Philip Hofmann Surface Physics An Introduction Surface Physics: An Introduction Written and published by Philip Hofmann Copyright (c) 2013 by Philip Hofmann ISBN 978-87-996090-1-7 This ebook is licensed for your personal use only. It may not be given away to other people and certainly not be re-sold. If you would like to share this book with another person, please purchase an additional copy for each recipient. If you are reading this book and did not purchase it, or it was not purchased for your use only, then please purchase your own copy. Thank you for respecting the licence and for thereby contributing to the idea of providing affordable and DRM free textbooks. For more information, please see www.philiphofmann.net. Contents 1 Introduction 7 2 From Solids to Surfaces 9 2.1 Introduction . 9 2.2 Lattice and reciprocal lattice . 10 2.2.1 Lattice . 10 2.2.2 Reciprocal lattice . 11 2.2.3 Directions in real and reciprocal space . 13 2.2.4 Lattice and reciprocal lattice at surfaces . 14 2.3 Electronic states . 20 2.3.1 Free electrons . 20 2.3.2 Electrons in a periodic potential: Nearly free electrons . 21 2.3.3 Electrons in a periodic potential: tightly bound electrons . 23 2.3.4 Calculating actual band structures . 29 2.3.5 Electronic states at surfaces . 32 2.4 Lattice vibrations . 39 2.4.1 Lattice vibrations in the harmonic crystal: phonons . 39 2.4.2 Vibrations at surfaces . 40 2.5 Further reading . 41 2.6 Discussion and Problems . 42 3 Ultra High Vacuum (UHV) 45 3.1 Vacuum requirements . 45 3.2 Construction, pumping and bakeout . 46 3.3 Pressure measurement . 52 3.4 Materials . 53 3.5 Flanges, viewports, electrical feedthroughs and movements . 54 3.6 Chemical analysis of the rest gas . 55 3.7 Surface cleaning . 56 3.8 Further reading . 58 3.9 Discussion and Problems . 58 4 Electron spectroscopy 61 4.1 Introduction . 61 4.2 Why electrons: The inelastic mean free path . 63 4.3 Physics of the inelastic mean free path . 64 4.4 Electron sources, detectors and energy filters . 71 4.5 Further reading . 74 4.6 Discussion and Problems . 74 5 Electron spectroscopy for chemical analysis 77 5.1 X-ray photoelectron spectroscopy (XPS) . 78 5.1.1 X-ray sources . 80 5.1.2 XPS cross sections . 83 5.1.3 XPS binding energies . 87 5.1.4 Qualitative analysis . 94 5.1.5 Quantitative analysis . 94 5.2 Auger electron spectroscopy (AES) . 95 5.2.1 Auger nomenclature . 96 5.2.2 Experimental . 97 5.2.3 Qualitative and quantitative analysis: typical spectra . 97 5.3 Further reading . 98 5.4 Discussion and Problems . 99 6 Adsorption, Desorption and Chemical Reactions 101 6.1 Introduction . 101 6.2 Physisorption . 102 6.3 Chemisorption . 104 6.4 Interaction between adsorbates . 113 6.5 Kinetics . 114 6.5.1 Adsorption . 114 6.5.2 Desorption . 118 6.5.3 Adsorption-desorption equilibrium . 121 6.6 Single-crystal adsorption calorimetry . 121 6.7 Chemical reactions and catalysis . 122 6.8 Further reading . 125 6.9 Discussion and Problems . 125 7 Surface Structure 127 7.1 Surface Thermodynamics and general crystal shape . 127 7.2 Surface geometry: truncated bulk, relaxation, reconstruction, defects and super-structures . 130 7.2.1 General phenomena . 130 7.2.2 Lattice and reciprocal lattice for reconstructions and overlayers 133 7.3 Low energy electron diffraction (LEED), LEED patterns and quantitative structure determination . 135 7.3.1 Instrumentation . 136 7.3.2 LEED diffraction pattern and their analysis . 137 7.3.3 Interpretation of LEED patterns . 143 7.3.4 Quantitative structure determination . 145 7.4 Some examples from LEED structure determination . 147 7.4.1 Metal surfaces . 147 7.4.2 Semiconductor surfaces . 151 7.5 Diffraction of x-rays and He atoms . 153 7.6 X-ray Absorption: EXAFS, SEXAFS, NEXAFS . 154 7.6.1 EXAFS . 154 7.6.2 SEXAFS . 158 7.6.3 NEXAFS . 159 7.7 Photoelectron diffraction (PhD, PED) . 162 7.7.1 Introduction . 162 7.7.2 Simple Theory . 