Scanning Probe Microscopy

Transcription

1 Bert Voigtlander Scanning Probe Microscopy Atomic Force Microscopy and Scanning Tunneling Microscopy ^ Springer

2 Contents 1 Introduction Introduction to Scanning Tunneling Microscopy Introduction to Atomic Force Microscopy A Short History of Scanning Probe Microscopy Summary 11 Part I Scanning Probe Microscopy Instrumentation 2 Harmonic Oscillator Free Harmonic Oscillator Driven Harmonic Oscillator Driven Harmonic Oscillator with Damping Transients of Oscillations Dissipation and Quality Factor of a Damped Driven Harmonic Oscillator Effective Mass of a Harmonic Oscillator Linear Differential Equations Summary 29 3 Technical Aspects of Scanning Probe Microscopy Piezoelectric Effect Extensions of Piezoelectric Actuators Piezoelectric Materials Tube Piezo Element Resonance Frequencies of Piezo Tubes Flexure-Guided Piezo Nanopositioning Stages Non-linearities and Hysteresis Effects of Piezoelectric Actuators Hysteresis Creep 49 ix

3 x Contents Thermal Drift STM Tip Preparation Vibration Isolation Isolation of the Microscope from Outer Vibrations The Microscope Considered as a Vibrating System Combining Vibration Isolation and a Microscope with High Resonance Frequency Building Vibrations Summary 63 4 Scanning Probe Microscopy Designs Nanoscope Inertial Sliders Beetle STM Pan Slider KoalaDrive Tip Exchange Summary 75 5 Electronics for Scanning Probe Microscopy Voltage Divider Impedance, Transfer Function, and Bode Plot Output Resistance/Input Resistance Noise Operational Amplifiers Voltage Follower/Impedance Converter Voltage Amplifier Current Amplifier Feedback Controller Proportional Controller Proportional-Integral Controller Feedback Controller in STM Implementation of an STM Feedback Controller Digital-to-Analog Converter Analog-to-Digital Converter High-Voltage Amplifier Summary 99

4 Contents xi 6 Lock-In Technique Lock-In Amplifier Principle of Operation Summary Data Representation and Image Processing Data Representation Image Processing Data Analysis Summary Artifacts in SPM Tip-Related Artifacts Other Artifacts Summary Work Function, Contact Potential, and Kelvin Probe Scanning Force Microscopy Work Function Effect of a Surface on the Work Function Surface Charges and External Electric Fields Contact Potential Measurement of Work Function by the Kelvin Method Kelvin Probe Scanning Force Microscopy (KFM) Summary Surface States Surface States in a One-Dimensional Crystal Surface States in 3D Crystals Surface States Within the Tight Binding Model Summary 141 Part II Atomic Force Microscopy (AFM) 11 Forces Between Tip and Sample Tip-Sample Forces Snap-to-Contact Summary Technical Aspects of Atomic Force Microscopy (AFM) Requirements for Force Sensors Fabrication of Cantilevers Beam Deflection Atomic Force Microscopy 161

5 Xll Contents Sensitivity of the Beam Deflection Method Detection Limit of the Beam Deflection Method Other Detection Methods Calibration of AFM Measurements Experimental Determination of the Sensitivity Factor in AFM Calculation of the Spring Constant from the Geometrical Data of the Cantilever Sader Method for the Determination of the Spring Constant of a Cantilever Thermal Method for the Determination of the Spring Constant of a Cantilever Experimental Determination of the Sensitivity and Spring Constant in AFM Without Tip-Sample Contact Summary Static Atomic Force Microscopy Principles of Static Atomic Force Microscopy Properties of Static AFM Imaging Constant Height Mode in Static AFM Friction Force Microscopy (FFM) Force-Distance Curves Summary Amplitude Modulation (AM) Mode in Dynamic Atomic Force Microscopy Parameters of Dynamic Atomic Force Microscopy Principles of Dynamic Atomic Force Microscopy I (Amplitude Modulation) Amplitude Modulation (AM) Detection Scheme in Dynamic Atomic Force Microscopy Experimental Realization of the AM Detection Mode Time Constant in AM Detection Dissipative Interactions in Non-contact AFM in the Small Amplitude Limit Dependence of the Phase on the Damping and on the Force Gradient Summary 204

