Atomic Force Microscopy E-Book

Greg Haugstad

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 811

Veröffentlichungsjahr: 2012

Beschreibung

This book enlightens readers on the basic surface properties and distance-dependent intersurface forces one must understand to obtain even simple data from an atomic force microscope (AFM). The material becomes progressively more complex throughout the book, explaining details of calibration, physical origin of artifacts, and signal/noise limitations. Coverage spans imaging, materials property characterization, in-liquid interfacial analysis, tribology, and electromagnetic interactions. "Supplementary material for this book can be found by entering ISBN 9780470638828 on booksupport.wiley.com"

Leseprobe

Contents

Cover

Title Page

Copyright

Dedication

Preface

Acknowledgments

Chapter 1: Overview of AFM

1.1 The Essence of the Technique

1.2 Property Sensitive Imaging: Vertical Touching and Sliding Friction

1.3 Modifying a Surface with a Tip

1.4 Dynamic (or “AC” or “Tapping”) Modes: Delicate Imaging with Property Sensitivity

1.5 Force Curves Plus Mapping in Liquid

1.6 Rate, Temperature, and Humidity-Dependent Characterization

1.7 Long-Range Force Imaging Modes

1.8 Pedagogy of Chapters

References

Chapter 2: Distance-Dependent Interactions

2.1 General Analogies and Types of Forces

2.2 van der Waals and Electrostatic Forces in a Tip–Sample System

2.3 Contact Forces and Mechanical Compliance

2.4 Dynamic Probing of Distance-Dependent Forces

2.5 Other Distance-Dependent Attraction and Repulsion: Electrostatic and Molecular Forces in Air and Liquids

2.6 Rate/Time Effects

References

Chapter 3: Z-Dependent Force Measurements with AFM

3.1 Revisit Ideal Concept

3.2 Force-Z Measurement Components: Tip/Cantilever/Laser/Photodetector/Z Scanner

3.3 Physical Hysteresis

3.4 Optical Artifacts

3.5 Z Scanner/Sensor Hardware: Nonidealities

3.6 Additional Force-Curve Analysis Examples

3.7 Cantilever Spring Constant Calibration

References

Chapter 4: Topographic Imaging

4.1 Idealized Concepts

4.2 The Real World

References

Chapter 5: Probing Material Properties I: Phase Imaging

5.1 Phase Measurement as a Diagnostic of Interaction Regime and Bistability

5.2 Complications and Caveats Regarding the Phase Measurement

5.3 Energy Dissipation Interpretation of Phase: Quantitative Analysis

5.4 Virial Interpretation of Phase

5.5 Caveats and Data Analysis Strategies when Quantitatively Interpreting Phase Data

References

Chapter 6: Probing Material Properties II: Adhesive Nanomechanics and Mapping Distance-Dependent Interactions

6.1 General Concepts and Interrelationships

6.2 Adhesive Contact Mechanics Models

6.3 Capillarity, Details of Meniscus Force

6.4 Approach–Retract Curve Mapping

6.5 High-Speed/Full Site Density Force-Curve Mapping and Imaging

References

Chapter 7: Probing Material Properties III: Lateral Force Methods

7.1 Components of Lateral Force Signal

7.2 Application of Lateral Force Difference

7.3 Calibration of Lateral Force

7.4 Load-Dependent Friction

7.5 Variable Rate and Environmental Parameters in AFM Friction and Wear

7.6 Transverse Shear Microscopy (TSM) and Anisotropy of Shear Modulus

7.7 Shear Modulation Methods

References

Chapter 8: Data Post-Processing and Statistical Analysis

8.1 Preliminary Data Processing

8.2 1D Roughness Metrics

8.3 2D-Domain Analysis

8.4 “Lineshape” Fitting

References

Chapter 9: Advanced Dynamic Force Methods

9.1 Principles of Electronic Methods Utilizing Dynamic AFM

9.2 Methods Using Higher Vibrational Modes

References

Appendices

Appendix 1: Spectral Methods for Measuring the Normal Cantilever Spring Constant k

Appendix 2: Derivation of van der Waals Force–Distance Expressions

Appendix 3: Derivation of Energy Dissipation Expression, Relationship to Phase

Appendix 4: Relationships in Meniscus Geometry, Circular Approximation

References

Index

Cover image: Courtesy of the author.

Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, [phone], fax [phone], or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, [phone], fax [phone], or online at http://www.wiley.com/go/permission.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at [phone], outside the United States at [phone] or fax [phone].

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.

Library of Congress Cataloging-in-Publication Data:

Haugstad, Greg, 1963–

Atomic force microscopy : understanding basic modes and advanced applications / Greg Haugstad.

p. cm.

Includes bibliographical references.

ISBN 978-0-470-63882-8

1. Atomic force microscopy. I. Title.

QH212. A78H38 2012

620′. 5–dc23

2012003429

To Laurie

Preface

Since its invention by Binnig and coworkers in 1986 and the appearance of commercial instruments by the end of that decade, atomic force microscopy (AFM) has become an essential tool for materials and biological research. AFM is present in core facilities at all major research universities and in many single-investigator labs, and is a standard capability in central research labs at large corporations. In more recent times AFMs have been acquired by 2-year and 4-year colleges and occasionally by smaller companies. But the latter typically seek AFM services, or training for independent use in nearby facilities. In addition, there are now more opportunities for AFM demonstrations and even summer research experiences for pre-college students.

What seems almost universally lacking in the above research settings is rigorous AFM education and training. Unlike transmission electron microscopy (TEM), for example, for-credit curricular classes focusing on AFM are almost nonexistent. AFM training sessions in many core facilities are “bare bones,” as confirmed in conversations with former graduate student users (i.e., later postdocs seeking self-described “remedial” AFM training). The trainer has some AFM experience but often little, or at most narrow, expertise in research applications as well as the plethora of artifacts, caveats and other interpretive issues that one encounters with the technique. There are also training sessions provided by AFM manufacturers, mostly relevant to the initial users of a newly installed instrument; but one often finds that these training sessions are not developed around fundamental AFM understanding (e.g., of interfacial forces) and broad research experiences.

Beyond AFM training issues, too often little knowledge exchange or “vetting” of data interpretations takes place between users of core facilities at universities or central analytical labs at companies. Together with the lack of formal education, a culture of understanding of AFM may not take root at a given institution, with the exception of a few single-investigator labs (with their own AFMs) whose research critically depends on the technique. This situation again differs from the learning environment around larger (i.e., more expensive) instruments such as TEM. Historically, TEMs have been heavily used by groups that take the time to fully understand the technique, even within a core-facility setting, because principal investigators cannot purchase “their own” instruments; and core-facility user fees are often high enough to preclude “casual” users. Similarly, groups at large research facilities such as synchrotron light sources, where usage proposals undergo peer review, develop a culture of understanding that is reinforced by “elbow-to-elbow” user interactions and “live-in” conditions. Finally, the peer review of journal publications or internal review of reports using AFM can be problematic. Typically the reviewers are experts in the material, biological, or technological issues of the samples studied, rather than knowledgeable of the AFM method. Often multiple techniques are employed such that AFM results are only tersely presented as part of a package of information, and thus correspondingly are often casually reviewed.

