Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy

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Scanning Probe Microscopy of Functional Materials

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Sergei V. Kalinin • Alexei Gruverman Editors

Scanning Probe Microscopy of Functional Materials Nanoscale Imaging and Spectroscopy

Editors Sergei V. Kalinin The Center for Nanophase Materials Sciences and Technology Division Oak Ridge National Laboratory 1 Bethel Valley Road 37831 Oak Ridge Tennessee USA [email protected]

Alexei Gruverman University of Nebraska - Lincoln Department of Materials Science and Engineering Department of Physics & Astronomy 202 Ferguson Hall 7 920 68588 Lincoln Nebraska USA [email protected]

ISBN 978-1-4419-6567-7 e-ISBN 978-1-4419-7167-8 DOI 10.1007/978-1-4419-7167-8 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010938721 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Scanning probe microscopy (SPM) has become a mainstream technique of nanoscience and nanotechnology by providing easy to use methodology for noninvasive imaging and manipulation on the nanometer and atomic scales. Beyond topographic imaging, SPM techniques have found an extremely broad range of applications in probing electrical, magnetic, optical and mechanical properties – often at the level of several tens of nanometers [1, 2], opening the way to an understanding material functionality and interactions at their fundamental length scales [3]. For more than a decade after the introduction of the first commercial microscopes in late 1980s, SPM evolved as a primarily qualitative imaging method. The surface topographic and functional (e.g., magnetic, electrostatic, or mechanical) images were acquired in parallel and were interpreted by an observer. A common feature for these measurements was that only a single or a small number of parameters describing the local properties were obtained; furthermore, information contained in complementary images was usually ignored (or interpreted solely within the limits of a cursory examination). These limitations stemmed primarily from the inherent limits of data processing electronics available at the time, the dearth of well-characterized probes, relative novelty of the field, and only a small number of available microscopic platforms. Nevertheless, even qualitative imaging capabilities have provided multiple opportunities in research for almost a decade. Ironically, this multitude of research opportunities has somewhat shifted the focus of research and development away from further technological advances in SPM. In contrast, the last several years have seen tremendous progress in force-based SPMs. The emergence of digital control and field-programmable gate array electronics have greatly increased the data acquisition and processing speed, allowing multiple information channels to be acquired without compromising image acquisition speed or quality. Similarly, recent advances in the theoretical understanding of contrast mechanisms in SPM and increasing market competition have lead to the rapid emergence of multimodal and spectroscopic SPM methods, including dual excitation frequency SPM (Asylum) [4–6], HarmoniX (Veeco) [7, 8], and configurable multiple frequency lock-ins by Agilent [9] and Nanonis [10]. This progress in fast data acquisition electronics and signal processing in SPM has allowed multiple information channels to be collected in the 1–10 ms range of a single pixel. This development in turn enabled several families of rapid multimodal and spectroscopic v

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imaging SPM techniques. Examples include band excitation [11] and digital lock-in [12] SPM, which allow rapid sampling of a response–frequency curve at each location on a surface, switching spectroscopy PFM [13] for mapping the ferroelectric behavior, rapid force–volume imaging [14] modes ushered in by small (high frequency) cantilever technology, torsional resonance imaging for mechanical property characterization [7], and many others. Advances in ultra-stable STM platforms resulted in a resurgence of STM-based spectroscopic methods, such as continuous imaging tunneling spectroscopy (CITS), dI/dV (density of states), dI/dz (work function), and d2I/dv2 (vibrational) imaging [15]. It is not an exaggeration to say that most of the recent advances in nanoscale science and condensed matter physics have been linked to the development of particular spectroscopic imaging modes – including imaging high-temperature superconductivity by Davies [16] and Yazdani [17], optically assisted SPM introduced by Ho [18], mechanical HarmoniX imaging introduced by Sahin [7, 8], and many others. In parallel with these instrumental developments, significant progress was achieved in development of SPM methods that combine novel experimental modalities, including thermal and mass-spectrometry assisted methods, novel electrical characterization modes, and combinations between SPM and beam techniques including focused X-ray and electron microscopy. Common to all of these methods is the acquisition of complex multidimensional data sets, typically comprised local spectroscopic responses of materials to external stimuli, or multiple parallel channels of information. At the same time, this allows not only the visualization of the structure of surfaces on the nanometer scale, but also insight into their functionalities. In this book, we aim to provide an overview of several notable recent developments in the field of functional SPM enabled by the advances in sample preparation and platform development, ultra-high resolution imaging, novel combined imaging modes, signal detection, data interpretation, and novel dynamic modes. In Chap. 1, Maksymovych delineates the applications of scanning tunneling microscopy and spectroscopy for probing chemical processes on a single-molecule level. While applications of STM for imaging surface structures on the molecular and atomic level has become common, he illustrates how STM can provide insight into chemical functionality of molecular systems. These range from tip-induced surface chemical reactions including long-range hot-electron induced phenomena to time spectroscopies of single molecule transformations to the minute details of the vibrational spectra probed by inelastic electron spectroscopy. High-resolution studies of biological functionality are addressed in the contribution by Malkin and Plomp (Chap. 2). Creatively combining the insights from the crystallization theory and high resolution atomic force microscopy imaging, the authors demonstrate that the molecular structure of the biological objects such as bacterial spores and viruses contains a wealth of information on their functionality and life cycle. Beyond providing a highly illuminating and often spectacular view of microscopic structure of these systems, these studies can be used to identify individual strains of bacterial systems, and establish their developmental pathways in response to changes in environment, chemical stimulants, and therapeutics.

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The recent advances in spectroscopic and multimodal SPMs enabled by novel data acquisition and analysis methods are summarized in Chaps. 3–6. Holscher et al. provide an in-depth description of dynamic force spectroscopy and microscopy in ambient conditions. Based on the precise measurements of the dynamic response of the cantilever, the complete force–distance curve and associated mechanical functionalities can be extracted. This topic is further developed in the contribution by Hurley (Chap. 4) who discusses probing mechanical functionality on the nanoscale, including mechanical properties and adhesive behavior, using Atomic Force Acoustic Microscopy-based methods. The signal formation mechanisms, detailed data interpretation, and multiple experimental examples are discussed. The new paradigm in dynamic SPMs – multiple frequency methods – is discussed in Chap. 5 by Proksch. While the classical SPMs utilize purely sinusoidal excitation signals corresponding to a single frequency in the Fourier domain, the use of multiple excitation and detection frequencies allows systematic mapping of frequency dispersion of the signal. Strategies for nanoscale mapping of dissipative interactions via multifrequency detection are discussed in detail. Finally, in Chap. 6 Sahin describes the tensional resonance method for probing dynamic mechanical properties. Utilizing decoupling between the flexural and torsional oscillation modes and difference in the corresponding resonant frequencies, the dynamic probing of the force–distance curve at each spatial pixel is possible. This approach is demonstrated for multiple applications, including phase transitions in polymers and high-resolution imaging of biological systems. The contribution by Ovchinnikova in Chap. 7 discusses in depth the rapidly emerging chemical imaging methods based on the combination of SPM and mass-spectrometry. While SPM is renowned for high spatial resolution, the amount of chemical information is typically limited. At the same time, modern massspectrometry methods provide ultimate information on the chemical structure of complex biological and pharmaceutical systems, often using minute amounts of material. The SPM-MS approach combines local thermal or optical excitation directed by an SPM tip, with subsequent pick-up of locally emitted products by the mass spectrometer, thus allowing local chemical identification. Critical for broad implementation of this approach is mass spectrometry at atmospheric pressures, and these methods are reviewed in detail. SPM methods for probing thermal phase transitions locally are summarized in the contribution by Nikiforov and Proksch (Chap. 8). Recent advances in SPM tip fabrication lead to the development of heated SPM probes with high heating– cooling rates. These probes enable a broad spectrum of thermal imaging methods. In one approach, the SPM tip concentrates the thermal field within the material, while the resulting surface deformation is detected by SPM electronics. The onset of melting transition below the probe results in probe penetration in the material, allowing the transition temperature to be identified. The combination of periodic heating and dynamic driving modes allows mapping of the glass transition temperatures as well. Beyond thermomechanical effects, these methods can be extended to probing local sample temperatures and heat conductivity, suggesting broad applicability for high-energy density material sand devices.

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The applications of SPM methods to probing electrical and electromechanical functionalities are discussed at length in Chaps. 9–13. In Chap. 9, Magonov et al. extend multiple frequency SPM to in-depth quantitative studies of electrical properties of semiconductors, ferroelectrics and self-assembled monolayers. Along with the overview of Kelvin Probe Force Microscopy and Electric Force Microscopy applications they discuss how frequency modulation realized in these modes can overcome uncertainties related to various mechanisms of response signal formation and improve spatial resolution in functional imaging. The contribution by Tian et al. (Chap. 10) describes the quantitative measurements of ferroelectric polarization distribution on the nanoscale by piezoresponse force microscopy (PFM). The force-based SPM signals scale linearly with tip-surface contact area resulting in a dearth of quantitative measurement capabilities in the range from molecular to mesoscopic (~100 nm) length scale. At the same time, the electromechanical signal in continuous approximation does not depend on the contact radius, enabling quantitative measurements of ferroelectric properties in the PFM mode. Using finite element simulation of the electric and elastic fields for various tip-sample interaction models, Tian et al. show that the real domain wall thickness can be extracted from experimental PFM line profiles across domain walls. This topic of PFM characterization of ferroelectrics is further developed by Huey and Nath in Chap. 11, who systematize a broad range of experimental studies of domain switching dynamics in ferroelectric thin films. By introducing high speed PFM, the rapid mapping of instantaneous domain patterns is possible at a rate of at least 100 times over standard PFM imaging. This is one of the most promising approaches in overcoming the PFM limitation in revealing the parameters of nucleation and fast domain wall motion as the basic mechanisms of polarization reversal in ferroelectric-based devices (notably ferroelectric memories) and understanding the role of structural defects in the thermodynamics of ferroelectric switching. The polar structure and polarization dynamics in relaxor ferroelectrics, one of the most mysterious classes of ferroic materials, are discussed in Chap. 12 by Shvartsman et al. The nanoscale ferroelectric ordering in relaxors presents a significant exploratory challenge but at the same time makes them the textbook example materials for demonstrating the superior capabilities of PFM in discerning the relationship between the polar structure and the unconventional dielectric properties. A detailed review of the PFM studies of several important groups of relaxors is presented highlighting experimental observation of temperature-induced transformation between ferroelectric and relaxor states. In Chap. 13, Ruediger reviews a complex problem of PFM image interpretation stemming from the tensorial nature of the electromechanical response, asymmetry in the local field distribution due to the sample defect structure or tip shape, surface modification and cantilever mechanics. Understanding these contributions allows one to avoid image misinterpretation and identify imaging artifacts while providing additional means for structural and electrical characterization of electronic materials.

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The novel functional SPM methods are discussed in Chaps. 14–17. In Chap. 14, Rose et al. discuss the perspectives of combined STM-focused X-ray measurements. The X-ray methods have evolved to provide in-depth information on the crystallographic structures and chemical identity of the surfaces, often with extremely high temporal resolution. However, spatial resolution is limited to several tens of nanometers. At the same time, STM-based methods routinely yield atomic spatial resolution, but are limited by 10–100 kHz bandwidth of amplifiers and are limited in chemical sensitivity. The potential for X-ray-STM combination and corresponding operational mechanism are discussed. The scanning ion conductance microscopy and its application for mapping surface structures and biological systems are discussed in detail by Rheinlander and Schäffer in Chap. 15. This method allows mapping ionic flows through the microcapillary and is ideally suited for studying the biological and electrochemical systems. This topic is further extended by Beyder and Sachs (Chap. 16), who describe the techniques that combine classical patch-clamp and AFM methods to probe electrophysiological properties on the cellular and subcellular levels. The contribution by Rodriguez et al. (Chap. 17) discusses in detail the novel problems that appear in the context of analysis of the multicomponent spectral data, and illustrates their applications for the voltage and time spectroscopies in PFM. The direct functional fits methods are discussed and compared with multivariate statistical methods including principal component analysis and correlation function analysis. Finally, the contribution by Gruverman (Chap. 18) reviews recent advances in probing and understanding polarization dynamics in ferroelectric capacitors. Although the PFM capability to detect the polarization state through the top electrode allows for direct studies of the dynamics of domain structure under the uniform field conditions, a major limitation was low time resolution. Discussion of the approach to extend the PFM studies into the 100 ns range is presented. The role of inhomogeneous domain nucleation and measurements of the switching parameters in conjunction with microstructural and scaling effects is discussed. Taken together, this book aims to give a prospective of new directions in functional SPM imaging. Many of the applications described in the book have appeared only in the last several years, and the future will undoubtedly see the emergence of a number of SPM modes for addressing materials functionality at the nanoscale. Sergei V. Kalinin Alexei Gruverman

References 1. E. Meyer, H.J. Hug, R. Bennewitz, Scanning Probe Microscopy: The Lab on a Tip (Springer, 2003) 2. S.V. Kalinin, A. Gruverman (eds.), Scanning Probe Microscopy: Electrical and Electromechanical Phenomena at the Nanoscale (Springer, 2006) 3. C. Gerber, H.P. Lang, Nat. Nanotechnol. 1, 3 (2006)

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4. R. Proksch, Appl. Phys. Lett. 89, 113121 (2006) 5. B.J. Rodriguez, C. Callahan, S.V. Kalinin, R. Proksch, Nanotechnol. 18, 475504 (2007) 6. http://www.asylumresearch.com 7. O. Sahin, S. Magonov, C. Su, C.F. Quate, O. Solgaard, Nat. Nanotechnol. 2, 507 (2007) 8. http://www.veeco.com 9. http://nano.tm.agilent.com/index.cgi?CONTENT_ID=253 10. http://www.nanonis.com 11. S. Jesse, S.V. Kalinin, R. Proksch, A.P. Baddorf, B.J. Rodriguez, Nanotechnol. 18, 435503 (2007) 12. A.B. Kos, D.C. Hurley, Meas. Sci. Technol. 19, 015504 (2008) 13. S. Jesse, B.J. Rodriguez, S. Choudhury, A.P. Baddorf, I. Vrejoiu, D. Hesse, M. Alexe, E.A. Eliseev, A.N. Morozovska, J. Zhang, L.Q. Chen, S.V. Kalinin, Nat. Mater. 7, 209 (2008) 14. D.A. Bonnell (ed.), Scanning Probe Microscopy and Spectroscopy: Theory, Techniques, and Applications (Wiley-VCH, 2008) 15. J.A. Stroscio, W.J. Kaiser (eds.), Scanning Tunneling Microscopy (Academic, Boston, 1993) 16. K. McElroy, R.W. Simmonds, J.E. Hoffman, D.H. Lee, J. Orenstein, H. Eisaki, S. Uchida, J.C. Davis, Nat. 422, 592 (2003) 17. K.K. Gomes, A.N. Pasupathy, A. Pushp, S. Ono, Y. Ando, A. Yazdani, Nature 447, 569 (2007) 18. S.W. Wu, N. Ogawa, W. Ho, Sci. 312, 1362 (2006)

Contents

Part I Spectroscopic SPM at the Resolution Limits 1 Excitation and Mechanisms of Single Molecule Reactions in Scanning Tunneling Microscopy.......................................................... Peter Maksymovych 2 High-Resolution Architecture and Structural Dynamics of Microbial and Cellular Systems: Insights from in Vitro Atomic Force Microscopy.......................................................................... Alexander J. Malkin and Marco Plomp

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Part II Dynamic Spectroscopic SPM 3 Dynamic Force Microscopy and Spectroscopy in Ambient Conditions: Theory and Applications.................................. Hendrik Hölscher, Jan-Erik Schmutz, and Udo D. Schwarz

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4 Measuring Mechanical Properties on the Nanoscale with Contact Resonance Force Microscopy Methods............................. D.C. Hurley

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5 Multi-Frequency Atomic Force Microscopy .......................................... 125 Roger Proksch 6 Dynamic Nanomechanical Characterization Using Multiple-Frequency Method.......................................................... 153 Ozgar Sahin Part III Thermal Characterization by SPM 7 Toward Nanoscale Chemical Imaging: The Intersection of Scanning Probe Microscopy and Mass Spectrometry........................ 181 Olga S. Ovchinnikova xi

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8 Dynamic SPM Methods for Local Analysis of Thermo-Mechanical Properties.......................................................... 199 M.P. Nikiforov and R. Proksch Part IV Electrical and Electromechanical SPM 9 Advancing Characterization of Materials with Atomic Force Microscopy-Based Electric Techniques.................................................. 233 Sergei Magonov, John Alexander, and Shijie Wu 10 Quantitative Piezoresponse Force Microscopy: Calibrated Experiments, Analytical Theory and Finite Element Modeling.......... 301 Lili Tian, Vasudeva Rao Aravind, and Venkatraman Gopalan 11 High-Speed Piezo Force Microscopy: Novel Observations of Ferroelectric Domain Poling, Nucleation, and Growth . ................. 329 Bryan D. Huey and Ramesh Nath 12 Polar Structures in Relaxors by Piezoresponse Force Microscopy..... 345 V.V. Shvartsman, W. Kleemann, D.A. Kiselev, I.K. Bdikin, and A.L. Kholkin 13 Symmetries in Piezoresponse Force Microscopy................................... 385 Andreas Ruediger Part V Novel SPM Concepts 14 New Capabilities at the Interface of X-Rays and Scanning Tunneling Microscopy..................................................... 405 Volker Rose, John W. Freeland, and Stephen K. Streiffer 15 Scanning Ion Conductance Microscopy................................................. 433 Johannes Rheinlaender and Tilman E. Schäffer 16 Combined Voltage-Clamp and Atomic Force Microscope for the Study of Membrane Electromechanics...................................... 461 Arthur Beyder and Frederick Sachs 17 Dynamic and Spectroscopic Modes and Multivariate Data Analysis in Piezoresponse Force Microscopy............................... 491 B.J. Rodriguez, S.Jesse, K. Seal, N. Balke, S.V. Kalinin, and R. Proksch

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18 Polarization Behavior in Thin Film Ferroelectric Capacitors at the Nanoscale.................................................................... 529 A. Gruverman Index.................................................................................................................. 541