6 . Contents xiii 15 Intermittent Contact Mode/Tapping Mode Atomic Force Microscopy with Large Oscillation Amplitudes Resonance Curve for an Anharmonic Force-Distance Dependence Amplitude Instabilities for an Anharmonic Oscillator Energy Dissipation in Dynamic Atomic Force Microscopy Properties of the Intermittent Contact Mode/Tapping Mode Summary Mapping of Mechanical Properties Using Force-Distance Curves Principles of Force-Distance Curve Mapping Mapping of the Mechanical Properties of the Sample Summary Frequency Modulation (FM) Mode in Dynamic Atomic Force Microscopy Non-contact Atomic Force Microscopy Principles of Dynamic Atomic Force Microscopy II Expression for the Frequency Shift Normalized Frequency Shift in the Large Amplitude Limit Recovery of the Tip-Sample Force Experimental Realization of the FM Detection Scheme Self-excitation Mode Frequency Detection with a Phase-Locked Loop (PLL) PLL Tracking Mode The Non-monotonous Frequency Shift in AFM Comparison of Different AFM Modes Summary Noise in Atomic Force Microscopy Thermal Noise Density of a Harmonic Oscillator Thermal Noise in the Static AFM Mode Thermal Noise in the Dynamic AFM Mode with AM Detection Thermal Noise in Dynamic AFM with FM Detection Sensor Displacement Noise in the FM Detection Mode Total Noise in the FM Detection Mode Comparison to Noise in STM Signal-to-Noise Ratio in Atomic Force Microscopy FM Detection Summary 267

7 xiv Contents 19 Quartz Sensors in Atomic Force Microscopy Tuning Fork Quartz Sensor Quartz Needle Sensor Determination of the Sensitivity of Quartz Sensors Summary 275 Part HI Scanning Tunneling Microscopy and Spectroscopy 20 Scanning Tunneling Microscopy One-Dimensional Potential Barrier Model Flux of Matter and Charge in Quantum Mechanics The WKB Approximation for Tunneling Density of States Bardeen Model for Tunneling Energy-Dependent Approximation of the Bardeen Model Tersoff-Hamann Approximation of the Bardeen Model Constant Current Mode and Constant Height Mode Voltage-Dependent Imaging Summary Scanning Tunneling Spectroscopy (STS) Scanning Tunneling Spectroscopy Overview Experimental Realization of Spectroscopy with STM Normalized Differential Conductance Relation Between Differential Conductance and the Density of States Recovery of the Density of States Asymmetry in the Tunneling Spectra Beyond the ID Barrier Approximation Energy Resolution in Scanning Tunneling Spectroscopy Barrier Height Spectroscopy Barrier Resonances Spectroscopic Imaging Example: Spectroscopy of the Si(7 x 7) Surface Summary 333

8 Contents xv 22 Vibrational Spectroscopy with the STM Principles of Inelastic Tunneling Spectroscopy with the STM Examples of Vibrational Spectra Obtained with the STM Summary Spectroscopy and Imaging of Surface States Energy Dependence of the Density of States in Two, One and Zero Dimensions Scattering of Surface State Electrons at Surface Defects Summary Building Nanostructures Atom by Atom Positioning of Single Atoms and Molecules by STM Electron Confinement in Nanoscale Cages Inducing a Single Molecule Chemical Reaction with the STM Tip Summary 357 Appendix A: Horizontal Piezo Constant for a Tube Piezo Element Appendix B: Fermi's Golden Rule and Bardeen's Matrix Elements Appendix C: Frequency Noise in FM Detection 371 References 375 Index 377