Then there is industry. As elucidating as advanced implementations of AFM can be, they have made only a meager foray into the R&D of technological and biomedical companies (with a few exceptions). It is this author's contention that academic research—especially that which is steeped in methods—must translate into advanced technological and biomedical R&D beyond academia. (Today's harsher political climate for public funding of universities can only underscore this contention.) Yet personnel from industry relate that they have received almost no training on AFMs for which they are charged to become local “experts.” We must do better in translating volumes of AFM methods development, as published in scientific journals over a period of more than two decades, into analytical practice in industry. My observation is that a broad range of structures, properties, and phenomena in the materials technologies of industry and biomedicine beg insightful analysis with AFM. Yet the usage of AFM exhibits a troubling footprint: a diversity of in-depth and creative methodologies implemented in academia by AFM-savvy research groups (not casual users of core facilities), and relatively minimal usage in industry. It behooves academics who are hands-on active in AFM to reach out much more to industry. Collaboration and consulting are two avenues (familiar to the author), but I believe an AFM monograph also is in need: one which explains underpinning concepts and operational issues, and how these lead to advanced applications.

This monograph is intended to address the above issues associated with the use of the AFM. Its chapters target a broad audience of AFM users ranging from pre-college students and technicians to PhD-level scientists. The materials derive in part from a diversity of curricular courses, training sessions, short courses and outreach programs at the University of Minnesota:

1. on site and internet-based demonstrations for precollege students;

2. a capstone fourth-semester characterization course within a Nanoscience Technology technical college (two-year) program;

3. a lab course on structural characterization within a Materials Science 4-year university degree program (5th semester);

4. a graduate course for students in their first or second year, taken primarily by Ph.D. candidates in chemistry, materials science, physics or chemical/mechanical/electrical engineering (for whom materials characterization is essential to later thesis research);

5. training courses for researchers to use instrumentation in a core facility;

6. short courses and demonstrations on advanced methods, primarily for industrial scientists and engineers.

I have taught more than a thousand curricular students and research trainees with a broad range of educational backgrounds and at various career stages, and have taught industrial users as well as academics from numerous institutions: not only research universities but also small colleges including visiting professors and undergraduates (e.g., Research Experiences for Undergraduates programs). In teaching the AFM technique, it has struck me that the knowledge required to understand its most basic operation and the simplest data (surface topography) is well within the grasp of this entire audience, given the intuitive nature of stylus profilometry and contact forces. Conversely, many of the less intuitive and more mathematical concepts (e.g., attractive and repulsive dynamic imaging regimes, raw versus processed data, piezoscanner nonidealities) often are murky for students and trainees at many levels of education, whether pre-college, 2-yr college, 4-yr college or graduate; even to professional scientists and engineers with PhDs. Often graduate students seek AFM training only to use it in a “zeroth-order” fashion, for seemingly simple measurements of surface roughness or step height. However, one cannot reliably determine even this simple information without addressing issues associated with attractive/repulsive imaging regimes, scanner cross coupling, nonlinearity and piezocreep, along with nanoscale contact mechanics; and issues of capillarity and tip-sample adhesion. In short: even if only the “simplest” information is sought from AFM, it does not follow that the simplest understanding of the technique will enable success.

Goals in the core facility that I manage, the Characterization Facility at the University of Minnesota, are to develop instructional materials

i. with minimal mathematics leading to an enabling understanding of AFM, insofar as it impacts the measurement of basic surface characteristics (like roughness or step height);

ii. that drill down into user-selectable rigor (calibration, physical origin of artifacts, signal/noise limitations, mathematical analysis of physical responses) to open avenues for in-depth experimentation and deeper understanding.

This monograph is thus written in a hierarchical fashion, rooted in basic understandings of distance-dependent intersurface forces, but drilling down into subtopics which are located in later subsections of early chapters or in late chapters and appendices. It seems that no existing books on AFM are based on such pedagogy. Often these (mainly edited) books consist of individual chapters derived from PhD or postdoctoral research projects, and thus assume a readership that is well into research applications and savvy of the difficulties associated with the AFM method. The writers typically do not introduce the technique in a way appropriate for a newcomer, and moreover do not get into the instrument realities with which one must wrestle to achieve success. These books usually emphasize advanced applications (e.g., viscoelastic properties of polymers, nanolithography, electrochemistry, single-molecule force spectroscopy) written by different authors with very different voices. Even if early chapters cover the “basics,” there is often an assumption of a readership with in-depth knowledge of physics, interfacial science, etc.... not the typical distribution of people who show up for AFM training! And in any case there usually is little in the way of “pointers” between chapters, because each is written by a different person.

