INTRODUCTION TO SCANNING TUNNELING MICROSCOPY

Transcription

1 INTRODUCTION TO SCANNING TUNNELING MICROSCOPY SECOND EDITION C. JULIAN CHEN Department of Applied Physics and Applied Mathematics, Columbia University, New York OXJORD UNIVERSITY PRESS

2 Contents Preface to the Second Edition Preface to the First Edition Gallery xxiii xxvii xxxiii Chapter 1: Overview The scanning tunneling microscope The concept of tunneling Transmission coefficient Semiclassical approximation The Landauer theory Tunneling conductance Probing electronic structure at atomic scale Experimental observations Origin of atomic resolution in STM The atomic force microscope Atomic-scale imaging by AFM Role of covalent bonding in AFM imaging Illustrative applications Catalysis research Atomic-scale imaging at the liquid-solid interface Atom manipulation Imaging and manipulating DNA using AFM 35 Part I Principles 41 Chapter 2: Tunneling Phenomenon The metal-insulator-metal tunneling junction The Bardeen theory of tunneling One-dimensional case Tunneling spectroscopy Energy dependence of tunneling matrix elements Asymmetry in tunneling spectrum Three-dimensional case Error estimation Wavefunction correction The transfer-hamiltonian formalism The tunneling matrix 63

3 viü Contents Relation to the Landauer theory Inelastic tunneling Experimental facts Prequency condition Effect of finite temperature Spin-polarized tunneling General formalism The spin-valve effect Experimental observations 76 Chapter 3: Tunneling Matrix Elements _ Introduction Tip wavefunctions General form Tip wavefunctions as Green's functions The derivative rule: individual cases s-wave tip state p-wave tip states d-wave tip states Complex tip states The derivative rule: general case An intuitive Interpretation 91 Chapter 4: Atomic Forces Van der Waals force The van der Waals equation of state The origin of van der Waals force Van der Waals force between a tip and a sample Hard-core repulsion Theionicbond The covalent bond: The concept Heisenberg's model of resonance The hydrogen molecule-ion Three regimes of interaction Van der Waals force Resonance energy as tunneling matrix element Evaluation of the modified Bardeen integral Repulsive force The covalent bond: Many-electron atoms 115

4 Contents ix The homonuclear diatomic molecules The perturbation approach Evaluation of the Bardeen Integral Comparison with experimental data 119 Chapter 5: Atomic Forces and Tunneling The principle of equivalence General theory The double-well problem Canonical transformation of the transfer Hamiltonian Diagonizing the tunneling matrix Case of a metal tip and a metal sample Van der Waals force Resonance energy between two metal electrodes A measurable consequence Repulsive force Experimental verifications An early experiment Experiments with frequency-modulation AFM Experiments with static AFM Non-contact atomic force spectroscopy Threshold resistance in atom manipulation 145 Chapter 6: Nanometer-Scale Imaging Types of STM and AFM images The Tersoff-Hamann model The concept The original derivation Profiles of surface reconstructions Extension to finite bias voltages Surface states: the concept Surface states: STM observations Heterogeneous surfaces Limitations of the Tersoff-Hamann model 166 Chapter 7: Atomic-Scale Imaging Experimental facts Universality of atomic resolution Corrugation inversion Tip-state dependence 171

5 x Contents Distance dependence of corrugation Intuitive explanations Sharpness of tip states Phase effect Arguments based on the reciprocity principle Analytic treatments A one-dimensional case Surfaces with hexagonal symmetry Corrugation inversion Profiles of atomic states as seen by STM Independent-orbital approximation First-principles studies: tip electronic states W Clusters as STM tip modeis Density-functional study of a W-Cu STM junction Transition-metal pyramidal tips Transition-metal atoms adsorbed on W slabs First-principles studies: the images Transition-metal surfaces Atomic corrugation and surface waves Atom-resolved AFM images Spin-polarized STM Chemical identification of surface atoms The principle of reciprocity 214 Chapter 8: Nanomechanical Effects Mechanical stability of the tip-sample junction Experimental observations Condition of mechanical stability Relaxation and the apparent G ~ z relation Mechanical effects on observed corrugations Soft surfaces Hard surfaces First-principles simulations Advanced topics The Pethica mechanism Force in tunneling-barrier measurements 238

6 Contents xi Part II Instrumentation 241 Chapter 9: Piezoelectric Scanner Piezoelectricity Piezoelectric effect Inverse piezoelectric effect Piezoelectric materials in STM and AFM Quartz Lead zirconate titanate ceramics Piezoelectric devices in STM and AFM Tripod Scanner Bimorph The tube Scanner Deflection In situ testing and calibration Resonant frequencies Tilt compensation: the s-scanner Repolarizing a depolarized tube piezo The shear piezo 265 Chapter 10: Vibration Isolation Basic concepts Environmental Vibration Measurement method Vibration isolation of the foundation Vibrational immunity of STM Suspension-spring Systems Analysis of two-stage Systems Choice of Springs Eddy-current damper Pneumatic Systems 282 Chapter 11: Electronics and Control Current amplifier Johnson noise and shot noise Frequency response Microphone effect Logarithmic amplifier Feedback circuit 289

7 xü Contents Steady-state response Transient response Computer interface Automatic approaching 298 Chapter 12: Mechanical design The louse The pocket-size STM The single-tube STM The Besocke-type STM: the beetle The walker The kangaroo The Inchworm The match 309 Chapter 13: Tip Treatment Introduction Electrochemical tip etching Ex situ tip treatments Annealing Field evaporation and controlled deposition Annealing with a field Atomic metallic ion emission Field-assisted reaction with nitrogen In situ tip treatments High-field treatment Controlled collision Tip treatment for spin-polarized STM Coating the tip with ferromagnetic materials Coating the tip with antiferromagnetic materials Controlled collision with magnetic surfaces Tip preparation for electrochemistry STM 328 Chapter 14: Scanning Tunneling Spectroscopy Electronics for scanning tunneling spectroscopy Nature of the observed tunneling spectra Tip treatment for spectroscopy studies 334

8 Contents xüi Annealing ControUed collision with a metal surface The Feenstra parameter Determination of the tip DOS Ex situ methods In situ methods Inelastic scanning tunneling spectroscopy Instrumentation Effect of finite modulation voltage Experimental observations 347 Chapter 15: Atomic Force Microscopy Static mode and dynamic mode The cantilever Basic requirements Fabrication Static force detection Optical beam deflection Optical interferometry Tapping-mode AFM Acoustic actuation in liquids Magnetic actuation in liquids Non-contact AFM Case of small amplitude Case of finite amplitude Response function for frequency shift Second harmonics Average tunneling current Implementation 369 Appendix A: Green's Functions 371 Appendix B: Real Spherical Harmonics 373 Appendix C: Spherical Modined Bessel Functions 377 Appendix D: Plane Groups and Invariant Functions 381 D.l A brief summary of plane groups 382 D.2 Invariant functions 385

9 xiv Contents Appendix E: Elementary Elasticity Theory 389 E.l Stress and strain 389 E.2 Small deflection of beams 391 E.3 Vibration of beams 394 E.4 Torsion 395 E.5 Helical Springs 397 E.6 Contact stress: The Hertz formulas 398