compared to earlier results for SWNTs on Au(111), where in the latter case the Fermi level was positioned next to the valence band edge of the SWNT [3]. This report stimulated interest in a more comprehensive UHV-STM study of SWNTs on Si(100), as the burgeoning field of Si-based molecular electronics [19,52] could be profoundly enriched by the integration of SWNTs.

5.3 Limitations of Solution Deposition of Carbon Nanotubes onto Conductive Substrates for UHV-STM Although solution deposition is arguably the simplest method to deposit SWNTs onto a surface for UHV-STM analysis, there are several drawbacks. First, SWNTs dispersed in organic solvents have a strong propensity to exist as bundles, rather than individual tubes. As a result, well-isolated SWNTs have represented only a small minority of the nanotube features observed with UHV-STM [4,53]. Solution processing of SWNTs can lead to structural defects due to ultrasonic agitation [54], unintentional doping by ionic species [55], and irreversible modification of their electronic structure due to nanotube-solvent interactions [56]. Accordingly, Ouyang et al. [57] noted that extreme care was taken to minimize solution processing of the SWNTs and ambient degradation of the Au(111) substrate. Finally, while ambient solution deposition of SWNTs is suitable for inert substrates (e.g., gold and graphite), the technique is incompatible with atomically clean semiconducting surfaces (e.g., Si(100)-2 × 1 and UHV-cleaved GaAs(110)) that degrade rapidly upon ambient exposure. Terada et al. [58] pulse-injected a nanotube/hexane mixture onto an Hterminated Si(100) substrate held in a high-vacuum chamber, and subsequently discovered with the UHV-STM that both nanotubes and a residual organic layer were present on the surface. Baluch et al. [59] demonstrated that an inert atmosphere glovebox was necessary for liquid-phase chemical processing of Si(100)2 × 1:H; treatments performed under ambient conditions resulted in degradation of the UHV-prepared surface. Both reports implicitly motivated an all-UHV method

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for the deposition of carbon nanotubes and other nonvolatile species onto a wide range of conductive surfaces for STM characterization.

5.4 Atomically Clean Deposition of Carbon Nanotubes onto Silicon Surfaces by Dry Contact Transfer Albrecht and Lyding [60] developed a dry contact transfer (DCT) technique for the in situ deposition of SWNTs onto the UHV-prepared Si(100)-2 × 1:H surface. Two key advantages of the DCT method are: (i) the deposition of SWNTs occurs in a UHV (∼10−10 Torr) environment, precluding degradation of the UHV-prepared Si(100)-2 × 1:H surface upon ambient exposure and subsequent liquid-phase treatment, and (ii) the DCT applicator can be prepared from SWNTs in powder form, which circumvents solution processing of SWNTs. The applicator consists of fiberglass sheath [61] coated with SWNTs. Following a short degas in UHV, the applicator is maneuvered into gentle mechanical contact with the Si surface to transfer the SWNTs. Although initially demonstrated with as-produced HiPco [62] SWNTs, the DCT technique has recently been extended to the deposition of CoMoCat [63] SWNTs onto H-passivated Si(100) [64].

6 UHV-STM of Carbon Nanotubes on Si(100) 6.1 Single-Walled Carbon Nanotubes on Si(100)-2 × 1:H

Figure 6(a) shows a three-dimensional rendering of a 10 × 10-nm2 STM topograph acquired near the end of an isolated SWNT on the Si(100)-2 × 1:H surface. The STM current image acquired concurrently with the topographic data is shown in Figure 6(b). The measured height of the SWNT (0.98 ± 0.03 nm) provides a reasonable estimate of its diameter. Individual Si dimers and the graphene lattice that constitutes the SWNT are simultaneously resolved, conveying the atomic-scale cleanliness of the SWNT/Si interface formed by DCT. Figure 7 shows a 50 × 50-nm2 STM topograph (Figure 7(a)) and current image (Figure 7(b)) of two distinct SWNTs deposited onto the Si(100)-2 × 1:H surface by in situ DCT. Within each of the three Si terraces, the Si dimer rows are clearly resolved, and residual contamination is negligible. The density of Si dangling bond defects, which appear as protrusions in the topographic image, is comparable to that observed prior to DCT. Interestingly, the two nanotubes are separated from one another on the surface rather than bundled together. The observation of primarily isolated SWNTs (rather than nanotube bundles) spanning largely contaminant-free regions of the Si substrate is consistent over numerous experimental trials incorporating the DCT technique. We hypothesize that during the DCT, individual SWNTs are detached from the exterior of large ropes due to van der Waals interaction with the H-Si(100) surface. Figure 8 shows 16 × 16-nm2 STM topographic (Figure 8(a)) and current images (Figure 8(b)) of the two distinct SWNTs depicted in Figure 7. The heights of the

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upper and lower SWNTs relative to the H-passivated Si(100) surface are 1.10 ± 0.05 nm and 1.05 ± 0.05 nm, respectively. In addition, the Si dimer rows are clearly evident between the two SWNTs. Figure 8(c) shows tunneling current-voltage (I -V ) spectra recorded for each SWNT along with the local Si(100)-2 × 1:H substrate. The absolute value of the tunneling current is plotted on a logarithmic scale as a function of the sample bias. I -V spectra acquired for both nanotubes reveal a conductance gap consistent with SWNTs of the semiconducting variety. Moreover, the conduction (empty states) band edges of both SWNTs are shifted closer to the Fermi level (V = 0 V) compared with that of the Si substrate. The ability to discern electronic features unique to the SWNT within the gap of the semiconducting substrate is an intriguing, yet highly reproducible, result. To explain this phenomenon,

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Sample Voltage (V) FIGURE 8. 16 × 16-nm2 UHV-STM (a) topographic image and (b) current image of the two distinct single-walled carbon nanotubes depicted in Figure 7.(c) Tunneling current-voltage (I-V) spectra for both nanotubes and the local Si(100)-2 × 1:H substrate.

Ruppalt et al. [65] have proposed a band-to-band recombination model after observing a Type-I band alignment for SWNTs on the cleaved GaAs(110) surface. In these measurements, the occupied and unoccupied states band edges of the SWNT were positioned inside of the band gap of the GaAs substrate. An isolated SWNT positioned near a step edge of the H-passivated Si(100) substrate is shown in Figure 9. The STM current image reveals atomic-level detail that was not as clearly elucidated in the topographic data. The differential conductance (dI /dV -V ) spectra for the nanotube and the Si substrate are shown in Figure 9(b). dI /dV provides a rough measure of the local electronic density of states at a particular energy. The nanotube dI /dV contains a peak near 0.5 V, likely associated with the first conduction subband in the density of states of the semiconducting SWNT [66]. A 35 × 35-nm2 STM current image of an individual SWNT on the Si(100)-2 × 1:H surface is shown in Figure 10. Several artifacts appear proximal to the real SWNT due to a multiple tip effect. The STM topograph is shown as the inset to Figure 10(a), with the prominent bright feature indicating the true position of the nanotube. Upon careful inspection of the current image, one finds that the nanotube axis is aligned with the nearest-neighbor hexagon rows of the sp2 -hybridized carbon lattice of the SWNT. This is evidence for an armchair metallic SWNT (a-SWNT) having chiral indices (n, n). Figure 10(b) shows the results of I-V spectroscopy performed to test this hypothesis. The dc I -V characteristic

(a)

dI/dV [arbitrary units]

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FIGURE 9. (a) 10 × 10-nm2 STM current image of a semiconducting SWNT oriented along a step edge of the Si(100)-2 × 1:H substrate. (b) Differential conductance (dI /dV ) versus sample bias (Vbias ) for the nanotube (solid line) and the substrate (dashed line).

for the Si(100)-2 × 1:H substrate contains well-defined valence and conduction band edges, separated by a ∼1.4 V gap. In contrast, the I -V characteristic of the nanotube is approximately linear over the range −1V ≤ Vbias ≤ 0.75 V. This behavior is consistent with that of an isolated a-SWNT rather than one contained in a rope. Specifically, the absence of a “pseudogap” at the Fermi level confirms that the n-fold rotational symmetry of the a-SWNT has not been broken by tubetube interactions arising in a bundle [57,67]. Locating a nanotube bundle on the Si(100)-2 × 1:H surface is actually a rare event following the in situ DCT process described previously. Figure 11(a) shows a 16 × 8.4-nm2 STM topograph of an isolated SWNT spanning several terraces of a vicinal Si(100)-2 × 1:H surface [68]. Experiments of this type provide an opportunity to explore the electrical and the mechanical properties

(a)

(b)

FIGURE 10. (a) 35 × 35-nm2 STM current image of an armchair metallic SWNT on Si(100)2 × 1:H. Inset: The corresponding STM topograph showing the primary (bright) SWNT feature and proximal tip artifacts. (b) Tunnel current (Itunnel ) versus sample bias (Vbias ) for the nanotube and the substrate, respectively.

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(a)

(c)

(b)

FIGURE 11. (a) 16 × 8.4-nm2 -filled states STM topographic image showing an isolated SWNT spanning several terraces of a highly stepped Si(100)-2 × 1:H surface. Tunneling parameters were −1.50 V, 25 pA. (b) STM current image acquired simultaneously with the STM topograph shown in (a), revealing the chiral lattice of the nanotube. (c) 6.6 × 6.6-nm2 empty states STM current image showing simultaneous atomic resolution of the SWNT and Si substrate. Tunneling parameters were +1.20 V, 20 pA.

of a carbon nanotube adsorbed on a stepped surface [69]. One end of the tube is visible near the left edge of the scan window. The current image (Figure 11(b)) was acquired in parallel with the topographic data, and reveals the SWNT chiral lattice and the Si dimers. The absence of surface contamination is again attributed to the cleanliness of the in situ DCT. Figure 11(c) shows a 6.6 × 6.6-nm2 STM current image, with simultaneous atomic resolution achieved for the Si substrate and the adsorbed SWNT.

6.2 Compatibility of Hydrogen-Resist STM Nanolithography with Carbon Nanotubes on Si(100)-2 × 1:H

The H-terminated Si(100) surface lends itself to nanolithographic patterning via H desorption with the STM tip [13]. One can then exploit the chemical contrast between the highly reactive Si dangling bonds and the relatively inert H-passivated background to engineer the local environment at an arbitrary position along a SWNT [70]. The 30 × 30-nm2 STM topographic image presented in Figure 12 shows a ∼4-nm-wide, ∼25-nm-long stripe of depassivated Si intercepting an isolated SWNT. Patterning conditions (+7 V sample bias, 0.1 nA, 10−4 C/cm dose) were not interrupted when the electron current intercepted the adsorbed SWNT approximately halfway through the nanolithography routine. The SWNT remained structurally intact, and more recent data suggests that even the Si dimers directly underneath the SWNT are depassivated by this process. Moreover, we have reproducibly leveraged this technique to stabilize SWNTs that were mechanically perturbed in the presence of the rastered STM tip due to an initially weak interaction with the Si substrate. Current image tunneling

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FIGURE 12. (a) 30 × 30-nm2 STM topograph of an individual SWNT after a ∼4-nm-wide, ∼25-nm-long stripe of depassivated Si was patterned by electron stimulated desorption of hydrogen by the STM probe. (b) Three-dimensional rendering of the topographic image shown in (a). The enhanced reactivity of the Si dangling bonds causes the rectangular pattern to appear as a protrusion under filled states imaging (Vsample = −1.5 V, Itunnel = 20 pA). (See also Plate 14 in the Color Plate Section.)

spectroscopy (CITS), where a full I-V or dI /dV-V characteristic is recorded at each pixel of a topographic image, may offer insight into local changes in the chemical and electronic interactions at the SWNT/Si interface (e.g., a transition from physisorption to chemisorption). Maltezopoulos et al. [71] have recently observed confined states in extended metallic SWNTs on Au/mica surfaces, which they attribute to backscattering by impurities and/or defect sites. This suggests the possibility for templating localized electronic states along the length of a SWNT adsorbed onto Si(100)-2 × 1:H by the nano-lithographic patterning of Si dangling bond defects in close proximity to the nanotube.

6.3 Single-Walled Carbon Nanotubes on Clean Si(100)-2 × 1

In addition to experiments conducted on the H-passivated Si(100) substrate, we have also performed UHV-STM of SWNTs in direct contact with the clean Si(100)2 × 1 surface [68]. The in situ DCT technique we have developed is essential for forming an atomically pristine SWNT/Si(100)-2 × 1 interface, as the clean Si(100) surface is incompatible with the ex situ solution-phase deposition of SWNTs due to the formation of native SiO2 upon ambient exposure. A 14 × 9-nm2 STM topograph of an individual SWNT on the clean Si(100) surface is shown in Figure 13(a), where the SWNT appears as two neighboring features due to a double tip artifact. The angle between the axis of the SWNT and the Si dimer rows is 40◦ , and from the measured height of the primary (bright) SWNT we estimate a tube diameter of 0.8 nm. Figure 13(b) shows dI /dV versus substrate bias for the SWNT (solid line) and the local p-type Si(100)-2 × 1 surface (dashed line), respectively. The SWNT dI /dV characteristic was found to be independent of position over the 15-nm-long interior section shown in Figure 13(a); the depicted spectrum represents the average of seven equally spaced measurements along the axis of the tube. This SWNT exhibits n-type semiconducting character, with the valence (filled states) and conduction (empty states) band edges separated by a

Peter M. Albrecht, Laura B. Ruppalt, and Joseph W. Lyding Differential tunneling conductance, dI/dV (arb. units)

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FIGURE 13. (a) 14 × 9-nm2 STM topograph showing the interior of an isolated SWNT on the UHV-cleaned Si(100)-2 × 1 surface. An artifact of the true SWNT appears due to a secondary imaging asperity at the apex of the STM tip. The SWNT is out of registration with the substrate; the angle between the nanotube axis and the Si dimer rows is 40◦ . Tunneling parameters were −1.4 V, 70 pA. (b) Differential tunneling conductance, dI /dV , versus substrate bias for the p-type Si(100) surface (dashed line) and the nanotube (solid line), respectively. The data suggest that the SWNT is an n-type semiconductor, with the Fermi level (V = 0 V) positioned closer to the onset of the conduction band. We also note the Type-II alignment of the dI /dV spectrum of the SWNT relative to that of the Si substrate.

0.9-eV gap. This value is in good agreement with the predicted gap from tight binding of E gap = 2γ0 aC−C /d ∼ 1 eV, where aC-C = 0.142 nm is the nearestneighbor C-C distance and γ0 = 2.9 eV is taken as the C-C tight-binding overlap integral. Avouris et al. [51] also identified n-doped semiconducting SWNTs on the Au(111) surface, where this n-type character was ascribed to substitutional impurities or species encapsulated by the SWNT. We also highlight the Type-II alignment of the two dI /dV spectra, where the SWNT conduction band edge is positioned inside the gap of p-Si(100). The identification of electronic features unique to the SWNT inside the substrate band gap is consistent with STS of SWNTs interfaced with H-passivated Si(100) [60].

7 STM of SWNTs on the GaAs(110) and InAs(110) Surfaces Apart from silicon, the most technologically relevant semiconductors are the IIIV materials, the majority of which possess a direct bandgap, giving rise to their valuable light-emitting properties and enabling their broad applicability in optoelectronics. Additionally, the precise control of layer growth provided by present MOCVD and MBE systems, combined with the ability to vary the material bandgap and lattice constant through deliberate alloying, allows for the fabrication of intricate and elaborate device structures impossible in other material systems. Coupling carbon nanotubes with such compound semiconductors could spur the development of novel device concepts and structures—it is conceivable that the optical properties of SWNTs, including their utility as polarized photodetectors [72], and

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their ability to act as optical emitters [44], could be more fully exploited when coupled with optically active III-V substrates. Additionally, the ability to tailor the III-V materials to provide specified material characteristics such as lattice constant and electronic band gap could provide a class of materials useful for the systematic study of nanotube-substrate interactions. While SWNT integration with various III-V materials has been explored theoretically [73], and initial reports of nanotube incorporation into Mn-doped GaAs structures have been made [74], experimental research on carbon nanotube/III-V systems has been limited, and a basic understanding of the nature of the physical and chemical forces governing a nanotube’s interactions with such compound materials is lacking. The STM, with its ability to resolve both physical and electronic features on an atomic level, when matched with the DCT method for nanotube transfer, offers an ideal method for the study of the fundamental SWNT-surface interactions in these systems. The DCT process provides a simple, UHV-friendly method of molecular deposition for ambient-incompatible substrates like the IIIV(110) surfaces that results in a nearly pristine system of unperturbed, isolated nanotubes distributed across the support, while subsequent STM imaging and spectroscopy can furnish detailed electronic and topographic information for both the nanotubes and the underlying substrate.

7.1 STM Imaging of SWNT/III-V(110) Systems To date, HiPco-produced SWNTs have been applied via in situ DCT to GaAs and InAs (110) surfaces obtained through cleavage in UHV [65,75,76], with a representative empty states STM image of an individual SWNT on the GaAs(110) surface shown in Figure 14. The results of SWNT depositions on the III-V materials mirror those observed on silicon surfaces in terms of the species transferred — primarily isolated SWNTs are applied to the surface, there being a notable absence of large nanotube bundles or ropes and little evidence of spurious contamination resulting from the deposition process. Furthermore, on these nonpolar III-V surfaces a strong directional preference for deposited nanotubes is observed, as a striking number of SWNTs align in the ¯ 110 direction, along the surface sublattice rows (Figure 15). This is in contrast to DCT-deposited nanotubes on Si-based substrates, for which there have yet been no published observations of a particular nanotube orientation inclination. It is believed that this directional dependence of SWNT alignment on the III-V(110) surfaces can be attributed to the stronger binding forces between nanotubes and the cations (Ga, In) of these compound semiconductors. For zigzag SWNTs commensurate with the underlying lattice, Kim et al. [73] predict the formation of a weak chemical bond between the electrons in the filled C-C π orbitals and the empty dangling bond orbitals of the cations of the III-V(110) surface, providing binding forces stronger than the expected van der Waals interactions. These enhanced binding forces may be responsible for the propensity of SWNTs to adhere more strongly, and thus be transferred from the DCT applicator more easily, when they are aligned ¯ along the 110 direction, where the linear density of surface cations is greatest.