Similarly, one can download application notes from AFM vendors, each application drilling down into a subtopic but without the context of an overall treatment rooted in basic principles. Some very good review articles exist, but newer ones are either about narrower special topics or are lengthy and exhaustively focused on a single methodology (e.g., force-distance measurements). Older review articles are shorter, shallower and broader in scope, but often contain flawed or at best outdated understandings. Finally there are basic tutorials at vendor and principal-investigator web sites, but the treatment of subtopics (e.g., frictional imaging) is usually minimal and sometimes physically incorrect when examined in detail.

A question that arises in any primer on AFM is at what point to move from quasistatic “contact mode” (or the newer force-distance mapping modes) to dynamic or “AC” (a.k.a. tapping mode) AFM. The former can be intuitively understood and tip-sample forces can be simply quantified, whereas the latter cannot be understood at even a base level without the physical concepts (and mathematics) of a driven oscillator with damping and nonmonotonic force-distance relationship. For some years now I have found that a majority of users need dynamic AFM because their materials are too soft, or because nano-objects are too weakly adhered to substrate, or because residual, mobile species are present at the surface (following film growth or surface modification or extraction from a vacuum chamber), preventing “clean” images. Although most of these users seek only topographic information, height is often sought at nanometer or subnanometer precision. Therein lies a problem, because one cannot accurately measure step heights or characterize roughness on this scale without carefully stabilizing the tip-sample interaction in the net repulsive or net attractive regime under delicate interaction conditions. Understanding regime bistability is essential even for casual users, and phase measurement is necessary for identifying and controlling the regime. But in the process of examining phase images, the novice stumbles across interesting contrast and naturally asks, “what does it mean”? Thus I do not relegate this topic to the last chapter on advanced methods, nor cover it early under superficial concepts. An introductory treatment must not, at the first stages of learning, mislead the user with oversimplified concepts such as “phase is equivalent to stiffness,” which is incorrect in many cases. Nevertheless, the most mathematically rigorous understandings of dynamic AFM and phase imaging have been assigned to Chapters 5 and 9 and Appendix 3.

As already hinted, an important question for any introductory book is the degree of mathematical formalism and exactness to invoke. An AFM primer cannot shy from mathematics, because it is the language of physics; and a method with “atomic” and “force” in its very name cannot possibly be understood while avoiding physics! Yet a book should be organized so as to invoke mathematics as painlessly as possible. This book begins with an overview chapter that contains essentially no mathematics, yet introduces several advanced things that AFM can do. In the ensuing early chapters, some physical concepts are first developed with appeal to analogy (e.g., radar, tuning fork), then a bit more formally such that the reader first dips only lightly into mathematics. Then in later chapters, the book delves into greater physical/mathematical detail and rigor, presumably as the user gains experience with the technique in parallel with reading and possibly coursework. But words such as “introductory” and “lightly” should not mean incorrect. I endeavor to clarify approximations and possibly incorrect assumptions (e.g., treating tip shape as a hemisphere) during the introduction of simplified topics, rather than relegate to later sections or chapters (or cited literature) that the reader may not visit for months or years while becoming familiar with the basics and reporting results from this work ... even submitting publications! Later, the reader who pushes through all the chapters, methods, and physics hopefully will be enabled to conduct more rigorous and ambitious research, additionally aided by the references (and perhaps consulting the authors).