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Contributors

John Alexander Agilent Technologies, 4330 W. Chandler Blvd., Chandler, AZ 85226, USA Vasudeva Rao Aravind Materials Science and Engineering, Pennsylvania State University, University Park, PA 16803, USA; Clarion University of Pennsylvania, Clarion, PA 16214, USA N. Balke Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA I.K. Bdikin Depto de Engenharia Cerâmica e do Vidro, CICECO, Universidade de Aveiro, 3810-193 Aveiro, Portugal Arthur Beyder Department of Medicine, Mayo Clinic, 200 First Street SW, Rochester, MN 55905, USA [email protected] John W. Freeland Advanced Photon Source Argonne National Laboratory, Argonne, IL 60439, USA Venkatraman Gopalan Materials Science and Engineering, Pennsylvania State University, University Park, PA 16803, USA [email protected] A. Gruverman Department of Physics and Astronomy, University of Nebraska, Lincoln, NE 68588-0111, USA [email protected] Hendrik Hölscher Institute for Microstructure Technology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany [email protected]

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Bryan D. Huey Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA [email protected] D.C. Hurley National Institute of Standards & Technology, 325 Broadway, Boulder, CO 80305, USA [email protected] S. Jesse Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA S.V. Kalinin The Center for Nanophase Materials Sciences and Technology Division, Oak Ridge National Laboratory, 1 Bethel Valley Road, 37831 Oak Ridge, Tennessee USA A.L. Kholkin Center for Research in Ceramic and Composite Materias (CICECO) & DECV, University of Aveiro, 3810-193, Aveiro, Portugal [email protected] D.A. Kiselev Depto de Engenharia Cerâmica e do Vidro, CICECO, Universidade de Aveiro, 3810-193 Aveiro, Portugal W. Kleemann Angewandte Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany Sergei Magonov Agilent Technologies, 4330 W. Chandler Blvd., Chandler, AZ 85226, USA [email protected] Peter Maksymovych Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA [email protected] Alexander J. Malkin Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA [email protected] Ramesh Nath Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA M.P. Nikiforov Oak Ridge National Laboratory (ORNL), Oak Ridge, TN 37831, USA [email protected]

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Olga S. Ovchinnikova Department of Physics and Astronomy, University of Tennessee, Knoxville 401 Nielsen Physics Building, 1408 Circle Drive, Knoxville, TN 37996-1200 [email protected] Marco Plomp Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA [email protected] Roger Proksch Asylum Research, Santa Barbara, CA 93117, USA [email protected] Johannes Rheinlaender Institute of Applied Physics, University of Erlangen-Nuremberg, Staudtstr. 7, Bldg. A3, 91058 Erlangen, Germany B.J. Rodriguez University College Dublin, Belfield, Dublin 4, Ireland [email protected] Volker Rose Advanced Photon Source Argonne National Laboratory, Argonne, IL 60439, USA [email protected] Andreas Ruediger Laboratory of Ferroelectric Nanoelectronics, Institut National de la Recherche Scientifique, Université du Québec, 1650, Blvd. Lionel-Boulet, Varennes, Canada J3X 1S2 [email protected] Frederick Sachs Center for Single Molecule Biophysics, Physiology and Biophysical Sciences, 301 Cary Hall, University at Buffalo, State University of New York, Buffalo, NY 14214, USA Ozgur Sahin The Rowland Institute at Harvard, Cambridge, MA, USA [email protected] Tilman E. Schäffer Institute of Applied Physics, University of Erlangen-Nuremberg, Staudtstr. 7, Bldg. A3, 91058 Erlangen, Germany [email protected] Jan-Erik Schmutz Center for Nanotechnology (CeNTech) and Physikalisches Institut, University of Münster, Heisenbergstr. 11, 48149 Münster, Germany

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Udo D. Schwarz Department of Mechanical Engineering, Yale University, New Haven, CT, USA K. Seal Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA V.V. Shvartsman Angewandte Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany Stephen K. Streiffer Argonne National Laboratory, Center for Nanoscale Materials, Argonne, IL 60439, USA Lili Tian Materials Science and Engineering, Pennsylvania State University, University Park, PA, 16803, USA Shijie Wu Agilent Technologies, 4330 W. Chandler Blvd., Chandler, AZ 85226, USA

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Part I

Spectroscopic SPM at the Resolution Limits

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Chapter 1

Excitation and Mechanisms of Single Molecule Reactions in Scanning Tunneling Microscopy Peter Maksymovych

Introduction Scanning tunneling microscopy (STM) achieves atomic-scale resolution due to the exponential dependence of the tunneling current on the distance from the tip to the surface. The majority of tunneling electrons traverse the junction elastically via coherent quantum mechanical coupling between the electronic states of the tip and the conducting substrate. However, a small fraction of tunneling electrons undergoes inelastic scattering, losing parts of their energy to available dynamic modes in the junction with the energy that is less or equal to the electrochemical potential of one of the tunneling leads relative to the Fermi level of the other. Depending on the atomic electronic structure of the tunneling junction and the tunneling conditions, the excited processes may include localized plasmons with subsequent photon emission [1–4], frustrated [5] and free [6] adsorbate motion, formation of charged species [7], molecular fluorescence [8], rotation [9], vibration [10], bond breaking [11, 12], and isomerization [13, 14]. The STM can therefore glimpse far beyond the local electronic structure of the junction and it has been extensively used to explore the dynamic functionality of surfaces, nanoparticles, and single molecules. This chapter will address a subset of such studies, focused on the electroninduced excitation of one or several chemical bonds of molecules located in close proximity of the STM tunnel junction. Such localized chemical reactions have been used to understand the fundamental aspects of molecule surface and intermolecular chemical interaction, manipulate single molecules or molecular aggregates to construct artificial nanostructures with new chemical or electronic properties, and control molecule-surface electronic coupling. Representative examples of such studies are shown in Fig. 1.1. Despite the striking diversity of the observed phenomena, the elementary processes initiating the motion of the molecule along the

P. Maksymovych (*) Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA e-mail: [email protected] S.V. Kalinin and A. Gruverman (eds.), Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy, DOI 10.1007/978-1-4419-7167-8_1, © Springer Science+Business Media, LLC 2010

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Fig. 1.1 (a) Linked-chevron arrangement of CO molecules assembled on Cu(111) surface using STM-tip-induced manipulation at T < 10 K (image size: 1.7 × 3.4 nm2). Blue (red ) dots mark the positions of the surface lattice atoms (CO molecules). Shifting of one molecule as shown by the green arrow triggers spontaneous cascade motion of CO molecules (blue arrows) along the assembled arrangement, until all the chevrons have decayed forming the structure in B. CO cascades were assembled into logic circuits, such as AND and OR gates (reproduced with permission from Heinrich et al. Science 298 (2002) 5597. Copyright (2002) by the American Association for the Advancement of Science. (b) Local manipulation of Kondo resonance by STM-tip-assisted attachment of single CO molecules to a Co atom on the Cu(100) surface. Models, STM topographies, and STS spectra in the center of the Co adatoms and complexes under investigation: (a) Co-adatom, (b) Co(CO)2, (c) Co(CO)3, (d) Co(CO)4. Models and topographies in (a)–(d) drawn to the same scale. The solid lines in the spectra are fits of a Fano function (redrawn with permission from Wahl et al. Phys. Rev. Lett. 95 (2005) 166601). Copyright (2005) by the American Physical Society. (c) Picometer-scale control of single-molecule dynamics. The image is STM topography of a biphenyl molecule on Si(100) surface (2 × 2 nm2, VS = –2 V, I = 0.56 nA). The tunnel current during the surface voltage pulse (VS = –2.5 V, duration 10 s) is shown for three different STM tip positions, P1, P2, and P3. Each step in the current trace corresponds to a single rotation of the molecules on the surface. Simply moving the tip between the three positions was found to change the rate of rotation by two orders of magnitude (reproduced with permission from Lastapis et al. Science 308 (2005) 1000) Copyright (2005) by the American Association for the Advancement of Science

1 Excitation and Mechanisms of Single Molecule Reactions

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reaction coordinate (RC) can be traced to a direct excitation of the RC mode by coherent [15] or incoherent [16] vibrational ladder climbing and an indirect excitation through anharmonic coupling to a mode excited by tunneling electrons [17]. Localized chemical reactions are therefore closely related to vibrational excitation of molecular bonds, which form the basis of inelastic electron tunneling spectroscopy (IETS). Inelastic spectroscopy has been successfully used for chemical identification of single adsorbed molecules and reaction products [18] and isotope purification on the nanoscale [19]. Conversely, the so-called action spectroscopy of single-molecule reactions [10] can provide additional information to what is directly accessible by IETS, as we will discuss later in the chapter. Several extensive reviews can be found in the literature that have highlighted the historic aspects of single-molecule chemistry and many examples of the kinds of reaction that can be induced and measured in the tunneling microscope [11, 12, 20]. Our goal here is to focus on the experimental approach to the measurement of the reaction rates and excitation thresholds, highlight the recent theoretical efforts to understand the mechanism of single-molecule reactions, and discuss emerging experiments on the collective reactivity in molecular complexes self-assembled on a surface.

Measurement of Single-Molecule Reactions The STM is usually operated in a constant current mode, where the resistance of the tunneling junction is maintained constant as the tip scans across the surface. To carry out a single-molecule chemical reaction, the tip is placed roughly on top of the feature that corresponds to an adsorbed molecule and the feedback loop is opened so as to maintain a roughly constant tip-molecule separation. The reaction is induced by increasing the tip bias which also leads to the increase of the tunneling current. After a certain time delay, the current abruptly drops or increases to a different constant value (Fig. 1.2). Once the voltage pulse ends, the feedback is reengaged. The rescan of the same area after the excitation pulse may reveal that the molecule has diffused, rotated, changed conformation, split into several other species, or desorbed. The procedure is thus very simple allowing thorough statistics to be derived from hundreds and even thousands of individual reaction events. Identifying the reaction products is not a straightforward problem, but it can often be solved from a careful inspection of the respective STM images (their shape, symmetry, orientation, and position relative to the underlying surface lattice), directly by applying conventional chemistry rules (law of mass conservation and knowledge about possible reaction scenarios) or through a direct measurement of the vibrational modes in the reaction products [10, 18]. For example, the author has done several experiments with electron-induced reactions of dimethyldisulfide (CH3SSCH3) molecule adsorbed on Au(111) [21, 22], shown in Fig. 1.2a, b. Electron excitation can in principle dissociate either a C–S, C–H, or an S–S bond in the molecule. However, the reaction products are always two identical species (Fig. 1.2b). This would be the case only upon rupturing of the S–S bond that produces two equivalent CH3S fragments. Curiously, the reaction itself is very likely initiated through the vibrational excitation of the C–H bond (which was confirmed

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Fig. 1.2 STM images (4.8 × 5.2 nm2, U = –40 mV, I = 20 pA) of CH3SSCH3 molecules adsorbed on Au(111) surface before (a) and after (b) electron-induced dissociation of the S–S bond by a 1–s current pulse at 1.0 V. The reaction products are two identical CH3S fragments. CO molecules co-adsorbed with CH3SSCH3 molecules have been used as markers of gold surface lattice atoms, allowing to identify the adsorption sites of the reactant molecules and product species on the surface (when combined with DFT calculations). Reproduced with permission from [P. Maksymovych, D. C. Sorescu and J. T. Yates, Jr. J. Phys. Chem. B 110 (2006) 21161]. Copyright (2006) by the American Chemical Society. [21]. (c) Seven consecutive traces of tunneling current acquired during electron-induced dissociation of CH3SSCH3 molecules on Au(100) surface. The abrupt drop of current marks the instant of the dissociation event, while Dt is the excitation time (Maksymovych, unpublished)

for a similar reaction on Cu(111) [10]), while the subsequent dissociation of the S–S bond occurs through the anharmonic coupling between two modes. Singlemolecule reactions are subject to detailed kinetic measurements, which can collectively reveal excitation mechanism with quantitative assignment of vibrational and electronic excitations leading to the reaction. One can measure the electron kinetics, rate constant, and energy threshold of the reaction.

Excitation Rate To overcome a potential barrier along the RC, the molecule needs to possess sufficient potential energy placed in the correct vibrational or electronic (or both) state. Once excited, a single molecule reacts on timescales that are comparable with the vibrational relaxation time of an adsorbate, on the order of 1–100 ps [23, 24]. This is at least nine orders of magnitude faster than the time resolution of even the best STM setups, which are typically bandwidth limited by the parasitic capacitance of conventional transresistance current preamplifiers to 1.3 V) [32] and methanethiol (>2.5 V) on Au(111) [69] and aromatic thiols on Cu(111) [70], localized reactions of aromatic halides on Si(111) [71], reversible displacement of a Sn ion through an adsorbed phthalocyanine molecule [72], isomerization of azobenzene on Au(111) [73], and others. The processes underlying these higher energy reactions, schematically shown in Fig. 1.6, can be traced to (1) electron or hole attachment to the molecular orbital above (below) Fermi level, (2) electron–hole pair attachment to a molecule decoupled from the metal substrate, and (3) formation of an excited molecular state, where an electron is excited from HOMO to LUMO state by inelastic scattering of tunneling electrons. These mechanisms can be differentiated to a certain degree by the polarity dependence of the reaction efficiency. Electron or hole attachment is a strongly unipolar process, Fig. 1.6a, b, determined by the position of the respective orbital relative to the Fermi level, and it will therefore exhibit strong bias dependence of the reaction rate. For example, in the author’s studies, the onset of dimethyldisulfide dissociation on Au(111) had a positive bias threshold at ~1.3 V and no observable reaction up to –2.0 V.


13

Fig. 1.6 Mechanisms of inelastic excitation in the tunneling junction beyond vibrational heating: (a) electron attachment; (b) hole attachment; (c, d) electronic transitions; (e, f ) electron–hole pair attachment. The latter two mechanisms may occur if the participant electronic states are decoupled from a substrate by a thin insulating layer (oxide, NaCl) (reproduced with permission from Mayne et al. [20])

This roughly agrees with the simple estimate for the position of the LUMO as the difference of the metal’s work function [j, 5.1 eV for Au(111)], vertical affinity of the adsorbate (EA, 1.7 eV for dimethyldisulfide [74]), and image charge interaction energy, ϕ − EA − e2 / 4 Z . The image charge stabilization of 1.5–2 eV is consistent with 4–2 Å distance of the molecular anion to the surface. Similar logic was used to identify the LUMO of azobenzene as the orbital involved in its electronically induced isomerization by ~1.7 eV electrons above Fermi level [9]. Desorption of hydrogen from Si(100) is also asymmetric in bias, with the onset of the hole attachment to 5s resonance at 4 V [31]. Electronic excitation via p → p* transition, Fig. 1.6c, d, was suggested to occur for an isomerization of polyaromatic 1,4″-paratriphenyldimethylacetone at a bias of ~4.0 V [75]. In general, one expects electronic excitation to have a weak

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P. Maksymovych

bias dependence by analogy with inelastic scattering. The process will, however, be complicated by the changes in the overall tunneling probability due to proximity of molecular resonances at high bias. A relatively high threshold coincident with weak bias dependence may also signal another electric-field induced excitation mechanism, which does not require inelastic electron scattering with a molecule. Only a few reactions of this type were suggested so far. They include reversible isomerization of Zn(II)-etioporphyrin [76], NO desorption from Si(111) [77], and isomerization of azobenzene on Au(111) [13]. In all these cases, the transformation involves a characteristic change in the shape of the molecule that changes its dipole moment, enabling efficient coupling to the electric field in the tip-surface junction. For example, from

Fig. 1.7 (a, b) STM images (3.3 × 3.3 nm2) along with the schematic structural models of ZnEtioI molecule on NiAl(110) surface. (c) Variations of threshold voltages for a ZnEtioI molecule to undergo the reversible conformational transitions from type I to type II and from type II to type I as a function of the change in tip–substrate separation (reproduced with permission from Qiu et al. [76])


15

direct inspection of the STM images before and after the reaction, Qiu et al. [76] established that the porphyrin ring undergoes symmetry reduction from C4h to C2d, manifested as the symmetric “indentation” of the flat shape of the central ring (as in the gas phase) shape due to additional interaction with the NiAl surface (Fig. 1.7a, b). The involvement of the electric field was established for the reverse process (flattening of the molecular ring) from a roughly linear dependence of the excitation voltage on tip-sample distance, justified if the simplest V/d expression for the electric field in the tunnel junction (d is the tip-surface distance) is valid (Fig. 1.7c). The voltage threshold for the direct process (indentation) was found to be independent of the tip-sample separation and was therefore assigned to inelastic electron-induced excitation of the molecule.

Rate Constant of a Single-Molecule Reaction In a recent study, Rao et al. [78] have demonstrated that it is also possible to extract valuable information from the value of the rate constant k in R ~ k ·I N . The authors compared the rate of single-molecule dehydrogenation of a series of halogenosubstituted thiophenols on Cu(111). The goal was to build a parallel to a wellknown Hammet equation [79], log(kx / k0 ) = ρ·σ , which predicts the effect of substituents (X) in the phenyl ring (Ph) on the rate of a particular reaction of a PhR → PhR¢, where R is a reactive center. k0 and s refer to the dissociation of benzoic acid in water (Ph–COOH), making r a unique descriptor of the relative reactivity of a variety of substituents and reactive groups. The Hammet equation and its several derivatives, Swain–Lupton, Taft, and Yukawa–Tsuno equations [80], have predictive power not only for the chemical identity of the substituent, but also its position in the phenyl ring, in particular meta- and para-substitutions (orthosubstituents introduce additional steric effects). Using the single-molecule averaging statistics described above, Rao et al. [78] have measured the linear rate of dehydrogenation of thiophenol and its para- chlorine, bromine, and fluorine derivatives – identifying single-electron kinetics for RSH → RS + H reaction in each case (Fig. 1.8). The rate constants, extracted from the corresponding slopes of R = f(I), revealed a systematic dependence on the substituent, which was used to calibrate r in the Hammet equation against the literature values of s for the corresponding molecules. The extracted value of r (~1.4) was then combined with literature values for meta-halo substituted molecules as well as the meta-methylphenyl. The actual measured values for the meta-substituted thiolphenols were found to be in very good agreement with the predictions of the Hammet equation for the surface reactions. The positive values of r furthermore indicate that the electron-withdrawing substituents in the phenyl ring stabilize the transition state, which thus indicates a strong likelihood of an anionic transition state [80]. Overall, systematic analysis of similar reacting molecules enables using single-molecule rate constants to glimpse onto the quantitative aspects of the transition state to which the molecule is excited by tunneling electrons.

