Amplitude Modulation Atomic Force Microscopy E-Book

Ricardo García

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 310

Veröffentlichungsjahr: 2011

Beschreibung

Filling a gap in the literature, this book features in-depth discussions on amplitude modulation AFM, providing an overview of the theory, instrumental considerations and applications of the technique in both academia and industry. As such, it includes examples from material science, soft condensed matter, molecular biology, and biophysics, among others. The text is written in such a way as to enable readers from different backgrounds and levels of expertise to find the information suitable for their needs.

Leseprobe

Contents

Preface

Annotation List

1 Introduction

1.1 Historical Perspective

1.2 Evolution Periods and Milestones

1.3 Tapping Mode or Amplitude Modulation Force Microscopy?

1.4 Other Dynamic AFM Methods

2 Instrumental and Conceptual Aspects

2.1 Introduction

2.2 Amplitude Modulation AFM

2.3 Elements of an Amplitude Modulation AFM

2.4 Cantilever–Tip System

2.5 Calibration Protocols

2.6 Common Experimental Curves

2.7 Displacements and Distances

3 Tip–Surface Interaction Forces

3.1 Introduction

3.2 Van der Waals Forces

3.3 Contact Mechanics Forces

3.4 Capillary Force

3.5 Forces in Liquid

3.6 Electrostatic Forces

3.7 Nonconservative Forces

3.8 Net Tip–Surface Force

4 Theory of Amplitude Modulation AFM

4.1 Introduction

4.2 Equation of Motion

4.3 The Point-Mass Model: Elemental Aspects

4.4 The Point-Mass Model: Analytical Approximations

4.5 Peak and Average Forces

4.6 The Point-Mass Model: Numerical Solutions

4.7 The Effective Model

Appendix A The Runge–Kutta Algorithm

5 Advanced Theory of Amplitude Modulation AFM

5.1 Introduction

5.2 Q-Control

5.3 Nonlinear Dynamics

5.4 Continuous Cantilever Beam Model

5.5 Equivalence between Point-Mass and Continuous Models

5.6 Systems Theory Description

5.7 Force Reconstruction Methods: Force versus Distance

5.8 Time-Resolved Force

6 Amplitude Modulation AFM in Liquid

6.1 Introduction

6.2 Qualitative Aspects of the Cantilever Dynamics in Liquid

6.3 Interaction Forces in Liquid

6.4 Some Experimental and Conceptual Considerations

6.5 Theoretical Descriptions of Dynamic AFM in Liquid

7 Phase Imaging Atomic Force Microscopy

7.1 Introduction

7.2 Phase Imaging Atomic Force Microscopy

7.3 Theory of Phase Imaging AFM

7.4 Energy Dissipation Measurements at the Nanoscale

8 Resolution, Noise, and Sensitivity

8.1 Introduction

8.2 Spatial Resolution

8.3 Image Distortion and Surface Reconstruction

8.4 Force-Induced Surface Deformations

8.5 Atomic, Molecular, and Subnanometer Lateral Resolution

8.6 High-Resolution Imaging of Isolated Molecules

8.7 Conditions for High-Resolution Imaging

8.8 Image Artifacts

9 Multifrequency Atomic Force Microscopy

9.1 Introduction

9.2 Normal Modes and Harmonics

9.3 Bimodal AFM

9.4 Mode-Synthesizing Atomic Force Microscopy

9.5 Torsional Harmonic AFM

9.6 Band Excitation

10 Beyond Topographic Imaging

10.1 Introduction

10.2 Scattering Near-Field Optical Microscopy

10.3 Topography and Recognition Imaging

10.4 Nanofabrication by AFM

References

Index

Related Titles

Sarid, D.Exploring Scanning Probe Microscopy with MATHEMATICA310 pages2007HardcoverISBN: 978-3-527-40617-3

Jena, B. P., Hoerber, J. K. H. (eds.)Force MicroscopyApplications in Biology and Medicine300 pages2006HardcoverISBN: 978-0-471-39628-4