Au: fix crashing characters

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(b)

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FIGURE 14. (a) Three-dimensional rendering of the 19.5 × 19.5-nm2 empty states topographic image displaying a SWNT on the n-type GaAs(110) surface shown in (c). (b) Concurrently captured current image. Nanotube chirality and individual Ga atoms of the substrate are simultaneously resolved. Both nanotube and substrate are completely intact following in situ deposition via dry contact transfer (DCT). Tunneling parameters were 1.6 V and 15 pA.

7.2 STS of SWNT/III- V(110) Systems STS performed on SWNT/III-V systems can be used to directly probe the electronic states of those systems and can provide valuable information regarding the electronic nature of the nanotube-surface interface. A comparison of room temperature

FIGURE 15. UHV-STM current images of SWNTs on the (a) GaAs(110) and (b) InAs(110) surfaces. Insets are topographic images. In both cases, the nanotubes are aligned along the sublattice rows of the (110) surface. Note that only a single nanotube is imaged in each figure—the adjacent artifacts resulted from a multiple tip. Imaging parameters: (a) 15 pA 10 pA, 1.7 V, 19.5 × 19.5 nm2 and (b) 10 pA, −1.4 V, 55.7 × 55.7 nm2 . (c) Schematic of the proposed bonding configuration between a carbon nanotube and the In cation of the (110) surface. Illustration after [73].

IV.3. UHV-STM Nanofabrication on Silicon

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FIGURE 16. (a) dI /dV -V distribution corresponding to the SWNT on GaAs (110) shown in the inset STM topograph, calculated from constant height I -V STS measurements. Imaging parameters: 8 pA, −1.5 V, 20 × 9.6 nm2 . (b) Illustration of STS-determined GaAs/ NT Type-I band alignment.

tunneling spectroscopy data collected from nanotubes on the GaAs(110) and InAs(110) surfaces as shown in Figures 16 and 17 prompt several noteworthy observations, as summarized below. On both material samples, electronic features associated with the deposited nanotubes are distinguishable within the electronic gap of the supporting substrate. This phenomenon appears consistently across semiconducting substrates, as comparable spectra are measured on SWNTs applied to the H-passivated Si(100) surface [60]. The detection of tunneling current in the absence of available substrate electronic states precludes the possibility of direct elastic tunneling in these systems, and is suggestive of an alternative carrier transport mechanism, potentially

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A pApplied p lie d VVoltage o lta g e(V) (V )

FIGURE 17. (a) As-recorded variable spacing dI /dV-V plot of a SWNT on InAs(110). The predicted bandgap value of 0.68 eV is in good agreement with the measured value of 0.70 eV. Imaging parameters: 50 pA, −1.4 V, 15.1 × 10.4 nm2 . (b) Schematic illustration of the Type-II InAs(110)/NT band alignment.

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a band-to-band scheme in which carriers injected from both the nanotube and the substrate recombine across the nanotube bandgap, generating a net current from STM tip to substrate [65]. Additionally, measurements of the semiconducting nanotube bandgaps in these systems are in good agreement with tight-binding theoretical values predicted by equating the nanotube diameter to the STM-measured tube height, indicating that the basic electrical structure of the nanotubes is not significantly altered by the transfer process or by integration onto the III-V substrate. Though the width of the electronic bandgap for a given SWNT appears relatively unchanged regardless of its supporting semiconductor substrate, the tube energy gap alignment with that of the supporting surface is highly dependent on the composition of the substrate itself. Tunneling spectra from the SWNT/GaAs(110) system provide evidence of a Type-I band alignment, with the nanotube bandgap contained wholly within the substrate gap, while dI /dV -V measurements of the SWNT/InAs(110) system reveal a Type-II band alignment, with the nanotube conduction band edge well within the conduction band of the InAs substrate. These findings are in excellent qualitative agreement with calculations performed by Kim et al. [77] and further confirm the sensitivity of the conducting character of SWNTs to their immediate environment. Additionally, the apparent doping of these HiPco SWNTs by virtue of their proximity to different III-V surfaces—those on the GaAs(110) surface appear approximately intrinsic while those in contact with the InAs(110) surface take on a p-type character—suggest the possibility of intentional nanotube doping and charge transfer through substrate engineering.

7.3 CITS of the SWNT/InAs(110) System In addition to conventional STS, current image tunneling spectroscopy (CITS), in which a full I -V or dI /dV -V spectrum is obtained at each pixel in the imaging mesh, can be used to obtain a rich array of electronic data from nanotube-based systems [78]. The STM topograph of Figure 18(a) depicts a SWNT with a central defect that was observed on the InAs(110) surface, with STS measurements verifying that this defect divides the tube into semiconducting (left) and conducting (right) segments, effectively creating an intramolecular semiconducting-metallic junction. Variable-spacing I -V spectra taken at a series of points along the length of the tube indicate that the electrical and physical junctions are not coincident, with the transition between semiconducting and metallic character occurring several nanometers to the left of the physical location of the defect, well within the “semiconducting” tube segment. The nature of the electrical junction can be further elucidated by acquiring I -V CITS spectra, recording the tunneling current characteristic at each imaging pixel as the voltage is swept from −2 V to +2 V. CITS data taken along the axis of the SWNT area depicted in Figure 18(a) is plotted in three-dimensional format in Figure 19, with the position along the nanotube measured on the x-axis and the voltage applied to the substrate measured along the y-axis. The height at a given (x, y) coordinate corresponds to the log of the

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FIGURE 18. (a) STM topograph of SWNT with central defect located at position 4. Imaging parameters: 50 pA, −2 V, 12.7 × 7.8 nm2 . (b) Variable-spacing ln(I)-V STS measurements acquired along the length of the tube at points indicated in topograph (a) verify the semiconducting and metallic character of the nanotube to the left and right of the central defect, respectively. The electronic transition occurs between spectra points 2 and 3, several nanometers to the left of the defect.

magnitude of the tunneling current recorded at the given spatial location, x, with the specified bias voltage, y, applied to the sample. Thus, a vertical slice parallel to the y-z plane corresponds to the STS I -V characteristic at the given x location. The location of the physical defect, as determined by correlation with simultaneously acquired topographic information, is indicated by an arrow.

FIGURE 19. 3D-rendering of CITS data from the junction region of the nanotube depicted in Figure 18(a). The black arrow indicates the physical location of the defect. The electronic character of the NT gradually transitions from metallic to semiconducting well to the left of the physical junction, indicative of the decay of the metallic electron wavefunction into the semiconducting tube segment.

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Peter M. Albrecht, Laura B. Ruppalt, and Joseph W. Lyding

At the leftmost x location, when the tip is positioned furthest into the semiconducting portion of the nanotube, the tube’s electronic energy gap of ∼1.0 eV is clearly visible as an elongated depression in the collected tunneling current. At the rightmost x location, however, the significant current contributions across the full range of applied bias gives evidence to the metallic nature of the right-hand tube segment. As the data is traversed from right to left, it is observed that the metallic character extends approximately 1.4 nm past the point of the physical defect into the “semiconducting” tube segment, then gradually transitions to complete semiconducting behavior over a ∼3.4-nm length. It is believed that this measurement of conducting behavior within the “semiconducting” portion of the nanotube can be ascribed to the decay of the metallic electron wave-funtion into the semiconducting nanotube segment.

8 Conclusions In this chapter, we have demonstrated the synergy of combining atomic-scale analysis and patterning with technologically relevant semiconductor surfaces. Atomically precise templates of Si dangling bonds for molecular adsorption and selective chemistry have been fabricated on Si(100)-2 × 1:H surfaces by locally desorbing hydrogen with the UHV-STM. A spin-off of this work has been the discovery of a giant isotope effect, prompting the use of deuterium to combat the effects of hot-carrier degradation in present-day CMOS technology. We have also developed a new dry contact transfer (DCT) method for the ultraclean in situ deposition of individual carbon nanotubes onto H-passivated and clean silicon as well as GaAs and InAs. STM spectroscopy has elucidated the connection between the relative nanotube-substrate orientation and the electronic properties of the nanotube; this effect will be of paramount importance in any future technological application of carbon nanotubes in nanoelectronic devices. Furthermore, the DCT method is generally extensible to a wide range of nanostructures and surfaces that are not amenable to other deposition schemes. Experiments are now in progress combining atomic scale modifications and selective chemistry to control the nanotube–silicon interface, while atomic scale characterization is being extended to study the expected rich behavior of carbon nanotubes interfaced with compound semiconductor heterostructures. Given its ability to probe and manipulate molecular structures with atomic precision, the value of the UHV-STM in controlling and investigating these and other novel hybrid systems on the sub-nanometer scale cannot be underestimated. Acknowledgments. The work reported in this chapter was supported under grants N00014-92-J-1519, N00014-98-I-0604, N00014-00-1-0234, N00014-03-1-0266 from the Office of Naval Research and by a grant from Intel Corporation. We are also grateful for valuable collaborations and interactions with Dr. Phaedon Avouris, Professor Karl Hess, and Dr. Isik C. Kizilyalli. P.M.A. and L.B.R. acknowledge support from the Department of Defense through NDSEG Graduate Fellowships.

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30. D. Menzel and R. Gomer, J. Chem. Phys. 41, 331 (1964); P. Redhead, Can. J. Phys. 42, 886 (1964). 31. J. W. Lyding, K. Hess, and I. C. Kizilyalli, Appl. Phys. Lett. 68, 2526 (1996). 32. A. B. Fowler, U.S. Patent No. 3,849,204 (1974). 33. S. Wolf, Silicon Processing for the VLSI Era, vol. 3—The Submicron MOSFET, (Lattice Press, 1995), pp. 559–674. 34. Z. Chen, K. Hess, J. Lee, J. W. Lyding, E. Rosenbaum, I. Kizilyalli, S. Chetlur, and R. Huang, IEEE Electron Device Lett. 21, 24 (2000). 35. Jinju Lee, K. Cheng, Z. Chen, K. Hess, and J. W. Lyding, Y.K. Kim, S.H. Lee, H.S. Lee, Y.H. Lee, Y.W. Kim and K.P. Suh, IEEE Electron Device Lett. 21, 221 (2000). 36. E. T. Foley, A. F. Kam, J. W. Lyding, and Ph. Avouris, Phys. Rev. Lett. 80, 1336 (1998). 37. C. G. Van de Walle and W. B. Jackson, Appl. Phys. Lett. 69, 2441 (1996). 38. S. Iijima and T. Ichihashi, Nature (London) 363, 603 (1993). 39. D. S. Bethune, C. H. Klang, M. S. deVries, G. Gorman, R. Savoy, J. Vazquez, and R. Beyers, Nature (London) 363, 605 (1993). 40. M. S. Dresselhaus, G. Dresselhaus, and Ph. Avouris (Eds.), Carbon Nanotubes: Synthesis, Structure, and Applications (Springer, Berlin, 2001). 41. R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998). 42. S. J. Wind, J. Appenzeller, R. Martel, V. Derycke, and Ph. Avouris, Appl. Phys. Lett. 80, 3817 (2002). 43. A. Javey, J. Guo, Q. Wang, M. Lundstrom, and H. Dai, Nature (London) 424, 654 (2003). 44. J. A. Misewich, R. Martel, Ph. Avouris, J. C. Tsang, S. Heinze, and J. Tersoff, Science 300, 783 (2003). ¨ unel, D. Roundy, T. A. Arias, and P. L. McEuen, Nature 45. V. Sazonova, Y. Yaish, H. Ust¨ (London) 431, 284 (2004). 46. J. Appenzeller, R. Martel, V. Derycke, M. Radosavljevi´c, S. Wind, D. Neumayer, and Ph. Avouris, Microelectron. Eng. 64, 391 (2002). 47. Y.-C. Tseng, P. Xuan, A. Javey, R. Malloy, Q. Wang, J. Bokor, and H. Dai, Nano Lett. 4, 123 (2004). 48. M. Tzolov, B. Chang, A. Yin, D. Straus, J. M. Xu, and G. Brown, Phys. Rev. Lett. 92, 075505 (2004). 49. A. Akturk, G. Pennington, and N. Goldsman, Proc. 3rd IEEE Conference on Nanotechnology 1, 24 (2003). 50. W. Orellana, R. H. Miwa, and A. Fazzio, Phys. Rev. Lett. 91, 166802 (2003). 51. Ph. Avouris, R. Martel, H. Ikeda, M. C. Hersam, H. R. Shea, and A. Rochefort, in Science and Application of Nanotubes, edited by D. Tomanek and R. J. Enbody (Kluwer Academic/Plenum Publishers, New York, 2000), pp. 223–237. 52. T. Rakshit, G.-C. Liang, A. W. Ghosh, and S. Datta, Nano Lett. 4, 1803 (2004). 53. D. J. Hornbaker, Ph.D. thesis, University of Illinois at Urbana-Champaign (2003). 54. K. L. Lu, R. M. Lago, Y. K. Chen, M. L. H. Green, P. J. F. Harris, and S. C. Tsang, Carbon 34, 814 (1996). 55. J. Chen, M. A. Hamon, H. Hu, Y. Chen, A. M. Rao, P. C. Eklund, and R. C. Haddon, Science 282, 95 (1998). 56. S. Niyogi, M. A. Hamon, D. E. Perea, C. B. Kang, B. Zhao, S. K. Pal, A. E. Wyant, M. E. Itkis, and R. C. Haddon, J. Phys. Chem. B 107, 8799 (2003). 57. M. Ouyang, J.-L. Huang, C. L. Cheung, and C. M. Lieber, Science 292, 702 (2001).

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58. Y. Terada, B. K. Choi, S. Heike, M. Fujimori, and T. Hashizume, Jap. J. Appl. Phys. 42, 4739 (2003). 59. A. S. Baluch, N. P. Guisinger, R. Basu, E. T. Foley, and M. C. Hersam, J. Vac. Sci. Technol. A 22, L1 (2004). 60. P. M. Albrecht and J. W. Lyding, Appl. Phys. Lett. 83, 5029 (2003). 61. Heat-treated braided fiberglass sleeving, SPC Technology, 4801 N. Ravenswood Ave., Chicago, IL 60640. 62. Carbon Nanotechnologies, Inc., 16200 Park Row, Houston, TX 77084. 63. SouthWest NanoTechnologies, Inc., 2360 Industrial Blvd., Norman, OK 73069. 64. K. A. Ritter, P. M. Albrecht, and J. W. Lyding (unpublished). 65. L. B. Ruppalt, P. M. Albrecht, and J. W. Lyding, J. Vac. Sci. Technol. B 22, 2005 (2004). 66. C. T. White and J. W. Mintmire, Nature (London) 394, 29 (1998). 67. P. Delaney, H. J. Choi, J. Ihm, S. G. Louie, and M. L. Cohen, Nature (London) 391, 466 (1998). 68. P. M. Albrecht and J. W. Lyding, AIP Conf. Proc. 723, 173 (2004). 69. Ph. Lambin, V. Meunier, and L. P. Biro, Carbon 36, 701 (1998). 70. P. M. Albrecht and J. W. Lyding, Superlattice Microst. 34, 407 (2003). 71. T. Maltezopoulos, A. Kubetzka, M. Moregenstern, R. Wiesendanger, S. G. Lemay, and C. Dekker, Appl. Phys. Lett. 83, 1011 (2003). 72. M. Freitag, Y. Martin, J. A. Misewich, R. Martel, and Ph. Avouris, Nano Lett. 3, 1067 (2003). 73. Y.-H. Kim, M. J. Heben, and S. B. Zheng, Phys. Rev. Lett. 92, 176102 (2004). 74. A. Jensen, J. R. Hauptmann, J. Nyg˚ard, J. Sadowski, and P. E. Lindelof, Nano Lett. 4, 349 (2004). 75. L. B. Ruppalt, P. M. Albrecht, and J. W. Lyding, in 2004 Fourth IEEE Conference on Nanotechnology, Munich, Germany (August 2004). 76. L. B. Ruppalt, P. M. Albrecht, and J. W. Lyding (to be published), 2005. 77. Y.-H. Kim, M. J. Heben, and S. B. Zhang, AIP Conf. Proc. 772, 1031 (2005). 78. S. G. Lemay, J. W. Janssen, M. van den Hout, M. Mooij, M. J. Bronikowski, P. A. Willis, R. E. Smalley, L. P. Kouwenhoven, and C. Dekker, Science 412, 617 (2001).

IV.4 Ferroelectric Lithography DONGBO LI AND DAWN A. BONNELL

The effects of domain orientation on the properties of ferroelectric surfaces are examined for single crystal BaTiO3 (100). Domain specific adsorption determined from surface potential variations suggests a mechanism for a new lithographic process. Three approaches (contact electrode, SPM, and e-beam) for patterning surface domains in the absence of a device metal electrode are explored. In particular the interaction of an electron beam with a ferroelectric surface is quantified and it is shown that it can cause both negative and positive surface charge depending on conditions. The domain specific reactivity and domain patterning are combined into a fabrication process that is demonstrated for several classes of nanostructures.

1 Introduction Ferroelectric compounds have been the basis of a large class of traditional electronic ceramic devices for over five decades and have provided a framework in which to study the physics of electron–lattice interactions. The last decade has seen a revitalized interest in this class of materials with advances in thin film processing that enable applications in silicon-based devices and nonvolatile storage [1,2]. Most recently, the potential of combined ferroelectric and magnetic interactions have suggested future nontraditional device applications [3]. A critical aspect of the new applications is that the dimensions of various features are in the nanometer length scale. Thin films have thicknesses on the order of 1–100 nm; grain sizes range from 70 to 200 nm, etc. Understanding the behavior of ferroelectric compounds at this scale has been the goal of much of the research of the last few years. These studies have been facilitated by the development of scanning probe tools that can access not only structure but properties at the nanometer-length scale. Of particular importance to this field is piezoresponse force microscopy [4] and transport-related scanning probes [5]. In sub-micrometer-sized ferroelectric devices, details of interface charge, residual stress, mechanical constraint, and domain stability dominate device performance. Scanning probes have enabled extensive studies that have addressed mechanisms of domain switching, the origins of imprint, and fatigue [6–9]. These 906

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studies have been aimed at determining the factors that affect device performance. Since device configurations involve a ferroelectric compound sandwiched between electrodes, many studies have involved a geometry with an electrode on top of a ferroelectric film. These experiments have led to insights regarding the effect of local electrostatic fields and strain at interfaces on domain switching and stability. The surface properties of ferroelectric compounds have received much less attention. The electronic structure of BaTiO3 has been examined by X-ray photo emission spectroscopy and found to be similar in nature to that of other transition metal oxides [10]. Several reconstructions have been observed and attributed to surface non-stoichiometry [11]. In the last few years, observations of surface interactions have led to a new field in which ferroelectric surfaces facilitate a lithographic approach for complex structure fabrication [12,13]. Ferroelectric nanolithography exploits the effect of ferroelectric polarization on local electronic structure to control chemical reactivity in a manner that allows complex multi component (metal nano particles, organic molecules, peptides, tubes, wires, etc) structures to be assembled in predefined configurations. This paper will describe the effect of polarization on surface properties in model ferroelectric compounds and illustrate three approaches to polarization patterning. The domain specific reactivity and patterning will then be combined into a fabrication process that is demonstrated on several classes of nanostructures.

