Preface p. 17
Introduction p. 22
Style p. 22
Mathematica Preparation p. 23
General p. 23
Example p. 24
Recommended Books p. 25
Mathematica Programming Language p. 25
Scanning Probe Microscopies p. 26
Uniform Cantilevers p. 27
Introduction p. 27
Bending Due to F[subscript z] p. 30
General Equations p. 30
Slope p. 31
Angular Spring Constant p. 31
Displacement p. 32
Linear Spring Constant p. 32
Numerical Example: Si p. 33
Numerical Example: PtIr p. 33
Buckling Due to F[subscript x] p. 36
General Equations p. 36
Slope p. 36
Angular Spring Constant p. 36
Displacement p. 37
Linear Spring Constant p. 37
Numerical Example: Si p. 37
Numerical Example: PtIr p. 39
Twisting Due to F[subscript y] p. 40
General Equation p. 40
Slope p. 41
Angular Spring Constant p. 41
Numerical Example: Si p. 42
Numerical Example: PtIr p. 42
Vibrations p. 42
Bending Resonance Frequencies p. 42
Characteristic Functions p. 44
Summary of Results p. 45
Exercises for Chapter 2 p. 45
References p. 46
Cantilever Conversion Tables p. 48
Introduction p. 48
Circular Cantilever p. 49
Square Cantilever p. 50
Rectangular Cantilever p. 52
Exercises for Chapter 3 p. 54
References p. 55
V-Shaped Cantilevers p. 56
Introduction p. 56
Bending Due to F[subscript z]: Triangular Shape p. 58
General Equations p. 58
Slope p. 59
Angular Spring Constant p. 59
Displacement p. 59
Linear Spring Constant p. 60
Numerical Examples p. 60
Buckling due to F[subscript x]: Triangular Shape p. 62
General Equations p. 62
Slope p. 63
Angular Spring Constant p. 63
Displacement p. 63
Linear Spring Constant p. 64
Numerical Examples p. 64
Bending due to F[subscript z]: V Shape p. 66
General Equations p. 66
Slope p. 67
Angular Spring Constant p. 67
Displacement p. 67
Linear Spring Constant p. 68
Numerical Examples p. 68
Buckling Due to F[subscript x]: V Shape p. 70
General Equations p. 70
Slope p. 71
Angular Spring Constant p. 71
Displacement p. 71
Linear Spring Constant p. 72
Numerical Examples p. 72
Vibrations p. 74
Resonance Frequencies p. 74
Characteristic Functions p. 76
Exercises for Chapter 4 p. 77
References p. 77
Tip-Sample Adhesion p. 78
Introduction p. 78
Indentation p. 81
Contact Radius and Contact Force p. 81
Indentation and Contact Radius p. 83
Indentation and Contact Force p. 84
Inverted Functions p. 85
Contact Force and Contact Radius p. 85
Contact Radius and Indentation p. 86
Contact Force and Indentation p. 86
Limits of Adhesion Parameters p. 87
Contact Pressure p. 88
Maximum Contact Pressure p. 89
Distribution of Contact Pressure p. 89
Lennard-Jones Potential p. 90
Total Force and Indentation p. 91
Push-in Region p. 91
Push-in Region in the Absence of Adhesion p. 91
Push-in Region in the Presence of Adhesion p. 92
Pull-out Region p. 93
Pull-out Region in the Absence of Adhesion p. 93
Pull-out Region in the Presence of Adhesion p. 93
Hysteresis Loop p. 93
Exercises for Chapter 5 p. 93
References p. 94
Tip-Sample Force Curve p. 95
Introduction p. 95
Tip-Sample Interaction p. 97
Lennard-Jones Potential p. 97
Lennard-Jones Force p. 98
Lennard-Jones Force Derivative p. 99
Morse Potential p. 100
Hysteresis Loop p. 101
Snap-in and Snap-out Points p. 102
Calculated Hysteresis Loop p. 103
Observed Hysteresis Loop p. 103
Evaluation of Hamaker's Constant p. 107
Animation p. 108
Exercises for Chapter 6 p. 108
References p. 108
Free Vibrations p. 110
Introduction p. 110
Equation of Motion p. 111
Analytical Solution p. 112
Equation of Motion p. 112
Steady-State Regime p. 113
Bimorph-Cantilever Phase p. 114
Q-Dependent Resonance Frequency p. 115
Frequency-Dependent Amplitude p. 116
