Atomic Force Microscopy (eBook)

Preface 7
Contents 9
1 Introduction 15
1.1 Scanning Tunneling Microscopy (STM) 18
1.2 Introduction to Atomic Force Microscopy 22
1.3 A Short History of Scanning Probe Microscopy 25
1.4 Summary 25
References 26
2 Harmonic Oscillator 28
2.1 Free Harmonic Oscillator 28
2.2 Free Harmonic Oscillator with Damping 31
2.3 Driven Harmonic Oscillator 32
2.4 Driven Harmonic Oscillator with Damping 34
2.5 Transients of Oscillations 39
2.6 Dissipation and Quality Factor of a Damped Driven Harmonic Oscillator 41
2.7 Effective Mass of a Harmonic Oscillator 42
2.8 Linear Differential Equations 44
2.9 Summary 45
References 46
3 Technical Aspects of Atomic Force Microscopy 47
3.1 Piezoelectric Effect 47
3.2 Extensions of Piezoelectric Actuators 50
3.3 Piezoelectric Materials 54
3.4 Tube Piezo Element 56
3.4.1 Resonance Frequencies of Piezo Tubes 59
3.5 Non-linearities and Hysteresis Effects of Piezoelectric Actuators 63
3.5.1 Hysteresis 63
3.5.2 Creep 65
3.5.3 Thermal Drift 66
3.6 Vibration Isolation 67
3.6.1 Isolation of the Microscope from Outer Vibrations 67
3.6.2 The Microscope Considered as a Vibrating System 71
3.6.3 Combining Vibration Isolation and a Microscope with High Resonance Frequency 73
3.7 Building Vibrations 76
3.8 Summary 78
References 79
4 Atomic Force Microscopy Designs 80
4.1 Coarse Positioners 80
4.1.1 Inertial Sliders 80
4.2 AFM Scanners 85
4.2.1 Flexure-Guided Piezo Nanopositioning Stages 85
4.2.2 Closed Loop Operation of Piezoelectric Nanopositioners 86
4.3 AFM Design with a Tube Scanner 89
4.4 AFM Design with Scanners Operating in Closed Loop 90
4.5 AFM Designs for Large Samples 92
4.6 AFM Designs for Vacuum Operation 93
4.6.1 Pan Slider 93
4.6.2 KoalaDrive 94
4.6.3 Tip Exchange 96
4.7 Summary 96
References 97
5 Electronics and Control for Atomic Force Microscopy 98
5.1 Time Domain and Frequency Domain 98
5.2 Voltage Divider 99
5.3 Impedance, Transfer Function, and Bode Plot 100
5.4 Output Resistance/Input Resistance 101
5.5 Noise 103
5.6 Operational Amplifiers 105
5.6.1 Voltage Follower/Impedance Converter 106
5.6.2 Voltage Amplifier 107
5.7 Current Amplifier 108
5.8 Feedback Controller 110
5.8.1 Proportional Controller 112
5.8.2 Integral Controller 113
5.8.3 Proportional-Integral Controller 115
5.8.4 Time Discrete Implementation of a PI Controller 116
5.8.5 Instabilities of a Feedback Loop 118
5.8.6 Measurement of Transfer Functions 120
5.9 Feedback Controller in AFM 121
5.10 Implementation of an AFM Feedback Controller 124
5.11 Digital-to-Analog Converter 126
5.12 Analog-to-Digital Converter 127
5.13 High-Voltage Amplifier 128
5.14 Summary 129
References 129
6 Lock-in Technique 130
6.1 Lock-in Amplifier–Principle of Operation 130
6.2 Summary 134
7 Data Representation and Image Processing 135
7.1 Data Representation 135
7.2 Image Processing 140
7.3 Data Analysis 142
7.4 Summary 145
References 145
8 Artifacts in AFM 146
8.1 Tip-Related Artifacts 146
8.2 Scanner-Related Artifacts 151
8.3 Feedback-Related Artifacts 152
8.4 Artifacts Due to Periodic Noise 153
8.5 Thermal Drift 154
8.6 Laser Interference 155
8.7 Summary 155
References 155
9 Work Function, Contact Potential, and Kelvin Probe AFM 157
9.1 Work Function 157
9.2 Effect of a Surface on the Work Function 158
9.3 Surface Charges and External Electric Fields 160
9.4 Contact Potential 163
9.5 Measurement of Work Function by the Kelvin Method 163
9.6 Kelvin Probe Scanning Force Microscopy (KPFM) 165
9.7 Summary 167
References 167
10 Forces Between Tip and Sample 168
10.1 Tip-Sample Forces 168
10.2 Tip-Sample Contact Mechanics 171
10.3 Capillary Tip-Sample Forces 175
10.4 Electrostatic Tip-Sample Force 176
10.5 Snap-to-Contact 177
10.6 Summary 182
References 183
11 Cantilevers and Detection Methods in Atomic Force Microscopy 184
11.1 Requirements for Force Sensors 184
11.2 Fabrication of Cantilevers 186