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P. Maksymovych

Fig. 1.8 Linear free-energy relationship of one molecule at a time. STM images and singlemolecule dissociation rates of substituted thiophenols (TP). (a–c) STM images of para-methyl-TP, meta-F-TP and meta-Cl-TP on Cu(111) at 16 K. The images have a petal shape because of molecular rotation around the anchor bond. (d) The linear dependence of the reaction rate on the tunneling current indicates a one-electron process. The k-values were used to buildup a surface analogue of Hammet equation (reproduced with permission from Rao et al. [78])

Theoretical Aspects of Single- and Multiple-Electron Processes To overcome an activation barrier, the energy of the inelastically scattered electrons has to be routed to a vibrational mode corresponding to the RC. This process can happen directly, when the electrons excite the RC mode by coherent [15] or incoherent vibrational ladder climbing [16], or indirectly when the inelastic tunneling current excites some vibrational mode in the molecule and the energy is subsequently transferred into the RC mode via anharmonic coupling [17], as schematically shown in Fig. 1.9. The latter process has been observed in those experiments, where the excitation threshold is observed to correspond to a vibrational mode that does not actually correspond to the breaking bond, exemplified by S–S bond dissociation of dimethyldisulfide on Cu(111), excited by a C–H stretch [56], and translation of ammonia (NH3) on Cu(100), excited by the N–H stretch [58]. The latter case is particularly interesting, because molecular desorption from the surface (which intuitively has a large activation barrier) can be induced at a smaller tunneling bias than molecular diffusion (Fig. 1.10). The reason behind this mode selectivity is that desorption can be induced by a direct excitation of the umbrella N–H bending mode with an energy of ~270 mV via a multiple-electron-scattering incoherent vibrational ladder climbing, while translation anharmonically couples to an N–H stretch excited at >400 mV.


17

Fig. 1.9 Schematics of a simple two-dimensional potential along the intramolecular stretch QA–B that is anharmonically coupled to the RC q. There are two ways to overcome EB: coherent or incoherent vibrational ladder climbing (green arrow) involving direct excitation of the RC mode by tunneling electrons; anharmonic coupling between the high-frequency A–B stretch mode excited by tunneling electrons (red arrow) and the low-frequency RC mode (reproduced with permission from Ueba et al. [88])

Very recently, Tikhodeev and Ueba [81] have analyzed an additional mechanism by which the vibrationally excited molecule can crossover the activation barrier for the reaction. Previous treatments considered only classical trajectories along the RC, whereby the molecule could overcome the reaction barrier only when the potential energy exceeded the barrier height. In light of recent experiments on the mobility of hydrogen atoms on Cu(100) [6], Co atoms on Cu(111) [59], and hydrogen exchange in water dimers on Cu(110) [82], quantum mechanical motion of the reacting species should also be considered if the effective mass of the particle is sufficiently light. Rotational tunneling (from the ground or excited rotational state) may also apply in a growing number of molecular rotors on the surface [83–85]. Tikhodeev and Ueba [81] modified the Pauli master equations (see below) to include the additional decay of the vibrational population via quantum mechanical tunneling across the potential barrier. The net result of their analysis is that the dependence of the reaction rate on the excitation bias may deviate from a power law (R ~ Vn) predicted by the models that consider only the classical trajectories. The power law itself originates from an Arrhenius type expression for the reaction rate, R ≈ Γ↑ exp( − EB / kTv ), Γ↑ rate of excitation into a given vibrational state, which is valid when “thermal” fluctuations in the presence of tunneling current (kTv) are much smaller than the vibrational quantum of the respective mode. Tv describes quasistationary population of the vibrational levels Γ↑ ≈ Γ↓ exp(− Ω / kTv ). The mechanism of vibrationally assisted tunneling was applied to hydrogen exchange in the water dimers [86], which was shown to be compatible with quantum tunneling from the lowest vibrational mode and first-excited vibrational mode (without the need for multiply excited states), while Co tunneling on Cu(111) [59] was reinterpreted as vibrationally assisted tunneling from many excited levels, which turns into classical behavior at large bias.

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P. Maksymovych

Fig. 1.10 (a) STM image of three NH3 molecules before and (b) after injecting 0.5 nA of 420 meV electrons on top of each molecule. Two of the molecules moved to a new site, and the third was desorbed. Statistics of electron energy onset leading to molecular motion: (b) The distribution of threshold energies for the reactions at low tunneling currents (It < 0.5 nA) NH3 shows a threshold at 400 mV (a), which shifts down to 300 mV for ND3 (b), matching correspondingly the energy of N–H and N–D stretch modes (dashed lines). The insets show traces of tunneling current during tip-induced excitation. These events induce molecular translation with ratio 0.6. (c) For It > 1 nA, an additional threshold appears gradually at 270 mV in NH3, consistent with the energy of two umbrella mode quanta (dash-dotted lines). Now, desorption dominates with ratio 0.75. In ND3, the corresponding onset at 200 mV is observed (d) only after reaching tunneling currents higher than 10 nA (reproduced with permission from Pascual [12])


19

Overall, the likelihood of electron-vibration coupling is determined by the properties of an adsorbate-induced resonance, its width (determined by coupling to the substrate and the tip), position relative to the Fermi level, the rate of vibrational deexcitation via electron–hole pair generation, and vibrational cooling down via the phonon bath of the surface. The involvement of the electronic resonance in the vibrational excitation is implicit in the theoretical models, where the tunneling process is mediated by the adsorbate-induced resonance [16, 40, 46, 50, 86]. Electron-vibration coupling is modeled by assuming that the energy of the resonance shifts linearly with the vibrational coordinate, typically within the first-order perturbative treatment, where the Hamiltonian operator is expanded in a Taylor series on the normal vectors and retaining only the first-order term [16]. The involvement of the electronic states in the electron-vibration coupling was recently directly confirmed by the Kawai’s group, in the analysis of CH3SSCH3 dissociation on Cu(111) using action spectroscopy [87]. The reaction was observed to have a threshold at the energy of the C–H stretch (~360 mV). However, the reaction rate was strongly bias dependent, being much faster at the positive sample bias. Furthermore, hopping of the CH3S fragments had symmetric thresholds at ±85 mV, but did not have a threshold at the energy of the C–H stretch. With the help of firstprinciples modeling, the interpretation of the bias asymmetry was that the dissociation reaction was assisted by the lowest unoccupied molecular orbital, which peaks at ~1.0 V above Fermi level (and is also very broad), and which stretches over the S–S and C–H bonds allowing the C–H stretch to be vibrationally excited. At the same time, the translation motion of the CH3S fragment was mediated by its LUMO and HOMO orbitals, which are spread relatively evenly around the Fermi level and coupled directly to the C–S bond. Neither of these orbitals had significant spatial concentration around the C–H bond, which served as a further indication that the excitation of the vibrational modes (and the corresponding reactions) did indeed depend on the availability of the adsorbate-induced resonance in the relevant tunneling window as well as its symmetry. Here we want to elaborate on one particular theoretical work that provides a kinetic framework for single- and multiple-electron excitation, and establishes the link between consecutive excitation processes and the power law of the reaction rate in current observed experimentally. Ueba et al. [88] considered the vibrational excitation scenario through the anharmonic coupling between a high-frequency mode (HF, levels labeled by n), directly excited by tunneling electrons, and reaction coordinate (RC, levels labeled by n), which may or may not be directly excitable, as schematically depicted in Fig. 1.11. For a one-electron process, the reaction can be symbolically represented as a sequence of two processes:

[υ : 0 → 1](υ :1 → 0 | RC : 0 → n) i.e., vibrational excitation of the ground into the first excited state, followed by simultaneous deexcitation and excitation of the RC from 0th to nth excited state.

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This representation clearly separates the excitation stage (accessible by STM) and the reaction rate. The reaction rate is by definition:

RRC =

∑τ

n > nth

1

N1,0

υ (1→ 0)RC(0 → n )

where τυ(1→0)RC(0→n ) is the rate of the anharmonic coupling, while N1,0 is the population of the first excited vibrational state. Note that the summation takes place over only those levels of the RC mode that are sufficient to overcome the activation barrier. N1,0 is subject to the following Pauli master equation reflecting the balance between inelastic scattering of tunneling current, vibrational relaxation, and reaction rate:

dN1,0 dt

= pν N 0,0 −

N1,0 τv

−∑ n

1 τv(1→0)RC(0→n )

N1,0

Here pν = ηv I is the inelastic fraction of the tunneling current (or the normalized probability of vibrationally exciting the HF mode), tv is the vibrational relaxation time of the HF mode and the third term is the reaction rate. The equation can be solved assuming a steady state condition of N1,0 = constant. The final expression for the reaction rate is RRC = τv,tot ηv I / τv,RC , where the total relaxation time tv,tot and the reaction time tv,RC are correspondingly:

1 τ v,tot

=

1 1 +∑ τv n τ v(1→ 0)RC(0 → n )

and

1 τv,RC

=

∑τ

n > nth

1 v(1→ 0)RC(0 → n )

The reaction rate of such a excitation/coupling mechanism is indeed directly proportional to the tunneling current, reflecting the one-electron excitation [u:0 → 1]. The analysis also reveals the terms that determine the total reaction rate: probability of inelastic scattering of the tunneling electron, total vibrational relaxation time of the HF mode, and the rate of the anharmonic coupling to the RC. Each one of these terms has been treated in several theoretical works over the years. For example, an earlier study by Persson and Ueba [89] has derived the analytical expression for the rate of anharmonic coupling of an HF mode to an RC frustrated translation/vibration mode, in competition with fast cooling of the HF mode by electron–hole pair excita2 3/ 2 −2 α tion in the metal: 1 / τ v,RC ≈ 1 / τ v (δω / EB ) α e , where dw is the anharmonic coupling, EB is activation barrier, hw is the energy of the RC mode, and alpha is α = EB / ω . Note that an increase of a will exponentially damp the reaction rate. To interpret this behavior, one needs to consider that upon reactive excitation the RC mode is promoted from its low-energy smooth ground-state wavefunction to a highly oscillatory wavefunction of the excited mode (which may even approach continuum), Fig. 1.11. The corresponding matrix element will be small, which ultimately affects the efficiency of anharmonic coupling and the total reaction rate [17]. The kinetic analysis applies also to multielectron excitation scenarios, although the final expression for the reaction rate becomes progressively more complex and


21

Fig. 1.11 Schematic illustration of a single-electron process. The decay of the high-frequency mode with the energy excites the low-frequency RC mode from the ground state localized at the bottom of the RC potential well to the unbound state just above the top of the barrier. Electron–hole pair excitation is a competing channel for deexcitation of the low-frequency mode (reproduced with permission from Ueba et al. [88])

parameter rich as the number of excitation channels and coupling modes increases. For a two-electron process, Ueba et al. considered the following three parallel scenarios, depending on how the RC mode is excited. For pure anharmonic excitation one arrives at:

[ υ : 0 → 1]( υ :1 → 0 | RC : 0 → m)[ υ : 0 → 1]( υ :1 → 0 | RC : m → n) + [ υ : 0 → 1][ υ :1 → 2]( υ : 2 → 1| RC : 0 → m)( υ :1 → 0 | RC : m → n) + [ υ : 0 → 1][ υ :1 → 2]( υ : 2 → 0 | RC : 0 → n) which is a sum of three (exclusive) processes: vibrational pumping of the RC mode via consecutive excitation–deexcitation of the HF mode, initial vibrational pumping of the HF mode to its second vibrationally excited state followed by two- or onestep anharmonic coupling to the RC mode. The resulting rate equation is RRC = τ (ηv τ v I ) 2 , where τ characterizes the total effect of the rates of the anharmonic couplings along the RC, while 1 / τ v is the rate of vibrational relaxation of the HF mode. In case the RC mode can also be excited directly, two other scenarios are possible

[ υ : 0 → 1]( υ :1 → 0 | RC : 0 → m)[RC : m → n] + [RC : 0 → m][ υ : 0 → 1]( υ :1 → 0 | RC : m → n)  v η RC τv τRC I 2 and for only direct exciwith the reaction rate equation RRC = τη tation [RC:0→m][RC:m→n] with the corresponding reaction rate of 0→ →mm mm→ →nn 22 = ((ηη0RC ηRC RRRC RC = RC η RC II )) // ττRC RC. Because each one of the scenarios involves a product of two consecutive excitations, the rate expressions of all three are in the form R µ I2, justifying the experimental determination of the corresponding kinetics. For the case of NH3 desorption from Cu(100) surface [58], Fig. 1.10, the low-energy

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two-electron process at V 3.3V, C60 films were observed to develop a beautiful ring structure (with diameters up to 20 nm) around the injection spot, Fig. 1.12, the size of which is dependent on the tunneling bias and duration of the excitation pulse. By analogy with chlorine diffusion, the formation of the ring structure was attributed to a reversible dimerization (and possibly partial polymerization) of the C60 molecules by hot-electrons, transported away from the tunneling junction via the surface band. The occurrence of the ring was explained as the initial dimerization of the molecules around the tip followed by a partial reverse monomerization in the immediate proximity of the tip. These reactions were previously established by the authors in local excitation experiments [94]. The barrier to polymerization and the reverse processes is different and so are the rates of the corresponding reactions. Because the surface current density of hot electrons scales as 1/r in purely two-dimensional transport (r, distance to the tip), after any excitation pulse, there will be slightly more polymerized than depolymerized molecules and they will be concentrated on the periphery of the excited region, where the net balance of polymerization–depolymerization is nonzero at the energy and current of hot electrons.


23

Fig. 1.12 Asymmetric rings of C60 polymers formed by carrier injection into close-packed layers with grain boundaries (line across the image). STM images acquired after (a) electron injection and (b) hole injection at 3 V into the marked points (reproduced with permission from Nouchi et al. [97])

Silicon surfaces possess well-expressed surface bands, allowing significant fraction of electrons to flow along the surface [95], which explains why such reactions are feasible. However, similar excitation phenomena can also be observed on almost all low-index metal surfaces of Au, Ag, and Cu, although the lifetime of hot carriers at >1 eV above EF is almost two orders of magnitude smaller (10–50 fs) [96, 97] than on silicon surfaces. Here, the surface state in the projected band gap of the surface and its derivative surface resonance play the role of the twodimensional transport medium [98, 99]. Delocalized electron excitation on metal surfaces was first suggested by Stipe et al. for oxygen dissociation on Pt(111) in a ~10-nm radius [100]. The author has observed delocalized excitation with the aforementioned model system of the electron-induced dissociation of CH3SSCH3, Fig. 1.13a–c, as well as CH3SH and C6H5I on Au(111), Au(100), and Cu(110),_ all with distinct thresholds. Notably, the projected _ band gap is centered at the X -point in the Brillouin zone for 100 [101] and at Y for 110-terminations of the fcc metals [99], which strongly reduces the fraction of tunneling electrons injected in these states. Nevertheless, delocalized excitation is very pronounced on these surfaces, because of the efficient electron attachment to a wide range of molecules, which have been traditionally studied in the framework of surface photochemistry. A particularly pronounced reaction yield was observed by Maksymovych et al. [102] with CH3SSCH3 molecules on Au(111) efficiently dissociating in a rather striking radius of up to 100 nm (Fig. 1.13 shows dissociation at a distance of ~50 nm) when the tunneling bias exceeds 1.4 eV (Fig. 1.13e). The effect was very reproducible between adjacent surface areas (Fig. 1.13d)

Fig. 1.13 STM images and structural models of electron-induced dissociation of CH3SSCH3 molecule (a) on the Au(111) surface producing CH3S fragments (b). Delocalized CH3SSCH3 dissociation induced by a single 2.5 V = 1.0 nA = 200-ms pulse at the (blue) point. (c) The inset is a surface area ( yellow square) located ~46 nm away from the pulse position. u marks unreacted and r marks reacted CH3SSCH3 molecules. (d) Total number of dissociation events per pulse obtained from 18 pulses of the same magnitude. (e) Total number of dissociation events per pulse (1.0 nA = 200 ms) as a function of pulse voltage (reproduced with permission from Maksymovych et al. [102])

25

Fig. 1.14 (a) Attenuation function of the delocalized CH3SSCH3 dissociation on Au(111) from two experiments using pulses at 1.8 V (average of 15 measurements) and 2.2 V (average of five measurements). Solid (red ) lines are exponential decay fits to the data (reproduced with permission from Maksymovych et al. [102]). (b) The radial probability g(r) of the delocalized electroninduced chlorine hopping on Si(111) at radial distance r from the tip position along the < 1 12 > direction. The oscillations are due to standing waves of the surface state on Si(111) at the excitation energy (reproduced with permission from Nakamura et al. [92])

and its hot-electron origin was established in a series of experiments, involving bias dependence of the effect, current injection through artificially created local nanoclusters, and a quantitative analysis of the spatial kinetics of the reaction events. In particular, the total reaction rate was derived to follow a kinetic equation:

−∑ ln(1 − Pr / N 0r ) = ktI 0g ∑ [ f (r )]g , r

r

where Pr and N0r is the reacted and initial numbers of molecules at a distance r from the tunneling junction, k is the rate constant, I0 is the tunneling current, g is the electron kinetic exponent, and f(r) is the intrinsic attenuation function. g was determined to be unity from experiments conducted at total constant tunneling charge (rather than current), further confirming the electron-induced kinetics. f(r) was closely fit by a simple monoexponential decay (Fig. 1.14a). Hot electrons emitted from the tunneling junction persist in the surface state (or resonance) of Au(111) surface with a lifetime less than 50 fs at energies exceeding 1.0 eV. The electron population will therefore decay exponentially in time and (correspondingly) distance. The decay exponent, Fig. 1.14a, extracted directly from properly normalized reaction probabilities is, in the first approximation, formally equal to twice the mean free path of the hot electrons at that energy [102]. By estimating the group velocity from the known band structure of Au(111), the relaxation times were estimated to be indeed on the order of 20–30 fs, in good qualitative

26

P. Maksymovych

agreement of spectroscopic measurements [102]. Similar statistics derived for chlorine jumps on Si(111), Fig. 1.14b, has revealed an oscillatory probability of a delocalized reaction which was assigned to the standing waves of the surface state on Si(111) at the excitation energy. Such measurements can therefore reveal the dynamics of hot electrons in a small region of the adsorbate-covered surface (in direct relevance to photochemistry), which is practically impossible to do using surface-resonance scattering techniques [97] at very high coverage due to the complexity of the scattering patterns and reactivity of the adsorbates. The advantage over averaging spectroscopic techniques is that the information can be extracted for a relatively localized region of the surface, which may contain a single-atom step, engineered defects, adlayers, etc. The application of the delocalized excitation for the characterization of chemical reactions allows one to remove tip artifacts (forces and fields) and has the potential to measure fast excitation kinetics for which single-molecule measurements would be limited by the measurement bandwidth of the STM.