2 Surface Properties of Ferroelectrics For a model system, i.e., a perfect single crystal, the termination of domains at a surface results in a large surface charge, the magnitude of which depends on the orientation of the polarization vector. This is illustrated in Figure 1 for BaTiO3 (100), which is a tetragonal perovskite that contains domains oriented along [100] directions, which are therefore oriented 90◦ or 180◦ with respect to each other. Note that the difference in surface charge between a and c domains is of a different magnitude than that between c+ and c− domains and that a–c domain intersections result in a physical surface corrugation due to lattice parameter differences in these directions. Surface domains are easily imaged by scanning surface potential microscopy (Kelvin force microscopy), as was first demonstrated on TGS and by piezoresponse force microscopy [14,15]. It is important to note that a large literature has been developed around the quantitative application of piezoresponse force microscopy [16–19]. Figure 2 illustrates two classes of surface domain patterns on single crystal BaTiO3 (100) surface. In a study of the effect of the ferroelectric-to-paraelectric phase transition on surface charge, Kalinin et al. [20,21] found that the charge exhibited different dynamics than did the structural phase transition. Figure 3 compares in situ measurements of the topographic structure that monitors corrugations associated with a–c domain boundaries with the surface charge associated with all boundaries. When the temperature passes the Curie point, the corrugations disappear instantaneously

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Domain structure

Potential Topography

(a)

(c)

(b)

FIGURE 1. Possible domain orientations intersecting a (100) surface of tetragonal BaTiO3 . Arrows represent the orientations of polarization vectors. (a) 90◦ a1–a2 boundary, (b) 90◦ c+ –a1 boundary, (c) 180◦ c+ –c− boundary. Shown below are the surface potentials (dot) and topographies (solid) expected along the dotted lines.

(on the time scale of the experiment); however, the surface charge initially increases by a factor of 10. On times scales characteristic of diffusion processes, the surface charge redistributes and becomes homogeneous. This is a clear indication that the measured surface charge is a combination of polarization charge and compensation charge. Charge can be compensated by the segregation of any mobile charge carriers in the lattice and/or by surface adsorption (since the measurement was carried out in ambient conditions). It has been shown that the time and

(a)

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10µm (d)

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(f (f)

10µm

FIGURE 2. Surface topography (a,d), surface potential (b,e), and schematics of domain structures (c,f) in an a-domain region with c-domain wedges (top) and a c-domain region with a-domain wedges (bottom). Reprinted with permission from [23]. Copyright 2001, APS. (courtesy of D. A. Bonnell).

IV.4. Ferroelectric Lithography

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(c)

(b)

(e)

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FIGURE 3. Surface topography (a,c,e) and potential (b,d,f) distribution at BaTiO3 (100) surface before ferroelectric phase transition at 125◦ C (a,b), 4 min after transition (c,d) and after 2.5 h annealing at 140◦ C (e,f). Scale is 0.1 V (b), 0.5 V (d), and 0.05 V (f). Reprinted with permission from [23]. Copyright 2001, APS (courtesy of D. A. Bonnell).

temperature dependence of surface charge contrast can be used to determine thermodynamic and kinetic parameters associated with charge compensation processes [22–24]. The situation, schematically illustrated in Figure 4, emphasizes several important points. First, the magnitude of the charge measured at the surface will be substantially lower than the polarization charge due to the compensation. This is realized in the data of Figure 1, in which the difference between a–c domains is on the order of 50 mV, while the difference in c+ –c− domains is on the order of 150–200 mV, orders of magnitude lower than the expected polarization charge. Second, the sign of the charge observed in a surface potential measurement is opposite that of the polarization charge. Finally, and most important for the present discussion, there is a separation of charge carriers depending on the sign of the domain. Positive charges or oriented dipoles compensate negative domains and vice versa. This suggests that domain polarization can have a significant effect on local surface interactions. Two types of polarization-dependent surface effects can occur on ferroelectric domains. Perhaps the most obvious is based on electrostatic interactions due to the surface charge. Charged molecules or particles will be attracted to domains terminating with opposite charge, much as shown in Figure 4. In fact, in the 1950s colloidal suspensions of micron-sized sulfur and lead oxide particles in hexane were used to decorate ferroelectric domains [25]. Under these conditions sulfur carries a positive charge and lead oxide a negative charge, which leads to

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- - - - + + + + + + + + - - - -

- - - - + + + +

(a)

(b)

- +

-

+

+

(c)

FIGURE 4. Schematic diagram of the surface charge compensation processes showing polarization charge terminating at the arrows and compensation charge. Below the Curie temperature (a), immediately after transition (b), and some time after phase transition (c).

attraction to oppositely charged domains. While electrostatic interactions will lead to deposition, the process will terminate as soon as the surface charge is passivated. A second class of interactions relies on the fact that the polarization charge at the surface affects the local electronic structure of the ferroelectric compound. Specifically, the energies of atomic orbitals at the surface are shifted in a manner that depends on the sign of the surface charge. For the case of titanates, the bottom of the conduction band is predominantly formed by Ti 3d orbitals, while the top of the valence band has predominantly O 2 p character. This relationship is illustrated in Figure 5. First-principle calculations for BaTiO3 and PbTiO3 indicate that while oxygen and titanium states may relax into the energy bandgap, no new bonding states are present at the surface [26,27]. This of course applies to perfect (1 × 1) terminations; the presence of defects or reconstructions will likely result in additional Ti-based deep-level surface states.

(a)

+

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(b) Possible reaction on c+ domain surface: Ag+ + e- = Ag

EC,Ti 3d

EC,Ti 3d

EF

EF

Ev,O 2p

-

-

+ hν Ev,O 2p +

+ Possibe Reaction on c- domain surface: Co2+ + h+ +2H2O = CoO(OH) + 3H+

hν

+

-

P Polarization

+

FIGURE 5. Schematic diagram of band bending in the ferroelectric perovskite crystals in the c− (a) and c+ (b) domain regions. For BaTiO3 and PbTiO3 E v is the top of the band associated with oxygen 2 p orbitals and E c is the bottom of the band associated with the titanium 3d orbitals. The band bending is a consequence of surface charge that results from polarization and is domain specific. The photo-generated carriers will respond to the local electric field at the surface such that reduction occurs at c+ domains surface while oxidation reactions occur at c− domains surface. Reprinted with permission from [49]. Copyright 2005, MRS (courtesy of D. A. Bonnell).

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(a)

(b)

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(c)

FIGURE 6. Scanning surface potential microscopy of BaTiO3 (100) before (a), during (b), and after (c) illumination with UV light. Optically generated carriers selectively accumulate at positive or negative domains and compensate the polarization charge.

The surface charge raises or lowers the energies of the orbitals in the vicinity of the surface, resulting in near-surface band bending and the formation of space charge regions. In regions with negative polarization (c− domains), the effective surface charge becomes more negative and, therefore, upward band bending occurs. In regions with positive polarization (c+ domains), surface charge is positive with associated downward band bending. From this description it is clear that a surface reaction that involved electron donation from the ferroelectric can occur over c+ domains but not over c− domains. Or more rigorously, electron donation reactions will occur at substantially higher rates at c+ domains than at c− domains. Of course, a reaction based on hole donation will occur over the negatively poled domains. Intrinsically, ferroelectric compounds are wide bandgap semiconductors with bandgaps ranging from 3 to 4.5 eV; therefore, an extrinsic source of carriers is necessary to implement this class of domain-specific reaction. Irradiation with super bandgap radiation results in the formation of electron-hole pairs that can separate in the space charge layer and concentrate at the appropriate domains. Gruverman et al. used photo-induced carriers to study domain pinning at interfaces [28]. A direct observation of this effect is illustrated in Figure 6, which shows in situ measurement of surface charge in the presence and absence of UV illumination of BaTiO3 (100). Before illumination the charge associated with a–c and c+ –c− domains is evident. As noted above, the difference in potential between upward-oriented (c+ ) and downward-oriented (c− ) domains observed under ambient conditions is a complex combination of polarization and screening and is on the order of 120∼150 mV [29–31]. On illumination the difference in surface potential between domains decreases to ∼10 mV, i.e., approaches “flat-band conditions” due to charge compensation by the generated electrons and holes. Switching off the light source yields the original domain structure indicating that the optical radiation did not switch the domains, it simply generated carriers. These interactions are complicated and are discussed in detail in [5]. Nevertheless, the time dependence of the potential difference demonstrates that the diffusion of electrons and holes in response to electric field gradients near the surface plays a large role in

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polarization compensation. These results show that carriers generated by optical radiation migrate to the appropriate domains and are available to participate in domain specific surface reactions.

3 Patterning Ferroelectric Polarization at Surfaces For ferroelectric substrates to be the basis of a lithographic process, the ability to pattern domains is implied. Poling domains under electrodes is the basis of the capacitor and nonvolatile storage industries, so the concept is not new. The question arises as to how to achieve polarization control at a surface and in patterns of small dimension. Three mechanisms for surface polarization patterning are considered here: microcontact electrode stamps, scanning probe tips, and electronbeam-induced charging.

3.1 Contact Electrode Patterning The drive for denser storage media has motivated efforts to fabricate and understand layered thin-film heterostructures with patterned top electrodes, i.e., small capacitors. Switching by applying a field to a contact electrode is thought to occur by heterogeneous domain nucleation at the interface followed by domain growth. Depending on local boundary conditions, such as the presence or absence of pinning sites, the amount of charge injection, etc., the relative rates of nucleation, lateral domain growth, and vertical domain growth can vary [2]. Nagarajan and Ramesh [32] have shown that capacitors with lateral dimensions as small as 70 nm are ferroelectric. Bune et al. recently demonstrated that a PZT thin film with thickness as small as 4 nm remains ferroelectric when strain is eliminated [33]. These demonstrations of domain stability at such small dimensions demonstrate that patterned electrodes for the control of surface domain orientation appear viable. Contact electrode switching for polarization patterning can be implemented with microcontact electrodes. For example, following the stamp fabrication process used for microcontact printing [34], small patterns can be achieved in a manner amenable to scalable processing and high throughput. The process is illustrated in Figure 7(a). The desired pattern is etched into a mold by whatever process is appropriate for the length scale. At this step high-precision, low-throughput methods such as e-beam lithography can be used. A liquid polymer such as PDMS is poured onto the mold and allowed to harden. It is then removed from the mold and coated with a metal. This patterned electrode can then be used to apply an electric field to the surface of a ferroelectric compound, producing a domain pattern. The pattern in Figure 7(b) is not particularly small but demonstrates the effectiveness of the stamp electrode in switching. The second approach to surface polarization patterning is to extend the concept of a contact electrode to a scanning probe tip (Figure 8 (a)). Soon after the development of scanning probe techniques capable of imaging ferroelectric domains, investigators began using a local field induced with an SPM tip to pattern

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(a) Upulse

Glass PDMS Au/Cr coating Conductive substrate

Ferroelectric film

(b)

FIGURE 7. Schematic diagram of microcontact electrode ferroelectric domain patterning (a), and an optical micrograph of pattern on a PZT thin film generated by microcontact electrode (b). Reprinted with permission from [12]. Copyright 2004, Advanced Materials. (courtesy of D. A. Bonnell).

polarization at surfaces. These studies were aimed at determining the minimum size of a stable domain and investigating domain wall dynamics. Domains in the sub-100-nm size range were produced in several studies [35]. In early studies characterization relied on scanning surface potential (Kelvin probe microscopy) to observe the domains and these results were influenced by compensation charge such as illustrated in Figures 2 and 3. A typical pattern is illustrated in Figure 8(b) for 150-nm PZT thin films with a 10-nm underlying Pt electrode. With probe tip electrodes the switching mechanism also involves the domain nucleation followed by forward growth and sidewise expansion processes, but the geometry of the field differs from that of a planar top electrode. This field decreases as 1/εz 2 in the polar direction z as the domain expands into the crystal. Due to the small size of the tip radius, the ultimate limit of domain patterning will be limited by the crystalline structure of the substrate.

3.2 Electron Beam Patterning The third approach to domain patterning is based on entirely different physics, specifically, the interaction of injected electrons with a ferroelectric surface. In

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FIGURE 8. Schematic of direct poling domains in ferroelectric thin film using AFM tip (a), and a PFM phase image (b) of a complex pattern written by AFM tip.

the early 1990s macroscopic features were produced on single crystal LiNbO3 [36,37] by e-beam irradiation. Recent studies have demonstrated that nanometer sized domain patterns on polycrystalline PZT thin films [38] can be produced by e-beam writing. This section focuses on the quantitative aspects of the poling mechanism as well as the beam dosage, energy and current density dependences of polarization reorientation in polycrystalline PZT thin films. The experimental setup is schematically shown in Figure 9. Electron-beam dosage, beam energy, and beam current were independently adjusted in order to determine the relationship between polarization reorientation and ferroelectric lithography conditions. When an insulator surface is irradiated by electrons, elastic and inelastic collisions in the crystal lead to the excitation of secondary electrons and back-scattering of incident electrons. Secondary electrons sufficiently close to the surface (less than 50 nm) are emitted from the surface, while the other electrons are either trapped in defect sites or self-trapped as polarons in the crystal. When the number of incident electrons is not equal to that of the emitted electrons, surface charge develops. If the field generated by the trapped charges is stronger than the coercive field of the ferroelectric compound, domain reorientation at the surface should occur. Figure 10 illustrates the process of surface charging and the underlying domain polarization reorientation in a PZT thin film. With positive surface charge developed, polarization is reoriented such that a negative domain terminates

IV.4. Ferroelectric Lithography FIGURE 9. Experimental setup for electron beam ferroelectric lithography and surface charge measurement. A scanning electron microscope equipped with lithography software is used to expose the sample to a focused electron beam. Electrons penetrate the sample to a depth (λ) and develop charge on surface. Electron penetration depth can be varied to be either greater or less than the film thickness (h) by changing the beam energy.

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Obj lens

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Metal sample holder

the surface. In contrast, negative surface charging leads to positive domain orientation. The dosage dependence of polarization switching, shown in Figure 11(a,b), is determined by a comparison of the fraction of irradiated area that is in the c− orientation. Note in Figure 11(b) that there is both a threshold dosage for the onset of switching and a saturation value at which the entire area is switched. Below 500 µC/cm2 no effect is observed, while at dosages higher than 1,500 µC/cm2 all domains are reoriented. In between these values there is a monotonic increase in the switched area. A reasonable explanation is based on the polycrystalline nature of the thin film. The orientation distribution starts out randomly. When the local electrical field reaches the critical value, domains with the most favorable orientation switch. The polarization switching process is schematically shown in Figure 11(c). Positive charge easily develops on an insulator surface because the cross sections for excitations leading to electron emission are relatively large. The development of negative charge is less straightforward. For a constant electron-beam energy, the dosage is related to the amount of charge that accumulates on the surface. In an insulating thin film irradiated by an electron beam, the surface potential is [39,40]: VS =

QT f, πε0 (1 + εr ) a

(1)

where Q T is the total trapped charge, εr is the relative permittivity of the material,

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Dongbo Li and Dawn A. Bonnell PE

SE

+++++++

c+++++++

BE

-------

c+

-------

FIGURE 10. Illustration of surface charging and underlying polarization reorientation by electron beam. PE are the primary incident electrons, SE are the secondary electrons and BE are the back-scattered electrons. Accumulation of positive charges on the surface causes the polarization to orient downwards (yielding the c− domains shown on left). In contrast, negative surface charging leads to positive domain orientation (c+ domains on right).

a is the spot diameter of electron beam, and f is a complex factor between 0 and 1 that accounts for the geometry of the thin film [41]. If electron trapping in the PZT thin film is due to intrinsic defects, and is assumed a reasonable defect density, 1020 cm−3 [42], the resulting surface potential is estimated to be less than 51 mV, resulting in a field much less than the coercive field (∼30–100 kV/cm) of PZT. Since the domains do in fact switch, the charge must be trapped by additional mechanisms. One possibility is that defects induced by e-beam irradiation increase the number of trapped charges, which in turn intensifies the internal electrical field in the film. The beam current dependence of domain reorientation is illustrated in Figure 12, which demonstrates that switching to both positive and negative orientations is

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FIGURE 11. (a) PFM phase image (over 20 × 20-µm area) showing negative domain polarization switched by electron beam of energy E = 10 keV, beam current of I = 30 pA, and dosages ranging from ∼500 to 5,000 µC/cm2 . The exposure is increased from left to right and from bottom to top in the figure with the dosage values (in µC/cm2 ) indicated for the corner positions. The darker regions are the negatively polarized domains. (b) The fraction of c− domains switched perpendicular to the surface increases with electron dosage. (c) Model of domain switching with electric field (E) as dashed arrows. For E greater than Ecritical the domains begin switching. The fraction of switched domains increases with electron dose until the reorientation saturates at a dosage of 1,500 µC/cm2 . Reprinted with permission from [38], Copyright 2004, AIP (courtesy of D. A. Bonnell).

possible. At beam currents 1 nA the surface charge is negative, resulting in c+ surface domains. At intermediate currents the sign of the charge depends on the beam energy. The current is related to surface charge through the electron emission yield, which is the intensity ratio of emitted electrons including secondary (I S ), back-scattered (I B ) and leakage electrons (I L ), to primary electrons (I0 ): σ =

I B + IS + IL . I0

(2)

For thin film geometry an important factor is the electron penetration depth [43]: 0.0276AE 1.67 (3) Z 0.89 d where A is the atomic weight in g/mole, E is electron beam energy in keV, Z is the average atomic number, and d is the density in g/cm3 (A = 235 g/mole, Z = 63, and d = 7.5 g/cm3 for PZT). The penetration depths for various beam energies are listed in Table 1. For thin films with a thickness h, when λ > h, some fraction of the electrons will contribute to the leakage current through the Pt film λ=

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FIGURE 12. Polarization reorientation dependence versus beam current. Dots represent experimental results under different irradiation conditions with the lines as guides to the eye. At high beam current (>1 nA), negative charges accumulate on the surface which switch the underlying domains in the positive direction (c+ ). At low beam current (1 nm/min), and application of multiple inks onto a single substrate provides avenues into exploring and comparing multiple SAMs simultaneously. Another interesting use for DPN is for the creation of templates. This method involves patterning the surface with a substituent that will bind the “material of interest”. This method has been used to create patterns of various proteins and nanoparticles [33,34] and the scope of this work has been reviewed extensively [1,27]. There are several questions that still exist on the fundamental mechanism that drives DPN. The mechanism of ink transport by the water meniscus is one of these questions. Another is the method by which hydrophobic molecules are transferred through this water meniscus, and yet another focuses on the need for the water

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FIGURE 3. (a) An array of features scaling from 45 nm to 920 nm in diameter generated by varying the contact time during the MHA writing phase with contact time increasing from A-I backfilled with ODT and developed with magnetic nanoparticles. (b) Lines produced by varying writing speeds from 0.1 µm/s to 1.3 µm/s creating line widths of 120 nm to 60 nm scaled from A to F. (c) A study of contact time versus feature diameter plotted via analysis of (a). (d) A plot of writing speed compared to fabricated line widths produced in (b). Reprinted with permission from [32]. Copyright 2002, WILEY-VCH Verlag GmbH.

