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