Tip Effects and Field-Induced Manipulation Given the striking complexity and intricacy of the processes involved in the singlemolecule reactions, it is not at all surprising that they can be strongly influenced by the shape, electronic states and electric field of the STM tip, and other parameters that cannot be easily controlled. The tip influence can be manifested in the excitation rate (change of vibrational relaxation and intermode coupling), excitation mechanism (kinetics of vibrational ladder climbing) and, ultimately, the potential energy landscape of the transition state. The tip effects were directly demonstrated by Sloan and Palmer [30] using dissociation of chlorobenzene on Si(111) as a model system and two different tip states to excite the system. While, the measurement of reaction kinetics was not affected by the tip state, the absolute measured rates differed by more than an order of magnitude. Furthermore, the ratio of molecular desorption to dissociation also revealed about an order of magnitude difference. An arguably good experimental test system to reveal the tip effects on the transition state of the molecule is the so-called localized or patterned reaction, the term first introduced by the Polanyi group [71] to describe a reaction which imprints the spatial configuration of the parent molecule onto the surface arrangement of the reaction products. Such chemical reactions, analogous to those in the field of surface-aligned photochemistry [104, 105], proceed through a tightly bound transition state involving surface atoms. Patterned reactions have been observed for a number of alkyl- and arylhalides adsorbed on silicon surfaces [71], while the author has found a similar behavior in the dissociation of dimethyldisulfide (CH3SSCH3) on Au(111) and Au(100) surfaces.


27

CH3SSCH3 is adsorbed on the gold surfaces in a characteristic trans-geometry [22], Fig. 1.13a, b, where the methyl groups are located on either side of the S–S bond, while the S–S bond itself is almost parallel to one of the three close-packed directions. The molecule has therefore six equivalent orientations, and each of these can be “imprinted” on the relative orientation of the reaction products (CH3S fragments). Substantial tip influence could then be inferred by observing the probability of “imprinting.” Upon single-molecule excitation, the “imprinted” reaction yield, Fig. 1.13b, was observed to be only ~10%, making it statistically equivalent to any other reaction scenario where the CH3S fragments rotate about the S–S bond during the reaction and diffuse on the surface around the location of the original molecule [22]. By decreasing the magnitude of the tunneling current, the “imprinted” scenario becomes dominant (~50%) and reaches a maximum fraction of 75% of the reaction events when the delocalized excitation is involved. The changes in the relative orientation of the CH3S fragments may originate from either the direct tip effect on the transition state of the dissociating molecule or a postfactum electron-induced rotation or diffusion of the CH3S fragments, provided the latter is efficient under the excitation conditions. Regardless of the details, the fact that a relatively high yield of the imprinted scenario can be recovered by tuning the excitation condition suggests that this scenario is representative of the transition state. Its symmetry is actually the same as the symmetry of the lowest unoccupied molecular orbital involved in the dissociation of the parent molecule via dissociative electron attachment mechanism [32]. It is tempting to suggest that a statistical analysis of the preferential scenarios in the remaining 25% of the reaction events where the transimprint is not observed will effectively produce a probabilistic description of the potential energy surface, experienced by hot CH3S fragments upon dissociation. To achieve this goal further theoretical analysis of this reaction is required, ideally in terms of wave packet propagation analysis that is similar to the decay of a charged Cs atom on Cu(111) surface [106]. In another study involving formation of a transient anion, Henningsen et al. [9] suggested that the electric field of the STM tip not only influences the transition state, but may also be necessary to direct the transient molecular anion of 3,3¢-dicyanoazobenzene on Au(111) toward the rotation of the phenyl ring about the N–N bond, which ultimately leads to trans–trans (3,3¢ to 3,5¢) isomerization of the molecule. While the tip effects may be undesirable to derive information about the excitation mechanism or the transition state of the dissociating molecule, they can be useful in molecular manipulation. Ohara et al. [107] have demonstrated that the direction of CH3S translation on the Au(111) surface, excited by inelastic electron scattering at 85 meV, can be controlled by positioning the tip slightly off-center on the molecule during excitation. The direction of motion could also be switched between away from and toward the tip by reversing the sign of the tip-sample bias, thereby allowing one to record arbitrary patterns on the surface Fig. 1.15. Notably, this is not a conventional scenario for single atom or molecule manipulation, which involves formation of a significantly strong tip-molecule bond and subsequent translation of the tip to “drag” the molecule or the atom along the surface.

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Fig. 1.15 STM images showing snapshots of construction of three letters, S, T and M using electric-field directed manipulation of vibrationally excited CH3S moieties on Cu(111) surface. Each image is 6x6 nm2 (reproduced with permission from M. Ohara et al. [107]). Copyright (2008) by the American Physical Society

Collective Reactivity of Molecular Aggregates Before concluding this chapter, a few comments are appropriate on several recent examples of collective chemical reactions observed in molecular assemblies or twodimensional polymers, where the energy of a localized inelastic excitation is channeled into a collective RC, rather than dissipating it into the electron–hole pair excitations and the phonon bath of the underlying substrate. The first example of such a reaction was reported by Okawa and Aono [108] using self-assembled diacetylene compound (10,12-nonacosadiynoic acid) on HOPG (Fig. 1.15). Application of a relatively high voltage/current pulse (~5 V) induced unidimensional polymerization of the molecules (RC≡CR–C≡CR→=(RC–CR=CR–C)= along the self-assembled rows, with the reaction surprisingly extending by tens of nanometers away from the excited position (Fig. 1.16b, c). Subsequently, the polymerized diacetylene rows were found to possess a delocalized electronic state, implying that this procedure can be used to make one-dimensional wires on the surface [109, 110]. The reaction of this type is not unexpected because polydiacetylene is a very well-known monomer [111], and formation of polydiacetylene moiety is thermodynamically very profitable. As a result, once initiated the reaction will self-propel. Furthermore, graphite has a zero-energy gap at the Fermi level [112], thus a low density of states and suppressed energy dissipation via electron–hole pair generation. Nevertheless, the degree of localization of this reaction is striking as is the accuracy and relative ease of initiation and propagation. A second example of an unconventional delocalized reaction was recently reported by Maksymovych et al. [32]. This time, the reaction took place on metal surfaces of Au(111) and Au(100), involving linear chains of CH3SSCH3 molecules


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Fig. 1.16 (a) STM image of self-assembled monolayer of diacetylene on HOPG (Vs = −1.0 V, It = 0.07 nA). (b) A bias pulse applied at a point shown by an arrow triggers one-dimensional polymerization of the diacetylene precursor. (c) STM image of the same area recorded immediately after (b). (d, e) Diagrams illustrating the initiation of chain polymerization with an STM tip (reproduced with permission from Okawa and Aono. J. Chem. Phys. 115 (2001) 2317)

that spontaneously form at T > 70 K. Upon electron attachment to any molecule in the chain of up to five molecules on Au(111) and up to ten molecules on Au(100), the S–S bonds of all the molecules were found to first break, and then all but one to reform, making new CH3SSCH3 molecules which relate as the offset mirror images to the initial molecules (ignoring the exact orientation of the CH3 groups), Fig. 1.17. Such a chain reaction can be therefore be visualized as a sequence of elementary steps, CH3S + CH3SSCH3 → CH3SSCH3 + CH3S, each of which is

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Fig. 1.17 STM images before and after electron-induced dissociation of CH3SSCH3 molecule chains self-assembled on Au(111) and Au(100) surfaces. (a) Chain reaction of CH3SSCH3 dimer and tetramer assemblies on Au(111) induced by a voltage pulse on top of the terminal molecule (blue dot, pulse voltage 0.9 V) leading to the synthesis of CH3SSCH3 molecules of opposite conformation. Schematic ball models of the selected structures are shown aside their STM images. (b) On Au(100) surface the reaction may involve as many as ten molecules in a row (reproduced with permission from Maksymovych et al. [32])

closely reminiscent of the photo-induced free-radical substitution reactions in the gas phase involving the thyil radical (RS·) [113]. The terminal CH3S fragments were found to bind to the twofold coordinated sites on the Au(111) surface. Unlike polymerization of the diacetylene cores, this reaction does not create stronger chemical bonds at each of its elementary steps (assuming a consecutive scenario), and its propagation is therefore quite intriguing in light of the presence of the Au(111) surface, which acts as an energy sink. The enabling chemical interactions in the interior of the chain were identified with the help of nudged elastic band density functional calculations. We have found that the energy to break an S–S bond in a single CH3SSCH3 molecule is nearly identical to the total energy required to react a trimer assembly of these molecules in a consecutive propagation scenario [32]. The main reason for the nearly activation-less reactions in the chains interior is the formation of a metastable complex where an intermediate atop-bonded CH3S species is stabilized by the neighbor CH3SSCH3 molecule. Experimental kinetic measurements have also revealed that the reaction is excited by relatively highenergy electrons, either two electrons at >0.8 eV or one electron at >1.3 eV. This high threshold and first-principles calculations of the electronic structure suggested that the chain reaction is initiated by electron attachment to the LUMO of the CH3SSCH3 molecules. A curious detail is that the LUMOs of the individual molecules form a delocalized state upon self-assembly of the chain reaction. Experimentally, the evidence for this state comes from a lower energy threshold for


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Fig. 1.18 Hydrogen exchange in a water dimer triggered by inelastic electron tunneling. (a) STM image of H2O and D2O dimers (5.5 × 5.5 nm2). (b) An enlarged image of the D2O dimer (2.4 × 2.0 nm2). The grid lines represent the lattice of Cu(110) that is depicted through nearby monomers centered on top of Cu atoms. The (H2O)2 dimer is observed to flip numerous times as the tip scans across. (b–d) represents step-by-step flipping of the (D2O)2 dimer. (c) The (D2O)2 dimer flipped between the two orientations as the tip was scanned horizontally across it. [Reproduced with permission from Kumagai et al. [82])

a chain reaction compared to an isolated molecule, which then poses a question of how the delocalized state participates in the initial excitation and whether more than one S–S bond in the chain is weakened by initial electron attachment. A third example of collective reactions is a hydrogen bond exchange within a water dimer formed by the tip-induced manipulation of the monomers on Cu(110) [82] (Fig. 1.18). The hydrogen exchange constituted a collective reorientation of the (H2O)2 and (D2O)2 molecules, so that the hydrogen bonding (O–H…O) would first be formed by the H atom of one molecule, and upon rearrangement switched for the H atom of the other. This is a surface analogue of a similar behavior of a free water dimer in the gas phase. What is peculiar is that much like the gas-phase reaction, the surface reaction is dominated by quantum tunneling, as evidenced from a large isotope effect. From the analysis of a bias dependence of the reaction rate, Tikhodeev and Ueba [81] concluded that this reaction proceeds through vibrationally

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assisted tunneling from the first vibrationally excited state. Overall, the growing experience in the field of atomically resolved imaging and single-molecule manipulation using scanning probe microscopy stimulates the studies of molecules and surfaces with increasing complexity, which is why we believe that collective reactivity will be observed more and more frequently in the future studies.

Conclusions and Outlook Single-molecule excitation in the tunneling junction is a versatile approach to chemical transformations that reveals the fundamental mechanisms of molecular reactivity on solid surfaces and the physical phenomena that govern the energy flow of a dynamic molecule-surface interaction. Statistical analysis of such reactions can address the electronic and vibrational interactions of adsorbed molecules in a way that is complementary to tunneling spectroscopy and, in some cases, is entirely exclusive (e.g., in the action spectroscopy of the vibrational modes). As such, it is poised to make many future discoveries that one day will enable us to tune chemical reactions by molecule-surface and inter-molecular interactions, harness singlemolecule machines and electronic circuitry and exploit molecules as a means to control the electronic properties of surfaces or thin films, including correlated electron behaviors. Many important steps have already been made, and we now have the statistical framework to analyze single-molecule reactions and a rather comprehensive understanding of the underlying mechanisms. The field is well positioned to take full advantage of the rapidly ongoing experimental developments in scanning probe microscopy, such as force sensitivity and mechanical energy dissipation on the single-molecule level and coupling to femto-second laser techniques. The increasing scope and scalability of ab initio theoretical methods enables complex systems and dynamic phenomena to be explored. We can thus proceed onto larger molecules, metal surfaces functionalized with insulating or polar thin films and molecular self-assemblies, all of which will present new dynamic functionality and new mechanisms for energy flow and dissipation that can eventually be resolved on the real timescale of single-molecule transformations. Acknowledgment The writing of this review was done at the Center for Nanophase Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy.

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Chapter 2

High-Resolution Architecture and Structural Dynamics of Microbial and Cellular Systems: Insights from in Vitro Atomic Force Microscopy Alexander J. Malkin and Marco Plomp

Introduction One of the great scientific challenges at the intersection of chemistry, biology and materials science is to define the biophysical pathways of cellular life, and in particular, to elucidate the complex molecular machines that carry out cellular and microbial function and propagate the disease. To study this in a comprehensive way, the fundamental understanding of the principal mechanisms by which cellular systems are ultimately linked with their chemical, physical, and biological environment are required. Complete genome sequences are often available for understanding biotransformation, environmental resistance, and pathogenesis of microbial and cellular systems. The present technological and scientific challenges are to unravel the relationships between the organization and function of protein complexes at cell, microbial, and pathogen surfaces, to understand how these complexes evolve during the bacterial, cellular, and pathogen life cycles, and how they respond to environmental changes, chemical stimulants, and therapeutics. Development of atomic force microscopy (AFM) for probing the architecture and assembly of single microbial surfaces at a nanometer scale under native conditions, and unraveling of its structural dynamics in response to changes in the environment has the capacity to significantly enhance the current insight into molecular architecture, structural and environmental variability of cellular and microbial systems as a function of spatial, developmental, and temporal organizational scales. In this chapter we will demonstrate, focusing on the work conducted in our group in the past several years, the capabilities of AFM in probing the architecture and assembly of bacterial surfaces and integument structures and their evolvement during bacterial life cycles, as well as in response to environmental changes. We have used AFM to investigate spore coat architecture and assembly, structural dynamics, and germination of several species of Bacillus [1–7] and Clostridium [8] A.J. Malkin and M. Plomp (*) Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA e-mail: [email protected] S.V. Kalinin and A. Gruverman (eds.), Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy, DOI 10.1007/978-1-4419-7167-8_2, © Springer Science+Business Media, LLC 2010

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spores. These include Bacillus thuringiensis, Bacillus anthracis, Bacillus cereus, Bacillus atrophaeus and Clostridium novyi-NT species spores. B. anthracis, the causative agent of anthrax, is a gram-positive spore-forming bacterium [9, 10]. The B. cereus species is environmentally ubiquitous and can cause bacteriemia and septicemia, central nervous and respiratory system infections, endocarditis and food poisoning [11]. B. atrophaeus spores have been used as a biological stimulant for decontamination and sterilization processes [12, 13], and bioaerosol detection development [14, 15]. B. thuringiensis spores are insect pathogenic species [16]. Clostridium novyi (C. novyi-NT) is a motile, spore-forming, gram-variable anaerobic bacterium. C. novyi can cause infections leading to gas gangrene in humans, particularly after traumatic wounds or illicit drug use [17]. The pathology of C. novyi is attributed to the lethal alpha-toxin [18], which is absent in an attenuated strain, C. novyi-NT [19]. C. novyi-NT is one of the most promising bacterial agents for cancer therapeutics [20]. Intravenous injection of C. novyi-NT spores into tumor-bearing mice was found to successfully eradicate large tumors, either in combination with radiation therapy [19] and chemotherapy [21], or by itself, as it can induce a potent immune response [22]. Here, we will also describe the development of AFM for immunolabeling of the proteomic structures of bacterial spore surfaces [5]. Finally, we will present data on the elucidation of bioremediation mechanisms of Arthrobacter oxydans. A. oxydans is a gram-positive and chromium (VI)-resistant bacterium, which can reduce highly mobile, carcinogenic, mutagenic, and toxic hexavalent chromium to less mobile and much less toxic trivalent chromium [23].

AFM Investigations of Spore Morphology, Structural Dynamics and Spore Coat Architecture When starved for nutrients, Bacillus and Clostridium cells initiate a series of genetic, biochemical, and structural events that results in the formation of a metabolically dormant endospore [24]. Bacterial spores can remain dormant for extended time periods and possess a remarkable resistance to environmental insults, including heat, radiation, pH extremes, and toxic chemicals [24]. Their unique structure, including a set of protective outer layers, plays a major role in the maintenance of spore environmental resistance and dormancy [24–26]. The Bacillus bacterial spore structure (Fig. 2.1) consists [25], starting from the center, of an inner core surrounded by the inner cytomembrane, a cortex, outer membrane and an exterior spore coat. In some bacterial species, including Bacillus thuringiensis and Bacillus anthracis, the coat is surrounded by a loosely attached exosporium. The spore core contains DNA and dipicolinic acid, which is associated predominantly with Ca2+. The major role of the spore cortex, which consists of a thick layer of species-dependent peptidoglycan, is to maintain spore heat resistance and dormancy [25].

