Introduction to Scanning Tunneling Microscopy

Introduction to Scanning Tunneling Microscopy

C. JULIAN CHEN

OXFORD UNIVERSITY PRESS

Introduction to Scanning Tunneling Microscopy

OXFORD SERIES IN OPTICAL AND IMAGING SCIENCES EDITORS

MARSHALL LAPP JUN-ICHI NISHIZAWA BENJAMIN B. SNAVELY HENRY STARK ANDREW C. TAM TONY WILSON

1. D. M. Lubman (ed.). 2. D. Sarid.

Lasers and Mass Spectrometry

Scanning Force Microscopy

With Applications to Electric, Magnetic, and Atomic Forces 3. A. B. Schvartsburg. 4. C. J. Chen.

Non-linear Pulses in Integrated and Waveguide Optics

Introduction to Scanning Tunneling Microscopy

Introduction to Scanning Tunneling Microscopy C. JULIAN CHEN IBM Research Division Thomas J. Watson Research Center Yorktown Heights, New York

New York Oxford OXFORD UNIVERSITY PRESS 1993

Oxford University Press Oxford New York Toronto Delhi Bombay Calcutta Madras Karachi Kuala Lumpur Singapore Hong Kong Tokyo Nairobi Dar es Salaam Cape Town Melbourne Auckland Madrid and associated companies in Berlin Ibadan

Copyright © 1993 by Oxford University Press, Inc. Published by Oxford University Press, Inc., 200 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Chen, C. Julian. Introduction to scanning tunneling microscopy / C. Julian Chen. p. cm. (Oxford series in optical and imaging sciences ; 4) Includes bibliographical references (p. ) and index. ISBN 0-19-507150-6 1. Scanning tunneling microscopy. I. Title. II. Series. QH212.S35C44 1993 502'.8'2—dc20 92-40047

Printed in the United States of America on acid-free paper 3 5 7 9 8 6 4 22

PREFACE It has been more than 10 years since the scanning tunneling microscope (STM) made its debut by resolving the structure of Si(l 11)-7X7 in real space (Binnig, Rohrer, Gerber, and Weibel, 1983). This new instrument has proved to be an extremely powerful tool for many disciplines in condensed-matter physics, chemistry, and biology. The STM can resolve local electronic structure at an atomic scale on literally every kind of conducting solid surface, thus also allowing its local atomic structure to be revealed. An extension of scanning tunneling microscopy, atomic force microscopy (AFM), can image the local atomic structure even on insulating surfaces. The ability of STM and AFM to image in various ambiances with virtually no damage or interference to the sample made it possible to observe processes continuously. For example, the entire process of a living cell infected by viruses was investigated in situ using AFM (Haberle et al., 1992). The field of scanning tunneling microscopy has enjoyed a rapid and sustained growth, phenomenal for a new branch of science. The growing number of papers presented at the six International STM Conferences documents the rising interest in this field: Year

Date

Location

Papers

1986

July 14-18

Santiago de Compostela, Spain

59

1987

July 20-24

Oxnard, California

110

1988

July 4-8

Oxford, UK

157

1989

July 9-14

Oarai, Japan

213

1990

July 23-27

Baltimore, Maryland

357

1991

August 12-16

Interlaken, Switzerland

580

Similarly, STMs are being developed commercially at an astonishing speed. As of summer 1991, over 30 companies have manufactured and marketed STMs and parts. Many beginning companies dedicated to STMs and AFMs are seeing their business expand rapidly. The recent performance of Digital Instruments, Park Scientific Instruments, WA Technology, Angstrom

