1. Integrated Cantilevers and Atomic Force Microscopes
Sadik Hafizovic, Kay-Uwe Kirstein, Andreas Hierlemann .... 1
1.1. Overview .............................................. 1
1.2. Active Cantilevers .................................... 2
1.2.1. Integrated Force Sensor ....................... 4
1.2.2. Integrated Actuation .......................... 8
1.3. System Integration ................................... 10
1.3.1. Analog Signal Processing and Conditioning .... 10
1.3.2. Digital Signal Processing .................... 13
1.4. Single-Chip CMOS AFM ................................. 16
1.4.1. Measurements .................................. 19
1.5. Parallel Scanning .................................... 19
1.6. Outlook .............................................. 21
References ................................................. 21
2. Electrostatic Microscanner
Yasuhisa Ando ........................................... 23
2.1. Introduction ......................................... 23
2.2. Displacement Conversion Mechanism .................... 24
2.2.1. Basic Conception ............................. 24
2.2.2. Combination with Comb Actuator ............... 25
2.2.3. Various Types of Displacement Conversion
Mechanism .................................... 27
2.3. Design, Fabrication Technique, and Performance ....... 29
2.3.1. Main Structure of 3D Microstage .............. 29
2.3.2. Amplification Mechanism of Scanning Area ..... 31
2.3.3. Fabrication Using ICP-RIE .................... 34
2.3.4. Evaluation of Motion of 3D Microstage ........ 37
2.4. Applications to AFM .................................. 39
2.4.1. Operation by Using Commercial Controller ..... 39
2.4.2. Evaluation of Microscanner Using
Grating Image ................................ 41
2.4.3. SPM Operation Using Microscanner ............. 45
References ........................................... 49
3. Low-Noise Methods for Optical Measurements of
Cantilever Deflections
Tilman E. Schäffer ...................................... 51
3.1. Introduction ......................................... 51
3.2. The Optical Beam Deflection Method ................... 52
3.2.1. Gaussian Optics .............................. 52
3.2.2. Detection Sensitivity ........................ 54
3.3. Optical Detection Noise .............................. 55
3.3.1. Noise Sources ................................ 55
3.3.2. Shot Noise ................................... 55
3.4. The Array Detector ................................... 56
3.5. Dynamic Range and Linearity .......................... 59
3.5.1. The Two-Segment Detector ..................... 59
3.5.2. The Array Detector ........................... 61
3.6. Detection of Higher-Order Cantilever
Vibration Modes ...................................... 62
3.6.1. Normal Vibration Modes ....................... 63
3.6.2. Optimization of the Detection Sensitivity .... 64
3.7. Calculation of Thermal Vibration Noise ............... 66
3.7.1. Focused Optical Spot of Infinitesimal Size ... 66
3.7.2. Focused Optical Spot of Finite Size .......... 67
3.8. Thermal Spring Constant Calibration .................. 69
References ................................................. 70
4. Q-controlled Dynamic Force Microscopy in Air and Liquids
Hendrik Hölscher, Daniel Ebeling, Udo D. Schwarz ........ 75
4.1. Introduction ......................................... 75
4.2. Theory of Q-controlled Dynamic Force Microscopy ...... 76
4.2.1. Equation of Motion of a Dynamic Force
Microscope with Q-control .................... 76
4.2.2. Active Modification of the Q-factor .......... 78
4.2.3. Including Tip-Sample Interactions ............ 80
4.2.4. Prevention of Instabilities by Q-control
in Air ....................................... 82
4.2.5. Reduction of Tip-Sample Indentation and
Force by Q-control in Liquids ................ 86
4.3. Experimental Applications of Q-control ............... 89
4.3.1. Examples for Q-control Applications
in Ambient Conditions ........................ 90
4.4. Summary .............................................. 94
References ................................................. 95
5. High-Frequency Dynamic Force Microscopy
Hideki Kawakatsu ........................................ 99
5.1. Introduction ......................................... 99
5.2. Instrumental ......................................... 99
5.2.1. Cantilever ................................... 99
5.2.2. Detection ................................... 102
5.2.3. Excitation .................................. 105
5.2.4. Circuitry ................................... 106
5.3. Experimental ........................................ 107
5.3.1. Low-Amplitude Operation ..................... 107
5.3.2. Manipulation ................................ 108
5.3.3. Atomic-Resolution Lateral
Force Microscopy ............................ 108
5.3.4. Other Techniques for High Frequency
Motion Detection ............................ 108
5.4. Summary and Outlook ................................. 109
References ................................................ 110
6. Torsional Resonance Microscopy and Its Applications
Chanmin Su, Lin Huang, Craig B. Prater,
Bharat Bhushan ......................................... 113
6.1. Introduction to Torsional Resonance Microscopy ...... 113
6.2. TRmode System Configuration ......................... 115
6.3. Torsional Modes of Oscillation ...................... 119
6.4. Imaging and Measurements with TRmode ................ 123
6.4.1. TRmode in Weakly-Coupled Interaction
Region ...................................... 123
6.4.2. TRmode Imaging and Measurement in
Contact Mode ................................ 127
6.5. Applications of TRmode Imaging ...................... 129
6.5.1. High-Resolution Imaging Application ......... 129
6.5.2. Electric Measurements Under Controlled
Proximity by TRmode ......................... 132
6.5.3. In-Plane Anisotropy ......................... 138
6.6. Torsional Tapping Harmonics for Mechanical
Property Characterization ........................... 140
6.6.1. Detecting Cantilever Harmonics Through