2 High-Resolution Architecture and Structural

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Fig. 2.1 Structure of a Bacillus spore: spore core (1), inner membrane (2), cortex (3), outer membrane (4), spore coat (5), exosporium (6), and appendages (7). Inset: spore coat with two crystalline layers of the outer spore coat

Bacillus and Clostridium Spore Morphology AFM images of various species of air-dried Bacillus and Clostridium-NT spores are presented in Fig. 2.2. As illustrated in Fig. 2.2, B. thuringiensis, B. cereus and B. anthracis native spores are enclosed within an exosporium sacculus (indicated with the letter E in Fig. 2.2a–d), which is larger than the dimensions of the spore body for two former species (Fig. 2.1a,c) and often tightly attached to the spore coat in the case of B. anthracis spores (Fig. 2.2d). The major part of the exposporium is reported to consist of two glycoprotein components [27, 28] and significant amounts of lipid (18%) and carbohydrate (20%), and smaller amounts of other components including amino sugars [29, 30]. It is constructed out of an inner part with three to four thin hexagonal crystalline layers, and an amorphous, hirsute layer on the outside [31, 32]. For B. anthracis spores, the exosporium is composed of a paracrystal basal layer and an external hair-like nap layer extending up to 600 nm in length [33] with approximately 20 exosporium-associated protein and glycoprotein species being identified [33–36]. The thickness of substrate-bound exosporium patches and of the hirsute layer as measured from the AFM height data (Fig. 2.2b) varied in the range 15–25 and 30–35 nm, respectively [1, 2], which corresponds well with earlier EM measurements [31, 32]. Apart from the 30–35 nm hirsute layer, the exosporium surface is frequently decorated with surface appendages [37–39]. These structures are most often described as hollow tubular filamentous extensions similar to pili of enterobacteria. The reported dimensions are variable but are in the range of 0.03–0.6 mm in width and 1.5–3.0 mm in length. These structures are most frequently described in the

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Fig. 2.2 AFM images of air-dried bacterial spores. (a, b) B. thuringiensis, (c) B. cereus, (d) B. anthracis, (e) B. atrophaes, and (f) C. novyyi-NT spores. In (b) AFM image of the B. thuringiensis exosporium showing a footstep (F) with numerous hair-like appendages (A2) and longer and thicker tubular appendage (A1). Surface ridges, extending along the entire spore length are indicated with white arrows in (a) and (c–e). Exosporium is indicated with letter E in (a–d). “Shell tail” in (f) is indicated with S. Images (b) and (c) reproduced, with permission from Ref. [1]. © (2005) Biophysical Society, USA

closely related B. cereus, B. anthracis and B. thuringiensis group. The number of appendages per spore varies from 3 to more than 20. It is not clear in the case of Bacillus spores if appendages originate on the spore coat or exosporium. These filaments could be of importance for spore attachment to surfaces or ligands. As illustrated in Fig. 2.2b, the filamentous exosporial appendages appeared to be attached to the outer surface of the exosporium. Two types of appendages were typically observed. The first type (indicated as A1) appeared to be tubular with a diameter and length in the range of 8–12 and 400–1,200 nm, respectively. Other appendages, such as those indicated as A2 in Fig. 2.1b, were 2.5–3.5 nm thick and typically 200–1,600 nm long. Six to ten appendages were seen on the exosporium surface. B. atrophaeus spores (Fig. 2.2e) do not possess exosporia, with the outer spore coat being the outermost surface. As illustrated in Fig. 2.2f, C. novyi-NT spores were encased in amorphous shells. Many spores exhibited ~200 nm thick shell “tails” at their poles (Fig. 2.2f) similar to “tails” visualized by EM [8]. Highresolution AFM images reveal that the outer shell surface typically consists of irregular amorphous material [8]. The most pronounced morphological features seen on the surfaces of air-dried Bacillus spores are ridges (indicated on several spores with arrows in Fig. 2.2),


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which typically extend along the long axis. Thickness of the ridges typically varies from 20 to 60 nm. Similar ridges were previously reported by electron microscopy [40] and AFM studies of various species of bacterial spores [1–3, 41].

Spore Size Distributions The interspecies distributions of spore length and width were determined for four species of Bacillus spores in aqueous and aerial phases (Fig. 2.3). It was found [1] that the dimensions of individual spores differ significantly depending upon species, growth regimes, and environmental conditions. Spores of B. thuringiensis are substantially larger (~50% higher and ~20% longer) than B. atrophaeus and

Fig. 2.3 Distribution of spore width (a) and length (b) for plate-grown (pg) and solution-grown (sg) B. atrophaeus and B. thuringiensis spores, and solution-grown B. subtilis spores. Images reproduced, with permission from Ref. [1]. © (2005) Biophysical Society, USA

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B. subtilis spores. The difference in average width and length between plate-grown and solution-grown spores of B. atrophaeus and B. thuringiensis suggest that environmental/physiological factors can have significant effects on spore dimensions. These findings could be useful in the reconstruction of environmental/preparation conditions during spore formation and for modeling the inhalation and dispersal of spores.

Spore Response to a Change in the Environment from Fully Hydrated to Air-Dried State AFM allows, for the first time, a direct comparison of fully hydrated and air-dried native spores visualized under water and in air, respectively [1]. Images of fully hydrated B. atrophaeus spores are presented in Fig. 2.4. Surface ridges, the prominent structural features of air-dried spores (Fig. 2.2), are typically absent from the surface of fully hydrated spores (Fig. 2.4). The surface morphology of fully hydrated

Fig. 2.4 AFM images showing the dynamic response of B. atrophaeus spores to dehydration. (a) Spore coat surface morphology of a fully hydrated spore. The area indicated with a square in (a) is shown at high resolution in (b). A shallow wrinkle on the surface is indicated in (b) with an arrow. In (c) the same area is shown after air-drying. The wrinkle seen in (b) developed into a fold/surface ridge (indicated with white arrow) with increased height and length. Structural alterations are seen in the surfaces morphology of a hydrated spore (d) and after air-drying (e). Formation of a surface ridge (indicated with an arrow) is seen in (e) and at higher resolution in (f) along with the emergence of a number of smaller folds


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and air-dried spores spans a wide range of folding motifs (Figs. 2.1 and 2.4). Therefore, direct visualization of individual spores is required in order to probe the dynamic response of this aqueous to aerial phase transition. This analysis was performed for 35 individual spores [1]. Spores were visualized under water, then air-dried for ~40 h, imaged in air (65% relative humidity), and reimaged after rehydration. Typical examples of hydration/dehydration ultrastructural transitions are presented in Fig. 2.4. As illustrated in Fig. 2.4a, the spore coat of a fully hydrated spore appears to be tightly attached to the cortex, excluding an area with an ~600 nm long wrinkle having a height of ~15–20 nm (Fig. 2.4a, b). Upon dehydration (Fig. 2.4c) this wrinkle becomes a surface ridge/fold extending along the entire length of the spore, accompanied by a height increase of ~50 nm. Similarly, the surface of another fully hydrated spore (Fig. 2.1d), exhibits an ~500 nm long fold (indicated with an arrow) having a height of ~30 nm. Upon dehydration, a new ~800 nm long surface ridge/fold (indicated with white arrow in Fig. 2.4e), having a height of ~40–60 nm and a number of smaller folds with a height range of ~10–30 nm, forms on the spore coat. These profound dehydrationinduced changes in spore surface architecture were found to be accompanied by a pronounced decrease in spore size. As illustrated in Fig. 2.5, the average width of 35 individual air-dried spores was reduced to 88% of the size measured for fully hydrated spores. Upon re-hydration of air-dried spores, they returned to 97% of their original size after 2 h in water, establishing the reversibility of the size transition (Fig. 2.5). The results from these individual spore measurements were confirmed by independent experiments (not presented here) where B. atrophaeus spore width was measured for two independent sets of ~200 spores in water and air, respectively. The width of the air-dried spore was again reduced to ~88% when compared with spores imaged in water. The observed decrease in the width of bacterial spores upon dehydration is apparently due to the contraction of the spore core and/or cortex. The ability of the coat to fold and unfold concomitant with changes in spore size was suggested [1, 41, 42] based on measurements of B. thuringiensis spore dimensions induced by humidity transients [43]. First direct visualization [1] of the response of native spores to dehydration/rehydration described above clearly demonstrates that the spore coat is itself does not shrink/expand but is flexible enough to compensate for the internal volume decrease of core/cortex compartments by surface folding and formation of ridges. These studies establish that the dormant spore is a dynamic physical structure. The observed folding could involve either the outer coat layer or the entire ensemble of inner and outer coat layers. In case of B. atrophaeus, if only the outermost rodlet layer (Fig. 2.4) was exclusively involved in folding, then due to the highly anisotropic rodlet structures, folding would most likely take place preferentially along the orientation of the rodlets. However, as seen in Fig. 2.4 folding of the coat takes place in arbitrary orientations with respect to the rodlet structures. This suggests that the whole spore coat folds with the inner surface of the coat disconnecting locally from the outer surface of the spore cortex. A number of ridges

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Fig. 2.5 Spore width variations of 35 individual B. atrophaeus spores, as a function of the size of the originally hydrated spore, following dehydration (24 h) (diamonds, dashed trend line) and rehydration (2 h) (triangles, dotted trend line). For ease of comparison, the original hydrated spore width is (redundantly) depicted as circles, which by definition lie on the solid y = x line. Thus, the three data points for one individual spore, depicted with the same color, are all on the same vertical line. Several spores detached from a substrate during rehydration experiments resulting in a smaller amount of experimental rehydration points (triangles). Solution-grown B. subtilis spores. Images reproduced, with permission from Ref. [1]. © (2005) Biophysical Society, USA

vary broadly for different Bacillus species. Thus the outer coat of B. thuringiensis spores typically exhibited less ridge formation when compared with B. atrophaeus and B. cereus spores. This finding suggests that the outer spore coat elastic properties may vary among spore-forming species.

High-Resolution Structure and Assembly of the Spore Coat The multilayer spore coat (Fig. 2.1) consists of structural proteins and small amounts of carbohydrate [24–26]. The spore coat plays an important role in spore protection and germination. Approximately 50 Bacillus spore coat proteins or coat protein orthologs have been identified by genomic and proteomic analysis [24–26, 44]. Despite the recent advances in biochemical and genetic studies [44], spore coat morphogenesis, which includes self-assembly of crystalline layers of the spore coat, is still poorly understood. In particular, it is not clear which spore coat


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proteins form the various spore coat layers, what their roles are in the coat assembly, and, finally, which proteins are surface-exposed and which ones are embedded beneath the surface. The elucidation of bacterial spore surface architecture and structure–function relationships is critical to determining mechanisms of pathogenesis, environmental resistance, immune response, and associated physicochemical properties. Thus, the development and application of high-resolution imaging techniques, which could address spatially explicit bacterial spore coat protein architecture at nanometer resolution under physiological conditions, is of considerable importance. We have directly visualized species-specific high-resolution native spore coat structures of bacterial spores including the exosporium and crystalline layers of the spore coat (Fig. 2.6) of various Bacillus [1–4, 6, 7] and Clostridium novyi-NT [8] species in their natural environment, namely air and fluid. For B. atrophaeus (Fig. 2.6a, b), and B. subtilis spores (data not shown here), the outer spore coat was composed of a crystalline rodlet layer with a periodicity of ~8 nm. Removal of the B. cereus and B. thuringiensis exosporium by sonication [1] or single cell French Press treatment [8] revealed crystalline rodlet (Fig. 2.6c) and hexagonal honeycomb (Fig. 2.6d) outer spore coat structures, respectively.

Fig. 2.6 High-resolution spore coat structures of Bacillus spores. The outer spore coats of B. atrophaeus (a, b), B. cereus (c), and B. thuringiensis (d) consist of crystalline layers rodlet and honeycomb structures. B. cereus spores contain a crystalline honeycomb structure (e) beneath the exterior rodlet layer (c). B. thuringiensis spore coats do not contain rodlet structures. Rodlet assemblies can be seen adsorbed to the substrate (f). Images reproduced, with permission from Ref. [1]. © (2005) Biophysical Society, USA

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The ~10 nm thick rodlet layer of B. cereus spores (Fig. 2.6c) is formed by multiple randomly oriented domains, comprised of parallel subunits with a periodicity of ~8 nm. The size of the domains is typically 100–200 nm. In contrast to the multi-domain rodlet structure of the B. cereus spore coat, typically only a single continuous domain was found to be present on the outer coat of B. atrophaeus (Fig. 2.6b) and B. subtilis spores. Multiple rodlet domains are less common. Generally, the main domain covers 60–100% of the spore surface, while 0–40% is covered by 0–10 smaller domains [3]. Complete removal of the exterior B. cereus rodlet layer by sonication revealed an underlying honeycomb structure (Fig. 2.6e) similar to the exterior spore coat layer of B. thuringiensis (Fig. 2.6d). For both species, the lattice parameter for the honeycomb structure is ~9 nm, with ~5–6 nm holes/pits (Fig. 2.6d, e). In case of B. thuringiensis spores, rodlet structures were not observed as an integral component of the spore coat [1, 3]; however, as illustrated in Fig. 2.6f, patches of extrasporal rodlet structures were observed adsorbed to the substrate [1, 3]. Rodlet width and thickness (Fig. 2.6f) were similar to those observed for B. atrophaeus, B. subtilis and B. cereus spore coat structures (Fig. 2.6a–c), which indicates that the similar rodlet proteins could be present during the sporulation in these three species of Bacillus spores. Similar rodlet and honeycomb crystalline structures to those seen in Fig. 2.6 were observed in freeze-etching EM studies of several species of Bacillus spores [32, 40] and AFM studies of fungal spores [45]. Note that in the case of B. thuringiensis, spore coat rodlet structures were not observed in freeze-etching EM [32, 40]. Little is known about the assembly, physical properties, and proteomic nature of these bacterial spore rodlets. The closest structural and functional orthologs to the Bacillus species rodlet structure (not its protein sequence) are found outside the Bacillus genus. Several classes of proteins, with divergent primary sequences, were found to form similar rodlet structures on the surfaces of cells of gram-negative Escherichia coli and Salmonella enterica, as well as on spores of gram-positive streptomycetes and various fungi (for the review see Ref. [46]). Hydrophobins, a new class of structural proteins [47], were shown to be necessary for and an integral component of rodlet fungal spore surface structures. Hydrophobins can self-assemble and produce layers of rodlet structures at water–air interfaces [47]. Fungal hydrophobin rodlet layers cause hyphal fragments and spores to become water-repellant, which enables escape from the aqueous environment and stimulates aerial release, dispersal and attachment to hydrophobic host surfaces [46]. However, while hydrophobin-like proteins are found in fungal spores, it has not been possible to identify orthologs of these proteins in bacterial spores [48]. These similarities in crystalline outer coat layer motifs found in prokaryotic and eukaryotic spore types are a striking and unexpected example of the convergent evolution of critical biological structures. Further investigation is required to determine the molecular composition of prokaryotic endospore rodlets and their evolutionary relationship to eukaryotic rodlet structures. To observe the structure of the C. novyi-NT spore coat beneath the amorphous shell, we developed procedures to remove the shells by chemical treatment with various reducing agents and detergents or by physical treatment using a French


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Press [8]. When either French Press or chemical treatments were used, the majority of the exposed spore coat surface is formed by an ~8–10 nm thick honeycomb layer with a periodicity of 8.7 ± 1 nm (Fig. 2.7a). We have found that during the germination, the spores often had partly or completely lost their honeycomb layers, revealing the underlying layers (Fig. 2.7b). Note that a number of spores, as judged by AFM observations, do not possess the amorphous layer. Furthermore, the presence of the amorphous material sandwiched between the spore coat and coat-associated honeycomb layers combined with the quick disappearance of these honeycomb layers during AFM germination experiments (Fig. 2.7) [8], all indicate that these C. novyi-NT honeycomb layers are not an integral part of the spore coat, as the “rodlet layer” or “honeycomb layer” is for Bacillus species (Fig. 2.6) [1–3], but rather are a parasporal layer with an increased affinity for the spore coat. As seen in Fig. 2.7b–e, the removal of the honeycomb layer revealed a multilayer structure formed by ~6 nm thick smooth layers. Typically, there were three to six layers exposed on the spore surface. The spore coat surface patterns (Fig. 2.7b–e) were very similar to ones observed on the surfaces of inorganic, organic, and macromolecular crystals [49–52]. As seen in Fig. 2.7b–e, these crystalline spore coat layers exhibited growth patterns typically observed on inorganic and macromolecular crystals. These patterns include steps and growth spirals originating from screw dislocations, such as those previously described in studies of the crystallization of semiconductors [53], salts [54], and biological macromolecules [51, 52]. In the middle of the growth centers, the dislocations cause depressions, typically 90%) cotE spores, the outermost structure is formed by three to five crystalline layers, each of which is ~6 nm thick (Fig. 2.10b), which likely correspond to the inner coat layers, as is the case for the coats of Clostridium novyi (Fig. 2.7) spores [8]. Note that remnants of small patches of rodlet structures or groups of several individual rodlets were seen on the majority of cotE spores (Fig. 2.10b). Furthermore, surfaces of some cotE mutant spores exhibit patches or large regions covering the spore of a hexagonal crystalline layer (located between the rodlet layer and the inner coat multilayer structure) (Fig. 2.10b). Surfaces of gerE spores were found to lack completely both amorphous and rodlet structures, being encased in several inner spore coat layers [7]. Note that the number of inner coat layers was found to be less on gerE spores compared with cotE spores. Finally, spores lacking both CotE and gerE proteins (cotEgerE spores) were found to lack all outer and inner coat structures [7]. The outer surface of CotEgerE spores was found to be quite smooth and corresponds likely to the spore cortex, which is typically located in wild type spores under the multilayer spore coat structure (Fig. 2.1). Our recent comprehensive analysis of a wide range of B. subtilis mutants, which lack various spore coat proteins (data are not presented here) here, have provided improved understanding of the spore coat architecture and assembly.