11.3 Beam Deflection Atomic Force Microscopy 188
11.3.1 Sensitivity of the Beam Deflection Method 189
11.3.2 Detection Limit of the Beam Deflection Method 191
11.4 Other Detection Methods 193
11.5 Cantilever Excitation in Dynamic AFM 194
11.6 Calibration of AFM Measurements 196
11.6.1 Experimental Determination of the Sensitivity Factor in AFM 197
11.6.2 Calculation of the Spring Constant from the Geometrical Data of the Cantilever 198
11.6.3 Sader Method for the Determination of the Spring Constant of a Cantilever 199
11.6.4 Thermal Method for the Determination of the Spring Constant of a Cantilever 200
11.6.5 Experimental Determination of the Sensitivity and Spring Constant in AFM Without Tip-Sample Contact 202
11.7 Summary 203
References 204
12 Static Atomic Force Microscopy 205
12.1 Principles of Static Atomic Force Microscopy 205
12.2 Properties of Static AFM Imaging 207
12.3 Constant Height Mode in Static AFM 208
12.4 Friction Force Microscopy (FFM) 209
12.5 Force-Distance Curves 210
12.6 Summary 214
References 214
13 Amplitude Modulation (AM) Mode in Dynamic Atomic Force Microscopy 215
13.1 Parameters of Dynamic Atomic Force Microscopy 215
13.2 Principles of Amplitude Modulation Dynamic Atomic Force Microscopy 216
13.3 Amplitude Modulation (AM) Detection Scheme in Dynamic … 222
13.4 Experimental Realization of the AM Detection Mode 225
13.5 Time Constant in AM Detection 227
13.6 Dissipative Interactions in the Dynamic AM Detection Mode 229
13.7 Dependence of the Phase on the Damping and on the Force Gradient 232
13.8 Summary 234
References 235
14 Intermittent Contact Mode/Tapping Mode 236
14.1 Dynamic Atomic Force Microscopy with Large Oscillation Amplitudes 236
14.2 Resonance Curve for an Anharmonic Force-Distance Dependence 242
14.3 Amplitude Instabilities for an Anharmonic Oscillator 245
14.4 Energy Dissipation in Tapping Mode Atomic Force Microscopy 249
14.5 General Equations for Amplitude and Phase in Dynamic AM … 252
14.6 Properties of the Intermittent Contact Mode/Tapping Mode 256
14.7 Summary 257
References 257
15 Mapping of Mechanical Properties Using Force-Distance Curves 259
15.1 Principles of Force-Distance Curve Mapping 259
15.2 Mapping of the Mechanical Properties of the Sample 262
15.3 Summary 263
References 263
16 Frequency Modulation (FM) Mode in Dynamic Atomic Force Microscopy—Non-contact Atomic Force Microscopy 264
16.1 Principles of FM Detection in Dynamic Atomic Force Microscopy 265
16.1.1 Expression for the Frequency Shift 268
16.1.2 Normalized Frequency Shift in the Large Amplitude Limit 271
16.1.3 Recovery of the Tip-Sample Force 273
16.2 Experimental Realization of the FM Detection Scheme 274
16.2.1 Self-Excitation Mode 274
16.2.2 Frequency Detection with a Phase-Locked Loop (PLL) 279
16.2.3 PLL Tracking Mode 282
16.3 The Non-monotonous Frequency Shift in AFM 284
16.4 Comparison of Different AFM Modes 286
16.5 Summary 287
References 288
17 Noise in Atomic Force Microscopy 289
17.1 Thermal Noise Density of a Harmonic Oscillator 289
17.2 Thermal Noise in the Static AFM Mode 292
17.3 Thermal Noise in the Dynamic AFM Mode with AM Detection 292
17.4 Thermal Noise in Dynamic AFM with FM Detection 293
17.5 Sensor Displacement Noise in the FM Detection Mode 295
17.6 Total Noise in the FM Detection Mode 296
17.7 Measurement of System Parameters in Dynamic AFM 297
17.8 Comparison to Noise in STM 299
17.9 Signal-to-Noise Ratio in Atomic Force Microscopy FM Detection 300
17.10 Summary 302
References 302
18 Quartz Sensors in Atomic Force Microscopy 303
18.1 Tuning Fork Quartz Sensor 303
18.2 Quartz Needle Sensor 304
18.3 Determination of the Sensitivity of Quartz Sensors 307
18.4 Summary 309
References 309
A Horizontal Piezo Constant for a Tube Piezo Element 310
B Spectral Density, Spectrum and their Experimental Calibration 313
C Corrections to the Thermal Method 318
D Frequency Noise in FM Detection 322
Index 325