vi

PREFACE

Technology, TopoMetrix, and RHK Technology are typical of such companies. Likewise, a number of major manufacturers of scientific instruments have expanded their wares to include STMs. Vacuum Generator, Newport Instrument, Omicron Vacuumphysik GmbH, Leica, JOEL, Nikon, and Seiko number among these manufacturers. Several other companies arc supplying STM parts and accessories, such as piezoelectric elements, steppers, and probe tips. Because of their broad endorsement by the scientific and commercial spheres, STMs and AFMs will stand alongside optical and electron microscopes for the foreseeable future as important instruments in laboratories around the world. Ten years in contemporary science is a long, long period. Myriad startling developments can take place in that amount of time. As Ziman says in Principles of the Theory of Solids: "Today's discovery will tomorrow be part of the mental furniture of every research worker. By the end of next week it will be in every course of graduate lectures. Within the month there will be a clamor to have it in the undergraduate curriculum. Next year, I do believe, it will seem so commonplace that it may be assumed to be known by every schoolboy." With the prolific activity in the field of scanning tunneling microscopy over the past 10 years, there remains a visible gap in the published material on that topic. Several edited collections of review articles on STM have already been published (for example, Behm, Garcia, and Rohrer, editors, Scanning Tunneling Microscopy and Related Methods, Kluwer, 1990, Giintherodt and Wicsendanger, editors, Scanning Tunneling Microscopy, Vols. I through III, Springer Verlag, 1991-1992, and a number of others.) A textbook on scanning force microscopy has already appeared (Sarid, Scanning Force Microscopy, Oxford University Press, 1991). Nevertheless, a coherent treatise or textbook on STM is still lacking. We have seen the use of STM and the information derived from it continue to expand rapidly. We have seen the potential of the STM in microelectronic and chemical industries for process control and diagnostics gradually becomes a reality. The need for a basic reference book and a textbook on STM is clearly evident. To satisfy this need is my goal in writing this work. In the iterative process of planning and writing the chapters of this book, I have encountered a number of unexpected difficulties. First, a treatise or a textbook must be presented in a logical sequence starting from a common knowledge background, for example, the standard undergraduate physics courses. However, there are many inconsistencies and discontinuities in the existing STM literature. To make a logically coherent presentation, the materials have to be digested carefully, and the numerous gaps have to be filled. A second unexpected difficulty springs from the fact that the field of STM is inherently cross-disciplinary. The roots of STM run deeply into quantum mechanics, solid-state physics, chemical physics, electronic engineering, mechanical engineering, and control theory. To organize the necessary information in a comprehensible and coherent manner for a broad spectrum of readers is no trivial task. Finally, the field of STM is evolving so rapidly that

PREFACE

vii

a painstakingly written treatise or textbook might be obsolete just as it has been printed. Based on those considerations, in this book I have chosen, to the best of my knowledge and judgement, only the topics that are fundamental, indispensable, and having a lasting value. The organization of the book is as follows: The first chapter, Overview, describes the basic facts, concepts, and a brief account of its history. This chapter is written at a general physics level and can be read as an independent unit. The last section, Historical Remarks, is an integrated part of the presentation of basic concepts in STM. As an introductory chapter of a textbook, it is not intended to be an authoritative and comprehensive treatment of the history of STM. However, serious efforts have been made to ensure the authenticity and accuracy of the historical facts. In addition to conducting an extensive literature search, I have consulted several key scientists in STM and related fields. Part I of the book is a systematic presentation of much of the fundamental physics in STM and AFM from a single starting point, a timedependent perturbation theory that is a modified version of the Bardeen approach. The Bardeen approach to tunneling phenomena is a perturbation theory for the understanding of the classical tunneling junction experiments. For atomic-scale phenomena as in STM and AFM, modifications to the original Bardeen approach are necessary. This approach can provide conceptual understanding and analytic predictions for both tunneling current and attractive atomic forces, as well as a number of tip-sample interaction effects. All essential derivations are given in full detail, to make it suitable as a textbook and a reference book. To understand Part I, some familiarity with elementary quantum mechanics and elementary solid-state physics is expected. For example, the reader is assumed to know elementary quantum mechanics equivalent to the first seven chapters of the popular Landau-Lifshitz Quantum Mechanics (Nonrelativistic Theory) and elementary solid-state physics equivalent to the first ten chapters of Ashcroft and Mermin's Solid State Physics. Part II of the book deals with basic physical principles of STM instrumentation and applications, with many concrete working examples. The reader is expected to know relevant materials routinely taught in the standard undergraduate curricula in the fields of physics, chemistry, materials science, or related engineering disciplines. Effort is taken to make every chapter independent, such that each chapter can be understood with little reference to other chapters. Piezoelectricity and piezoelectric ceramics, which are not taught routinely in colleges, are presented from the basic concepts on. Elements of control theory, necessary for the understanding of STM operation, are presented for physicists and chemists in the main text and in an Appendix. As in Part I, all essential derivations are given in full detail. For specific applications, preliminary knowledge in the specific fields of the reader's interest (such as physics, chemistry, electrochemistry, biochemistry, or various engineering sciences) is assumed.