Fig. 2.10 AFM images of B. subtilis spores of different strains. The spores analyzed were wildtype (a), cotE (b), gerE (c), and cotEgerE (d). Images reproduced, with permission from Refs. [6, 7]. © (2008) American Society for Microbiology


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Mechanisms of Spore Germination Upon exposure to favorable conditions, metabolically dormant Bacillus and Clostridium spores break dormancy through the process of germination [81–83] and eventually reenter the vegetative mode of replication. A comprehensive understanding of the mechanisms controlling spore germination is of fundamental importance both for practical applications related to the prevention of a wide range of diseases by spore-forming bacteria (including food poisoning and pulmonary anthrax), as well as for fundamental studies of cell development. Germination involves an ordered sequence of chemical, degradative, biosynthetic, and genetic events [81, 83]. While significant progress has been made in understanding the biochemical and genetic bases for the germination process [81], the role of the spore coat in the germination remains unclear [24, 81]. Spore coat structure regulates the permeation of germinant molecules [84, 85]. It is believed that penetration of germinants proceeds through pores in the coat structure and may involve GerP proteins [85]. We have recently developed [4, 8] in vitro AFM methods for molecular-scale examination of spore coat and germ cell wall dynamics during spore germination and outgrowth. To obtain a comprehensive understanding of the role of the spore coat in germination, AFM imaging on a nanometer scale is required. At this scale, the outer layer of the B. atrophaeus spore coat is composed of a crystalline rodlet array (Figs. 2.6a, b and 2.11a) containing a small number of point and planar (stacking fault) defects [3]. Upon exposure to the germination solution, disassembly of the rodlet structures was observed [4]. During the initial stages of germination, the disassembly was initiated through the formation of 2–3 nm wide micro etch pits in the rodlet layer (Fig. 2.11b). Subsequently, the etch pits formed fissures (Fig. 2.11b–d) that were, in all cases, oriented perpendicular to the rodlet direction. Simultaneously, etching commenced on the stacking faults (Fig. 2.11e,f) revealing an underlying hexagonal inner spore coat layer (Fig. 2.11g). Note that the hexagonal layer was previously observed [6] beneath the rodlet layer on B. subtilis spores (Fig. 2.10b). During later stages of germination, further disintegration of the rodlet layer (Fig. 2.11e, f) proceeded by coalescence of existing fissures, their autonomous elongation (at a rate of ~10–15 nm/h) and widening (at ~5 nm/h), and by continued formation of new fissures. Disassembly of the higher-order rodlet structure began prior to the outgrowth stage of germination (Fig. 2.12). Disaggregation of the rodlet layer occurred perpendicular to the orientation of individual rodlets resulting in the formation of banded remnants (Fig. 2.12). Further structural disruption led to the formation of extended, 2–3 nm wide, fibrils (indicated with arrows in Fig. 2.12e) which were also oriented perpendicular to the rodlet direction. The AFM studies presented here elucidate the time-dependent structural dynamics of individual germinating spores and reveal previously unrecognized nano-structural alterations of the outer spore coat. Disassembly of the higher-order rodlet structure initiates at micro-etch pits, and proceeds by the expansion of the pits to form

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Fig. 2.11 Disintegration of the spore coat layer. (a) The intact rodlet layer covering the outer coat of dormant B. atrophaeus spores is ~11 nm thick, and has a periodicity of ~8 nm (1–3). (b–d) Series of AFM images tracking the initial changes of the rodlet layer after (b) 13 min, (c) 113 min, and (d) 295 min of exposure to germination solution. Small etch pits (indicated with arrows in b) evolve into fissures (indicated with an arrow in c) perpendicular to the rodlet direction. The fissures expand both in length and width. (e, f) Series of AFM images showing another germinating spore. The spore long axis, as well as major rodlet orientation is left–right. Enhanced etching at stacking faults (running from left to center and indicated with an arrow in e), as well as increased etching at the perpendicular fissures were visible following (e) 135 min and (f) 240 min of germination. Fissure width and length increased from 10–15 and 100–200 nm (135 min) to 15–30 and 125–250 nm (240 min), respectively. (g) Etching and/or fracture of the rodlet layer at a stacking fault revealed the underlying hexagonal layer of particles with a 10–13 nm lattice period. Images reproduced, with permission from Ref. [4]. © (2007) National Academy of Sciences, USA

fissures perpendicular to the rodlet direction. What causes this breakdown of the rodlet layer? We proposed [4] that rodlet structure degradation is caused by specific hydrolytic enzyme(s), located within the spore integument and activated during the early stages of germination. The highly directional rodlet disassembly process suggests that coat degrading enzymes could be localized at the etch pits, and either recognize their structural features, or that the etch pits are predisposed to structural deformation during early stages of spore coat disassembly.


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Fig. 2.12 (a–d) Series of AFM height images showing the progress of rodlet disassembly. In the circled regions, banded remnants of rodlet structure (a) disassemble into thinner fibrous structures (d). Time between images was 36 min (a, b); 3 min (b, c) and 6 min (c, d), for a total time between (a, d) of 45 min. In (b), the area imaged in (c) is indicated with a light grey box. In (b, c) the area imaged in (a, d) is indicated with a dark grey box. In (e), which is an enlarged part of (d), arrows indicate the end point of rodlet disruption, i.e. fibrils with a diameter of 2–3 nm, oriented roughly perpendicular to the rodlets. Images reproduced, with permission from Ref. [4]. © (2007) National Academy of Sciences, USA

The gradual elongation of the fissures suggests that once hydrolysis is initiated at an etch pit, processive hydrolysis propagates perpendicular to the rodlet direction and to neighboring rodlets. The locations of the small etch pits may coincide with point defects in the rodlet structure. These point defects could be caused by misoriented rodlet monomers or by the incorporation of impurities into the crystalline structure. In both cases, point defects could facilitate access of degradative enzymes to their substrate in an otherwise tightly packed structure. Recent proteomic and genetic studies suggest that the inner and outer spore coats of Bacillus subtilis, which is closely related to Bacillus atrophaeus, are composed of over 50 polypeptide species [24]. However, it is unknown which of these proteins form the surface rodlet layer of the spore coat or how this outer spore coat layer is assembled. We have shown previously for B. cereus [1] and B. subtilis [7] spores and here for Bacillus atrophaeus spores (Fig. 2.11g) that the outer spore coat rodlet layer is underlain by a crystalline honeycomb structure.

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Several classes of proteins, with divergent primary sequences, were found to form similar rodlet structures on the surfaces of cells of gram-negative Escherichia coli and Salmonella enterica as well as spores of gram-positive streptomycetes and various fungi [46]. These rodlets were shown to be structurally highly similar to amyloid fibrils [46]. Amyloids possess a characteristic cross b-structure and have been associated with neural degenerative diseases (i.e., Alzheimer’s and prion diseases) [86]. Amyloid fibrils or rodlets form microbial surface layers [46], which play important roles in microbial attachment, dispersal, and pathogenesis. We have proposed [4] that the structural similarity of B. atrophaeus spore coat rodlets and the amyloid rodlets found on other bacterial and fungal spores suggests that Bacillus rodlets have an amyloid structure. AFM characterization of the nanoscale properties of individual amyloid fibrils has revealed that these self-assembled structures can have a strength and stiffness comparable to structural steel [87]. The extreme physical, chemical, and thermal resistance of Bacillus endospores suggests that evolutionary forces have captured the mechanical rigidity and resistance of these amyloid selfassembling biomaterials to structure the protective outer spore surface. Structural studies of amyloids have identified an array of possible rodlet assemblies, each consisting of several (two or four) individual cross-b-sheet fibrils, which are often helically intertwined [46]. The number of fibrils determines the diameter of the rodlet. Most amyloids resulting from protein-folding diseases, and some naturally occurring amyloids, form individual fibrils or disorganized rodlets networks. In spore coats of B. atrophaeus, the higher-order rodlet structure is organized as one major domain of parallel rodlets covering the entire spore surface [3]. Rodlet domain formation requires there must be periodic bonds in the rodlet direction (“parallel bonds”) as well in the direction perpendicular to it (“perpendicular bonds”) [88]. In the case of amyloid-like rodlets, the intra-rodlet, parallel bonds are known and consist primarily of hydrogen bonds associated with the cross-b sheets that form the backbone of the rodlet fibrils. However, the nature of the perpendicular bonds, i.e., the inter-rodlet bonds that keep the rodlets tightly packed, is unknown. Interestingly, for B. atrophaeus the ratio of length (parallel to rodlet direction) and width (perpendicular to rodlet direction) of the rodlet domains is on average ~1, indicating that during formation of these domains, growth velocity was similar in both directions, and hence parallel and perpendicular bonds were similar in strength. Based on these rodlet features, one might expect that during germination individual rodlets would detach or erode, leaving a striated pattern parallel to the rodlet direction. Surprisingly, striations perpendicular to the rodlet direction were observed (Fig. 2.12), and 2–3 nm wide fibrils perpendicular to the rodlet direction (Fig. 2.12e) were the culmination product of coat degradation. This result indicates that during germination, perpendicular rodlet bonds are stronger, or are more resistant to hydrolysis, than bonds parallel to the rodlet direction. Second, and most surprisingly, these perpendicular structures facilitate the formation of 200–300 nm long fibers perpendicular to the rodlet direction. It is unclear how microbial amyloid fibers form these perpendicular structures. One possibility is that during formation of the rodlet layer, both intra-rodlet parallel


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Fig. 2.13 (a–d) Series of sequential AFM amplitude images showing passage of sub-surface steps during the early stages of germination. The central step visible in (a, b) has a height of 18 nm and a velocity of ~10 nm/s. Scan direction is down (a, c), up (b, d); time between images is 36 s. (e) AFM amplitude image showing sub-surface permanent ring structures, corresponding to a height difference of 4–8 nm, at 65 min into germination. In general, observed step heights range from –10 to 0 to 25 nm, and velocities range from 0 to 100 nm/s

bonds and inter-rodlet perpendicular bonds form, similar in strength and leading to tern. During germination, the intra-rodlet parallel bonds are hydrolyzed, while the inter-rodlet perpendicular bonds remain intact over longer time periods. Spore coat hydrolytic enzymes could target a specific residue or structure (in this case, that of the cross-b sheets) and leave other (here, perpendicular) residues or structures intact. Identification of the gene(s) encoding the rodlet structure and the enzymes responsible for rodlet degradation are important areas for future research. Although in vitro AFM is a surface imaging technique, internal structural changes that are physically separated from the probe tip by the thin rodlet layer could be visualized, much as the arrangement of ribs beneath the skin is apparent to a finger passing over them, or, as in other AFM applications, the visualization of the cytoskeleton network beneath the surface of the cell [89]. During early stages of the germination process, movement of 2–10 nm steps beneath the rodlet structure was consistently recorded (Fig. 2.13a–d), which resulted in the formation of a pronounced ring structure beneath the outer spore coat surface (Fig. 2.2e). Moving steps were either ascending or descending with step velocities up to ~100 nm/s.

Emergence of Vegetative Cells Etch pits were the initiation sites for early germination-induced spore coat fissure formation. During intermediate stages of germination, small spore coat apertures developed that were up to 70 nm in depth (Fig. 2.14b). During late stages of germination these apertures dilated (Fig. 2.14c–e) allowing vegetative cell emergence (data not shown).

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Fig. 2.14 Emergence of vegetative cells. (a–g) Series of AFM height images showing 60–70 nm deep apertures in the rodlet layer (indicated with arrows in (b)) that gradually enlarged (c, d), and subsequently eroded the entire spore coat (e). Germ cells emerged from these apertures. (e) Prior to germ emergence from the spore coat, the peptidoglycan cell wall structure was evident. (f) At an early stage of emergence, the cell wall was still partly covered by spore remnants, while (g) immediately prior to cell emergence, the cell wall was free of spore integument debris. The germ cell surface contained 1–6 nm fibers forming a fibrous network enclosing pores of 5–100 nm. Images in (a–g) were collected on the same spore as those shown in Fig. 11e,f. Elapsed germination time (in h:min) was (a) 3:40, (b) 5:45, (c) 7:05, (d) 7:30, (e) 7:45, (f) 7:15, (g) 7:50. (h) In separate experiments, cultured vegetative B. atrophaeus cells were adhered to gelatin surfaces and imaged in water. AFM height images show a slightly denser, similar fibrous network compared with the germ cell network structure (g), with 5–50 nm pores. In the inset, the imaged part (h) of the entire cell is indicated with a white rectangle. Images reproduced, with permission from Ref. [4]. © (2007) National Academy of Sciences, USA


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In vitro AFM visualization of germling emergence allowed high-resolution visualization of nascent vegetative cell surface structure (Fig. 2.14e–g). Vegetative cell wall structure could be recognized through the apertures approximately 30–60 min prior to germ cell emergence. The emerging germ cell surface was initially partially covered with residual patches of spore integument (Fig. 2.14f). During the release of vegetative cells from the spore integument, the entire cell surface consisted of a porous fibrous network (Fig. 2.14g). In order to compare the cell wall structure of germling and mature vegetative cells, we carried out separate experiments in which cultured vegetative B. atrophaeus cells were adhered to a gelatin-coated surface [4], and imaged with AFM in water. As seen in Fig. 2.14h, the cell wall of mature vegetative cells contained a porous, fibrous structure similar to the structure observed on the surface of germling cells (Fig. 2.14g). The bacterial cell wall consists of long chains of peptidoglycan that are crosslinked via flexible peptide bridges [91, 92]. While the composition and chemical structure of the peptidoglycan layer vary among bacteria, its conserved function is to allow bacteria to withstand high internal osmotic pressure [91]. The length of peptidoglycan strands varies from 3 to 10 disaccharide units in S. aureus to ~100 disaccharide units in B. subtilis, with each unit having a length and diameter of ~1 nm [92]. The fibrous network observed on the germ cell surface with 5–100 nm pores (Fig. 2.14e, g), and the fibrous network observed on mature vegetative cells with 5–50 nm pores (Fig. 2.14h) appear to represent the nascent peptidoglycan architecture of newly formed and mature cell wall, respectively, and is comprised of either individual or several intertwined peptidoglycan strands. The cell wall density of mature cells appears to be higher with, on average, smaller pores and more fibrous material, as compared to the germ cells. These results are consistent with murein growth models whereby new peptidoglycan is inserted as single strands and subsequently cross-linked with preexisting murein [93]. The AFMresolved pore structure of the nascent B. atrophaeus germ and vegetative cell surfaces is similar to the honeycomb structure of peptidoglycan oligomers determined by NMR [91]. Note, the AFM data presented here suggests that peptidoglycan structure rearrangement may occur prior to the formation of the fibrous cell wall network. As seen in Fig. 2.13, during the early stages of germination, movement of 0–25 nm steps beneath the outer spore coat and formation of pronounced ring structures occurred. Similar concentric rings were observed by EM [94] and AFM [95] in newly divided gram-positive cell walls. It was suggested [95] that these rings were caused by peptidoglycan structural rearrangements during cell division. The rings and steps observed during the early stages of germination could be caused by peptidoglycan restructuring that accompanies maturation of the nascent sacculus [96]. The structural dynamics of C. novyi-NT [8] and B. atrophaeus germinating spores appears to be similar. Thus, at later stages of the germination process, the C. novyi-NT spore coat layers seen in Fig. 2.15, which are exposed at early stages of germination start to dissolve (Fig. 2.15). Thus this process was initiated by the formation of fissures (Fig. 2.15a), which subsequently widened and elongated

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Fig. 2.15 Dynamic AFM height imaging of degrading C. novyi-NT spore coat layers. Fissures first appeared (a, b), then laterally expanded into wide gaps (c–e) and eventually resulted in the removal of whole layers, exposing the underlying layer (e, f, arrows in (e)). One expanding fissure is indicated with a white oval in (a–f). Time in germination medium in h:min was 0:45 (a), 0:50 (b), 0:55 (c), 1:00 (d), 1:05 (e), 1:10 (f). Images reproduced, with permission from Ref [8]. © (2007) American Society for Microbiology

(Fig. 2.15b–e), resulting in isolated islands of remnant coat layers (Fig. 2.15e, f). The dissolution of coat layers revealed an underlying undercoat layer (marked with arrows in Fig. 2.15e). Similarly to B. atrophaeus spore germination mechanisms described above, coat degradation likely occurs under the influence of germination-activated lytic enzymes. In fact, such lytic enzymes are known to be encoded within the C. novyiNT genome [97]. Interestingly, C. novyi-NT spores contain mRNA, and these mRNA molecules are enriched in proteins that could assist with cortex and other degradation [97]. At the final stages of germination, the coat layers dissolved completely (Fig. 2.16a), fully exposing the ~20–25 nm thick undercoat layer. In the following stage of germination this layer also disintegrated. This proceeded through the formation and slow expansion of ~25 nm deep flat-bottomed apertures (Fig. 2.16a–f). The cortex was fully lysed by the time spore coat layers dissolved. Hence, the flatbottomed apertures in this undercoat layer show the underlying cell wall of the emerging C. novyi-NT vegetative cell, which, based on its lighter AFM phase contrast (Fig. 2.16f), has different physicochemical properties or/and hence, composition than the surrounding coat remnants. The nascent surface of the emerging germ cell appears to be formed by a porous network (Fig. 2.16e–f) of peptidoglycan fibers, similar to one described above for B. atrophaeus vegetative cells (Fig. 2.14g, h).


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Fig. 2.16 (a–e) AFM height images of the final outgrowth stage. (a) After the ~6 spore coat layers were largely dissolved, the underlying structural layer was exposed. (b–e) In this layer, 25 nm deep apertures appeared and grew laterally. (f) Phase image zoom-in of the largest aperture depicted in (c–e), showing the pronounced phase contrast, indicating the different material properties of the emerging cell wall (light) and remaining spore layer (dark). Inset in (f) is the concurrent height image, showing the 25 nm deeper position of the cell wall with respect to the surrounding spore layer. Time in germination medium in h:min was 1:40 (a), 2:15 (b), 2:50 (c), 3:35 (d), 3:50 (e), 3:55 (f). Images reproduced, with permission from Ref. [8]. © (2007) American Society for Microbiology

Note that the spore coat degradation process presented in Figs. 2.11–2.16 appears not to be affected by the scanning AFM tip [48]. The shapes of fissures and apertures remained unaltered after repeated scanning. Furthermore, when we zoomed out to a larger previously non-scanned area after prolonged scanning on a smaller spore area, the initially scanned area did not display any tip-induced alterations (such as a larger degree of coat degradation). Finally, when we did not image spores for more than an hour between two scans, the coat degradation pattern had developed similarly when compared with spores that were scanned continuously. Spore germination provides an attractive experimental model system for investigating the genesis of the bacterial peptidoglycan structure. Dormant spore populations can be chemically cued to germinate with high synchrony [81], allowing the generation of homogenous populations of emergent vegetative cells suitable for structural analysis. Proposed models for the bacterial cell wall structure posit that peptidoglycan strands are arranged either parallel (planar model) or orthogonal (scaffold model) to the cell membrane [90, 91]. Existing experimental techniques are unable to confirm either the planar or the orthogonal model. The experiments described here do not contain sufficient high-resolution data, in particular of individual peptidoglycan

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strands, to deduce with certainty the tertiary three-dimensional peptidoglycan structure. The pore structures (Figs. 2.14 and 2.16) of the emergent germ and mature vegetative cell wall – an array of pores – suggest a parallel orientation of glycan strands with peptide stems positioned in stacked orthogonal planes [91]. More detailed studies of germ cell surface architecture and morphogenesis will be required to confirm this peptidoglycan architecture and to investigate whether glycan biosynthesis precedes peptide cross-linking. The results presented here demonstrate that in vitro AFM has the capacity to provide important insight into peptidoglycan architecture and the biological role of the cell wall in critical cellular processes and antibiotic resistance.