Throughout the book I also point out some unfortunate “realities.” One is the variegated terminology for expressing a given concept (e.g., “tapping mode” and its synonyms), as easily found in journal papers, books, digital presentations, manuals, and so on; and in some cases I comment on appropriateness. So rather than invoke a single terminology and a pedagogical strictness, I attempt to make the reader aware of the diversity of terms in the “real world.” Another reality is the prevalence of instrument shortcomings. These include (i) the “leakage” of optical interference, AC electrical signal and building vibrations into AFM data, generating variable background in images and plots; (ii) nonideal behavior in the split photodiode (central to instrument performance), resulting in misleading data trends; (iii) calibration issues arising from operation under liquid immersion; (iv) feedback oscillations due to tip contamination in dynamic AFM; and related topics. I endeavor to explain the fundamental origins of these shortcomings, and present manifestations of artifacts in real data and images, such that suggested mitigations can be better understood.

Another question involves the degree of emphasis on custom methods. I have rooted this book in what I consider to be core methods available on most research-grade commercial systems, needing no special attachments. This includes “secondary” probes like lateral force, phase in dynamic mode, X-Y mapping of force-Z curves, and interleave-based scanning (electrostatic methods). To this I have added examples of simple but useful custom methods, often requiring BNC signal breakout (commonly available on commercial AFMs for at most a small additional expense), using (1) a function generator and signal adder circuit (easy to build with an op amp and a few resistors), (2) additional lock-in amplifier (e.g., to analyze an external periodic signal such as used in shear modulation), (3) LabView computer with high-speed DAQ card running commercial virtual instruments (e.g., logger, oscilloscope, digital signal analyzer), and (4) Witec's Pulsed Force Mode because I consider it to be a hugely enabling add-on (especially the digital version), and one that dovetails with the pedagogy of force-vs-distance and intermittent contact AFM. Inexpensive function generators, lock-in amplifiers and LabView are often available even in 4-year colleges. Configuring these special measurements is a good way to reinforce a student's or technician's understanding of what is being measured and how, and what are the limitations (signal magnitude, time/frequency domain), while at the same time expanding capabilities.

A further educational tool that is missing from nearly all books on AFM is the use of digital files for the manipulation of real data and illustrating concepts. During my career as an experimental and analytical scientist, nothing has elucidated better than manipulation of numbers and seeing results rendered in graphical form. This is particularly true for AFM. I have elected to create Microscoft Excel workbooks available from the Wiley web site, given the ubiquity of this software. (Many other programs that are more advanced in graphics and curve fitting, such as Origin, MATLAB, SigmaPlot, Kaleidagraph, etc., can open Excel files.) In addition to real AFM data, I have generated several theoretical/mathematical constructs to illustrate concepts, for example Fourier decomposition of surface topography and force- distance relationships within adhesive contact mechanics models. I also incorporate usage of the freeware and open-source AFM program Gwyddion for AFM data processing/rendering.

A final, related question is the number of Scanning Probe Microscopy techniques to cover in a single book. It is worth noting that this capitalized term and its acronym, SPM, is almost unknown to the diversity of first or second-year graduate students that show up for AFM training in a core facility (at least in the US), and to the range of personnel in companies who seek AFM services from their central analytical labs or from university facilities. Yet the majority of edited books that might be useful to these users (usually at a much later date), or conference symposia and workshops of potential interest, use the acronym “SPM.” This reflects the inclusion of additional measurement modes and methods (some of which are not force based) such as scanning tunneling microscopy, conducting AFM (measuring current through tip under bias but in contact under force control), electrochemical AFM (in liquid under bias), scanning capacitance microscopy, scanning ion conductance microscopy, scanning near-field optical microscopy, piezoresponse force microscopy, and more. As already stated, this book focuses on core methods available on most research-grade commercial systems, methods requiring no special attachments, and which are force based (including force gradient), and are applicable to a broad range of material/biological systems and research questions. The reader is referred to other books on the previously listed SPM techniques.