viii

PREFACE

The Appendices cover a number of topics that are not standard parts of an average science or engineering undergraduate curriculum, and are relatively difficult to glean from popular textbooks. To understand those Appendices, the reader is assumed to have the average undergraduate background of a science or engineering major. This introductory book, moderate in size and sophistication, is not intended to be the ultimate STM treatise. The first part of this book, especially, is not intended to be a comprehensive review of all published STM theories. More sophisticated theoretical approaches, such as those directly based on first-principle numerical calculations, are beyond the scope of this introductory book. With its moderate scope, this book is also not intended to cover all applications of STM. Rather, the applications presented are illustrative in nature. Several excellent collections of review articles on STM applications have already been published or are in preparation. An exhaustive presentation of STM applications to various fields of science and technology needs a book series, with at least one additional volume per year. Moreover, this book does not cover the numerous ramifications of STM, except a brief chapter on AFM. The references listed at the back of the book do not represent a catalog of existing STM literature. Rather, it is a list of references that would have lasting value for the understanding of the fundamental physics in STM and AFM. Many references from related fields, essential to the understanding of the fundamental processes in STM and AFM, are also included. A preliminary camera-ready manuscript of this book was prepared in 1991. To ensure that its content was well-rounded, reasonably truthful and accurate, the book manuscript was sent to many fellow scientists for reviewing, mostly arranged by Oxford University Press. I am greatly indebted to those reviewers who have spent a substantial amount of time in scrutinizing it in detail and providing a large number of valuable comments and suggestions, both as reviewing reports and as marked on the manuscript. Those comments greatly helped me to correct omissions, inaccuracies, and inconsistencies, as well as improving the style of presentation. Among the reviewers are, in alphabetical order, Dr. A. Baratoff (IBM Zurich Laboratory), Dr. I. P. Batra (IBM Almaden Laboratory), Professor A. Briggs (University of Oxford), Dr. S. Chiang (IBM Almaden Laboratory), Dr. R. Feenstra (IBM Yorktown Laboratory), Professor N. Garcia (Universidad Atonoma de Madrid), Professor R. J. Hamers (University of Wisconsin, Madison), Professor J. B. Pethica (University of Oxford), Professor C. F. Quate (Stanford University), Dr. H. Rohrer (IBM Zurich Laboratory), Professor W. Sacks (Universiti Pierre et Marie Curie), Professor T. T. Tsong (Pennsylvania State University), and Dr. R. D. Young (National Institute of Standard and Technology). In addition, a number of fellow scientists reviewed specific parts of it. Also, in alphabetical order, Dr. N. Amer (IBM Yorktown Laboratory, Chapter 15), R. Borroff (Burleigh Instrument Inc., Chapter 12), Dr. F. J. Himpsel (IBM Yorktown Laboratory, Chapter 3), R. I. Kaufman (IBM Yorktown Laboratory, Chapter