Frequency at the Steepest Slope p. 117
Average Power p. 117
Numerical Solutions p. 117
Equation of Motion p. 117
Transient Regime p. 118
Bimorph-Cantilever Phase Diagram p. 118
Displacement-Velocity Phase Diagram p. 119
Exercises for Chapter 7 p. 119
References p. 120
Noncontact Mode p. 122
Introduction p. 122
Tip-Sample Interaction p. 124
Lennard-Jones Potential p. 124
The Equation of Motion p. 126
Numerical Solution of the Equation of Motion p. 126
Approximate Analytical Solution of the Equation of Motion p. 129
Exercises for Chapter 8 p. 132
References p. 132
Tapping Mode p. 133
Introduction p. 133
Lennard-Jones Potential p. 135
Indentation Repulsive Force p. 136
Total Tip-Sample Force p. 137
General Solution p. 137
Transient Regime p. 138
Steady-State Regime p. 139
Tapping Phase Diagram p. 140
Displacement-Velocity Phase Diagram p. 140
Numerical Value of the Phase Shift p. 140
Summary of Results p. 144
Exercises for Chapter 9 p. 144
References p. 144
Metal-Insulator-Metal Tunneling p. 146
Introduction p. 146
Tunneling Current Density p. 148
General Solution p. 148
Small Voltage Approximation p. 148
Large Voltage Approximation p. 149
The Image Potential p. 150
Barrier with an Image Potential p. 152
The Barrier p. 152
The Barrier Width p. 153
Average Barrier Height p. 154
Comparison of the Barriers p. 154
The General Solution with an Image Potential p. 156
Apparent Barrier Height p. 157
Exercises for Chapter 10 p. 157
References p. 158
Fowler-Nordheim Tunneling p. 160
Introduction p. 160
Fowler-Nordheim Current Density p. 161
Numerical Example p. 163
Oxide Field and Applied Field p. 164
Oscillation Factor p. 165
Averaged Oscillations p. 167
Effective Tunneling Area p. 168
Exercises for Chapter 11 p. 169
References p. 169
Scanning Tunneling Spectroscopy p. 170
Introduction p. 170
Fermi-Dirac Statistics p. 172
Feenstra's Parameter p. 173
Scanning Tunneling Spectroscopy p. 174
STS Data File p. 174
Data Processing p. 175
Spectroscopic Data p. 175
Comparison of STS Results p. 176
Exercises for Chapter 12 p. 177
References p. 177
Coulomb Blockade p. 179
Introduction p. 179
Capacitance p. 180
Sphere-Plane Capacitance p. 181
Sphere-Sphere Capacitance p. 182
Quantum Considerations p. 182
Requirements and Approximations p. 184
Coulomb Blockade and Coulomb Staircase p. 184
Electrostatic Energy Due to the Charging of the Quantum Dot p. 185
Electrostatic Energy Due to the Applied Bias p. 185
Total Electrostatic Energy p. 185
Tunneling Rates p. 186
Tunneling Current p. 186
Examples p. 187
Example 1 p. 187
Example 2 p. 188
Example 3 p. 189
Example 4 p. 190
Example 5 p. 191
Temperature Effects p. 192
Parameters p. 192
Very High Temperature Operation p. 193
Very Low Temperature Operation p. 193
Finite Temperature Operation p. 194
Exercises for Chapter 13 p. 196
References p. 197
Density of States p. 198
Introduction p. 198
Sphere in Arbitrary Dimensions p. 199
Density of States in Arbitrary Dimensions p. 201
Density of States in Confined Structures p. 203
Quantum Wells p. 203
Quantum Wires p. 204
Cubical Quantum Dots p. 204
Spherical Quantum Dots p. 205
Interband Optical Transitions and Critical Points p. 207
Exercises for Chapter 14 p. 208
References p. 209
Electrostatics p. 211
Introduction p. 211
Isolated Point Charge p. 212
Point Charge and Plane p. 212
Point Charge and Sphere p. 213
Isolated Sphere p. 214
Sphere and Plane p. 215
Position of Charges Inside the Sphere p. 215
Magnitude of Charges Inside the Sphere p. 216
Position of Charges Outside the Sphere p. 216
Magnitude of Charges Outside the Sphere p. 216