FIGURE 4. Polygons written with MHA preformed with varying writing times. The darkened square 3 × 3-µm region was patterned afterwards by writing with ODT. Reprinted with permission from [30]. Copyright 1999, American Association for the Advancement of Science.

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meniscus. To date, the answers to these questions are still up for speculation with some arguing both for [35] and against [36,37] the necessity of the water meniscus. These experiments and their interpretation are reviewed in more detail elsewhere [1,27].

4 Substitution Lithography The third form of writing is that of substitution lithography where first the background canvas is removed and then replaced with a second type of ink. Substitution lithography is based upon the ability to remove an existing monolayer and replace it with another in the removal region [1]. The advantage of this approach is that it retains a chemical identity in all regions on the substrate and allows the comparison of two or more different SAMs simultaneously [38]. In an early example, this method was used to pattern monolayer-protected gold with a thin layer of silver by elevating the bias of a silver-coated platinumiridium tip over a scanned region of the monolayer. Upon elevating the bias the monolayer was removed and the silver was deposited. Subsequent scanning over the region revealed that no silver had been deposited outside of the scan area [39]. A second example of this method was the substitution of decanethiol into a dodecanethiolate monolayer [38]. In this experiment a low current STM was used to remove the dodecanethiolate monolayer in a dodecane solution containing decanethiol. Interestingly, upon replacement the decanethiolate replaced regions illustrated a higher apparent height as compared to the dodecanethiolate background. This reversed apparent height contrast was attributed to the tunneling gap of the dodecane solution having a higher conductance than the monolayer as had been predicted previously [40]. This technique has also been employed to create monolayers composed of both insulating and electroactive regions by removing lines from a dodecanethiolate background in a solution of ferrocenylundecanethioacetate (Fc-C11-SAc) and three component monolayers consisting of two electroactive regions separated by the insulating dodecanethiolate background [41]. Another interesting experiment performed with this technique was the creation of chemical gradients in which a Fc-C11SH gradient was fabricated into a dodecanethiolate monolayer and a mercaptoundecanoic acid gradient was fabricated into a dodecanethiolate monolayer [42]. Examples of substitution lithography have also been illustrated with CS-AFM in which hexanethiol, octanethiol and decanethiol were replaced into a monolayer of octadecanethiolate [43]. AFM can also be used to remove the monolayer in a solution of replacement thiol [44]. Interestingly, the patterns produced by this method (termed ‘nanografting’) form at least one order of magnitude faster and have fewer defect sites than monolayers formed from solution (Figure 5) [45]. A wide variety of two component monolayers have been created using nanografting both in situ and ex

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FIGURE 5. (A) An AFM image of C10 S SAM prior to fabrication. (B) Patterning of two 10 × 50-nm C18 S- lines with 20-nm spacing. (C) Removal of one of the C18 S- lines and reintroduction of the C10 S- into the region. (D) Fabricating another C18 S- line 65 nm in length. Reprinted with permission from [48]. Copyright 1999, American Chemical Society.

situ. One interesting example of ex situ patterning was the binding of proteins to nanografted areas of mercaptopropionic acid in a dodecanethiolate background [46,47]. Early studies performed by Xu and Liu [44] utilized the mechanical attributes of AFM in order to displace “matrix monolayer” components from substrates. Through the application of an increase in the force used during scaning, nanoshaving was observed as they had previously reported. However, with the addition of dodecanethiol (C12 SH) or decanethiol (C10 SH) in supporting solution it was observed that the replacing “ink” adsorbed into the freshly etched regions. Thus the term “nanografting” was conceived. In the course of experimenting with nanografting, the ability to “erase” lines fabricated within the monolayer as well as reform them demonstrated a vast range of control in the selectivity of structural manipulation through AFM [48]. Also, structures fabricated through this methodology illustrated control in line resolution, given the reproducible 10-nm line width and 50-nm length. Formation of lines with these dimensions resulted from the application of 5.2 nN setpoint force during the writing scan with 0.1 mM concentration of replacing molecules in 2-butanol solution. In order to confirm the replacement, scans were taken with a reduced 0.3 nN setpoint force. Changes in the relative height of the replaced region agreed with the difference in lengths of the

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C18 S- and C10 S-molecules suggested the complete replacement of the monolayer in the selected region. A second classification of substitution lithography is tip induced modification of the terminal head group in the SAM [1]. In this process, the underlying chain is left unperturbed with only the chemical functionality of the terminal headgroup affected. STM, AFM and CS-AFM have been used in this process. An interesting example is the chemical modification of an amine terminated organosilane by the low energy electron beam applied to the sample during STM imaging [49]. After exposure to the low energy electrons from the STM tip the functionality of the exposed surface was destroyed and therefore would not ligate ions in subsequent steps. The undamaged regions were then exposed to aqueous Pd+2 followed by ex situ exposure to an electroless nickel plating bath. The Pd+2 was bound only to the unexposed regions and the nickel plated only on the Pd+2 regions [49]. In another example, CS-AFM was used to induce an nanoelectrochemical oxidation of the terminal methyl group of a n-octadecyltrichlorosilane monolayer [50]. After oxidation of the terminal methyl group, the sample was reacted with a vinyl-terminated silane which created a bilayer in the oxidized region. The vinyl group could then be reacted to form various other terminal groups and further layers or functionalities could be added. These examples indicate that substitution lithography on SAMs is another useful method along with addition lithography and elimination lithography in preparing and manipulating the components at a monolayer substrate interface.

5 Apparent Height The ability to distinguish and characterize regions of replacement relies on the properties of replacing molecules compared to that of the background SAM. Through the use of STM and AFM several distinctive measurements are possible. The use of relative heights and conductance measurements provide information into the structural and electrical properties of regions in the SAM. Apparent height contrast, the relative difference between two distinct regions of the SAM, provides both a visual representation of replacement domains as well as comparative height measurements. In exploring the relative conductance and height differences, several factors contribute towards providing clear-cut responses including the length and relative tilt of the molecules in the replaced region, and how the relative conductance of the tip-molecule-substrate junction varies with applied bias. Bias dependent apparent height contrast is based upon molecules having a nonlinear increase in tunneling current as the tip-sample bias is increased. Gorman et al. [41] demonstrated that a ferrocenyl-terminated SAM region shows little or no apparent height contrast with the background dodecanethiolate SAM at a 150 mV setpoint bias. However, if the bias was increased to 1,000 mV then the ferrocenyl-terminated regions appeared much taller than the C12 background (Figure 6).

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FIGURE 6. Replacement lithography images showing an FcC11 SH molecules replaced into a C12 S-SAM. Also illustrated is bias-dependent apparent height contrast shown by the dark letters Fc at 150mV and brightened Fc at 1,000 mV with a set point current of 10 pA. Reprinted with permission from [41]. Copyright 2001, American Chemical Society.

FIGURE 7. A series of replacement lithography experiments imaged by STM with FcC11 Sas replacing molecule and background monolayer indicated at the left side of each image. Each scanned image illustrates the effect of varying the applied bias within each monolayer while maintaining constant humidity ∼55% and writing speed 20 nm/s. Reprinted with permission from [54]. Copyright 2004, American Chemical Society.

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The mechanism behind this apparent height contrast is suggested to be resonant tunneling [51]. Resonant tunneling occurs when the Fermi energy levels in the tip and a suitable level of the redox active molecule come into alignment. At low potentials the Fermi level of the tip is too low to access a molecular orbital associated with the molecule and therefore little excess tunneling current is observed. However if the Fermi level of the tip is brought into alignment with a MO on the molecule the tunneling current increases dramatically and an apparent height difference is seen between the insulating background and the electroactive molecule. This effect has been modulated by installing the electroactive groups reversibly using non-covalent interactions [52] and by capping the electroactive group (in this case, binding the ferrocenyl groups with β-cyclodextrin) [53]. The ability to characterize SPL fabrication relies on the interpretation of the surface features formed during the process. In an attempt to characterize the process of replacement lithography, Lewis and Gorman characterized the efficacy of replacement based on the apparent height response [54]. In doing so, the establishment of visible and measurable desorption trends based on the length of the initial monolayer were established (Figure 7).

6 Concluding Thoughts The field of scanning probe lithography on self-assembled monolayers evolving is quickly and is already enjoying utility in materials science and life science investigations. As this work continues to progress, we hopefully will learn more about the mechanisms of these lithographic operations. Moreover, we will undoubtedly see a further expansion of the range of investigations where nanopatterning of this type is useful.

References 1. Kr¨amer, S., Fuierer, R. R., and Gorman, C. B., Chem. Rev. 103 (11), 4367 (2003). 2. Soh, H. T., Guarini, K. W., and Quate, C. F., Scanning Probe Lithography (Kluwer Academic Publishers, Boston, 2001). 3. Ross, C. B., Sun, L., and Crooks, R. M., Langmuir 9 (3), 632 (1993). 4. Schoer, J. K., Ross, C. B., Crooks, R. M. et al., Langmuir 10 (3), 615 (1994). 5. Schoer, J. K., Zamborini, F. P., and Crooks, R. M., J. Phys. Chem. 100 (26), 11086 (1996). 6. Schoer, J. K. and Crooks, R. M., Langmuir 13 (8), 2323 (1997). 7. Lercel, M. J., Redinbo, G. F., Craighead, H. G. Sheen, C. W., and Allara, D. L., Appl. Phys. Lett. 65 (8), 974 (1994). 8. Liu, G. Y. and Salmeron, M. B., Langmuir 10 (2), 367 (1994). 9. Touzov, I. and Gorman, C. B., J. Phys. Chem. B 101, 5263 (1997). 10. Kelley, S. O., Barton, J. K., Jackson, N. M., McPherson, L. D., Potter, A. B., Spain, E. M., Allen, M. J., and Hill, M. G., Langmuir 14 (24), 6781 (1998). 11. Zhou, D. J., Sinniah, K., Abell, C. and Rayment, T., Langmuir 18 (22), 8278 (2002).

IV.5. Patterned Self-Assembled Monolayers via Scanning Probe Lithography 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.

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Zhao, J. W. and Uosaki, K., Langmuir 17 (25), 7784 (2001). Wold, D. J. and Frisbie, C. D., J. Am. Chem. Soc. 123 (23), 5549 (2001). Wold, D. J. and Frisbie, C. D., J. Am. Chem. Soc. 122 (12), 2970 (2000). Leatherman, G., Durantini, E. N., Gust, D., Moore, T. A., Moore, A. L., Stone, S., Zhou, Z., Rez, P., Liu, Y. Z., and Lindsay, S. M., J. Phys. Chem. B 103 (20), 4006 (1999). Rawlett, A. M., Hopson, T. J., Nagahara, L. A., Tsui, R. K., Ramachandran, G. K., and Lindsay, S. M., Appl. Phys. Lett. 81 (16), 3043 (2002). Sugimura, H., Okiguchi, K., Nakagiri, N., and Miyashita, M., J. Vac. Sci. Technol. B 14 (6), 4140 (1996). Sugimura, H. and Nakagiri, N., Langmuir 11 (10), 3623 (1995). Zheng, J. W., Zhu, Z. H., Chen, H. F., and Liu, Z.-F., Langmuir 16 (10), 4409 (2000). Li, Q. G., Zheng, J. W., and Liu, Z.-F., Langmuir 19 (1), 166 (2003). Kim, S. M., Ahn, S. J., Lee, H., and Kim, E. R., Ultramicroscopy 91 (1–4), 165 (2002). Ara, M., Graaf, H., and Tada, H., Appl. Phys. Lett. 80 (14), 2565 (2002). Xia, Y. N., Mrksich, M., Kim, E., and Whitesides, G. M., J. Am. Chem. Soc. 117 (37), 9576 (1995). Koide, Y., Such, M. W., Basu, R., Evmenenko, G., Cui, J., Dutta, P., Hersam, M. C., and Marks, T. J., Langmuir 19 (1), 86 (2003). Jun, Y., Le, D., and Zhu, X. Y., Langmuir 18 (9), 3415 (2002). Hurley, P. T., Ribbe, A. E., and Buriak, J. M., J. Am. Chem. Soc. 125 (37), 11334 (2003). Ginger, D. S., Zhang, H., and Mirkin, C. A., Angew. Chem. Int. Ed. 43 (1), 30 (2004). Piner, R. D. and Mirkin, C. A., Langmuir 13 (26), 6864 (1997). Hong, S. H., Zhu, J., and Mirkin, C. A., Langmuir 15 (23), 7897 (1999). Piner, R. D., Zhu, J., Xu, F., Hong, S., and Mirkin, C. A., Science 283, 661 (1999). Hong, S. H., Zhu, J., and Mirkin, C. A., Science 286 (5439), 523 (1999). Liu X., F. L., Hong S., Dravid V. P., Mirkin C. A., Adv. Mater. 14 (3), 231 (2002). Lee, K. B., Park, S. J., Mirkin, C. A., Smith, J. C., and Mrksich, M., Science 295 (5560), 1702 (2002). Smith, J. C., Lee, K. B., Wang, Q., Finn, M. G., Johnson, J. E., Mrksich, M., and Mirkin, C. A., Nano Lett. 3 (7), 883 (2003). Rozhok, S., Piner, R., and Mirkin, C. A., J. Phys. Chem. B 107 (3), 751 (2003). Schwartz, P. V., Langmuir 18 (10), 4041 (2002). Sheehan, P. E. and Whitman, L. J., Phys. Rev. Lett. 88 (15) (2002). Gorman, C. B., Carroll, R. L., He, Y. F., Tian, F., and Fuierer, R. R., Langmuir 16 (15), 6312 (2000). Zamborini, F. P. and Crooks, R. M., J. Am. Chem. Soc. 120 (37), 9700 (1998). Weiss, P. S., Bumm, L. A., Dunbar, T. D., Burgin, T. P., Tour, J. M., and Allara, D. L., Ann. N. Y. Acad. Sci 852, 145 (1998). Gorman, C. B., Carroll, R. L., and Fuierer, R. R., Langmuir 17 (22), 6923 (2001). Fuierer, R. R., Carroll, R. L., Feldheim, D. L., and Gorman, C. B., Adv. Mater. 14 (2), 154 (2002). Zhao, J. W. and Uosaki, K., Nano Lett. 2 (2), 137 (2002). Xu, S. and Liu, G.-Y., Langmuir 13 (2), 127 (1997). Xu, S., Laibinis, P. E., and Liu, G.-Y., J. Am. Chem. Soc. 120 (36), 9356 (1998). Browning-Kelley, M. E., Wadu-Mesthrige, K., Hari, V., and Liu, G.-Y., Langmuir 13 (2), 343 (1997). Wadu-Mesthrige, K., Xu, S., Amro, N. A., and Liu, G.-Y., Langmuir 15 (25), 8580 (1999).

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48. Xu, S., Miller, S., Laibinis, P. E., and Liu, G.-Y., Langmuir 15 (21), 7244 (1999). 49. Marrian, C. R. K., Perkins, F. K., Brandow, S. L., Koloski, T. S., Dobisz, E. A., and Calvert, J. M., Appl. Phys. Lett. 64 (3), 390 (1994). 50. Maoz, R., Frydman, E., Cohen, S. R., and Sagiv, J., Adv. Mater. 12 (10), 725 (2000). 51. Tao, N. J., Phys. Rev. Lett. 76 (21), 4066 (1996). 52. Credo, G. M., Boal, A. K., Das, K., Galow, T. H., Rotello, V. M., Feldheim, D. L., and Gorman, C. B., J. Am. Chem. Soc. 124 (31), 9036 (2002). 53. Wassel, R. A., Credo, G. M., Fuierer, R. R., Feldheim, D. L., and Gorman, C. B., J. Am. Chem. Soc. 126, 295 (2004). 54. Lewis, M. S. and Gorman, C. B., J. Phys. Chem. B 108, 8581 (2004).

IV.6 Resistive Probe Storage: Read/Write Mechanism SEUNGBUM HONG AND NOYEOL PARK

We define probe storage in a broad sense, which includes most of the mechanically addressing storage devices such as hard disk drives and optical disk drives. Its history is briefly discussed from the era of inscription, which leads to the application of scanning probe microscopy (SPM), to probe storage devices. Most of the current activities regarding the SPM based probe storage device are reviewed with special emphasis on resistive probe storage and related methods that use ferroelectric materials as information media. We present the principle of the read/write mechanism using the resistive probe accompanied by a servo/tracking concept. Such resistive probes can be implemented into probe storage devices with ferroelectric media development, which shows promise for the terabit era.

