Introduction to Scanning Tunneling Microscopy

Transcription

1 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

2 CONTENTS List of Figures xvii Gallery of STM Images (follows page xxii) 1 Overview l 1.1 The scanning tunneling microscope in a nutshell Tunneling: an elementary model Probing electronic structure at an atomic scale Semiconductors Metals Organic molecules Layered materials Spatially resolved tunneling spectroscopy Lateral resolution: Early theories The Stoll Formula The s-wave-tip model Origin of atomic resolution in STM Tip-sample interaction effects Historical remarks Imaging individual atoms Metal-vacuum-metal tunneling 43 PARTI IMAGING MECHANISM 2 Atom-scale tunneling Introduction The perturbation approach The image force The Square-barrier problem Apparent barrier height Uncertainty-principle considerations 64

3 Xll CONTENTS 2.5 The modified Bardeen approach The transition probability The modified Bardeen integral Error estimation Wavefunction correction Comparison with exact solutions Effect of image force on tunneling 72 3 Tunneling matrix elements Introduction Tip wavefunctions Green's function and tip wavefunctions The derivative rule: individual cases The derivative rule: general case An intuitive interpretation 88 4 Wavefunctions at surfaces Types of surface wavefunctions The jellium model Concept of surface states Field emission spectroscopy Photoemission studies Atom-beam diffraction The Esbjerg-Nrirskov approximation The method of Harris and Liebsch Atom charge superposition First-principles theoretical studies The density-functional formalism Electronic structures of bulk solids Surface electronic structures Imaging crystalline surfaces Types of STM images Surfaces with one-dimensional corrugation Leading-Bloch-waves approximation Topographic images Surfaces with tetragonal symmetry Surfaces with hexagonal or trigonal symmetry 5.5 Corrugation inversion The s-wave-tip model 142

4 CONTENTS 6 Imaging atomic states Slater atomic wavefunctions Profiles of atomic states as seen by STM Apparent radius and apparent curvature Comparison with experiments The Na-atom-tip model Images of surfaces: Independent-orbital approximation General expression for the Fourier coefficients Application to the images of Si(l 11)2X Application to close-packed metal surfaces Atomic forces and tunneling Effect of atomic force in STM Attractive atomic force as a tunneling phenomenon Three regimes of interaction van der Waals force Resonance energy as tunneling matrix element Evaluation of the modified Bardeen integral Repulsive force Attractive atomic force and tunneling conductance Tip-sample interactions Local modification of sample wavefunction The point of view of momentum space Uncertainty principle and scanning tunneling spectroscopy 8.2 Deformation of tip and sample surface Mechanical amplification of corrugation amplitudes The Pethica mechanism Corrugation of attractive force and its effect Stability of STM at short distances Force in tunneling barrier measurements 207 PARTH INSTRUMENTATION 9 Piezoelectric scanner Piezoelectric effect Lead zirconate titanate ceramics Tripod scanner Bimorph Tube scanner 224

5 XIV CONTENTS 9.6 In situ testing and calibration Resonance frequencies Repoling a depoled piezo Vibration isolation Basic concepts Environment vibration Suspension springs Analysis of two-stage systems Choice of springs Eddy-current damper Stacked plate - elastomer system Pneumatic systems Electronics and control Current amplifier Johnson noise and shot noise Frequency response Microphone effect Logarithmic amplifier Feedback circuit Steady-state response Transient response Computer interface Automatic approaching Coarse positioner and STM design The louse Level motion-demagnifier Single-tube STM Spring motion demagnifier Inertial steppers Thelnchworm Tip treatment Introduction Electrochemical tip etching Ex situ tip treatments Annealing Field evaporation and controlled deposition Annealing with a field Atomic metallic ion emission 289

6 CONTENTS 13.4 In situ tip treatments High-field treatment Controlled collision Scanning tunneling spectroscopy Electronics for scanning tunneling spectroscopy Nature of the observed tunneling spectra The role of tip DOS Uncertainty-principle considerations Effect offinitetemperature Tip treatment for spectroscopy studies The Feenstra parameter Ex situ determination of the tip DOS In situ determination of tip DOS Atomic force microscopy Introduction Tip and cantilever Deflection detection methods Vacuum tunneling Mechanical resonance Optical interferometry Optical beam deflection AFM at the liquid-solid interface Illustrative applications Surface structure determination Periodic structures Aperiodic structures Nucleation and crystal growth Local tunneling spectra of superconductors Surface chemistry Organic molecules Electrochemistry Biological applications 341 Appendix A Real wavefunctions 343 Appendix В Green's functions 347 Appendix С Spherical modified Bessel functions

7 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