PREFACE

ix

11), Dr. V. Moruzzi (IBM Yorktown Laboratory, Chapter 3), C. Near (Morgan Matroc Inc., Vernitron Division, Chapter 9), Dr. E. O'Sullivan (IBM Yorktown Laboratory, sections on electrochemistry), R. Petrucci (Staveley Sensors Inc., EBL Division, Chapter 9), Dr. D. Rath (IBM Yorktown Laboratory, sections on electrochemistry), and Dr. C. Teague (National Institute of Standard and Technology, Chapter 1). After all the revisions were made, I felt that this book would serve the readers better than its preliminary version, and I had no regrets about delaying its printing. I would also like to thank the senior editor in Physical Sciences, Mr. J. Robbins, and Miss A. Lekhwani of Oxford University Press in assisting in the publication, especially the painstaking reviewing process of the manuscript. Also, special thanks to Elizabeth McAuliffe of IBM Yorktown Laboratory for her development and assistance in the BookMaster software enabling me to prepare the camera-ready manuscript, which was essential for the preprinting reviewing process. Numerous colleagues provided original STM and AFM images, which enabled me to compile a gallery of 30 spectacular images in the high-quality printing section, which are acknowledged on each page. Finally, I would like to admit that, even with such extensive reviews and revisions, the book is still neither perfect nor does it represent the last word. Especially in such an active field as STM and AFM, new concepts and new measurements come out every day. I expect that substantial progress will be made in the years to come. Naturally, I am looking forward to future editions. I am anxious to hear any comments and suggestions from readers, with whose help, the future editions of this book would be more useful, more truthful, and more accurate. Thus spake Johann Wolfgang von Goethe:'

Oft, wenn es erst durch Jahre durchgedrungen, Erscheint es in vollendeter Gestalt. Was gldnzt, istfiir den Augenblick geboren, Das Echte bleibt der Nachwelt unverloren.

October 1992, at Yorktown Heights, New York

C. J. C.

1 Often, after years of perseverance, it emerges in a completed form. What glitters, is born for the moment. The Genuine lives on to the aftcrworld. Faust, Vorspiet aufdem Theater.

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CONTENTS List of Figures

xvii

Gallery of STM Images

1 Overview

(follows page xxii)

l

1.1 The scanning tunneling microscope in a nutshell 1.2 Tunneling: an elementary model 3 1.3 Probing electronic structure at an atomic scale 1.3.1 Semiconductors 10 1.3.2 Metals 18 1.3.3 Organic molecules 19 1.3.4 Layered materials 20 1.4 Spatially resolved tunneling spectroscopy 21 1.5 Lateral resolution: Early theories 26 1.5.1 The Stall Formula 27 1.5.2 The s-wave-tip model 28 1.6 Origin of atomic resolution in STM 32 1.7 Tip-sample interaction effects 36 1.8 Historical remarks 38 1.8.1 Imaging individual atoms 39 1.8.2 Metal-vacuum-metal tunneling 43

PARTI IMAGING MECHANISM 2 Atom-scale tunneling 2.1 2.2 2.3 2.4

53

Introduction 53 The perturbation approach 55 The image force 56 The Square-barrier problem 59 2.4.1 Apparent barrier height 62 2.4.2 Uncertainty-principle considerations

64

1 10

xii

CONTENTS

2.5 The modified Bardeen approach 65 2.5.1 The transition probability 65 2.5.2 The modified Bardeen integral 68 2.5.3 Error estimation 69 2.5.4 Wavefunction correction 70 2.5.5 Comparison with exact solutions 71 2.6 Effect of image force on tunneling 72

3 Tunneling matrix elements 3.1 3.2 3.3 3.4 3.5 3.6

75

Introduction 75 Tip wavefunctions 76 Green's function and tip wavefunctions 78 The derivative rule: individual cases 81 The derivative rule: general case 83 An intuitive interpretation 88

4 Wavefunctions at surfaces

91

4.1 4.2 4.3 4.4 4.5 4.6

Types of surface wavefunctions 91 The jellium model 92 Concept of surface states 98 Field emission spectroscopy 101 Photoemission studies 104 Atom-beam diffraction 107 4.6.1 The Esbjerg-N U(z), the electron has a nonzero momentum pz. On the other hand, the electron cannot penetrate into any region with E < U(z), or a potential barrier. In quantum mechanics, the state of the same electron is described by a wavefunction i|/(z), which satisfies Schrodinger's equation,

Consider the case of a piecewise-constant potential, as shown in Fig. 1.3. In the classically allowed region, E> U, Eq. (1.2) has solutions

Fig. 1.3. The difference between classical theory and quantum theory. In quantum mechanics, an electron has a nonzero probability of tunneling through a potential barrier. (After Van Vleck; see Walmsley, 1987.)