1 Introduction 1.1 Definition of Probe Storage What comes to mind when you hear the words “probe storage”? Most of the people involved in SPM community might think of SPM tip arrays moving across the media. However, we would challenge such a perception with a broader definition by examining “probe storage” word by word. In this broader sense, “probe storage” can be defined as a storage device where the “probe” serves as the reader/writer of a storage device. The “probe” is a movable energy-emitting/sensing unit. Some might call such a device a “mechanically addressable storage device,” because mechanical positioning of the probe to the desired bit is the way it addresses the information. Examples of such devices include the pen and notebook you bring to the lecture room. The pen is the probe you use for writing the information, and your eyes are the probes you use for reading it back. The notebook is the media for storing it. You move your pen to write down information in the form of characters. You align the first character of each paragraph to the left margin. The indentation is a kind of marker where you position each paragraph macroscopically. For example, if you

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wanted to locate the sentence above, you might refer to the third paragraph and eighth line. The pen and the paper of your notebook have chemical interactions where the ink is deposited in the line form. If you want to correct a word or rewrite a sentence, you might need an erasing pen by means of which you overcoat the character with white ink. What else can we think of as an example of “probe storage”? Edison’s phonograph, CDs, and hard disk drives are good examples of our broad definition of “probe storage.” They have a stylus, optical pickup, or head as moving probes and their media vary from polymers to a magnetic coating. They use rotational motion of media and linear or quasi-linear probe motion. Probe-positioning technology is called servo/tracking in the hard disk drive industry.

1.2 History of Probe Storage In the 19th century, the phonograph was invented by Edison and commercialized. In view of our broad definition of probe storage, this could be thought of as an early version—yet not quite so early as inscription—of a probe storage device. The microgroove that containing the frozen data of musical notes was the format of data and it transferred its data in the form of micrometer movement of magnetic pickups (probe), which, in turn, transduced the mechanical motion into electrical signal through induced current in the coil of the probe. Probe wear was the main problem for reliability, so diamond probes were preferred above any other type of probe like sapphire, osmium, etc. [1]. Optical disc drives (ODDs) also fall into the category of probe storage devices if we consider their pickups as probes. Polymers or phase change media serve the role of storing the information in the form of pits or phase-changed areas. The reflectance change of the laser incident from the probe is the signal detected at the probe, which translates into a corresponding data stream. The probe is positioned linearly in the radial direction by a motor and in the circular direction by disc rotation. Hard disc drives have separate readers and writers, as in the case of optical disk drive (ODD) [2]. The writer has been an inductive coil, although it evolved from a bulky form into a thin film magnet. The reader has undergone an exponential density increase, which started with the inductive coil and progressed through the magneto-resistance (MR) head to the giant magneto-resistance (GMR) head. Likewise the media has evolved from longitudinal magnetic recording media to perpendicular magnetic recording media due to the superparamagnetic limit of the media [3]. The arm moves in a nearly radial direction on the disc and the motor rotates the disc. Servo and tracking are performed by means of servo-patterns and burst signals embedded in the disc. One might readily recognize, the common concept implemented in conventional probe storage devices such as phonographs, ODDs, and HDDs—all the components are mechanically assembled and the probes have arms or cantilevers that support them mechanically. In addition, the media rotate around their axes and the arms around the pivots where the center of mass coincides with the pivot. This

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scheme provides a mechanically stable configuration, especially against lateral vibration or shock. Moreover, the data are written serially, which allows coding technology to take part in density increase and error corrections. Recently, the amount of information being created has exploded [4], and the need for ever-smaller form factors is driving the whole storage device industry toward mobile high-density devices. Good examples of this are the 1- or 0.85-inch HDDs and mini-ODD which have been implemented in MP3 players, digital still cameras, and PDAs (personal digital assistants) to name a few currently popular devices. However, these devices are facing big challenges in further miniaturization, which led to a paradigm shift from mechanical assembly to silicon processing like MEMS or NEMS design for further miniaturization of probe storage devices. Such an insight was first provided by IBM researchers at the time they invented SPM (scanning probe microscopy), a tool that can image atoms and molecules by means of silicon probes [5]. As mentioned above, IBM developed the STM (scanning tunneling microscope) and AFM (atomic force microscope) and showed that atoms and molecules can be detected and imaged by a scanning probe, which was a sharp tip of nanoscale radius attached to either a metallic wire or a silicon cantilever. Binnig and Vettiger developed the application beyond simple measurement and imaging into probe storage devices; they knew that the same probe technology could be applied to storage devices if combined with MEMS and HDD technology. The working principle is similar to the old phonograph in the sense that the data are written in the form of nanogrooves indented by the heated tip. The probe acts as a heater and indenter when it heats itself and hits the media with mechanical force to form an indentation mark. The silicon heater also acts as a reader when it scans over the indentation by using the temperature-dependent resistance of the doped silicon probe. The heat dissipation rate changes depending on the air gap between the cantilever and the media surface, which, in turn, determines the temperature and accordingly the resistance of the probe. This is the reason it is called a thermo-mechanical probe storage mechanism. IBM started a probe storage project in 1996 and has continued developing it to this day. Recently, they showed a prototype where the multiprobe layer and MEMS stage was sandwiched and packaged on a PCB board to show eight channels of text read/write. They claim that the potential recording density reaches over 400 Gb/in2 even on the system level [6].

1.3 Global Trends: Companies and Universities Since the first announcement of the IBM millipede concept, there has been criticism regarding its read/write mechanism. Many have raised reliability issues such as probe/media wear, rewritability, read/write speed, and shock resistance. In particular, few believed that the indentation scheme would allow rewritable scheme.

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TABLE 1. Comparison of probe storage devices under development in various companies Recording physics

IBM

LG

Canon

Samsung

Write

Indentation

Indentation

Phase change

Polarization switching

Read

Resistance change

Piezoelectric change

Resistance change

Resistance change

Media

PMMAa

PMMA

Polyimide

PZTb

Demonstrated density

1

TB/in2

∼200GB/in2

1

TB/in2

∼115GB/in2

Write/read time

5 µs/5 µs

5 µs/5 µs

10 µs/2 µs

Write cycles

(105 )

(105 )

1

(1012 )

Weakness

Reliability, speed

Low SNR, speed

Write once

Low level of maturity

Strength

High density, maturity

Stable signal detection

High density, simple processing

Fast acquisition, high rewritability

a

30 ns/10 ns

PMMA: Polymethyl methacrylate. Pb(Zr,Ti)O3 .

b PZT:

Even though IBM claimed and showed experimental proof that they can indent and fill the indentations by neighborhood heating, there remains doubt in the capacity for rewritability up to 105 cycles, which is the minimum requirement for storage applications. One more disadvantage of thermal scheme comes from the fact that it consumes a lot of power, and it inherently has latency time on the order of microseconds. The power consumption problem might be solved with proper probe/media design such as lowering the tip-sample distance to the enhance heating and thermo-resistance effects or lowering the glass transition temperature (Tg ) of the media to make possible a lower-temperature heating scheme. However, the latency effect will not decrease unless the probe heaters are scaled down to nanoscale dimensions as in PRAM (phase-change random access memory). One might argue that parallel multiplexing will increase the speed, but there also exist limitations for integrating the necessary channels into the signal-processing chip. Fueled by doubt about and hope in IBM millipede, there have been a lot of efforts around the world to integrate faster and more reliable read/write mechanisms into the probe storage scheme. To the knowledge of the authors, the companies that have been involved in such research activities include IBM, HP, Seagate, Philips, Canon, Nanochip, Canon, Pioneer, LG, and Samsung. Among those companies, IBM, LG [7], HP [8], Canon [9], and Samsung are known as those that publicly announce the status of their projects and publish the results in relevant conferences or journals. Here, the comparison of recording physics is presented in Table 1 based on results published via websites, journals, and mass media. Those groups which have not demonstrated recording experimentally were not taken into account. There are two groups of media that have been mostly investigated for probe storage applications: polymer and ferroelectric. IBM and LG share writing methods and media, while LG has a different reading scheme, i.e., piezoelectric sensing,

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which has the advantages of more stable signal detection without offset current. Canon uses polymer media where the phase can be changed by voltage application and detected by resistance change measured through the tip. Samsung adopts ferroelectric media and uses a resistive probe as a writer and reader where simple voltage application through the tip induces local polarization switching beneath the tip and the surface-bound charge of the written domain changes the resistance of the resistive probe. The demonstrated density reached beyond 1 Tb/in2 for the case of IBM’s polymer media coupled with thermo-mechanical probe. The ultimate density for such kind of writing and reading will be limited by minimum thickness of elastic stress frozen area, which is not clear now. However, it seems that a few Tb/in2 is achievable. Since LG uses similar media to that of IBM, the same arguments apply even though it has demonstrated lower density results than IBM. Canon has also published a remarkable bit arrays showing potential density above 1 Tb/in2 , but its scheme is confined to WORM (write once–read many)-type storage devices since the media are not rewritable. HP has published some results on ferroelectric media, phase change media, and thermo-mechanical writing media, but a complete consistent read/write scheme is not available [8]. Samsung has published its first result of read/write on ferroelectric media using a resistive probe, which was only to show feasibility of working principle of its newly designed probe [23]. The demonstrated density was below 1 Gb/in2 ; however, the read/write scheme reached 100 ns extremely quickly. Recently, Samsung has come up with upgraded result of 115 Gb/in2 with 10-ns response time. The detailed read/write mechanism of resistive probe storage will be explained in section 2. It is still not clear where the physical limit will occur for resistive probe storage, but one can get a clue from the first work on nanoscale ferroelectric bit writing and imaging [15]. It is quite promising that a couple of research groups around the world have detected 20-nm ferroelectric domain bits, which correspond to nearly 2 Tb/in2 (See Table 2). This demonstrates that the limiting factor for 1 Tb/in2 density is the resolution and sensitivity of the resistive probe rather than the ferroelectric materials. As one can see from Table 2, the main reading mechanism for ferroelectric domains is piezoelectric force microscopy (PFM). This lock-in–based technique has a sub-10-nm spatial resolution. It employs a simple conducting probe or tip to both write and read the information in the form of ferroelectric polarization. However, the main reasons that PFM was not considered as a competitive candidate for probe storage devices are as follows: r Lock-in technique necessitates at least 1 ms of integration time for acquisition, which is too slow for high data transfer rate r Integration of a lock-in circuit into the chip is challenging due to size considering the necessary numbers of chips. Although it is a powerful tool to investigate issues related to ultimate bit density of ferroelectric materials, retention properties at nanoscale dimensions, and

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TABLE 2. Comparison of domain writing and reading in ferroelectric media by various research groups Univ. Geneve [10] C/Pa PFMb 40 nm 94 nm 40 nm PZT/NbSTO Processing Off-axis rf sputtering Write Read Single bit Array Thickness Material

Tohoku Univ. [11] C/P SNDMc 12 nm 20 nm 70 nm Single-crystal CLTd Melt grown and etched

KAIST/ Himeji Inst. Univ. SAIT/ Technol. [12] ETHZ [13] Maryland [14] INOSTEK C/P PFM 40 nm N/A 250 nm PZT/SRO/ STO MOCVD

C/P PFM 80 nm 360 nm 120 µm BaTiO3 crystal Remeika method

C/P PFM 20 nm N/A N/A PZT/STO/ Si PLD

C/P PFM 33 nm 66 nm 75 nm PZT/Pt Sol-gel

a C/P:

conducting probe. piezoelectric force microscopy. c SNDM: scanning nonlinear dielectric microscopy. d CLT: congruent lithium tantalate. b PFM:

writability, PFM is not a promising candidate as an integrated reader for storage devices. An alternative method called scanning nonlinear dielectric microscopy (SNDM) was proposed by a group in Tohoku University, which is a unique, fast, and highresolution imaging technique applicable to ferroelectric materials. This method has proven that it can form and detect ferroelectric domains down to 20 nm or below in diameter [11]. It is not yet clear whether one can fabricate the probe structure by full silicon processing because it requires a ring-type shield around the tip, which forms LC resonant structure. The inductor (L) component would be also a challenge to implement in the multi-probe scheme. Figure 1 shows bit arrays formed in ferroelectric media by the conductive probe and imaged by SNDM or PFM in different research groups. It demonstrates that 33–94 nm bits can be stored in statistically reliable ways. However, in the storage industry, one needs to prove that bit error rate is less than 10−4 at the raw data level, which necessitates acquisition of at least 10,000 bit arrays, and there has been no published report available yet with such a large number of bit arrays in ferroelectric media.

2 Resistive Probe Storage 2.1 Overview The resistive probe storage device consists of three main layers: the signal processing/control layer, multi-probe layer, and media on a nanostage layer as shown in Figure 2.

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FIGURE 1. Bit arrays formed and detected by (a) SNDM (bit size of 47 nm), (b) PFM (piezoresponse image, bit size of 94 nm), and (c) PFM (phase images, bit size of 33 nm). Reprinted with permission from (a) [16], copyright 2004, IPAP; (b) [10], copyright 2001, AIP.

The first layer, the signal processing and control unit, processes the information data and servo/tracking signals. The second layer, the multi-probe unit, consists of arrays of nanoheads which serve as readers and writers of information data. The last layer, media on a nanostage unit, moves the media with embedded servo-codes for position control. From the technology viewpoint, resistive probe storage can be described in terms of three major components: 1. Resistive probe: Transistor-on probe (TOP) structure As shown in Figure 3(a), the resistive probe has an n-type dopant region on the inclines of the tip with a small overlap on the tip. The body consists of p-type doped silicon. Therefore, the structure is a transistor-on probe-type structure.

FIGURE 2. Schematic diagram of a resistive probe storage device, which consists of three main layers (see detailed description of each layer in the text).

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Seungbum Hong and Noyeol Park

FIGURE 3. (a) Schematic diagram of a resistive probe showing dopant distribution profile inside. The left scale bar shows the doping level in terms of the exponent of 10 (/cm3 ) (b) SEM image of a resistive probe.

2. Surface charge media: Ferroelectric thin films Since the resistive probe detects the local electric field on the surface of the media, the storage media should be one that has a surface charge like ferroelectric thin films, as shown in Figure 4. Currently, PZT is of primary interest, not only because one can utilize the most conventional media fabrication technology in the field, but also it has large remnant polarization and fatigue endurance far above 105 cycles. 3. Dynamic Dedicated Servo/Tracking A servo-algorithm locates the probe at the position where data will be written or read, and a tracking algorithm enables the probe to track the centerline of the data stream and to synchronize the moment the probe travels above the bit center with the events of either writing or reading. Min et al. proposed a servo-algorithm for resistive probe storage which is a type of dedicated servo-algorithm [18]. A certain number of probes are assigned as servo-probes; they read each digit at every position and construct an address number in binary codeword. It works like a position encoder where the absolute position of the probe is known. Figure 5(a) shows the schematic diagram of the servo-algorithm where P servoprobes read the data in the corresponding servo-fields, and these values become the bit values of the servo-codes as S = s P s P−1 s P−2 . . . s2 s1 .

(1)

FIGURE 4. (a) Ferroelectric thin film with domain structure (100% c-domain) (reprinted with permission from [17]; copyright 2002, Elsevier) and (b) the perovskite ferroelectric unit cell showing permanent dipole moment along z-axis.

IV.6. Resistive Probe Storage:

n

951

n

N s1

m

(i,j)

m

s2

P

M

sp

dx

p

sy

decomposition signals

tx ty

tracking field

n × m absolute coordinates servo f ield data field

dy

sx

(i,j)

synchronization error ex ∫T

∫T

ey off-track error

y ux uy T

position detector

FIGURE 5. Schematic diagrams of (a) servo-algorithm showing data and servo-fields with servo-probes on an arbitrary position at (i, j), which is represented by a binary codeword S (see Eq. (1)), and (b) tracking method where a saw wave is applied to the movement of the probe to multiply the resulting probe signal with decomposition signals that provide the off-track error and synchronization error simultaneously and continuously. Reprinted with permission from [18]. Copyright 2005, IEEE.

The P-bit servo-code S in Eq. (1) can indicate 2P different positions with oneto-one correspondence such as S = G (i + ( j − 1) × n, P) ,

(2)

where i(1 ≤ i ≤ n) and j(1 ≤ j ≤ m) are the coordinates of data bits and G(·,P) is a function that generates a P-bit Gray code, which is generally adopted for position encoding of mechanical sensors for its reliability. For the tracking approach, Min et al. proposed a dynamic approach, where a periodic movement perpendicular to the scan direction is added to extract the offtrack error and synchronization error, where the former is the position error from the track and the latter that from the bit center in scanning direction at writing and reading events (see Figure 5(b)). Figure 6 shows the roadmap to the final product, which consists of two major paths—namely, recording technology and system integration. The recording technology is the core component, which defines the ultimate density, speed, and reliability limit. Depending on the physical interactions between the probe and media, one can expect different physical limits. As there are several candidates for

Au: Is this correct?

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Seungbum Hong and Noyeol Park

FIGURE 6. Roadmap to final product with key issues addressed in (a) recording technology and (b) system integration prospects.

Au: Date of copyright?

non-volatile random access memories such as FeRAM [19], MRAM [20], PRAM [21], and OxRAM [22], depending on which physical interactions are used to store and read data, there are several approaches for probe storage systems, as outlined in Table 1. The key parameters to consider at the early stages are ultimate bit density, read/write speed and cycles, retention time, and power consumption. For ferroelectric media, the research for finding the minimum stable domain size is expanding and the record is beaten every year. Ten- to twelve-nanometer bit formation gives us the hope that we can reach beyond 4 Tb/in2 limit. A switching speed below 1 ns in ferroelectric media and 10 ns for a resistive probe is a positive landmark for Gbps data transfer rate [23,24]. Retention studies by Gruverman et al. showed the important role of grain boundaries on back-switching [25], and more recently by Kim et al. [26] indicated that grain size should be statistically decreased to ensure uniform bit size written under identical electrical condition. Unlike FeRAM, probe storage requires modest fatigue endurance of about 105 cycles, which is the criterion for a FLASH device. This is a relatively low target for ferroelectric media, where many groups have reported above 1010 cycles for endurance [27,28]. However, one should note that top electrode-less structure might pose different boundary conditions for the media, which necessitates a different approach on the subject [29]. Resistive probe storage is in the first stage in the roadmap. One needs to further elaborate on the servo- and recording pattern, which will serve as a stepping stone for servo/tracking concept. Finally, one has to consider the multiplexing and probe selection scheme, which would influence the data capacity and data transfer rate. Once recording technology is completely developed, one needs at each stage to develop processing technology that can realize the read/write concept. This is named system integration technology and it will enormously affect the cost and practical performance of the product. As the ultimate goal is to achieve a sandwiched structure of three silicon layers which go through silicon batch processing, one needs to clarify all the factors that may determine the yield and cost of the device.