Potential and Field p. 217
Potential Along the Axis of Symmetry p. 217
Capacitance p. 217
Sphere-Plane Capacitance p. 218
Example p. 218
Two Spheres p. 218
Capacitance: Exact Solution p. 219
Capacitance: Approximate Solution p. 219
Example p. 219
Electrostatic Force p. 220
Exercises for Chapter 15 p. 220
References p. 221
Near-Field Optics p. 222
Introduction p. 222
Far-Field Solution p. 224
Vector Potential p. 224
Electric Field p. 224
Electric Vector Field in the x-z Plane p. 225
Electric Vector Field in the x-y Plane p. 225
Magnetic Field p. 226
Poynting Vector and Intensity p. 227
Intensity in the x-z Plane p. 228
Intensity in the x-y Plane p. 229
Near-Field Solution p. 229
Transformation p. 229
Electric Field p. 230
Electric Field in the x-y Plane p. 230
Magnetic Field p. 233
Poynting Vector and Intensity p. 233
Discussion of the Models p. 236
Electric Field p. 236
Intensity p. 237
Scattered Electric Fields Around Patterned Apertures p. 238
Exercises for Chapter 16 p. 238
References p. 241
Constriction and Boundary Resistance p. 242
Introduction p. 242
A Metal as a Free Electron Gas p. 244
Lorenz Number, N[subscript Lorenz], and the Wiedemann-Franz Law p. 244
Fermi Velocity, v[subscript F] p. 244
Fermi Temperature, T[subscript F] p. 245
Fermi k-Vector, k[subscript F] p. 246
Electron Density, N[subscript e] p. 246
Mean Free Path, l p. 246
Ratio of l/[sigma] p. 247
Electronic Density of States, D[subscript e] p. 247
Electronic Specific Heat, C[subscript e] p. 248
Constriction Resistance p. 248
Electrical Resistance in the Maxwell Limit p. 248
Electrical Resistance in the Sharvin Limit p. 251
Combined Electrical Resistance p. 254
Boundary Resistance p. 256
Thermal Boundary Resistance of General Media p. 256
Thermal Boundary Resistance of Metallic Media p. 258
Electrical Boundary Resistance of Metallic Media p. 260
Exercises for Chapter 17 p. 261
References p. 261
Scanning Thermal Conductivity Microscopy p. 263
Introduction p. 263
Theory of Thermal Response p. 267
Electrical and Thermal Circuits p. 267
Cantilever Thermal Resistance and Temperature p. 268
Tip-Sample Thermal Resistance p. 269
Tip Thermal Resistance and Temperature p. 270
Thermal and Mechanical Cantilever Bending p. 271
Mechanical Bending p. 271
Thermal Bending p. 272
Combined Solution p. 273
Results p. 275
Tip-Side Coating, Upward Thermal Bending: Si and SiO[subscript 2] p. 275
Top-Side Coating, Downward Thermal Bending: Si and SiO[subscript 2] p. 277
Tip- and Top-Side Coating n-Dependent Apparent Height p. 279
Tip- and Top-Side Coating k-Dependent Apparent Height p. 279
Exercises for Chapter 18 p. 280
References p. 281
Kelvin Probe Force Microscopy p. 282
Introduction p. 282
Capacitance Derivatives p. 285
Tip-Sample Capacitance Derivative p. 285
Cantilever-Sample Capacitance Derivative p. 287
Measurement of Contact Potential Difference p. 287
Tip-Sample and Cantilever-Sample Electrostatic Forces p. 287
Harmonic Expansion of Tip-Sample Force p. 289
Thermal Noise Limitations p. 291
Exercises for Chapter 19 p. 291
References p. 292
Raman Scattering in Nanocrystals p. 293
Introduction p. 293
Raman Scattering in Bulk Silicon Crystals as a Function of Temperature p. 295
Introduction p. 295
Linewidth and Frequency Shift p. 295
Spectra p. 296
Raman Spectra in Nanocrystals at Room Temperature p. 298
Introduction p. 298
Linewidth and Frequency Shift p. 299
Spectra p. 299
Raman Spectra in Nanocrystals as a Function of Temperature p. 300
Introduction p. 300
Linewidth and Frequency Shift p. 301
Spectra p. 302
Exercises for Chapter 20 p. 302
References p. 303
Index p. 305