4

INTRODUCTION TO SCANNING TUNNELING MICROSCOPY

where

is the wave vector. The electron is moving (in either a positive or negative direction) with a constant momentum p, = hk = [2m(E- U)Vn, or a constant velocity vz = pjm, the same as the classical case. In the classically forbidden region, Eq. (1.2) has a solution

where

is the decay constant. It describes a state of the electron decaying in the +z direction. The probability density of observing an electron near a point z is proportional to | I|J(0) 1 e~ 2KS which has a nonzero value in the barrier region, thus a nonzero probability to penetrate a barrier. Another solution, \\i(z) = vK0)eK:, describes an electron state decaying in the -z direction. Starting from this elementary model, with a little more effort, we can explain some basic features of metal-vacuum-metal tunneling, as shown in Fig. 1.4. The work function 4> of a metal surface is defined as the minimum energy required to remove an electron from the bulk to the vacuum level. In general, the work function depends not only on the material, but also on the crystallographic orientation of the surface (see Section 4.2). For materials commonly used in STM experiments, the typical values of 4> are listed in Table 1.1. (The work functions for alkali metals are substantially lower, typically 2-3 eV.) Neglecting the thermal excitation, the Fermi level is the upper limit of the occupied states in a metal. Taking the vacuum level as the reference point of energy, E,, = — 4>. To simplify discussion, we assume that the work functions of the tip and the sample are equal. The electron in the sample can tunnel into the tip and vice visa. However, without a bias voltage, there is no net tunneling current. Table 1.1. Typical values of work functions, After Handbook of Chemistry and Physics, 69th edition, CRC Press (1988).

Element

Al

Au

Cu

Ir

Ni

Pt

Si

W

<MeV)

4.1

5.4

4.6

5.6

5.2

5.7

4.8

4.8

OVERVIEW

5

Fig. 1.4. A one-dimensional nietal-vacuum-metal tunneling junction. The sample, left, and the tip, right, are modeled as semi-infinite pieces of free-electron metal.

By applying a bias voltage V, a net tunneling current occurs. A sample state i|»,, with energy level En lying between EF-eV v and EF has a chance to tunnel into the tip. We assume that the bias is much smaller than the value of the work function, that is, eV. The probability w for an electron in the nth sample state to present at the tip surface, z = W, is

where i|;,,(0) is the value of the nth sample state at the sample surface, and

is the decay constant of a sample state near the Fermi level in the barrier region. Using eV as the unit of the work function, and A"1 as the unit of the decay constant, the numerical value of Eq. (1.8) is

In an STM experiment, the tip scans over the sample surface. During a scan, the condition of the tip usually does not vary. The electrons coming to the tip surface, z — W, have a constant velocity to flow into the tip. The tunneling

6

INTRODUCTION TO SCANNING TUNNELING MICROSCOPY

current is directly proportional to the number of states on the sample surface within the energy interval eV, which are responsible for the tunneling current. This number depends on the local nature of the sample surface. For metals, it is finite. For semiconductors and insulators, the number is very small or zero. For semimetals, it is in between. By including all the sample states in the energy interval eV, the tunneling current is

If V is small enough that the density of electronic states does not vary significantly within it, the sum in Eq. (1.10) can be conveniently written in terms of the local density of states (LDOS) at the Fermi level. At a location z and energy E, the LDOS ps(z, E) of the sample is defined as

for a sufficiently small e. The LDOS is the number of electrons per unit volume per unit energy, at a given point in space and at a given energy. It has a nice feature as follows. The probability density for a specific state, | \\in! , depends on the normalization condition: its integral over the entire space should be 1. As the volume increases, the probability density | \\i,, | of a single state decreases; but the number of states per unit energy increases. The LDOS remains a constant. The value of the surface LDOS near the Fermi level is an indicator of whether the surface is metallic or insulating. The tunneling current can be conveniently written in terms of the LDOS of the sample:

The typical value of work function is 4>«4 eV, which gives a typical value of the decay constant K«1 A"1. According to Eq. (1.12), the current decays about