IV.6. Resistive Probe Storage:

(a)

(b)

953

600

Bit S ize (nm)

500 400 300 200 100 0

Bit Depth (nm)

300

0

5

10

0

5

10

15

20

25

30

15

20

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30

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100

0

V o lta g e (V )

FIGURE 7. (a) Schematic diagram of electric field distribution inside ferroelectric thin film when the resistive probe is in contact with the film and (b) graphs showing bit size and depth dependence on pulse voltage for 300-nm-thick Pb(Zr,Ti)O3 film (reprinted with permission from [30]; copyright, AVS), where bit size and depth refer to the lateral and depth dimensions of the switched domain.

2.2 Read/Write Mechanism The write mechanism is similar to that of PFM-type experiments. Both terminals are short-circuited, and electric potential is applied when the bottom electrode is grounded. The electric field in the thickness direction is distributed in a way depicted in Figure 7(a). The region where the electric field exceeds the coercive field expands both in depth and lateral directions as the applied voltage increases. Depending on the thickness of the film, tip radius, and applied voltage and pulse width, the lateral size and vertical depth of the switched domain (bit) will be determined as in Figure 7 (b). As reported by Woo et al. [30,31], fully penetrating bits in the thickness direction occur at certain threshold voltages, below which non-penetrating bits with smaller later size are formed. This prediction was confirmed by PFM measurement for different pulse voltage and width conditions and is illustrated in Figure 8. Since pulse voltage creates nonuniform electrical field distribution inside the film, the switched domain first experiences forward domain growth toward the electrode. As the pulse voltage increases, the territory confined by coercive field contour expands not only vertically but also laterally, which leads to enlargement of bit size as it touches the electrode to be a fully penetrating bit. Non-penetrating bits are less stable than fully penetrating ones, as confirmed by Woo et al. [30], so one needs to apply sufficient voltage to form fully

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FIGURE 8. Comparison between (a) fully penetrating and (b) non-penetrating bits. Ring structure in amplitude images of PFM measurement is a landmark for fully penetrating bits. PFM amp and phi refer to the amplitude and phase of the tip vibration signal at the frequency of voltage modulation applied to the tip.

penetrating bits for thermal stability. At the same time, to form bits with small lateral size, which is relevant to the recording density of the medium, one has to decrease the film thickness. This is the reason ultrathin film fabrication [32] and the physical limit of ferroelectricity in scaling down the thickness [33] are important. The read mechanism of the resistive probe was previously examined in a work published by Park et al. [23]. The surface charge on the ferroelectric medium depletes or accumulates the carrier inside the low-doped region of the resistive probe, which increases or decreases the resistance between the two highly doped terminals formed on both inclines of the tip (Figure 9(a)). Figure 9(b) shows the experimental result of sensitivity, which is defined as [IR (VG = 1V)−IR (VG = 0V)]/IR (VG = 0V), as a function of gate voltage applied to the bottom electrode. This result implies that the resistive probe can detect surface charges of both positive and negative polarities.

2.3 Probe and Media Design and Fabrication Implementing the field-effect transistor onto the probe has been suggested and realized by Westervelt’s group in Harvard University [34] and also demonstrated by Seo et al. [35] in Seoul National University. In addition, the single-electron transistor probe was designed and fabricated via a natural shadowing method using evaporation onto tapered glass fiber [36]. However, we found two major problems with the design and processing flow for mass-production of multi-probe arrays. Either the operating temperature was

IV.6. Resistive Probe Storage:

(a)

High doped n-type

955

(b)

Low doped n-type electric field

S (%)

6

VD = 2.5 V

4 2 -10

-5

0 -2

electric field

0

5

10 VG (V)

-4 -6

FIGURE 9. (a) Schematic diagram showing the reading mechanism of the resistive probe and (b) the sensitivity measurement result as a function of gate voltage applied to the bottom electrode. Upward polarization induces accumulation of electrons in the low-doped region and thereby decreases the resistance between the two highly doped n-type regions (upper figure in (a)), while downward polarization depletes the electrons, which leads to higher resistance between the two regions (lower figure in (a)).

too low for probe storage devices, or the fabrication methods suggested did not allow Si wafer processing with high reproducibility. Figure 11 shows the optical microscope and SEM images of a fully processed resistive probe. The cantilever length, tip height, and tip radius were 180 µm, 800 nm, ∼50 nm. The spring constant was measured using dimensions and resonance frequency of 146.9 kHz, which leads to a value of 32 N/m [37]. Therefore, Park et al. have developed a breakthrough approach shown in Figure 10, referred to as a self-aligning process [23]. The key idea is to use part of the implantation mask as a tip mask and perform isotropic etching to form a pyramidal tip with a self-aligned channel. Since the channel is first electrically defined by a 2D process, which is followed by tip etching; reproducibility and channel size reduction are expected to be better than those of other known methods. The media structure of the resistive probe storage device resembles that of the ferroelectric capacitor in FeRAM device. The main difference is that it does not have the top electrode deposited on top of the ferroelectric layer. In addition, it requires a flat planar structure without patterning for continuous media. Figure 12(a) shows the schematic diagram of the media structure, which consists of overcoat (not indicated), ferroelectric, conductive, and nucleation layers on oxidized silicon substrate.

956

Seungbum Hong and Noyeol Park FIGURE 10. Schematic diagram of key process flow of the resistive probe, which consists of (a) ion implantation after oxide mask patterning (stripe shape), (b) oxide mask reshaping after diffusion, and (c) silicon etching followed by sharpening oxidation. Reprinted with permission from [23]. Copyright 2004, AIP.

The key design requirements for media are summarized in Table 3, where domain size instead of capacitor area is more important and roughness of the film takes an important role for reliable data acquisition. Previous study on retention properties of fully penetrating and non-fullypenetrating bits written in ferroelectric thin film suggested that the former type outlasts the latter one in terms of retention time (Figure 13) [31]. It was suggested that for forming a fully penetrated domain with a conductive probe and minimizing the domain size at the same time, it is necessary to reduce the thickness and form a bit of which diameter is comparable to the thickness. Kim et al. recently found that the size deviation of bits written under identical electrical pulses has a bell-shape dependence on the ratio of bit size to grain size, the peak of which is located where the ratio equals one as shown in Figure 14(a). This implies that the deviation reaches the maximum when the bit size

FIGURE 11. (a) Optical micrograph and SEM images of full-processed resistive probes showing (b) cantilever and (c) pyramidal tip structures.

IV.6. Resistive Probe Storage:

(a)

(b)

Doman Size

Media Structure

d

Ferroelectric Layer Conducting Layer Nucleation Template Silicon Oxide Silicon Substrate

(c)

10 nm 10 nm 1 µm

40 Potential [V]

957

20 0

∆φ

-20 -40 0

15 5 10 Distance [µm]

20

FIGURE 12. Schematic diagrams of (a) media structure showing ferroelectric layer on top of conducting layer; (b) domain structure with up and down polarizations where domain size, d, determines the recording density; and (c) surface potential distribution across alternating domains where surface potential difference, φ, influences the signal to noise ratio of media which, in turn, determines the bit error rate of the device. Reprinted with permission from [38]. Copyright 2004, Springer.

equals the grain size [26]. For analysis of the trend, PFM images overlapped with corresponding topography images were mapped as in Figure 14 (b) for each regime where regime (1) represents the case of bit size > grain size, regime (2) the case of bit size = grain size, and regime (3) the case of bit size < grain size. As is clearly shown in the figure, grain boundary influences the shape of the bit boundary, which contributes to the fluctuation of the bit size. Based on our results, we proposed that the media should either have very large grain size, which will ultimately lead to single crystal or full epitaxy, or have very small grain size, which leads to nanograin films, which is in agreement with Gruverman’s early suggestion for nanoscale FeRAM [39]. For ferroelectric thin films, both directions can be found [11,40]; however, there are almost no reports available for either epitaxy or single crystals grown on Si substrates. Therefore, while not definitely excluding the direction toward single crystals, we proposed that a nanograin structure be the direction for PZT thin films on Si substrate. Figure 15 summarizes our design guidelines for ferroelectric media. The dark circle in the center of (a) represents the information bit written by the resistive probe and the black boundary the grain boundary. One bit covers several grains

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Seungbum Hong and Noyeol Park

TABLE 3. Required design parameters of media for the resistive probe storage device and related phenomena to be studied Category

Parameter

Media Parameter

Phenomenon

Performance parameter

Recording density

Domain size, surface potential

Local volume energy, screen charge effect

Recording speed

Switching speed

Switching mechanism

Bit error rate

Roughness, grain boundary, 2nd phase

Film growth mechanism

Bit lifetime

Retention time

Backswitching, imprint

Endurance

Fatigue cycles

Fatigue

Reliability parameter

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Normalized Number of Bits

1 µm 1.0 0.8 0.6 0.4

1 ms 3 ms 5 ms

0.2 0.0

0

50

150 100 Temperature (°C)

200

FIGURE 13. PFM images (a,c,e,g, amplitude; b,d,f,h, phase) of fully penetrating (a,b,e,f) and non-penetrating (c,d,g,h) bit arrays at room temperature (a–d) and once elevated to 100◦ C for 30 min and cooled to room temperature (e–h). (i) Graph of normalized number of bits remaining as a function of elevated temperature for three different types of bit arrays formed by different pulse widths. Reprinted with permission from [31]. Copyright 2002, AIP.

IV.6. Resistive Probe Storage:

959

FIGURE 14. (a) Plot of normalized bit size fluctuation as a function of bit to grain size ratio, and (b) PFM phase images overlapped by topography showing grain boundaries for different sizes of bits corresponding to the regions of (1), (2), and (3) in (a).

so that the grain boundary effect on the bit shape becomes minimized to ensure statistically averaged-out uniform bit size.

2.4 Probe and Media Characterization The resistive probe was characterized by a semiconductor parameter analyzer (HP4145), atomic force microscope (AFM, PSI M5), and high-speed oscilloscope (LeCroy 9354AL), a detailed configuration of which can be found in our previous publication [23,30]. Figure 16(a) shows the source-drain current as a function of the source-drain voltage for different gate voltages applied to a standard test sample, which is an oxidized Si substrate. The curve shape resembles that of the IBM millipede, since it has the same n + -n-n + structure for heating [41]. The difference lies in the fact that we utilize the depletion and accumulation effects by the external field, while they use the thermo-resistance effect by heat dissipation through the air gap. Figure 16(b) shows the response characteristics of the resistive probe to the external gate voltage pulse. The rise time of the probe current was measured with a high-speed oscilloscope and the 10–90% transition region gave us about a 10-ns (a)

(b) Probe

FIGURE 15. Schematic (a) plan view and (b) cross section image of ferroelectric media. The black dot represents the information bit and black line the grain boundary. The lateral size of the bit exceeds that of the film thickness.

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FIGURE 16. (a) The I-V characteristics of the resistive probe at various external voltages applied to a Si wafer of low resistivity with 500-nm-thick thermal oxides on top of it. The inset shows the measurement setup configuration. Reprinted with permission from [23]. Copyright 2004, AIP. (b) The response characteristics of the resistive probe to the voltage pulse (gate voltage) applied to the Si wafer in the inset of (a). The transition time was determined by the 10–90% region, which leads to ∼10 ns.

response time, which is extremely fast in comparison to other read/write probes for probe storage devices (see Table 1 for comparison). Figure 9(b) plots sensitivity versus gate voltage, which shows a linear character. It implies that it has lower sensitivity for low surface potential difference of domains, which could be detrimental when we reduce the written bit size. As we proved that the fabricated resistive probe responds to the external field, we implemented the probe on an AFM and performed a preliminary read/write experiment. The first experiment was to image the well-known TGS single crystal where the typical domain images can be found [42]. Lenticular-shaped domains were observed, as shown in Figure 17(b), which was decoupled from the simultaneously

IV.6. Resistive Probe Storage:

961

FIGURE 17. (a) Topography and (b) domain images of a TGS single crystal acquired by the resistive probe microscopy over the 40 × 40-µm scan area. (c) Four alternatively poled domains by the resistive probe over the 25 × 25-µm scan area. (d) Line profile of the read signal over A–A′ line, which shows a transition length of about 800 nm across opposite domains. Reprinted with permission from [23]. Copyright 2004, AIP.

obtained topography of Figure 17(a). The next step was to prove that the resistive probe is able to write and read the domains using PZT samples. The writing experiment consisted of applying voltage above the coercive voltage through the source and drain across the film, and grounding the bottom electrode while scanning the probe. Four alternating regions were poled with either positiveor negative-bias voltage to form the checkerboard pattern, as shown in Figure 17(c). The right image shows the transition width between two adjacent domains, which was ∼800 nm. After a process revision and test bed upgrade, we could enhance the resolution up to ∼100 nm, as evidenced by the transition width between alternating domains in Figure 18. For media characterization, all the PZT films were preferentially oriented for the composition from 20:80 to 40:60, while the other compositions from 52:48 to 70:30 showed mixture of and . Moreover, the SEM observation showed second-phase segregation in the composition range for rhombohedral phases. Therefore, for our media study, we focused on the tetragonal phases that cover the composition range from 20:80 to 40:60. The microstructure was observed by SEM (Figure 19) and the grain size was measured using the line-crossing method. As shown in Figure 19, no secondary

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FIGURE 18. (a) Image of domains written and visualized by the resistive probe over a 5× 5-µm area and (b) line profile of the read signal over the A–A′ line.

phases could be detected, and the average grain size increased from ∼90 nm to ∼150 nm as the Zr/Ti ratio increased (Figure 20). Since the resistive probe detects the surface potential variation, the larger the surface potential difference between the opposite domains gets, the higher becomes the signal to noise ratio of the media. Therefore, the local surface potential measurement is important for designing high-SNR media (see Figure 12(c)). Kelvin force microscopy (KFM) suits the purpose of local detection of surface potential [43–45]. We used a commercially available KFM (SPA 400, Seiko Instruments). For calibration, we applied 20 mV, 40 mV, and 80 mV to a gold-sputtered silicon wafer, and measured the resulting surface potential of the gold surface. The average measured potential read 20.66, 40.42, and 79.87 mV, respectively, which gave a good agreement with the applied potential.

FIGURE 19. Plan SEM observation of PZT thin films of composition from (a) 20/80, (b) 25/75, (c) 30/70, (d) 35/65, and (e) 40/60 in terms of Zr/Ti ratio. The film thickness is 100 nm.

IV.6. Resistive Probe Storage: FIGURE 20. Plot of grain size vs. composition in terms of Zr/Ti ratio.

963

Average Grain Size (nm)

200

150

100

50

0

20/80

25/75

30/70

35/65

40/60

Composition (Zr/Ti ratio)

Figure 21(a) shows the KFM contrast as a function of PZT composition, of which trend is not well understood. The remnant polarization measured with Pt top electrode showed a different trend (see Figure 21(b)), not only from the wellknown curve from the literature where Pr increases monotonously as composition approaches Ti-rich (20/80 in our case) [46], but also from the surface potential trend shown in Figure 21(a). Even though the trend may differ from reference to reference, the variation of Pr does not exceed 50%, and in Figure 21(b) the maximum variation was 6%. This is far from the variation observed in the local surface potential measurement, where the maximum variation reached 400%. Reports on the behavior of KFM contrasts as a function of elapsed time and writing voltage might give us a clue about the complex trend shown in Figure 21 35

(a)

400

(b)

30 Pr (µC/cm )

300

2

KFM contrast (mV)

500

200

25

100 0

20/80

25/75

30/70

35/65

PZ T composition (Zr/Ti ratio)

40/60

20

20/80

25/75

30/70

35/65

40/60

PZ T Compostion (Zr/Ti ratio)

FIGURE 21. (a) Plot of surface potential difference between positively poled and negatively poled domains as a function of PZT composition in terms of Zr/Ti ratio. The size of poled region was 5 × 5 µm. (b) Plot of remnant polarization, Pr , vs. PZT composition, which was measured on top electroded capacitors.

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FIGURE 22. (a) PFM phase image of bit arrays formed by voltage pulses of −20 V, 30 ns to the conductive probe over 1 × 1 µm. (b) shows the line profile across A–A′ in (a).

[44,47]. The exponential decay behavior of surface potential as a function of time in the span of minutes due to surface charge migration, and evidence showing surface charge trapping on the media, complicates the surface potential difference as a function of composition [47]. Depending on the surface condition, the decay time constant as well as surface charge-trapping effect might vary a lot. Our current understanding of surface potential behavior as a function of composition limited the choice of the optimum condition based on the experimental results. The composition so chosen were 25/75 and 40/60 based on the assumption that Figure 21(a) represents the typical results for our specific system. The domain writing and reading experiments by PFM have been performed and reported in the previous publication [30,31], where the detailed experimental conditions can be found. Based on the fact that scaling down the thickness of PZT film is crucial for stable domain configuration, we reduced the thickness to 50 nm. However, 50 nm films showed poor leakage properties, which prevented us from using it as proper media. Therefore, the optimum thickness was chosen to be 75 nm, where the grain sizes were 75 nm and 101 nm for 25/75 and 40/60, respectively. Figure 22 shows PFM phase images of bit arrays formed by −20 V, 30 ns voltage pulses to the conductive probes over a 1 × 1-µm area after poling the whole area by 20 V. The line profile of the bits formed is shown in Figure 22(b), where the average bit size was 33 nm with a standard deviation of 14 nm. The large variation of the bit size was due to the interaction between grains and domains, as shown in Figure 14(b).

