Atomic Force Microscopy

GREG HAUGSTAD, PhD, is a technical staff member and Director of the Characterization Facility in the College of Science and Engineering at the University of Minnesota. He has collaborated with industry professionals on such technologies as medical X-ray imaging media, lubrication, inkjet printing, and more recently on biomedical device coatings. He teaches undergraduate and graduate AFM courses, as well as short professional courses, and has trained over 600 AFM users.

• Preface xiiiAcknowledgments xxi1. Overview of AFM 11.1. The Essence of the Technique 11.2. Property Sensitive Imaging: Vertical Touching and Sliding Friction 61.3. Modifying a Surface with a Tip 131.4. Dynamic (or “AC” or “Tapping”) Modes: Delicate Imaging with Property Sensitivity 161.5. Force Curves Plus Mapping in Liquid 211.6. Rate, Temperature, and Humidity-Dependent Characterization 241.7. Long-Range Force Imaging Modes 281.8. Pedagogy of Chapters 30References 312. Distance-Dependent Interactions 332.1. General Analogies and Types of Forces 332.2. Van der Waals and Electrostatic Forces in a Tip–Sample System 382.2.1. Dipole–Dipole Forces 382.2.2. Electrostatic Forces 412.3. Contact Forces and Mechanical Compliance 442.4. Dynamic Probing of Distance-Dependent Forces 512.4.1. Importance of Force Gradient 512.4.2. Damped, Driven Oscillator: Concepts and Mathematics 562.4.3. Effect of Tip–Sample Interaction on Oscillator 602.4.4. Energy Dissipation in Tip–Sample Interaction 642.5. Other Distance-Dependent Attraction and Repulsion: Electrostatic and Molecular Forces in Air and Liquids 672.5.1. Electrostatic Forces in Liquids: Superimposed on Van der Waals Forces 672.5.2. Molecular-Structure Forces in Liquids 692.5.3. Macromolecular Steric Forces in Liquids 722.5.4. Derjaguin Approximation: Colloid Probe AFM 762.5.5. Macromolecular Extension Forces (Air and Liquid Media) 782.6. Rate/Time Effects 832.6.1. Viscoelasticity 842.6.2. Stress-Modified Thermal Activation 852.6.3. Relevance to Other Topics of Chapter 2 86References 883. Z-Dependent Force Measurements with AFM 913.1. Revisit Ideal Concept 913.2. Force-Z Measurement Components: Tip/Cantilever/Laser/Photodetector/Z Scanner 933.2.1. Basic Concepts and Interrelationships 933.2.2. Tip–Sample Distance 963.2.3. Finer Quantitative Issues in Force–Distance Measurements 993.3. Physical Hysteresis 1063.4. Optical Artifacts 1093.5. Z Scanner/Sensor Hardware: Nonidealities 1133.6. Additional Force-Curve Analysis Examples 1183.6.1. Glassy Polymer, Rigid Cantilever 1183.6.2. Gels, Soft Cantilever 1233.6.3. Molecular-Chain Bridging Adhesion 1263.6.4. Bias-Dependent Electrostatic Forces in Air 1293.6.5. Screened Electrostatic Forces in Aqueous Medium 1313.7. Cantilever Spring Constant Calibration 133References 1354. Topographic Imaging 1374.1. Idealized Concepts 1384.2. The Real World 1434.2.1. The Basics: Block Descriptions of AFM Hardware 1434.2.2. The Nature of the Collected Data 1494.2.3. Choosing Setpoint: Effects on Tip–Sample Interaction and Thereby on Images 1564.2.5. Realities of Piezoscanners: Use of Closed-Loop Scanning 1674.2.6. Shape of Tip and Surface 1804.2.7. Other Realities and Operational Difficulties—Variable Background, Drift, Experimental Geometry 182References 1865. Probing Material Properties I: Phase Imaging 1875.1. Phase Measurement as a Diagnostic of Interaction Regime and Bistability 1895.1.1. Phase (and Height, Amplitude) Imaging as Diagnostics 1895.1.2. Comments on Imaging in the Attractive Regime 2005.2. Complications and Caveats Regarding the Phase Measurement 2025.2.1. The Phase Offset 2025.2.2. Drift in Resonance Frequency, Phase Offset, Quality Factor, and Response Amplitude 2075.2.3. Change of Phase and Amplitude During Coarse Approach 2115.2.4. Coupling of Topography and Phase 2145.2.5. The Phase Electronics and Its Calibration 2215.2.6. Nonideality in the Resonance Spectrum 2305.3. Energy Dissipation Interpretation of Phase: Quantitative Analysis 2345.3.1. Variable A/A0 Imaging 2355.3.2. Fixed A/A0 Imaging 2405.3.3. Variable