Kumar, C. S. S. R. (ed.)Nanosystem Characterization Tools in the Life Sciences413 pages with 178 figures and 28 tables2006HardcoverISBN: 978-3-527-31383-9

The Author

Prof. Dr. Ricardo GarcíaInstituto de Microelectronica de Madrid (CSIC)Tres Cantos. Madrid, [email protected]

Cover pictureSpiesz Design, Neu-Ulm

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Cover Design Grafik-Design Schulz, Fußgönheim

ISBN: 978-3-527-40834-4

The intellect of man is forced to chooseperfection of the life, or of the work,And if it take the second must refuseA heavenly mansion, raging in the dark.When all that story’s finished, what’s the news?In luck or out the toil has left its mark:That old perplexity an empty purse,Or the day’s vanity, the night’s remorse.

(William Butler Yeats, The Choice)

To my wife Begoña and children Leonardo and Adriano.To my parents Graciana and Santiago.

Preface

This book has two goals. First, it aims to describe how the physical forces acting between a vibrating probe and the sample atoms are transformed into amplitude and phase shift variations. Second, it aims to explain how from these variations it is possible to generate a high-resolution image and to extract information on the properties of the sample surface.

My first experiment with an amplitude modulation atomic force microscope happened in the spring of 1993. Then, I was a postdoctoral fellow working with Carlos Bustamante. At that time, Bustamante’s laboratory was at the forefront of AFM applications in biology. Tapping mode AFM was generating images of DNA and single proteins in liquid with an unprecedented resolution. The intellectual atmosphere of the laboratory was exuberant. Passionate discussions about image resolution were frequent. Sometimes, the emphasis was placed on the sample preparation, at others on the size and lifetime of the probe. We knew little about the cantilever dynamics. Mostly, we assumed that a microscope that provided impressive images had to have a well-established theory behind it. After a few years of hard work, it emerged that further improvements in lateral resolution and material properties characterization would require a better understanding of the cantilever–tip dynamics.

About 3 years ago, an editor from Wiley-VCH invited me to write a book on amplitude modulation AFM. I had mixed feelings. Was this happening at the right time? Is it worth to devote time and energy to write a scientific book at the beginning of the twenty-first century? The writing process has not been easy. On several occasions, I had to pause because I realized that my knowledge on dynamic AFM was uneven. It took me about 8 months to reach a steady writing rhythm. On other occasions, especially when I was under pressure of different submission deadlines, I went introspective. At the end, the aspirations harbored during the undergraduate and graduate years had more weight than other professional considerations.

The text is structured to satisfy the needs of beginners and experts alike. Every chapter starts with an introduction that summarizes the topics of the chapter. Most of the chapters can be read independently. Chapter 1 offers a historical perspective on the development of amplitude modulation force microscopy. Chapter 2 summarizes the minimum knowledge that is required to properly operate the microscope. Chapter 3 introduces to the tip–surface forces. Chapters 4 and 5 present several aspects of the cantilever dynamics in air. Chapter 6 extends the cantilever dynamics to liquid environments. Chapter 7 deals with the theory and applications of phase imaging AFM. Chapter 8 describes the factors that control lateral and vertical resolution of the instrument. Chapter 9 delves into the multifrequency AFM methods based on the use of several modes or harmonics. Finally, Chapter 10 presents some applications that go beyond topographic imaging such as nanolithography, near-field optics, or molecular recognition imaging.

The number of people who directly or indirectly have helped me understand atomic force microscopy is larger than I could cope to realize. However, I specifically want to acknowledge the graduate students that have trodden with me the manifold aspects of dynamic AFM. Javier Tamayo, Alvaro San Paulo, and Tomás R. Rodríguez belong to the first wave of graduate students involved in theoretical simulations of cantilever dynamics. They were genuine pioneers. Nicolás F. Martínez, José R. Lozano, Christian Dietz, and Elena T. Herruzo are contributing to expand amplitude modulation AFM into the multifrequency domain. I also want to acknowledge the graduate students and postdocs who carried some of its applications. Monserrat Calleja, Marta Tello, and Ramsés Martínez performed some key experiments to materialize the potential of AFM nanolithography. Javier Martínez, Carlos Gómez, Nuria S. Losilla, Jorge R. Ramos, and Marco Chiesa have participated in several projects where the AFM played a crucial role.