2.5 Servo/Tracking Concept If one compares the traveling speed of a few dozen meters per second in the case of HDD, 12 mm/s maximum speed is very slow. However, if one compares the number of probes that reaches 4,096, it is a huge number of heads in comparison to the single head in a HDD. Why do we compare the speed and number of probes

IV.6. Resistive Probe Storage:

965

or heads for both probe storage devices in wide sense? It is because the exact positioning mechanism depends heavily on the velocity jitter and the number of servo-probes. When the head moves very fast with low jitter, there is less need to check frequently whether the head is on track or not. On the contrary, for the resistive probe storage device, it is necessary to have frequent feedback whether the probes are on track or not, because the probe moves relatively slowly, and it may suffer from more severe jitter in comparison to the head of HDD. The other thing to consider is that we can use multi-probes for identifying the position more robustly. We have proposed a robust method of servo/tracking for resistive probe storage considering the pros and cons of the mechanical system under investigation, which will be explained in detail below. The storage medium consists of M × N data fields and P servo-fields as shown in Figure 5(a). A data field is defined as a sectioned storage medium where m × n data bits can be stored (Figure 5(a)). A servo-field is similarly defined, except that servo-information is stored. Accordingly, a probe array consists of M × N data probes for M × N data fields and P servo-probes for P servo-fields. P servoprobes read the data in the corresponding servo-fields, the values of which become the bit values of the servo-codes as described in Eq. (1). The P-bit servo-code S in Eq. (1) can indicate 2 P different positions with one-to-one correspondence as described in Eq. (2). For example, if the data bit is of radius 50 nm and written with 100 nm spacing, a data field of 100 × 100-µm size can store less than 218 bits. Therefore, 18 probes are required for indicating all bit positions. The stage must be controlled such that a probe can track exactly the centerline of the data stream and be located at the bit center every reading or writing timing. Therefore, the two-axis positions must be known: off-track error and synchronization error. The off-track error is the position error from the track, whereas the synchronous error is that from the bit center in scanning direction at writing and reading events. Since the servo-algorithm discussed in the previous section can detect the position bit-wise, it cannot detect the position error smaller than the bit size. In addition, the scanner is very sensitive to disturbances, since it moves slowly. Therefore it must detect position errors smaller than a bit size frequently or even continuously. Many off-track detection techniques in probe storages have been proposed, and can be categorized into two groups: static and dynamic approaches. As a static approach, like HDD, some precise burst patterns are written at the head of data stream and an off-track error is calculated in a discrete manner [48,49]. There is another static approach that uses different pitches between the data bits and the servo-probes, by which the off-track error can be obtained continuously [50]. As a dynamic approach, the off-track error is modulated by vibrating the stage at a high frequency and then demodulated using the lock-in technique of SPM [51]. Also similar but not vibrating at as high a frequency as the above case, is the simple tracking method [52]. These dynamic approaches do not require highly precise servo-patterns but have the limit of scanning speed.

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2R

y R o1 x d

(a) y

yd

4R

6R

l1

8R

R o 2

x l2

-R ta

(b) p

tb

tc

td t

(c) u y

t

(d) u x

t

(e) ty

t

(f) tx

t 0

T/4

T/2

3T/4

FIGURE 23. The illustrative waveforms to explain the tracking algorithm: (a) scanner vibration on the y-axis, (b) probe signal, (c) decomposition signal of y-axis, (d) decomposition signal of the x-axis, (e) probe signal multiplied by the decomposition signal of the y-axis, (f) probe signal multiplied by the decomposition signal of the xaxis. Reprinted with permission from [18]. Copyright 2005, IEEE.

T

We propose a tracking algorithm for probe storage devices. It can detect the two-axis position error smaller than a bit size quickly and almost continuously. A tracking probe reads the bits in the tracking field (in Figure 23(a), o1 and o2 ) in which all data are written as “1”s. Along the x-axis, the scanner is moved at constant velocity Vs . On the y-axis, the scanner is moved in a saw wave with magnitude R and frequency of Vs /8R, as shown in Figure 23(a). If a disturbance causes deviation from bit centers (xd and yd ), the probe detects the signal p between ta and tb , and between tc and td , as the scanner is vibrated on the y-axis (see the probe trajectory, lines l1 and l2 intersect the data bits, circles o1 and o2 in Figure 23(a)). These crossing times have the following conditions: 4 (2xd + yd ) + 5Vs 4 (2xd − yd ) + tc + td = 5Vs

ta + tb =

4R Vs . 12R Vs

(3)

It is assumed that all data bits are written in a circle with a radius R, and the sensor signal of the probes is abrupt, as shown in Figure 23(b). The deviation of each axis can be obtained if we sum or subtract the two equations as shown in Eq. (4). To do this, the two decomposition signals u x and u y in Figure 24(c,d) are multiplied with the probe signal p, resulting in the signals tx and t y (Figure 24(e,f)) as tx = p × u x . ty = p × u y

(4)

IV.6. Resistive Probe Storage:

967

0.6 0.5 estimated error real error disturbance

error(R)

0.4 0.3 0.2 0.1 0 -0.1 0

5

10

15 bit(R)

20

25

30

FIGURE 24. Transient response of the closed-loop controlled tracking system. Reprinted with permission from [18]. Copyright 2005, IEEE.

If these signals are integrated during T and the deviations xd and yd are constant during T , the estimated position errors xˆd and yˆd can be estimated as xˆd = yˆd =





T

T

+   T /4 + tx dt = − ta

+   T /4 + t y dt = − ta

tb T /4

+

tb T /4

−



3T /4 tc



3T /4 tc

− +



td 3T /4



td 3T /4

,

,

dt =

4T xd 5R .

(5)

2T yd dt = 5R

Note that the estimated errors in Eq. (5) are decoupled to each other and proportional to their real position errors. Since the estimated position error on the x-axis can be used for synchronizing the writing or reading timing with the center of the bit, no additional timing recovery circuit is needed. We can control these errors to be zero in a closed-loop manner. The proposed error detection algorithm is simulated by MATLAB. The scanner is modeled as an ideal linear second-order system and controlled to move constantly along x-axis and is vibrated along the y-axis, as shown in Figure 23(a). The scanner parameters, controller gains, and operation conditions are given in Table 4. Figure 24 shows that the tracking algorithm works well with a simple PI controller, although the step disturbance equivalent to 0.5R is applied. Equation (5) is derived when the slope of the vibration l1 is 1/2 (see Figure 23(a)). In the general case of the slope m, the factors will be 1/(1 + m 2 ) and m/(1 + m 2 ) instead of 4/5 and 2/5, respectively. If the stage is not vibrated, i.e., m = 0, we can estimate only the x-axis position error with maximum gain.

968

Seungbum Hong and Noyeol Park TABLE 4. Simulation Conditions Parameter

Value

Mass Damping ratioa Bit radius Proportional gain a Closed-loop

10−3

1× 0.7 50 nm 0.1

Parameter kg

freq.a

Natural Scanning speed Sampling time Integral gain

Value 500 Hz 0.5 mm/s 0.8 ms 1,500

controlled scanner.

The above results are derived under several assumptions: infinite bandwidth of the scanner, abrupt readback signal, exact bit location, constant radius of bits, and constant magnitude vibration of the scanner. In practical, these assumptions limit the performance of the position-sensing algorithm and reduce the operating range. For example, in Figure 23, the scanner is assumed to vibrate in a saw-wave pattern, but in actuality it moves in a sinusoid pattern because of the finite bandwidth of the scanner. Usually the scanner has a resonant frequency below several kHz and it move faster than the resonant frequency. Figure 25 shows the sensor characteristics of the x-axis when the scanner is vibrated in a saw-wave and sinusoid pattern. Although the sensor gain is reduced about 11.0% from their regression models, it remains linear, which can be easily compensated for. Similarly, the sensor gain of the y-axis increases about 18.6% and it can be easily compensated for. However, the proposed algorithm is expected to be effective and applicable for a probe storage device when feedback controllers with a robust design technique are used [53]. 0.5 0.4

finite bandwidth (sinusoid) finite bandwidth (saw wave)

0.3

sensor output

0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -1.5

-1

-0.5 0 0.5 normalized position error(R)

1

1.5

FIGURE 25. Gain characteristics of the x-axis sensor in the case that the scanner has infinite and finite bandwidth. Reprinted with permission from [18], Copyright 2005, IEEE.

IV.6. Resistive Probe Storage:

969

3 Outlook One of the major hurdles in the development of probe storage devices is to make a uniform multi-probe array, which leads to the question of why we need a multiprobe scheme for probe storage devices. The first reason is because it can reduce the seek time to the desired position; the second one is because it can enhance the data transfer rate and total capacity. However, as one increases the number of probes, the challenges of making a uniform array of probes becomes more and more difficult. Therefore, there is an upper limit for increasing the number of probes. On the other hand, the lower limit for decreasing the number of probes comes from the fact that currently available MEMS stages can only travel up to 120 µm. The other limitation comes from the fact that the fastest possible scan frequency does not exceed 1 kHz. Therefore, finding the optimum number of probes depends on the processing technology of the probe arrays and the MEMS stage. Taking all the facts into account, the most probable scenario will likely be an approximately 64 by 64 multi-probe array with a 120-µm travel range and a maximum speed of 12 mm/s for the MEMS stage. This will lead to 40 GB capacities with 200 Mbps in a 13 × 13× 1.5-mm form factor. If we focus on the challenges to developing resistive probe storage devices, the major problems fall into three major categories, as shown in Table 5. Among them, the physical limit of the resistive probe and its wear properties are the most urgent challenges. Preliminary works on probe and media wear showed [54] that probe wear was more severe than media wear, which necessitates a proper anti-wear design for the resistive probe. The contact scheme should also be specified so that one can determine whether simple passive loading or a sophisticated non-contact scheme should be employed. The potential recording density is mainly determined by the resolution of probe and the minimum bit size formed in the media. Up to now, the potential bit size studied by the PFM showed better performance than the resolution of the resistive probe. Therefore, we need to find the optimum design for the resistive probe, which can detect 25-nm domains. Reliable signal generation from the bit in the media determines the bit error rate. The surface charge state influences the signal, which is affected by screen charges or trapped charges by external injection. The clear identification of surface TABLE 5. Major Challenges and Responses Category

Detailed Items

Response

Probe design

Resolution wear Screen charge Reliability

New structure Anti-wear design /non-contact scheme Surface treatment Anti-shock design

Media design Stage design

970

Seungbum Hong and Noyeol Park

(a) Process Simulation

FIGURE 26. Schematic flow diagram of (a) process simulation that covers all processing steps, (b) field simulation that includes ferroelectric media, and (c) device simulation where source and drain are defined. The structure developed in the process simulation becomes the input with the media surface charge information for field simulation, which in turn, becomes the input for device simulation. The ultimate output is the device performance parameters such as sensitivity and spatial resolution.

screening or charge trapping phenomena will lead to a design breakthrough in the resistive probe storage media. We developed an electrostatically driven xy stage showing ±40 µm at 10 V with a dc gain of 3.0 µm/V at 4 V. The remaining challenges are the reliability against shock and the areal efficiency [55]. The future direction is illustrated in Figure 6, in which the direction toward the ultimate resistive probe storage device is clearly shown. One of the main strategies to help achieve the goal is to build a simulation process to find the optimum design condition for the resistive probe. A simulation process which covers process, field, and device simulation as shown in Figure 26 is currently being developed at Samsung. Another simulation tool includes media domain simulation and servo/tracking simulation, with which we can develop a design tool for a new recording technology such as the resistive probe storage device. Acknowledgments. Our probe storage device team members at the Samsung Advanced Institute of Technology provided all the materials presented in this chapter, and I gratefully acknowledge their contribution. The list of team members includes H. Ko, D. K. Min, H. Park, J. Jung, Y. W. Nam, S. Buehlmann, C. Park, Y. Seo, and J. Y. Shim.

IV.6. Resistive Probe Storage:

971

Fruitful discussions with Y. Kim and J. Woo at KAIST, and J. Yoo, C. S. Kim, J. S. Shim, Y. S. Kim at SAIT are acknowledged. Last but not least, we acknowledge with gratitude the collaborations with Prof. K. No at KAIST, Prof. H. Shin at Kookmin Univ., Prof. H. C. Shin at Seoul National Univ., Prof. J. U. Jeon at Ulsan Univ., and Dr. S. H. Kim at INOSTEK.

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51. H. Nose, T. Miyazaki, T. Oguchi, K. Sakai, and T. Kawase, US patent 5,404,349 (1995). 52. R. V. Lapshin, Rev. Sci. Instr. 71(12), 4607–4610 (2000). 53. D.-K. Min, S. Hong, IEEE Conference on Sensors, 601–604 (2004). 54. K.-H. Chung, Y.-H. Lee, D.-E. Kim, J. Yoo, S. Hong, IEEE Trans. Magn. 41(2), 849–854 (2005). 55. H. Shin, Nanoscale Phenomena in Ferroelectric Thin Films, edited by S. Hong (Kluwer Academic Publisher, Boston, 2004), Chapter 11.

Index

Adhesion, 517–518 Adsorbates effect on transport SPM, 396 effect on PFM, 663 AFM, 283–285, 267, 290–295, 297–299, 301–302, 304–308 Conductive probe, 32, 137, 932–933 Current-sensing, 135, 932 Alkanethiols, 419, 605, 729–730, 778 Antenna, 217–219, 226, 235, 243, 256, 264, 326–328 Angle-Resolved Photoemission Spectroscopy, 489 Atomic Force Acoustic Microscopy, 616 Attenuation, 176, 178, 200, 321 Azo-compounds, 274 BaTiO3 , 160, 185, 198, 907, 910–911, 918 Battery Lead acid, 290–291, 298 Lithium ion, 292–293 BiFeO3 , 164 Biomolecules, 603–604, 611, 627 Bit array, 947–948, 958, 964 depth, 953 error rate, 948, 957, 969 size, 949, 953, 956–957, 964–965, 969 Breakdown, 143–144, 259, 562, 572, 574–576, 578, 844, 871 Break junction 726, 732, 784 C-V curve, 93–94, 96, 99–100, 105. 107, 699 local measurement, 699 Cabrera-Mott theory, 859, 872 CaCu3 Ti4 O12 , 164, 166 Calibration electrostatic tip shape, 303

974

PFM, 182–183, 620 SCM, 50, 59 SSRM, 37, 41, 44–45, 49, 57, 66 Cantilever frequency response, 152 effect on PFM, 178 surface capacitance, 137, 150 Carbon nanotubes, 156, 270, 423–436, 890 bundle, 889 chirality, 423, 443 contacts, 436 CVD growth, 580 decay length, 449 defects, 449 integration with Si, 881 junctions, 444 field-effect transistor, 424 memory effect, 429, 451 metallic, 435 network, 442, 443 semiconductive, 476 STM, 466 Cavity perturbation approach, 233 Capacitor ferroelectric, 750, 756, 761 switching, 189 Charge writing, 834, 843–844, 847–848 Chemical-Vapour Deposition 286 Conductive probe AFM, 778, 842 Contact Potential Difference, 114–115, 457, 519, 610, 664, 676, 694–696, 704 Coherent Anti-Stokes Raman Scattering, 270 Collagen, 615, 617–620 Contact mechanics DMT, 528 Hertzian, 528 Maugis, 528

Index Correlated oxides, 2–3 Corrosion, 298 Coulomb gap, 354 blockade, 360 Cross-correlation, 403–404 CuGaSe2 , 669, 671, 673 Curie temperature Ferroelectric, 331 Current Image Tunneling Spectroscopy, 900 Defects transport across, 161 in SAMs, 396 in SWNT, 900 surface, 709 Density of states local, 25, 350–351, 391, 462, 466, 471–472, 493, 502 Density Functional Theory, 465, 467, 470, 888 Dentin, 620–622, 624 Derjaguin, Muller, Toropov, 528 Depletion width, 158, 563, 569 Dielectric Constant, 99, 117, 166–167, 196, 241, 257, 817 Films, SCM, 99 Dielectric response Linear, 236 Non-linear, 236 Dip-pen nanolithography electrochemical, 838 DNA, 405, 432, 603–604, 609–610, 613, 717, 725, 731–734, 735 DMT model, 528 Dopant 3D profiling, 634 activation mechanism, 68 profiling by SCM, 90 profiling by SSRM, 73 Double exchange, 539 Dye, 264, 274, 595, 610, 736 Dynamic force microscopy, 506 charge imaging, 518 energy dissipation, 529 on insulators, 523 spectroscopy, 622 on semiconductors, 514 Eddy current microscopy, 240 Eigenfrequency, 469, 508–510 Electret, 618, 834, 844 Electric Force Microscopy, 209, 788, 790

975

cantilever-sample interaction, 792 resolution, 792 sensitivity, 806 theory, 793 Electrochemical AFM, 281 Etching, 304 Electrochemical cell two electrode, 282 three electrode, 282 four electrode, 282 Electrochemical SPM, 280 active probe, 283 passive probe, 283 probe requirement, 283 Electrochemical STM, 834–835 Electron Spin Resonance Microscopy, 241 Electromechanical forces, 176, 178–180 Electromigration, 23, 784 Electron electron interaction, 349, 352, 355 gas, 692 phases, 349 phase separation, 350 standing wave, 25, 493 Electrooptical, 184, 186 Electrostatic forces Tip–surface, 355 Electrostatic Force Microscopy -337, 355 of quantum systems, 337 single electron, 422 Enamel, 620 Energy depolarization, 185 dissipation, 226 Helmholtz, 317 Evanescent field, 218 Fatigue, 906, 950 Fatigue endurance, 950, 952 Fermi level, 47, 114, 123, 354, 357–358, 360, 375 golden rule, 374 vector, 352 Ferroelectric bit, 947 capacitors, 173, 182 Data storage, 935 domains, 156, 164, 173 domain growth, 188–189 hysteresis, 96, 105, 193 imaging by NSOM, 334 imprint, 204