A/A0 via Z-Dependent Point Measurements 2435.4. Virial Interpretation of Phase 2475.5. Caveats and Data Analysis Strategies when Quantitatively Interpreting Phase Data 248References 2556. Probing Material Properties II: Adhesive Nanomechanics and Mapping Distance-Dependent Interactions 2586.1. General Concepts and Interrelationships 2596.2. Adhesive Contact Mechanics Models 2616.2.1. Overview and Disclaimers 2616.2.2. JKR and DMT Models 2636.2.3. Ranging Between JKR and DMT: The Transition Parameter l 2666.2.4. The Maugis–Dugdale Model 2706.2.5. Other Formal Relationships Relevant to Adhesive Contact Mechanics 2736.2.6. Summary Comments and Caveats on Adhesive Contact Mechanics Models 2746.3. Capillarity, Details of Meniscus Force 2776.3.1. Framing the Issues 2786.3.2. Basic Elements of Modeling the Meniscus 2806.3.3. Mathematics of Meniscus Geometry and Force 2836.3.4. Experimental Examples of Capillarity 2876.3.5. Capillary Transfer Phenomena: Difficulties and Opportunities 2936.4. Approach–Retract Curve Mapping 2966.4.1. Motivation and Background 2966.4.2. Traditional Force-Curve Mapping 2986.4.3. Approach–Retract Curve Mapping in Dynamic AFM 3066.4.4. Approach–Retract Curve Mapping of Liquidy Domains in Complex Thin Films 3136.5. High-Speed/Full Site Density Force-Curve Mapping and Imaging 3156.5.1. Liquidy Domains in Complex Thin Films 3176.5.2. PBMA/PLMA Blend at Variable Ultimate Load 3196.5.3. PBMA/Dexamethasone Mixture at Variable Temperature 3206.5.4. Arborescent Styrene–Isobutylene–Styrene Block Copolymer Plus Drug Rapamycin 3226.5.5. Comments on “Force Modulation” Mode 323References 3247. Probing Material Properties III: Lateral Force Methods 3307.1. Components of Lateral Force Signal 3307.2. Application of Lateral Force Difference 3367.3. Calibration of Lateral Force 3437.4. Load-Dependent Friction 3467.4.1. Motivations 3467.4.2. Load Stepping and Ramping Methods 3477.5. Variable Rate and Environmental Parameters in AFM Friction and Wear 3527.5.1. Motivations 3527.5.2. Interplay of Rate, Temperature, Humidity, and Tip Chemistry in Friction 3547.5.3. Wear Under Variable Rate and Temperature 3597.5.4. Musings on the Spectroscopic Nature of Friction and Other Measurements 3627.6. Transverse Shear Microscopy (TSM) and Anisotropy of Shear Modulus 3647.7. Shear Modulation Methods 3667.7.1. Motivations and Terminology 3667.7.2. Shear Modulation During 1D Lateral Scanning 3687.7.3. Diagnostics of Sliding Under Shear Modulation 3717.7.4. Complementarity of Shear Modulation Methods to TSM 3727.7.5. Shear Modulation Within Force Curves: Material Creep 373References 3758. Data Post-Processing and Statistical Analysis 3798.1. Preliminary Data Processing 3798.2. 1D Roughness Metrics 3838.3. 2D-Domain Analysis 3858.3.1. Slope and Surface Area Analysis 3858.3.2. 2D-Domain Fourier Methods for Spatial Analysis 3868.3.3. Fourier Methods for Time-Domain Analysis 3918.3.4. Grain or Particle Size Analysis 3948.4. “Lineshape” Fitting 396References 3989. Advanced Dynamic Force Methods 4009.1. Principles of Electronic Methods Utilizing Dynamic AFM 4019.1.1. Shifted Dynamic Response due to Force Gradient 4029.1.2. Interleave Methods for Long-Range Force Probing 4059.1.3. Interleave-Based EFM/KFM on Different Metals and Silicon 4089.1.4. KFM of Organic Semiconductor, Including Cross-Technique Comparisons 4129.2. Methods Using Higher Vibrational Modes 4149.2.1. Mathematics of Beam Mechanics: The Music of AFM 4149.2.2. Probing Tip–Sample Interactions via Multifrequency Dynamic AFM 4199.2.3. Contact Resonance Methods 4259.2.4. Single-Pass Electric Methods 429References 433Appendices 437Appendix 1: Spectral Methods for Measuring the Normal Cantilever Spring Constant K 437A1.1 Plan-View/Resonance Frequency Method 438A1.2 Sader Method 441A1.3 Thermal Method 442Appendix 2: Derivation of Van der Waals Force–Distance Expressions 443Appendix 3: Derivation of Energy Dissipation Expression, Relationship to Phase 447Appendix 4: Relationships in Meniscus Geometry, Circular Approximation 449References 450Index 453