164 7.7.3 Structure determination: experimental results . 167 7.8 Scanning Tunnelling Microscopy . 172 7.8.1 Basic principle and experimental setup . 172 7.8.2 Theory of operation . 177 7.8.3 Clean metal surfaces . 178 7.8.4 Adsorbates on metal surfaces . 179 7.8.5 Semiconductor surfaces . 183 7.9 Atomic force microscopy (AFM) . 184 7.10 Further reading . 190 7.11 Discussion and Problems . 191 8 The electronic structure of surfaces 195 8.1 Work function . 195 8.2 Electronic surface states: basic ideas . 198 8.3 Measuring the electronic structure of surfaces with angle-resolved pho- toemission . 206 8.3.1 Introduction . 206 8.3.2 Instrumentation . 208 8.3.3 The photoemission process . 209 8.3.4 Photoemission and band mapping of two-dimensional states . 212 8.3.5 Photoemission and band mapping of three-dimensional states . 216 8.3.6 Some surface states investigated by ARPES . 221 8.4 Determining surface electronic structure using the STM . 240 8.4.1 Scanning tunnelling spectroscopy . 240 8.4.2 Standing electron waves on surfaces . 243 8.5 Further Reading . 246 8.6 Discussion and Problems . 247 9 Vibrational properties of surfaces 251 9.1 Surface vibrations: basic ideas . 251 9.2 Electron energy loss spectroscopy . 257 9.3 Optical spectroscopy: IRAS . 263 9.4 He Atom scattering . 265 9.5 Vibrational spectroscopy with the STM . 267 9.6 Further reading . 268 9.7 Discussion and Problems . 268 10 Optical properties of surfaces 271 10.1 Reflection of Light at a Surface . 272 10.2 Surface plasmon polaritons . 275 10.3 Reflection Anisotropy Spectroscopy (RAS) . 279 10.4 Second Harmonic Generation . 281 10.5 Further reading . 283 10.6 Discussion and Problems . 283 Preface The scope of this book is to give an introduction into the physics of solid, crystalline surfaces as well as an overview over the experimental techniques used to study such surfaces. Theoretical concepts are only briefly introduced when they are needed. The main focus lies on the phenomena and their experimental investigation. The text covers only a fraction of the field and the choice is rather subjective. The most important physical phenomena and experimental techniques should be covered, however. There are many other general books on surface physics. Here are some that can serve for further reading: • Modern Techniques of Surface Science by T. A. Delchar, and D. P. Woodruff, Cambridge Solid State Science Series, 1994. • Physics at Surfaces by A. Zangwill, Cambridge Univ. Press, 1988. • Solid Surfaces, Interfaces and Thin Films by H. L¨uth,Springer, 2010. • Concepts in Surface Physics by M. C. Desjonqueres, D. Spanjaard, Springer, 2012. • Physics of Surface and Interfaces by H. Ibach, Springer, 2006. A more specific list for further reading is given in the end of each Chapter and some references are given in the text. Note, however, that this is a textbook and not a review article and the references are merely intended to help you with finding a more in-depth discussion of the subjects. Each Chapter ends with a list of discussion questions you can use to test your under- standing of the text and with a few problems to further deepen your understanding of the concepts introduced. The problems marked by (*) are more difficult and meant as a challenge. This book is self-published as an ebook and both of these concepts are new to me. My hope is that this new approach of publishing will provide the student with a useful text at at more affordable price than the usual textbooks, while at the same time ensuring that the costs for the technical realisation, ISBN numbers, distribution and so are covered. An important issue for this approach to publishing is quality control, something that 5 can only be ensured through testing. I am therefore very grateful to my colleagues Jeppe Vang Lauritsen at Aarhus University and Christoph Tegenkamp at the University of Hannover, as well.