976

Index

Ferroelectric (cont.) fatigue, 204 lithography, 915 local hysteresis loops, 194 Random Access Memories, 204 relaxors, 206 size effect, 201 storage medium, 965 surface potential, 911 switching, 178 switching kinetics, 190 Ferroelectroelastic, 185 Ferromagnets, 215, 240, 384 domains, 391 Field Effect Transistor Body under source, 654 Cross-sectional imaging, 636, 645 Metal-oxide-semiconductor, 677 Multiple Gate, 70 Organic, 925 Force capillary, 611, 720 electrostatic, 114 Lennard-Jones, 528 London, 467 Lorentz, 354 power law, 512 Van der Waals, 152 Force-distance curve deconvolution, 525, 527, 808 Frequency response 92, 105 cut-off, 772 Fresnel fringes, 319 Friedel oscillations, 24, 492 GaAs, 26, 59, 337, 355, 494, 516 Gain, 529 GaN, 690–691 Gate voltage, 429, 443, 448, 451 Ge-H surface, 273 Grain boundaries, 19, 21, 671 CaCu3 Ti4 O12 , 166 Double Schottky barriers 143 SrTiO3 , 158 Transport across, 165–166 ZnO, 143 Green’s function imaging, 465 surface, 465 transport, 719

Hall effect, 239 quantum, 349 Hamiltonian tip-surface system, 456 Hanning window, 405 Harmonic oscillator, 321, 432, 794 Haversian system, 618 High Temperature Superconductors, 241, 538 HOPG, 118, 120–121, 293–294 Hund’s rule, 535 Hydroxyapatite, 617, 620 III-V nitrides, 690 semiconductors, 349, 351, 354, 367 I-V curves, 17, 37, 41, 44, 486 reconstruction, 44 InP, 24, 59, 73 International Technology Roadmap for Semiconductors, 89 Image deconvolution in KPFM, 127 Impedance, 132 electric tip, 226 magnetic tip, 228 Impedance spectroscopy, 308 2 probe, 263 4 probe, 263 Cole-Cole plot, 145, 166 microelectrodes, 134 Jahn-Teller effect, 549 Kelvin Probe Force Microscopy, 113–115, 299, 663 Amplitude detection, 113 Frequency detection, 113 Resolution, 114 La0.8 Sr0.2 MnO3 , 242 La0.7 Sr0.3 MnO3 , 23, 542–543, 545 Landau level, 356–357, 360–361 Landauer formula, 493 theory, 24 Laser buried heterostructures, 561, 574, 583–585 diode, 561, 572, 589 solid state, 308 ridge waveguide, 561, 563, 572, 578 LC oscillator, 217, 225, 239 LCAO, 457–458, 461–462 Leakage Current, 154, 161, 575, 578, 655, 702

Index LEIS-AFM, 285–286, 307, 309 Legendre transformation, 794 LiNbO3 , 185, 190, 237, 914 Lightning-rod effect, 257, 259–261, 264–266 Linear Imaging theory, 157 LSMO, 242, 539–540, 543, 545–546 Local Electrochemical Impedance Spectroscopy, 285, 30–309 Lock-in amplifier, 375, 381, 431, 441, 590, 602, 747, 761, 771 Low-dimensional electron systems, 349 Luttinger liquid, 424 Magnetic Force Microscopy, 155, 339, 382, 545, 924 Magnetoresistance, 374, 534, 936 colossal, 21, 536, 538, 540, 554–555 giant, 936 Manganites, 534 charge ordering, 537 phase separation, 552 Meissner state, 216 MEMS, 288, 945, 969 Metal-insulator transition, 535–536 Metamaterials, 245 Microcoils, 329 Microscopic 4 point probe, 480 Microwave, 215 Millipede, 834, 945–946, 959 Mn3 N2 , 377 Mobile charges Effect on SIM and SSPM, 161 Molecular conductance switching, 396 conformation, 416, 718 current path, 716 electronics, 736 internal rotation, 416 latching, 416 motion, 410 wire, 416 Mott-Hubbard insulator, 538 Nanoimpedance Microscopy, 132, 136, 146 experimental set-up, 132 probe selection, 132 resolution, 145 Nanoimpedance Spectroscopy, 145 Nanolithography by NSOM, 223 Elimination, 922 Addition, 925 Ferroelectric, 924–925

977

Dip-pen, 934 Substitution, 928 Nanomanipulation, 273, 527 Nanooxidation, 7 Nanowire Au, 483 silicide, 499 SnO2 , 160 Nafion 149–150, 309, 834 Near-Field Microwave Microscopy, 215, 223 aperture based probes, 221 apertureless probes, 221 resolution, 221 Noise Johnson, 332 Thermal, 19, 24 Non-contact AFM, 140 Non-volatile random access memories, 952 Numerical aperture, 261, 263, 273 Oxygen Reduction Reaction (ORR), 149 Optoelectronics, 73, 424, 633 Pattern Ag, 835 Biotin-IgG, 852 Charge, 853 Domain, 165 Particle, 850 Polyaniline, 838 Polymer, 836 Patterning 2D electron gas, 875 beam, 853 domain, 186 electrochemical, 835 lithographic, 895 mask, 956 monolayers, 956 oxide, 956 remote, 875 resist, 841 silicon, 31, 945 p-n junction, 26, 55, 95 PbMg1/3 Nb2/3 O3 , 206 PbZn1/3 Nb2/3 O3 , 206 PbTiO3 , 206 Pentacene, 788–789, 793 Perovskite, 21, 166, 181, 204 Piezoelectric biopolymers, 617, 628 tensor, 617, 625–626, 629 semiconductors, 919

978

Index

Piezoresponse Force Microscopy, 2, 173 adsorbate effect, 173 biological systems, 615 contrast formation, 177 experimental set-up, 175 domain switching, 175 III-nitrides, 696 orientation dependence, 617 principle, 175 Piezoresponse Force Spectroscopy, 164 local hysteresis loops, 194 switching spectroscopy mapping, 200 Phase transition insulator-metal, 537, 547 ferroelectric, 237, 909 Phase-locked loop, 223 Phenylene-ethynylene oligomers, 397, 399 Photoexcitation, 25 Photosystem I, 605–606 PMMA, 323, 328, 841, 843, 845 Plasmon, 219, 245, 256–257 Point charge model, 186, 189 Polarizability, 321–322, 325 Polaron, 548, 552, 717 Polyaniline, 790, 837–838 Polyethileneoxide, 432 Positive Temperature Coefficient of Resistance, 152 Potential electrochemical, 566, 568, 796,723 electrostatic, 125 Lennard-Jones, 468, 523 Pr0.5 Sr0.5 MnO3 , 537 Probe array, 834, 965, 969 coaxial, 238, 234, 328 magnetic dipole, 329 multifunctional, 334 resistive, 947 storage, 947 PZT, 950, 957 capacitor, 191 composition, 963 thick film, 332 thin film, 176, 761 Q-factor, 231–232 Quantum dot electrostatically defined, 366 GaAs, 644 Quantum point contact, 363 well, 589, 366

Raman spectroscopy, 256, 270, 294 Relaxors, 206 Resistance across atomic step, 495 contact, 500–501 Maxwell, 40 Schottky, 46 Sharvin, 41 sheet, 203–231 step bunches, 496 Resolution dopant gradient, 34, 55 spatial in KPFM, 127 spatial in NIM, 308 spatial in NSOM, 318 spatial in PFM, 210 spatial in probe storage, 966 spatial in SCM, 58 spatial in SIM, 150 spatial in SSRM, 39 Resonance optical, 246 surface plasmon, 239 Resonators Cavity, 220 Coaxial, 220 Slot, 329 Transmission line, 225 Sample preparation for cAFM, 432 for SCM, 89 for SSRM, 26 Schottky barriers, 367, 425–426, 447, 452 in 1D systems, 425 grain boundary, 425 surface estate, 447 Scanning Capacitance Microscopy, 34, 88, 90–91, 239, 350, 361, 564, 634, 663 Constant V mode, 91 Constant V mode, 93 Cross-sectional, 634 Dopant profiling, 634 Failure analysis, 634 Optical pumping, 106 Resolution, 91 Scanning Conductance Microscopy, 424, 430, 432 Scanning Differential Spreading Resistance Microscopy, 562, 588–589 Scanning Electrochemical Microscopy, 134, 281, 285, 827

Index probe development, 302 applications, 302 Scanning Impedance Microscopy, 132, 135, 150, 285, 308, 424 resolution, 135 Scanning Gate Microscopy, 363, 425, 471 2DEG, 363 spectroscopic mode, 471 Scanning Maxvell Stress Microscopy, 601, 865 Scanning Near Field Optical Microscopy, 254, 261, 351, 457 field enhancement, 257 low-dimensional electronic systems, 351 probe, 254 scattering, 351 Scanning Noise Potentiometry, 18, 21 Scanning Nonlinear Dielectric Microscopy, 948 Scanning probe oxidation, 858 Scanning Single Electron Transistor, 357 Scanning Spreading Resistance Microscopy, 31, 39, 114, 135, 564, 663, 675 Resolution, 31 Scanning Surface Potential Microscopy (also see KPFM), 28, 135, 151, 606 Scanning Thermal Microscopy, 424, 435 Scanning Tunneling Microscopy, 11, 66, 217, 223, 272, 335, 372, 433, 456–457, 507, 534, 805 Constant current mode, 375 Constant height mode, 457 EPR, 223 inelastic, 465 induced desorption, 465 feature tracking, 403 Green’s function 465 multiprobe, 945 Spin polarized, 372 surface photovoltage, 664 Scanning Tunneling Potentiometry, 3, 11–12, 27, 536, 540 Ac/dc feedback, 12 Interrupted feedback, 12 Scanning Tunneling Spectroscopy, 11, 17, 335, 350–351, 378, 481, 536, 540, 543 Scanning Voltage Microscopy, 561–595 artifacts, 583 theoretical interpretation, 565 probe selection, 563 resolution, 583 Self-assembled monolayers, 929–940 alkanethiols, 778 insertion, 414

defects, 414 ordering 550 Self-assembly templated, 885 Sensitivity KPFM, 114 SSRM, 114 Shear-force control, 223, 235 Silicon-on-insulator, 641, 654 Single-Electron Transistor, 357, 424, 791, 954 Single-Spin Microwave Microscopy, 244 SnO2 , 160, 847 Solar cell, 6, 114, 664, 668–669 SQUID, 11, 222, 240, 335 Sr3 Bi4 Ti6 O21 , 334 SRAM, 638, 641, 643 SrTiO3 , 23, 38, 158, 189, 204, 308, 542, 763 Grain boundary, 158 Space charge, 124, 482, 487, 497, 562, 812 Spin-orbital interaction, 391 Spin polarized STM, 373 constant current mode, 373 differential magnetic mode, 555 spectroscopic mode, 388 tip preparation, 385 Surfaces Au(111), 290, 835, 889, 896 CaF2 (111), 523 Co (0001), 382 Cr (001), 376 InAs (110), 352–353, 896, 899 Mn3 N2 (010), 377 NiO (110), 522 Pd (111), 288 Pt (100), 290 Pt(111), 204, 288 Rh(111), 288 Si(110), 499 Si (111), 526–527 Si (557), 491 W (110), 376 Surface Relaxation, 517 Surface conductivity anisotropy, 487–488 Surface state, 685 band bending, 685, 721 conduction, 473 effect on SSRM, 33 tunneling, 41 Surface potential inversion, 161

979

980 Tersoff-Hamann model, 372 TGS, 907, 960 Thermoelectric voltage, 24–25 Schottky barriers, 18 Thiols, 399, 727, 934 Tip CrO2 , 376 CoFeSiB, 387 Tip-enhanced optical lithography, 271 Tip-surface capacitance, 156, 167, 428, 431, 476, 694 Tip-surface contact area estimation, 138 equivalent circuit, 150 electrical properties, 33 mechanical properties, 33 pressure effects, 48 Thermionic emission, 581, 586, 591, 816 Thermodynamics of domain switching, 184, 186 Transconductance, 502–503 Transmission line, 209 Model of probe, 229 Resonant, 217, 230 Transistor bipolar junction, 644 field effect, 201, 425, 443, 448, 472, 793, 797 organic, 114, 797

Transport defects, 24 drift-diffuusion, 566 frequency dependent, 163 grain boundaries, 163 metal-semiconductor interface, 161 p-n junctions, 26 Tuning fork oscillator, 223 damping, 152 Tunneling, 578, 708, 716 AFM, 135, 433 current, 12–15, 18–19, 224, 337, 373–376, 381, 388–389, 413 magnetoresistance, 374 Ultramicroelectrode, 126, 293, 288 Underpotential deposition, 284, 827 Vanessa Virginiensis, 627 Waveguide, 217–222, 232, 240, 255–256, 320, 323 Work function, 118–122, 129, 152, 519 Wurtzite, 691–692, 696 X-ray photoemission, 681 ZnO, 142–143 ZrNx , 860, 874 Zr/Ti ratio, 962

PLATE 1. Surface topography and surface potential images of polycrystalline ZnO varistor ceramics. Shown are images at zero lateral bias and +10 and −10 biases. On grounded surface, potential variations on second-phase inclusions are clearly seen. On laterally biased surface, potential barriers developed at grain boundaries are illustrated. Figure courtesy of S. Kalinin (ORNL) and D. Bonnell (U. Penn).

Topography Vector PFM Domain Writing

Piezoresponse Force Microscopy

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Domain dynamics and evolution

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Temperature dynamics and phase transitions

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PFM

Work of switching

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Inactive Grain -10 -8 -6 -4 -2 0 2 4 6 8 10 Tip bias, V

PFM spectroscopy

(a)

Switching 500 nm Spectroscopy Mapping

PLATE 2. Schematic illustration of PFM capabilities in nanoscale characterization of ferroelectrics.

PLATE 3. Dynamic force spectroscopy performed with atomic resolution on Si(111)-(7×7). The frequency shift vs distance curves plotted in A) were measured at the positions marked in the topographical image shown in Fig. 14B). The atoms labeled “2” and “3” represent inequivalent adatoms (cf. also the cross section displayed in C);DFS is able to distinguish differences in their bonding strength (see insert in A). Experiments have been performed at a temperature of T = 7.2 K. (Images reproduced from Lantz et al. [64].)

PLATE 4. Orientational imaging of the protein fiber in tooth. (a) Surface topography of polished tooth enamel (vertical scale 20 nm). (b) Vertical and (c) lateral PFM images of the same region as in (a) with a modulation bias of 10 V applied to the tip. A protein fibril embedded within a non-piezoelectric matrix can be clearly seen in the center of the PFM images. Circles and arrows in (b) and (c), respectively, show the orientation of the piezoresponse vector. (d) Vector PFM map of local electromechanical response. Color indicates the orientation of the electromechanical response vector, while the intensity provides the magnitude (color wheel diagram).

PLATE 5. (a) Optical photograph of Vanessa virginiensis (courtesy of Jeffrey Pippen, Duke University) and (b) optical micrograph of the wing scales. (c) AFM surface topography of the wing (vertical scale is 1 µm). (d) AFAM elasticity image (vertical scale is 18% of the average signal) of the wing obtained simultaneously with (c).

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PLATE 6. (a) Vertical and (b) lateral PFM images of the same area of the wing. (c) Color representation of the VPFM and LPFM data. Note the presence of the strong positiondependent PFM signal, indicative of the piezoelectric properties of the butterfly wing. (d) Angle distribution histogram of data in (c) that indicates the predominant orientation of the chitin fibers in the wing scale.

PLATE 7. Surface topography (a) and vector PFM images (b,c) of deer antler. Vector PFM illustrates finer details of internal antler structure, including the presence of region with different keratin orientation. The characteristic keratin fiber size in PFM image is ∼200 nm. Note that there is no correlation between PFM and topographic images, suggesting absence of cross-talk. Reprinted with permission from [42]. Copyright 2006, Elsevier, Inc.

PLATE 8. Sequence of SCM images of an n-channel BUSFET following a total dose radiation exposure of 500 krad. (a) At VG = 0 V, the SCM image shows the source and drain isolated from one another, the yellow-red-yellow contrast being indicative of the n + p junction. The most notable effect of radiation exposure can be seen at the buried oxide/substrate interface. The SCM image shows a light yellow layer at the top of the p-type substrate, which represents the accumulation of electrons caused by radiation-induced trapped charge (net positive) in the buried oxide. Just beneath the accumulation layer is a green region (dC/d V = 0 V), which represents the depletion region formed between the accumulated electrons and the p-type substrate. (b) Increasing the gate voltage to VG = 0.4 V resulted in the carriers reconfiguring in the body region such that the source and drain appear to extend toward one another, while at (c) VG = 0.75 V, the source and drain appear continuous. (d) An I D − VG curve of the irradiated BUSFET (solid) plotted along with pre-exposure data (open), both generated from in situ electrical measurements. The red circles show the biasing conditions for the SCM images in (a) through (c).

PLATE 9. SCM image of a 1.0 × 1.0 µm2 area of an InGaN surface showing indiumrich aggregation domains (bright regions) as small as 50 nm. Image courtesy of Veeco Instruments, Santa Barbara, CA. STM Tip

Tunnel Gap Conjugated Molecules

PLATE 10. Schematic drawing of conductance measurements using STM. Conductive Cantilever (Au Pt coated)

V

Molecules

I

PLATE 11. Schematic drawing of conductance measurements by CPAFM.

PLATE 12. (b) On an atomically flat gold surface, the legend “NANO” is written by applying successive voltage pulses across the tunneling gap. The letters are about 30 nm tall and 25 nm wide and are made up of lines of 5 nm width and 0.24 nm depth. In average each letter represents 5,000 missing gold atoms. Reprinted with permission from [47]. Copyright 1998, Springer-Verlag GmbH.

PLATE 13. Scanning tunneling microscope (STM) images and diagrams showing the process of controlling the initiation and termination of linear chain polymerization with an STM tip. STM images were obtained in air at room temperature in constant-current mode. Reprinted with permission from [3]. Copyright 2001, Nature Publishing Group.

PLATE 14. Three-dimensional rendering of a 30 × 30-nm2 STM topography of an individual SWNT after a ∼4-nm wide, ∼25-nm-long stripe of depassivated Si (red) was patterned by electron stimulated desorption of hydrogen by the STM probe.

PLATE 15. Optical micrographs of nanoparticles photo reacted on patterned PZT substrates. Au and Ag simultaneously deposited on c+ domains (a), Ag and Au sequentially deposited on c+ domains (b). Ni-based (c) and Fe-based (d) particles on c+ domains. Co-based particles deposited on c− domains (e). Co-based particles on c− domains followed by Ag on c+ domains (f). Reprinted with permission from [49]. Copyright 2005, MRS (courtesy of D. A. Bonnell).