Bacteria–Mineral Interactions on the Surfaces of Metal-Resistant Bacteria We are currently conducting studies on the elucidation of bioremediation mechanisms of Arthrobacter oxydans metal-resistant bacteria. A. oxydans is a gram- positive and chromium (VI)-resistant bacterium, which can reduce highly mobile, carcinogenic, mutagenic, and toxic hexavalent chromium to less mobile and much less toxic trivalent chromium. Toxic compounds and heavy metals can be removed from contaminated cites or waste by chemical and physical techniques, which are both difficult and expensive. The extraordinary ability of indigenous microorganisms, like metal-resistant bacteria, for biotransformation of toxic compounds is of considerable interest for the emerging area of environmental bioremediation. However, the underlying mechanisms by which metal-resistant bacteria transform toxic compounds are currently unknown and await elucidation. Stress response pathways are sure to play an important role in the niche definition of metal-resistant bacteria and their effect on the biogeochemistry of many contaminated environments. The present technological and scientific challenges are to elucidate the relationships between the stress-induced organization and function of protein and polymer complexes at bacterial cell wall surfaces, to understand how these complexes respond to environmental changes and chemical stimulants, and to predict how they guide the formation of biogenic metal phases on the cell surface. We have visualized air-dried A. oxydans bacteria and revealed the differences in surface morphology and flagella arrangements during different stages of bacterial growth. Thus, bacteria during the exponential stage growth (Fig. 2.17a) appear to have a rather smooth surface and show a peritrichous flagellar arrangement with flagella seen over the entire cellular surface. The surface of air-dried bacteria grown during the stationary phase (Fig. 2.17b) appears to be tubular (Fig. 2.17b, inset) and these bacteria show the lophotrichous flagellar arrangement with several flagella seen only at one pole of the cell. We have further visualized for the first timestress responses of A. oxydans bacteria in response to the exposure to the toxic environment. Thus, as illustrated in Fig. 2.17c, the formation of a supramolecular crystalline hexagonal structure on the


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Fig. 2.17 AFM and SEM images of A. oxydans bacteria. (a, b) Growth-dependent morphologies; (c) stress-induced supramolecular crystalline hexagonal layer on the bacterial surface; (d) stressinduced microbial extracellular polymers (MEP) layer covering a microbial colony; (e–f) SEM images of bacteria as a function of exposure time to Cr (VI). (e) 18 days; (d) 1 year

surface of A. oxydans bacteria exposed to 35–50 ppm Cr (VI) was observed. Since similar crystalline layers are not seen on control samples, this structure appears to be stress-induced in response to Cr (VI) exposure. At higher Cr (VI) concentrations, we have observed the formation of microbial extracellular polymers (MEP), which are seen in Fig. 2.17d, to cover a small microbial colony. Our AFM observations of the appearance of stress-induced layers on the surfaces of A. oxydans bacteria exposed to Cr (VI) are consistent with biochemical and electron microscopy (EM) studies of stress responses of A. oxydans bacteria. Thus, it was reported that A. oxydans grown with chromate concentrations above 40 mg/L significantly increased the production of a cell wall protein that had an apparent molecular mass of 60 kDa [98]. Presumably, this protein could form, as seen in Fig. 2.17c, a highly organized particulate layer on the surface of A. oxydans bacteria exposed to Cr (VI). The hexagonal stress-induced structure (Fig. 2.17c) is formed by a protein with the size of ~10–11 nm. High-resolution images (Fig. 2.17c, inset) reveal that these particles are oligomers, composed of monomers with a size of ~5 nm. Assuming the globular shape of the protein, this size corresponds well to the molecular mass of ~60 kDa. This 60 kDa protein was found to be positively charged and to act as an ion trap to bind negatively charged ions such as the soluble chromium anion (CrO4)2- [98]. Indeed, scanning electron microscopy (SEM) images of A. oxydans exposed to 40–50 ppm of chromate clearly showed that the surface of A. oxydans grown

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with Cr(VI) was coated with an array of particles (Fig. 2.17e). These nanoparticles remained on the surface of A. oxydans for months before they were released into the immediate environment either individually or with other cell envelope materials as a shell (Fig. 2.17f), thereby maintaining basic vital processes such as growth and division, as well as nutrient transport. We are currently developing procedures for in vitro high-resolution AFM characterization of the surface architecture, and structural dynamics of metal-resistant bacteria in response to changes in the environment and various chemical stimuli. It is expected that these experiments will improve the fundamental understanding of bioremediation mechanisms. The results presented here demonstrate that in vitro AFM is a powerful tool for revealing the structural dynamics and architectural topography of the microbial and cellular systems. AFM allows new approaches to high-resolution real-time dynamic studies of single microbial cells under native conditions. Environmental parameters (e.g., temperature, chemistry or gas phase) can be easily changed during the course of AFM experiments, allowing dynamic environmental and chemical probing of microbial surface reactions. Further incorporation of AFM-based immunolabeling techniques could allow the identification of spore coat proteins that play a role in spore germination, and provide a structural understanding of how these proteins regulate spore survival, germination, and disease. Acknowledgments The authors thank B. Vogelstein, T.J. Leighton, P. Setlow and H.-Y. Holman for spore and bacteria preparations, and helpful discussions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract number DE-AC52–07NA27344. This work was supported by the Lawrence Livermore National Laboratory through Laboratory Directed Research and Development Grants 04-ERD002 and 08-LW-027, and was funded in part by the Federal Bureau of Investigation.

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Part II

Dynamic Spectroscopic SPM

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Chapter 3

Dynamic Force Microscopy and Spectroscopy in Ambient Conditions: Theory and Applications Hendrik Hölscher, Jan-Erik Schmutz, and Udo D. Schwarz

Introduction Since its introduction in 1986 [1] the atomic force microscope become a standard tool in surface physics. In early experimental setups, a sharp tip located at or near the end of a microstructured cantilever profiled the sample surface in direct mechanical contact (contact-mode) to measure the force acting between tip and sample. Maps of constant tip–sample interaction force, which are usually regarded as representing the sample’s “topography,” were then recovered by keeping the deflection of the cantilever constant. This is achieved by means of a feedback loop that continuously adjusts the z-position of the sample during the scan process so that the output of the deflection sensor remains unchanged at a preselected value (setpoint value). Despite the widespread success of contact-mode AFM in various applications, the resolution was found to be limited in many cases (in particular for soft samples) by lateral forces acting between tip and sample. In order to avoid this effect, it has been proven to be advantageous to vibrate the cantilever in vertical direction near the sample surface. AFM imaging with oscillating cantilever is often denoted as dynamic force microscopy (DFM). In most cases, short-range tip–sample forces, which might be repulsive as well as attractive in nature, are responsible for the topographic contrast observed in AFM or DFM. Since the oscillation amplitudes of the oscillating cantilever are typically much higher than the interaction range of these forces, the tip “feels” the influence of the surface only during a short period of an individual oscillation, making nanoscale cantilever dynamics in atomic force microscopes inherently nonlinear.

H. Hölscher (*) Institute for Microstructure Technology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany e-mail: [email protected] S.V. Kalinin and A. Gruverman (eds.), Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy, DOI 10.1007/978-1-4419-7167-8_3, © Springer Science+Business Media, LLC 2010

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To further complicate matters, cantilever dynamics is additionally governed by the specifics of how the oscillation is performed, as several distinct methods to drive the cantilever exist. For instance, the historically oldest scheme of cantilever excitation in DFM imaging is the external driving of the cantilever at a fixed excitation frequency chosen to be exactly at or very close to the cantilever’s first resonance [2–4]. For this driving mechanism, different detection schemes measuring either the change of the oscillation amplitude or the phase shift between driving signal and resulting cantilever motion were proposed. Over the years, the amplitude modulation (AM) mode, where the actual value of the oscillation amplitude is employed as a measure of the tip–sample distance, has been established as the most widely applied technique for ambient conditions and liquids. Another method to oscillate the cantilever is the frequency-modulation (FM) mode. It was primarily developed for application in vacuum where standard AFM cantilevers made from silicon or silicon nitride exhibit very high quality factors Q, what makes the response of the system slow if driven in AM mode. Therefore, Albrecht et al. [5] introduced in 1991 the FM mode, which works well for high-Q systems and consequently developed into the dominating driving scheme for DFM experiments in ultrahigh vacuum (UHV) [6–9]. In contrast to the AM mode, this approach features a so-called self-driven oscillator [10, 11], which uses the cantilever deflection itself as drive signal, thus ensuring that the cantilever instantaneously adapts to changes in the resonance frequency. In this review, we present a detailed theoretical analysis of the basic features of DFM driven in any of these two modes. For this purpose, we first highlight the similarities and differences between externally driven and self-driven cantilevers before we explicitly include tip–sample interactions. We close our overview by some experimental examples demonstrating the features of dynamic force spectroscopy (DFS) using the FM mode.

General Theory of Dynamic Force Microscopy Formulation of the Problem and Basic Equation of Motion A sketch of the experimental setup of a dynamic force microscope utilizing the amplitude-modulation technique is shown in Fig. 3.1. The deflection of the cantilever is typically measured with the laser beam deflection method as indicated [12, 13], but other displacement sensors such as interferometric sensors [14–16] can be applied as well. During operation in conventional AM mode, the cantilever is driven at a fixed frequency by a constant-amplitude signal originating from an external function generator, while the resulting oscillation amplitude and/or the phase shift are detected by a lock-in amplifier. The function generator supplies not only the signal for the dither piezo; its signal serves simultaneously as a reference for the lock-in amplifier in the analyzer electronics.

3 Dynamic Force Microscopy and Spectroscopy in Ambient Conditions photo diode

laser

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analyzer phase or frequency amplitude amplifier

z

piezo

D+2A

aexc

d D

θ0

sample

PID

function generator

amplitude

phase shifter

setpoint

x−y−z−scanner

Fig. 3.1 Schematic drawing of the experimental setup of a dynamic force microscope where the driving of the cantilever can be switched between amplitude-modulation (AM) mode (solid lines) or frequency-modulation (FM) mode (dashed lines). While the cantilever in the AM mode is externally driven with a frequency generator producing a fixed frequency, the FM mode exhibits a feedback loop consisting of a time (“phase”) shifter and an amplifier. In both cases we assume that the laser beam deflection method is used to measure the oscillation of the tip which oscillates between the nearest tip–sample position D and D + 2A. The equilibrium position of the tip is denoted as d

In contrast, a dynamic force microscope driven in the FM mode has no external driving imposing a fixed frequency, but a feedback circuit consisting of an amplifier and a phase shifter (dashed lines in Fig. 3.1). The properly amplified and time- (i.e., phase-)shifted displacement sensor signal is then used to excite the dither piezo driving the cantilever.1 Two different driving techniques have been established for use with the FM mode: The original constant-amplitude (CA) driving scheme, where the oscillation amplitude of the cantilever is held constant by an automatic gain control (AGC) [5] and the constant-excitation (CE) driving scheme [18, 19], where the excitation amplitude of the cantilever driving is kept constant. Both the CE driving scheme [20–24] as well as the CA driving scheme [25–28] are frequently used in air and liquids. However, since the amplitude can be used as a feedback signal for scanning in the CE driving scheme, its implementation is easily possible for an existing DFM build for AM mode applications in air and liquid (cf. Fig. 3.1). Therefore, a comparison of both modes is especially straightforward by focussing just on the constant-excitation driving scheme if operating in FM mode. It is also possible to implement the FM-mode with the help of a phase-looked loop (PLL) [17].

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Based on the above description of the experimental setup, we can formulate the basic equation of motion describing the cantilever dynamics in DFM [29, 30]:

mz(t ) +

2 π f0 m z(t ) + cz ( z(t ) − d ) = Fts [z(t ), z(t )]    Q0 tip − sample force

 aexc cz cos(2πfd t )  +  aexc  − A cz z(t − t0 )

for AM mode,

(3.1)

for FM mode.

Here, z(t) is the position of the tip at the time t; cz, m, and f 0 = (cz / m) / (2π) are the spring constant, the effective mass, and the eigenfrequency of the cantilever, respectively. Somewhat simplifying, it is assumed that the quality factor Q0 unites the intrinsic damping of the cantilever and all influences from surrounding media such as air or liquid, if present, in a single overall value. The equilibrium position of the tip is denoted as d. The (nonlinear) tip–sample interaction force Fts is introduced by the first term on the right side of the equation. The two operational modes (AM or FM) are considered by the distinction on the right side of the equation. For the AM mode, an external driving force of the cantilever is used, where the driving signal is modulated with the constantexcitation amplitude aexc at a fixed frequency fd. The self-excitation of the cantilever used in the FM mode is described by the retarded amplification of the displacement signal, i.e., the tip position z is measured at the retarded time t − t0. Nonetheless, a consideration of the time shift by a phase difference q0 is also possible, giving equivalent results. Therefore, we use “time shift” and “phase shift” as synonyms throughout this review and notice that both parameters are scaled by q0 = 2pfdt0. Before finishing this introductory paragraph, we would like to add some words of caution regarding the validity of the equation of motion (3.1), as it disregards two effects that might become of importance under specific circumstances. First, we describe the cantilever by a spring-mass-model and neglect in this way higher modes of the cantilever. This is justified in most cases as the first eigenfrequency is by far dominant in typical AM-AFM experiments (see, for example, Fig. 1 in [31]). Thus, a mathematical treatment that ignores higher modes is still able to describe and explain all major general features experimentally observed in standard DFM imaging, which is the limited goal of this review. Comparison with studies that include higher harmonics by numerical means (see, e.g., [32–35]) confirms this statement. It might, however, not apply if advanced signal analysis in certain DFM spectroscopy modes is intended. Second, we assume in our model equation of motion that the dither piezo applies a sinusoidal force to the spring, but do not consider that the movement of the dither piezo simultaneously also changes the effective position of the tip at the cantilever end by the current value of the excitation aexccos(2pfdt) [34, 36, 37]. This effect

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becomes important when aexc is in the range of the cantilever oscillation amplitude. Fortunately, for conditions characterized by sufficiently high quality factors, this effect can be neglected. This is usually safely the case for measurements in air, where oscillation amplitudes typically exceed excitation amplitudes by several hundred times. During operation in liquids, however, the Q factor is low, and the oscillation amplitudes might be comparable with aexc [37]. Finally, in order to avoid confusion with other literature we would like to mention some words regarding the terminology used throughout this review. Due to the frequently occurring intermitted contact between tip and sample at the lowest point of the oscillation, the amplitude modulation mode introduced above has often been denoted as tapping mode [3]. Over the years, use of the term “tapping mode” has then evolved into a synonym for the AM mode in many publications, disregarding whether the tip is actually making intermitted contact or not. On the other hand, if it is the operator’s firm believe that no contact is established during the oscillations, the AM mode is sometimes also referred to as “noncontact” mode. Please note, however, that the term “noncontact atomic force microscopy (NC-AFM)” is often employed in connection with the frequency-modulation mode, which is mostly applied in UHV (see, e.g., [7]). This simple example shows how to different driving modes might be mixed up if we use the assumed type of tip–sample interaction to define a DFM technique. Therefore, in order to avoid confusion in this review, we will always use the suitable expressions for the driving technique (AM or FM mode) to describe the applied technique.

Driven and Self-Driven Cantilevers in Dynamic Force Microscopy In order to analyze the specific features of the AM and FM mode, it is instructive to first examine the difference of both driving terms. For simplicity, we assume in these preparatory considerations that the cantilever vibrates far away from the sample surface. Consequently, we can neglect tip–sample forces (Fts º 0), resulting in a greatly simplified equation of motion (3.1). This restriction will be abandoned later. First, we consider the situation where the DFM is driven in the AM mode. Under these circumstances, the equation motion reduces to the well-known case of a driven and damped harmonic oscillator:

mz(t ) +

2 π f0 m z(t ) + cz ( z(t ) − d ) = aexc cz cos(2 π fd t ) . Q0

(3.2)

The external driving forces the cantilever to oscillate exactly at the driving frequency fd. Therefore, the steady-state solution is given by the ansatz

z(t  0) = d + A cos(2 π fd t + φ) ,

(3.3)

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where f is the phase difference between the excitation and the oscillation of the cantilever. Introducing this ansatz, we obtain two functions for the amplitude and phase curves: A=

aexc 2

 fd 2   1 fd  1 − +  f0 2   Q0 f0 

tan φ =

2

,

fd / f0 1 . Q0 1 − fd 2 / f0 2

(3.4a)

(3.4b)

The features of such an oscillator are well-known from introductory physics courses, and we will thus skip their further discussion at this point. In contrast, the case where the cantilever is entirely self-driven is much less discussed in the literature. Here the corresponding equation of motion reduces to

mz(t ) +

2 π f0 m a z(t ) + cz ( z(t ) − d ) = − exc cz z(t − t0 ) . Q0 A

(3.5)

As the cantilever is not excited with a specific externally set frequency, the cantilever itself serves as the frequency determining element. Therefore, we make the ansatz [10, 38]

z(t  0) = d + A cos(2 π ft ) ,

(3.6)

and introduce it into (3.6) into (3.5). As a result we obtain a set of two coupled trigonometric equations:

aexc cos(2 π ft0 ) =

f02 − f 2 , f02

aexc 1 f sin(2 π ft0 ) = . A Q0 f0

(3.7a)

(3.7b)

The two equations can be decoupled with the assumption that the time shift t0 is set to a value corresponding to t0 = 1 / (4 f 0 ) ( = 90 ˚ ), which simultaneous corresponds to the by far most common choice for t0. For this value, the solution of (3.7) is given by

f = f0 ,

(3.8a)

A = aexc Q0 .