I have enjoyed the friendship and the intellectual rigor of many colleagues, in particular, Carlos Bustamante, Arvind Raman, Roger Proksch, Fabio Biscarini, José M. Soler, Rubén Pérez, Ozgur Sahin, Artuto Baró, Peter Hinterdorfer, Ali Passian, Julio Gómez, and Alexis Baratoff. Ron Reifenberger made a short visit to the laboratory in 1997. His genuine appraisal of the simulations we were conducting had a considerable effect on me to keep my interest on dynamic AFM.

The type of symbols to be used or the terms selected to describe a given concept posed some unexpected challenges. The books by Robert Gomer “Field Emission and Field Ionization” and Jacob Israelachvili “Intermolecular Forces and Surface Forces” provided some examples or served as models.

Tres Cantos, SpainFebruary 25, 2010

Ricardo Garcia

Annotation List

AamplitudeAspset-point amplitudeA0free amplitudeacontact radiusa0intermolecular distanceBfrequency bandwidthdinstantaneous tip–surface distanceE, EeffYoung’s modulusEdisenergy dissipated per cycleFadadhesion forceFDMTforce as given by the DMT modelFtstip–surface forceFvdWvan der Waals forceF0external driving forceffrequencyGshear modulusggain factor in Q-controlHHamaker constanthcantilever thicknessIarea moment of inertiakforce constantkBBoltzmann constantknforce constant nth eigenmodeLcantilever lengthllateral resolutionmccantilever massmeffective massQquality factorQnquality factor nth eigenmodeR, Rttip’s radiusTperiod of the oscillationttimeVexternal voltageWcantilever widthw(x,t)deflection of a continuous cantileverzinstantaneous cantilever deflectionz0average cantilever deflectionzcaverage tip–surface distanceγeffective force damping factor, surface tensionδindentationεdielectric constant, strainneigenvalue of spatial argumentcantilever densityϕphase shift of the tip’s oscillationφphase shift in Q-controlωexcitation angular frequencyω0fundamental angular frequencyωnangular frequency of an eigenmode or higher harmonic

1

Introduction

1.1 Historical Perspective

The invention of scanning probe microscopy is considered one of the major advances in materials science since 1950 [1, 2]. Scanning probe microscopy includes a large family of microscopy methods that share two operational elements: the use of a sharp probe (tip) and the feedback mechanism. The feedback loop is characterized by keeping at a constant value the interaction parameter while the probe is scanned across the sample surface. Scanning probe microscopy started with the invention of the scanning tunneling microscope (STM) by Gerd Binnig and Heinrich Rohrer in 1982 [3, 4]. The STM works by detecting the current that flows between a metallic tip situated a few angstroms above a conductive surface when an external voltage is applied. The limitations of the STM to image poorly conducting materials such as biomolecules served as a motivation for Gerd Binnig, Calvin Quate, and Christoph Gerber to invent the atomic force microscope (AFM) in 1986 [5, 6]. The first AFM operated by measuring the static deflection of the probe. This method is called contact mode AFM. One year later Martin, Williams, and Wickramasinghe implemented the dynamic operation in force microscopy [7]. They wanted to use the AFM to measure long-range forces over a distance range of 3–15 nm. They noticed that the amplitude of the tip’s oscillation changed with the tip–surface distance. These changes were related to the gradient of the tip–surface force. At the same time, they proposed to use the amplitude in a feedback loop to get an image of the surface. Such an early start would have anticipated a sudden rise in the number of articles dealing with amplitude modulation AFM. However, it did not happen that way (). In 1987, the technique was so new that only a handful of groups could master the instrumental and conceptual challenges to design and operate a dynamic AFM [7–11].