For an industrial lab, the payback on investments into AFM systems and personnel come from the wealth of information obtained by broad-based applications of AFM to imaging, materials property characterization, in-liquid interfacial analysis, tribology, and more, by a staff spanning from technicians to PhDs. I hope that this book will aid in understanding the use of AFM in these applications, and will help different corporate laboratories to understand the various components of a complex technology (e.g., medical devices). Similarly, I hope that this book will fit the missions of research university core facilities, especially those serving a broad clientele. And of course I hope that graduate students or postdocs, whose research project benefits from a more penetrating application of AFM, will be aided by this book. Another important potential use of this book is as a textbook or supplementary reference in advanced undergraduate or graduate courses.

Greg Haugstad

July 2012

Acknowledgments

My introduction to atomic force microscopy occurred in late 1991 as a postdoc in an industry-collaborative project, with Wayne Gladfelter in the Department of Chemistry at the University of Minnesota and Mike Keyes of DuPont Medical Products in Brevard, North Carolina, in basic research relevant to medical X-ray film. Considering my then-minimal knowledge of chemistry and zero experience with AFM, silver halides and polymers (rather, a background in semiconductor physics and ultrahigh-vacuum synchrotron work), I must heartily thank these two scientists for opening the door to AFM. In a short time I fell in love with the technique and, relatedly, nanotribology and polymer/organic thin-film systems. (Some of this love derived from a love of physics, first nurtured at Gustavus Adolphus College through the teaching of Dennis Henry, Richard Fuller and John Bolkcum.) I also quickly experienced the open-endedness of AFM research within an industrial collaboration, repeated in several projects up to the present day. I am thus indebted to industrial collaborators who encouraged exploration and methods development: Libby and Rolf Weberg, Richard Jones, Andrew Avery, Ed Parsonage and Klaus Wormuth. (I further thank Klaus for valuable feedback on early partial drafts of this book.) My growth as an applied scientist/consultant, with one foot in academia and the other in industry, would not have been possible without the countless hours in discussion with these individuals. Nor would my broad interests in AFM have flourished.

I am also eager to thank several former and current PhD students for whom I have been privileged to serve as a thesis co-advisor, including Jon Hammerschmidt, Ron Schmidt, Craig Dykstra, Donna Staarup, Srini Somayajula, Kanan Puntambekar, Vivek Kalihari, Dave Ellison, Dabien Chen, Yanfei Wu, Pranav Agarwal, Govind Saraswat, Kirby Liao and Peng Li; also, postdocs Susheng Tan, Jinping Dong and Francois Ahimou, with whom it was a joy to work. Some of these research projects have contributed data and/or understandings of AFM methods contained in this book; in particular, those involving friction and wear, shear modulation, force curve mapping, transverse shear microscopy and Kelvin-probe force microscopy. In this co-advisor role I have benefitted from the collegiality and intellectual exchange with faculty collaborators Wayne Gladfelter, Mike Semmens, Paige Novak, Dan Frisbie, Raj Suryanarayanan, Ron Siegel, Tianhong Cui, Murti Salapaka, Andre Mkhoyan and Chris Macosko.

I further thank Wayne Gladfelter for championing the importance of PhD-level scientific staffing to core facilities, including roles in curricula, methods development, research (both independent and collaborative), and interaction with industry. I believe this to be a model for core facilities in a twenty-first century research university. To grow hands-on expertise in analytical techniques over a period of decades is in many respects a privilege, and a lot of fun. But it's also the right way to staff the research enterprise.

Finally I must thank my wife, for patiently awaiting returns from weekend and late-night work sessions, for allowing the author to quietly write from the passenger's seat, and for managing the home front including (among other things) sons' activities; and all the while, providing cheerful encouragement.

