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
CONTENTS List of Figures xvii Gallery of STM Images (follows page xxii) 1 Overview l 1.1 The scanning tunneling microscope in a nutshell 1 1.2 Tunneling: an elementary model 3 1.3 Probing electronic structure at an atomic scale 10 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 Stoll 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 53 2.1 Introduction 53 2.2 The perturbation approach 55 2.3 The image force 56 2.4 The Square-barrier problem 59 2.4.1 Apparent barrier height 62 2.4.2 Uncertainty-principle considerations 64
Xll 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 75 3.1 Introduction 75 3.2 Tip wavefunctions 76 3.3 Green's function and tip wavefunctions 78 3.4 The derivative rule: individual cases 81 3.5 The derivative rule: general case 83 3.6 An intuitive interpretation 88 4 Wavefunctions at surfaces 91 4.1 Types of surface wavefunctions 91 4.2 The jellium model 92 4.3 Concept of surface states 98 4.4 Field emission spectroscopy 101 4.5 Photoemission studies 104 4.6 Atom-beam diffraction 107 4.6.1 The Esbjerg-Nrirskov approximation 4.6.2 The method of Harris and Liebsch 4.6.3 Atom charge superposition 111 4.7 First-principles theoretical studies 112 4.7.1 The density-functional formalism 4.7.2 Electronic structures of bulk solids 4.7.3 Surface electronic structures 117 109 110 112 115 5 Imaging crystalline surfaces 121 5.1 Types of STM images 121 5.2 Surfaces with one-dimensional corrugation 5.2.1 Leading-Bloch-waves approximation 5.2.2 Topographic images 125 5.3 Surfaces with tetragonal symmetry 128 5.4 Surfaces with hexagonal or trigonal symmetry 5.5 Corrugation inversion 137 5.6 The s-wave-tip model 142
CONTENTS 6 Imaging atomic states 149 6.1 Slater atomic wavefunctions 149 6.2 Profiles of atomic states as seen by STM 151 6.2.1 Apparent radius and apparent curvature 152 6.2.2 Comparison with experiments 155 6.3 The Na-atom-tip model 157 6.4 Images of surfaces: Independent-orbital approximation 159 6.4.1 General expression for the Fourier coefficients 159 6.4.2 Application to the images of Si(l 11)2X1 164 6.4.3 Application to close-packed metal surfaces 167 7 Atomic forces and tunneling 171 7.1 Effect of atomic force in STM 171 7.2 Attractive atomic force as a tunneling phenomenon 173 7.2.1 Three regimes of interaction 174 7.2.2 van der Waals force 175 7.2.3. Resonance energy as tunneling matrix element 177 7.2.4. Evaluation of the modified Bardeen integral 181 7.2.5 Repulsive force 185 7.3 Attractive atomic force and tunneling conductance 185 8 Tip-sample interactions 195 8.1 Local modification of sample wavefunction 195 8.1.1 The point of view of momentum space 196 8.1.2 Uncertainty principle and scanning tunneling spectroscopy 8.2 Deformation of tip and sample surface 198 8.2.1 Mechanical amplification of corrugation amplitudes 199 8.2.2 The Pethica mechanism 201 8.2.3 Corrugation of attractive force and its effect 202 8.2.4 Stability of STM at short distances 204 8.2.5 Force in tunneling barrier measurements 207 PARTH INSTRUMENTATION 9 Piezoelectric scanner 213 9.1 Piezoelectric effect 213 9.2 Lead zirconate titanate ceramics 217 9.3 Tripod scanner 221 9.4 Bimorph 222 9.5 Tube scanner 224
XIV CONTENTS 9.6 In situ testing and calibration 229 9.7 Resonance frequencies 234 9.8 Repoling a depoled piezo 235 10 Vibration isolation 237 10.1 Basic concepts 237 10.2 Environment vibration 242 10.3 Suspension springs 244 10.3.1 Analysis of two-stage systems 245 10.3.2 Choice of springs 247 10.3.3 Eddy-current damper 248 10.4 Stacked plate - elastomer system 249 10.5 Pneumatic systems 250 11 Electronics and control 251 11.1 Current amplifier 251 11.1.1 Johnson noise and shot noise 252 11.1.2 Frequency response 254 11.1.3 Microphone effect 256 11.1.4 Logarithmic amplifier 258 11.2 Feedback circuit 258 11.2.1 Steady-state response 258 11.2.2 Transient response 261 11.3 Computer interface 266 11.3.1 Automatic approaching 268 12 Coarse positioner and STM design 269 12.1 The louse 269 12.2 Level motion-demagnifier 271 12.3 Single-tube STM 273 12.4 Spring motion demagnifier 274 12.5 Inertial steppers 275 12.6 Thelnchworm 278 13 Tip treatment 281 13.1 Introduction 281 13.2 Electrochemical tip etching 282 13.3 Ex situ tip treatments 285 13.3.1 Annealing 286 13.3.2 Field evaporation and controlled deposition 287 13.3.3 Annealing with a field 288 13.3.4. Atomic metallic ion emission 289
CONTENTS 13.4 In situ tip treatments 291 13.4.1 High-field treatment 291 13.4.2 Controlled collision 293 14 Scanning tunneling spectroscopy 295 14.1 Electronics for scanning tunneling spectroscopy 295 14.2 Nature of the observed tunneling spectra 296 14.2.1 The role of tip DOS 297 14.2.2 Uncertainty-principle considerations 298 14.2.3 Effect offinitetemperature 301 14.3 Tip treatment for spectroscopy studies 301 14.4 The Feenstra parameter 303 14.5 Ex situ determination of the tip DOS 306 14.6 In situ determination of tip DOS 308 15 Atomic force microscopy 313 15.1 Introduction 313 15.2 Tip and cantilever 315 15.3 Deflection detection methods 317 15.3.1 Vacuum tunneling 317 15.3.2 Mechanical resonance 318 15.3.3 Optical interferometry 319 15.3.4 Optical beam deflection 321 15.4 AFM at the liquid-solid interface 323 16 Illustrative applications 325 16.1 Surface structure determination 325 16.1.1 Periodic structures 325 16.1.2 Aperiodic structures 328 16.2 Nucleation and crystal growth 331 16.3 Local tunneling spectra of superconductors 332 16.4 Surface chemistry 334 16.5 Organic molecules 338 16.6 Electrochemistry 339 16.7 Biological applications 341 Appendix A Real wavefunctions 343 Appendix В Green's functions 347 Appendix С Spherical modified Bessel functions
XVI CONTENTS Appendix D Two-dimensional Fourier series 353 Appendix E Plane groups and invariant functions 357 E. 1 A brief summary of plane groups 358 E.2 Invariant functions 361 Appendix F Elementary elasticity theory 365 F. 1 Normal stress and normal strain 365 F.2 Shear stress and shear strain 366 F.3 Small deflection of beams 367 F.4 Vibration of beams 370 F.5 Torsion 372 F.6 Helical springs 373 F.7 Contact stress: The Hertz formulas 374 Appendix G A short table of Laplace transforms 377 Appendix H Operational amplifiers 379 References 383 Index 405