Torsional Detection ......................... 142
6.6.2. Reconstruction of Time-Resolved Forces ...... 142
6.6.3. Force-Versus-Distance Curves ................ 143
6.6.4. Mechanical Property Measurements and
Compositional Mapping ....................... 144
6.7. Conclusion .......................................... 145
References ................................................ 146
7. Modeling of Tip-Cantilever Dynamics in Atomic
Force Microscopy
Yaxin Song, Bharat Bhushan ............................. 149
7.1. Introduction ........................................ 155
7.1.1. Various AFM Modes and Measurement
Techniques .................................. 155
7.1.2. Models for AFM Cantilevers .................. 161
7.1.3. Outline ..................................... 163
7.2. Modeling of AFM Tip-Cantilever Systems in AFM ....... 163
7.2.1. Tip-Sample Interaction ...................... 164
7.2.2. Point-Mass Model ............................ 166
7.2.3. The ID Beam Model ........................... 168
7.2.4. Pure Torsional Analysis of TRmode ........... 171
7.2.5. Coupled Torsional-Bending Analysis .......... 177
7.3. Finite Element Modeling of Tip-Cantilever
Systems ............................................. 187
7.3.1. Finite Element Beam Model of Tip-
Cantilever Systems .......................... 188
7.3.2. Modeling of Tapping Mode .................... 192
7.3.3. Modeling of Torsional Resonance Mode ........ 196
7.3.4. Modeling of Lateral Excitation Mode ......... 199
7.4. Atomic-Scale Topographic and Friction Force
Imaging in FFM ...................................... 200
7.4.1. FFM Images of Graphite Surface .............. 202
7.4.2. Interatomic Forces Between Tip
and Surface ................................. 204
7.4.3. Modeling of FFM Profiling Process ........... 205
7.4.4. Simulations on Graphite Surface ............. 208
7.5. Quantitative Evaluation of the Sample's Mechanical
Properties .......................................... 213
7.6. Closure ............................................. 216
A. Appendices .......................................... 217
A.l. Stiffness and Mass Matrices of 3D
Beam Element ................................ 217
A.2. Mass Matrix of the Tip ...................... 218
A.3. Additional Stiffness and Mass Matrices
Under Linear Tip-Sample Interaction ......... 219
References ................................................ 220
8. Combined Scanning Probe Techniques for In-Situ
Electrochemical Imaging at a Nanoscale
Justyna Wiedemair, Boris Mizaikoff, Christine Kranz .... 225
8.1. Overview ............................................ 227
8.2. Combined Techniques ................................. 228
8.2.1. Integration of Electrochemical
Functionality ............................... 230
8.2.2. Combined Techniques Based on Force
Interaction ................................. 231
8.2.3. Combined Techniques, Based on Tunneling
Current ..................................... 232
8.2.4. Combined Techniques Based on Optical
Near-Field Interaction ...................... 233
8.2.5. Theory ...................................... 234
8.2.6. Combined Probe Fabrication .................. 234
8.3. Applications ........................................ 243
8.3.1. Model Systems ............................... 244
8.3.2. Imaging Enzyme Activity ..................... 246
8.3.3. AFM Tip-Integrated Biosensors ............... 249
8.3.4. Combined SPM for Imaging of Living Cells .... 253
8.3.5. Measurement of Local pH Changes ............. 255
8.3.6. Corrosion Studies ........................... 257
8.4. Outlook: Further Aspects of Multifunctional
Scanning Probes ..................................... 259
References ................................................ 261
9. New AFM Developments to Study Elasticity
and Adhesion at the Nanoscale
Robert Szoszkiewicz, Elisa Riedo ....................... 269
9.1. Introduction ........................................ 270
9.2. Contact Mechanics Theories and Their Limitations .... 271
9.3. Modulated Nanoindentation ........................... 273
9.3.1. Force-Indentation Curves .................... 273
9.3.2. Elastic Moduli .............................. 276
9.4. Ultrasonic Methods at Local Scales .................. 278
9.4.1. Brief Description of Ultrasonic Methods ..... 278
9.4.2. Applications of Ultrasonic Techniques in
Elasticity Mapping .......................... 281
9.4.3. UFM Measurements of Adhesion Hysteresis
and Their Relations to Friction at the
Tip-Sample Contact .......................... 282
References ................................................ 284
10. Near-Field Raman Spectroscopy and Imaging
Pietro Giuseppe Gucciardi, Sebastiano Trusso,
Cirino Vasi, Salvatore Patane, Maria Allegrini ......... 287
10.1. Introduction ........................................ 287
10.2. Raman Spectroscopy .................................. 289
10.2.1. Classical Description of the Raman Effect ... 289
10.2.2. Quantum Description of the Raman Effect ..... 291
10.2.3. Coherent Anti-Stokes Raman Scattering ....... 295
10.2.4. Experimental Techniques in
Raman Spectroscopy .......................... 296
10.3. Near-Field Raman Spectroscopy ....................... 299
10.3.1. Theoretical Principles of the Near-Field
Optical Microscopy .......................... 300
10.3.2. Setups for Near-Field Raman Spectroscopy .... 302
10.4. Applications of Near-Field Raman Spectroscopy ....... 306
10.4.1. Structural Mapping .......................... 307
10.4.2. Chemical Mapping ............................ 312
10.4.3. Probing Single Molecules by Surface-
Enhanced and Tip-Enhanced Near-Field
Raman Spectroscopy .......................... 314
10.4.4. Near-Field Raman Spectroscopy and Imaging
of Carbon Nanotubes ......................... 321
10.4.5. Coherent Anti-Stokes Near-Field
Raman Imaging ............................... 324
10.5. Conclusions ......................................... 326
References ................................................ 326
Subject Index ................................................. 331
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