Greg Haugstad

Minneapolis, Minnesota

Chapter 1

Overview of AFM

1.1 The Essence of the Technique

Atomic force microscopy or AFM is a method to see the shape of a surface in three-dimensional (3D) detail down to the nanometer scale [1,2]. AFM can image all materials—hard or soft, synthetic or natural (including biological structures such as cells and biomolecules)—irrespective of opaqueness or conductivity. The sample is usually imaged in air, but can be in liquid environments and in some cases under vacuum. The surface morphology is not perceived in the usual way, that is, by line-of-sight, reflections, or shadows.1 Rather, at each point or pixel within a 2D array over the surface, a measurement of surface height is made using a sharp solid force probe. One could thus say that AFM is “blind microscopy”; it essentially uses touch to image a surface, unlike light or electron microscopes. The force probe may move over a stationary sample or remain stationary as the sample is moved under the probe, as discussed in Chapter 4. Typically, one chooses to display the height measurements as colors or tints, some variant of dark-is-low/bright-is-high, with a gradient of color or grayscale in between. Thus, an image of surface topography is obtained for viewing purposes, as exemplified in Figure 1.1, for several surfaces relevant to hard and soft materials science, nanotechnology, and biology. The typical range of these measurements is several micrometers vertically with subnanometer height resolution and several tens of micrometers laterally, ranging up to ~100 μm, with a highest lateral resolution of ~1 nm (when not limited by the pixel density of the image, i.e., physical resolution as opposed to digital resolution).

Figure 1.1 In-air surface topography images of (a) silver rods (15-nm tall) grown from a AgBr(111) surface by photoreduction, 5 × 5 μm [3]; (b) gold and aluminum lines (~50-nm tall) lithographically created on silicon, 25 × 25 μm; (c) surface of a ~1-μm thick polymer film (deepest valleys ~100 nm) of a 75:25 blend of butyl and lauryl methacrylates (spin coated onto a silicon wafer), 8 × 8 μm; (d) wastewater bacterium (170-nm tall) on filtration membrane, 3 × 3 μm [4].

Given that the image is constructed from height numbers, one also can measure peak-to-valley distances, compute standard deviations of height, compile the distribution of heights or slopes of hills..., and even Fourier-analyze a surface to identify periodic components (ripples or lattices) or dominant length scales (akin to a scattering technique). These metrics of topography can be relevant to technological performance or biological function, whether in microelectronics (e.g., roughness of layers or grain size, in deposition processes), tribology (e.g., friction and wear on hard disk read heads), polymer–drug coatings (e.g., surface contour area impacting drug release rate), intrabody medical devices (e.g., shape of surface in contact with cells, tissues), cellular membranes and surface components (e.g., phospholipid bilayer, protein receptors), and much more.

As a bonus, with real height numbers in hand, one can render images in 3D perspective. The example in Figure 1.2 is an image of the dividing bacterium rendered in 2D in Figure 1.1d. Computer-simulated light reflections and shadows are incorporated to give the sense of a macroscale object and to enhance the perception of texture, even though the features may be nanoscale (i.e., below the resolution of real light microscopes). The angle of simulated illumination as well as the angle of “view” can be adjusted. The vertical scale has been exaggerated; the height of the bacterium is 180 nm, but is made to appear almost twice that high in comparison to the lateral scale. This is typical; often 3D-rendered AFM images exaggerate height by an even greater factor to bring out features for viewing.2

Figure 1.2 Wastewater bacterium (170-nm tall) on filtration membrane, 3 × 3 μm.

A bacterium, or for that matter anything hundreds of nanometers tall, is in fact a large object for AFM. With AFM's high precision, one can measure molecular or atomic crystal structures and indeed image striking, meandering steps. Figure 1.3 contains an image of five terraces on a surface of single crystal SrTiO3, in ambient air. The steps between terraces comprise a “staircase” of increasing brightness from top right to bottom left. Also shown is a histogram representation or population of heights in the image: the number of pixels counted within narrow increments or “bins” of height (further discussed in Chapter 4), with the height scale increasing from left to right. One sees five well-resolved histogram peaks, spaced by 4 Å between adjacent peaks, the signature step size between adjacent (100) planes of SrTiO. The area under each peak—the total count of pixels—quantifies the relative surface area of each terrace within the imaged region. The shapes of step contours and extent of terraces are interesting for many reasons; for example, these may provide information on the and by which steps and terraces form during material growth processes [5].