(3.8b)


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This simple calculation demonstrates the very specific behavior of a self-driven oscillator if the phase (or time) shift is set to 90 ˚ . In this case, the cantilever oscillates exactly with its eigenfrequency f0. Due to this specific feature revealed by (3.8a), we define that the cantilever is in resonance if this condition is fulfilled. The linear relationship between the oscillation and excitation amplitude is described by (3.8b).

Tip–Sample Interaction Force in Air During surface imaging, the vibrating cantilever is brought closely to the sample in order to monitor changes in the oscillation behavior induced by the tip–sample interaction. Therefore, we have to include a suitable model for the tip–sample interaction into our analysis. Assuming that the tip experiences long-range attractive forces described by a van der Waals term and short-range repulsive forces upon contact has been regarded by many authors as an adequate approximative description for the tip–sample interaction at ambient conditions [34, 39–44]. A geometrical characterization of the tip–sample system by a sphere of radius R over a flat surface then results in reasonably simple equations, which allow to reproduce most features of the amplitude-modulation DFM applied in ambient conditions. In this approach [34, 40–43], the long-range van der Waals force is described by

FvdW ( z ) = −

AH R , 6z2

(3.9)

where AH is the Hamaker constant. If the tip comes very close to the sample surface, the repulsive forces between tip and sample become significant. For simplicity, we assume that the geometrical shape of tip and sample does not change until contact has been established at z = z0 and that afterwards, the tip–sample forces are given by the DMT-M model, denoting Maugis’ approximation to the earlier Derjaguin– Muller–Toporov model [45]. In this approach, an offset FvdW(z0) is added to the well-known Hertz model, which considers the adhesion force between tip and sample surface. Therefore, the DMT-M model is often also referred to as Hertzplus-offset model [45]. The resulting overall force law is given by

 FvdW ( z ) Fair ( z) =  4 E∗ R ( z0 − z )3/2 + FvdW ( z0 )  3

for z ≥ z0 , for z < z0 .

  

(3.10)

The effective elastic modulus E *

(1 − m t2 ) (1 − ms2 ) 1 = + E∗ Et Es

(3.11)

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tip-sample force (nN)

6 4 2 0 −2 −4 −1.5

−1.0

−0.5

0.0

z0 0.5

1.0

1.5

2.0

tip-sample distance (nm)

Fig. 3.2 Tip–sample model force for air (3.10) using the parameters given in the text. The dashed line marks the position z0 where the tip touches the surface

depends on the Young’s moduli Et,s and the Poisson ratios mt,s of tip and sample, respectively. Figure 3.2 displays the assumed tip–sample model force. For the plot, the following parameters were used, which are typical for DFM measurements in air: AH = 0. 2 aJ, R = 10 nm, z0 = 0. 3 nm, µ t = µs = 0.3 , Et = 130 GPa, and Es = 1 GPa. The eigenfrequency, the quality factor, and the spring constant of the cantilever were chosen to be f0 = 300 kHz, Q0 = 300, and cz = 40 N/m, respectively.

Theory of AM Mode Including Tip–Sample Forces The mathematical form of realistic tip–sample forces is highly nonlinear for almost all cases of tip–sample systems. This fact complicates the analytical solution of the equation of motion (3.1) even for the assumed simplified model introduced in (3.10). However, for the analysis of DFM experiments, we need to focus on steadystate solutions of the equation of motion with sinusoidal cantilever oscillation. Therefore, it is advantageous to expand the tip–sample force into a Fourier series Fts [ z(t ), z(t )] ≈ fd Ú

1/ fd 0

+ 2 fd Ú + 2 fd Ú +…,

Fts [ z(t ), z(t )]dt

1/ fd 0 1/ fd 0

Fts [ z(t ), z(t )]cos(2p fd t + φ)dt × cos(2p fd t + φ) Fts [ z(t ), z(t )]sin(2p fd t + φ)dt × sin(2p fd t + φ) (3.12)


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where z(t) is given by (3.3). In the following, we assume that the tip–sample force is so small and the Q-factor so high that, as a consequence, higher harmonics can be neglected. It has been shown by Cleveland et al. [31] and Rodriguez and García [33] that this condition is well fulfilled in many practical cases. The first term in the Fourier series reflects the averaged tip–sample force over one full oscillation cycle, which shifts the equilibrium point of the oscillation by a small offset Dd from d to d0. Actual values for Dd, however, are typically small. For amplitudes commonly used in AM-AFM in air (some nm to some tens of nm), the averaged tip–sample force is in the range of some pN. The resulting offset Dd is less than 1 pm for typical sets of parameters [46]. Since this is well beyond the resolution limit of an AM-DFM experiment in air, we neglect this effect in the following and assume d » d0 and D = d − A. For the further analysis, we now insert the first harmonics of the Fourier series (3.12) into the equation of motion (3.1), obtaining two coupled equations [44, 47]

−

f02 − fd2 a = I + (d , A) + exc cos φ , A f02

(3.13a)

1 fd Q0 f0

(3.13b)

= I − (d , A) +

aexc sin φ , A

where the following integrals have been defined:

2 fd 1/ fd Fts [ z(t ), z(t )]cos(2p fd t + φ)dt cz A ∫0

I + (d , A) = =

1 p cz A2

I − (d, A) =

∫

d+ A

d−A

( F↓ + F↑ )

z−d A − ( z − d )2 2

dz ,

(3.14a)

2 fd 1/ fd Fts [ z(t ), z(t )]sin(2p fd t + φ)dt cz A ∫0

=

1 p cz A2

=

1 DE (d, A) . p cz A2

∫

d+ A

d− A

( F↓ − F↑ )dz

(3.14b)

Both integrals are functions of the actual oscillation amplitude A and cantileversample distance d. Furthermore, they depend on the sum and the difference of the tip–sample forces during approach (F↓) and retraction (F↑) as manifested by the labels “ + ” and “ − ” for easy distinction. The integral I + is a weighted average of

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these tip–sample forces ( Fts = ( F↓ + F↑ ) / 2 ). On the other hand, the integral I − is directly connected to DE, which reflects the energy dissipated during an individual oscillation cycle. Consequently, this integral vanishes for purely conservative tip– sample forces, where F↓ and F↑ are identical. A more detailed discussion of these integrals can be found in [48] and [49]. Equations (3.13) can be used to calculate the resonance curves of a dynamic force microscope driven in AM mode including tip–sample forces. The results are ad A= , 2 2    1 fd  fd 2 (3.15a)  1 − f 2 − I + (d , A) +  Q f + I − (d , A) 0 0 0 1 fd + I − ( d , A) Q0 f0 tan φ = . fd 2 1 − 2 − I + (d , A) f0

(3.15b)

Equation (3.15a) describes the shape of the resonance curve, but it is an implicit function of the oscillation amplitude A and cannot be plotted in a direct way. Nonetheless, the equation can be simplified for the case we consider here. Since the assumed tip–sample force is conservative, the integral function I − vanishes. Due to this simplification, (3.15a) can be written as a fourth-order equation, and the relationship between driving frequency and oscillation amplitude can be obtained from the relationship [50] 2

 fd  1 − I + ad2 1 1 I = 1 − − ± − + 2 . + 2 4 2  f  2Qeff 4Qeff Qeff A 0 ±

(3.16)

Figure 3.3 contrasts this equation (solid lines) with the numerical solution (symbols). As pointed out by various authors (see, e.g., [34, 40, 50–55]), the amplitude vs. frequency curves are multi-valued within certain parameter ranges. Moreover, as the gradient of the analytical curve increases to infinity at specific positions, some branches are unstable. The resulting instabilities are reflected by the “jumps” in the simulated curves (marked by arrows in Fig. 3.3), where only stable oscillation states are obtained. Obviously, they are different for increasing and decreasing the driving frequency. This is a well-known effect frequently observed in nonlinear oscillators (see, e.g., [56, 57]). The analysis of the resonance curve, however, gives no direct insight into the characteristics of DFM imaging, as during scanning, the driving frequency is set to a fixed value (and not swept) and the oscillation amplitude (or the phase, respectively) is used to control the cantilever-sample distance. Therefore, we need to examine the change of the oscillation amplitude as a function of the cantileversample distance.


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11 amplitude (nm)

10

AM-mode (Q = 300)

9 8 7 6 299.2

299.6

300.0

300.4

300.8

driving frequency (kHz)

Fig. 3.3 Resonance curve if the cantilever oscillates near the sample surface with a distance of d = 8. 5 nm and a free amplitude of A0 = 10 nm, thereby experiencing the tip–sample force given by (3.10). The solid line represents the analytical result of (3.15a), while the symbols are obtained from the numerical solution of the equation of motion (3.1). The dashed line reflects the resonance curve without tip–sample force and is shown purely for comparison. The resonance curve including the tip–sample force exhibits instabilities (“jumps”) during a frequency sweep. These jumps take place at different positions (marked by arrows) depending on whether the driving frequency is increased or decreased

In amplitude-modulation DFM, the cantilever might be oscillated at any frequency located well within the resonance peak. However, for first analysis we restrict ourselves to a single well-defined situation and assume that the driving frequency is set exactly to the eigenfrequency of the cantilever (fd = f0). With this choice, we have defined imaging conditions, which lead to a handy formula suitable for further analysis. From (3.15a), we obtain the following relationship between the free oscillation amplitude A0, the actual amplitude A, and the equilibrium tip position d:

A0 = A 1 + (Q0 I + [ d , A]) . 2

(3.17)

For the derivation of this formula, we used the approximation that the maximal value of the free oscillation amplitude at resonance is given by A0 » aexcQ0. Solving this equation allows us to calculate an amplitude vs. distance curve as shown in Fig. 3.4. As observed before in the resonance curves stable and unstable branches manifest, which can unambiguously be identified by a comparison with numerical results (symbols). Most noticeably, the AM mode curve exhibits jumps between unstable branches, which occur at different locations for approach and retraction. The resulting bistable regime then causes a hysteresis between approach and retraction, which has been well examined in numerous experimental and theoretical studies (see, e.g., [34, 42, 50–62]). This instability divides the tip–sample interaction into two regimes [34, 42, 50, 62]. Before the instability occurs, the tip interacts during an individual oscillation exclusively with the attractive part of the tip–sample force. After jumping to the higher branch, however, the tip senses also the repulsive part of the tip–sample interaction.

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10 bistable regime amplitude (nm)

8 6 AM-mode (Q0 = 300)

4

A(d)-curve approach retraction

2 0

0

2

4 6 8 distance d (nm)

10

12

Fig. 3.4 Amplitude vs. distance curves for conventional AM mode (“tapping mode”) with the parameters A0 = 10 nm, f0 = 300 kHz, and a tip–sample interaction force as given in Fig. 3.2. The dashed lines represent the analytical result, while the symbols are obtained from the numerical solution of the equation of motion (3.1). The overall amplitudes decrease during an approach towards the sample surface, but instabilities (indicated by arrows) occur during approach and retraction leading to a hysteresis

Our analysis dealt only with the case where the cantilever is driven exactly at resonance frequency, as this leads to clearly defined imaging conditions. In practice, however, experimentalists often drive the cantilever not exactly at, but somewhere else within the resonance peak (“detuned”), hoping for benefits while imaging the sample surface (see [43, 46, 59] for a more detailed discussion of this issue).

Measuring the Tip–Sample Interaction Force In the above subsections, we have outlined the influence of the tip–sample interaction on the cantilever oscillation based on the assumption of a specific model force. However, in practical imaging, the tip–sample interaction is not a priori known. In contrast, the ability to measure the continuous tip–sample interaction force as a function of the tip–sample distance would add a tool of great value to the force microscopist’s toolbox. Since the cantilever reacts to the interaction between tip and sample in a highly nonlinear way, one might wonder how that could be done. Surprisingly, despite the over 15 years that AM-AFM is used, it was only recently that solutions to this inversion problem have been suggested [63–65]. We start our analysis by applying the transformation D = d − A to the integral I+ (3.14a), where D corresponds to the nearest tip–sample distance as defined in Fig. 3.1. Next, we note that due to the cantilever oscillation, the current method intrinsically recovers the values of the force that the tip experiences at its lower turning point, where F↓ necessarily equals F↑. We thus define Fts = ( F↓ + F↑ ) / 2 , and (3.14a) subsequently reads as


I+ =

2 p cz A2

D+2 A

∫

Fts

D

z−D−A A − ( z − D − A)2 2

83

dz .

(3.18)

The amplitudes commonly used in AM mode are considerably larger than the interaction range of the tip–sample force. Consequently, tip–sample forces in the integration range between D + A and D + 2A are practicably insignificant. For this so-called “large amplitude approximation” [66, 67], the last term can be expanded at z ® D to (z − D − A) / A2 − ( z − D − A)2 ≈ − A / 2( z − D) , resulting in

I+ ≈ −

2 p cz A3/ 2

D+2 A

∫

D

Fts z−D

dz .

(3.19)

Introducing this equation into (3.13a), we obtain the following integral equation:

cz A3/ 2  ad cos(f ) f02 − fd2  1 −  = A f02  p 2    

D+2 A

∫

D

Fts z−D

dz .

(3.20)

κ

The left hand side of this equation contains only experimentally accessible data, and we denote this term as k. The benefit of these transformations is that the integral equation can be inverted [67] and, as a final result, we find

Fts ( D ) = −

∂ ∂D

D+2 A

∫

D

k (z) z−D

dz .

(3.21)

It is now straightforward to recover the tip–sample force using (3.21) from a “spectroscopy experiment,” i.e., an experiment where the amplitude and the phase are continuously measured as a function of the actual tip–sample distance D = d − A at a fixed location. With this input, one first calculates k as a function of D. In a second step, the tip–sample force is computed solving the integral in (3.21) numerically. Additional information about the tip–sample interaction can be obtained noticing that the integral I− is directly connected to the energy dissipation DE. By simply combining (3.13b) and (3.14b), we get

 1 fd aexc  DE =  + sin φ p cz A2 . Q f A  0 0 

(3.22)

The same result has been found earlier by Cleveland et al. [31] using the conservation of energy principle. However, exceeding Cleveland’s work, we suggest to plot the energy dissipation as a function of the nearest tip–sample distance

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D = d − A in order to have the same scaling as for the tip–sample force (see Fig. 3.5d). A verification of the algorithm is shown in Fig. 3.5, where we present computer simulations of the method by calculating numerical solutions of the equation of motion with a fourth-order Runge-Kutta method [68]. In order to be able to check both (3.21) and (3.22), we need to add a dissipative component to our original model interaction force Fair (cf. (3.10)). Instead of exploring elaborate energy dissipation mechanisms, it is sufficient for principle demonstration to simply add an additional dissipative force term Fdiss, i.e., Fts = Fair + Fdiss. To characterize Fdiss,

phase (degree)

b

c

−40 −50 −60 −70 −80 −90 −100 −110 −120

8 force (nN)

10 9 8 7 6 5

d

6 8 10 12 cantilever position (nm)

4

Fts reconstructed

0 −4 −0.5 0.0 0.5 1.0 1.5 2.0 tip-sample distance (nm)

6 8 10 12 cantilever position (nm)

dissipation (eV)

amplitude (nm)

a

40 30 20

∆E reconstructed

10 0 −0.5 0.0 0.5 1.0 1.5 2.0 tip-sample distance (nm)

kappa (Nm1/2x10−15)

e 40 20 0 −20 −40 −0.5 0.0 0.5 1.0 1.5 2.0 tip-sample distance (nm)

Fig. 3.5 A numerical verification of the proposed algorithm. Based on the equation of motion (3.1), the amplitude (a) and phase (b) vs. distance curves during the approach toward the sample surface have been numerically calculated. Both curves show the instability that is typical for AM-DFM operation in ambient conditions. As described in the text, the data is used for the reconstruction of the tip–sample force (c) and the energy dissipation (d). The assumed tip–sample model interactions according to (3.10) (c) and (3.23) (d) are plotted by solid lines. Finally, (e) reflects the k(D)-values that can be computed from the amplitude and phase values given in (a) and (b)


85

we chose viscous damping with an exponential distance-dependence: Fdiss = F0 exp(− z / ζ 0 ) z . The energy dissipation caused by this type of dissipation is given by [69]

 D + A  A  DE = 4p 2 fd AF0z 0 exp  − I1 ,  z 0   z 0 

(3.23)

where I1 is the modified Bessel function of the first kind. Figure 3.5 displays the resulting amplitude and phase vs. distance curves during approach, respectively. The assumed parameters and the conservative force are the same as already given in section “Mapping of Tip-Sample Interactions in Ambient Conditions” while the following parameters have been used for the dissipative force: F0 = 10−6 Ns/m and z0 = 0. 5 nm. Again the amplitude curve shows the previously discussed discontinuity caused by an instability. The subsequent reconstruction of Fts and DE based on the data provided by the amplitude and phase vs. distance curves is presented in Fig. 3.5c, d. The assumed tip–sample force and energy dissipation are plotted by solid lines, while the reconstructed data is indicated by symbols; the excellent agreement demonstrates the reliability of the method. Nonetheless, it is important to recognize that the often observed instability in amplitude and phase vs. distance curves affects the reconstruction of the tip–sample force. If such an instability occurs, experimentally accessible k(D)-values will feature a “gap” at a specific range of tip–sample distances D. This issue is illustrated in Fig. 3.5e, where the gap is indicated by an arrow. As a consequence, one might be tempted to interpolate the missing k-values in the gap. This is a workable solution if, as in our example, the accessible k-values appear smooth and, in particular, the lower turning point of the k(D)-values is clearly visible. In most realistic cases, however, the k(D)-values are unlikely to look so smooth as in our simulation and/or the lower turning point might not be reached, and we thus advise to uttermost caution in applying any inter- or extrapolation. Finally, let us note two more issues: (1) The reconstruction of the energy dissipation does not require the continuous knowledge of k-values. Thus, it is not influenced by the instability and gives reliable values also after the jump Fig. 3.5d. (2) The “large amplitude approximation” is not a prerequisite for the inversion of the tip–sample forces from the amplitude and phase data. The application of other numerical methods where the amplitude is not restricted to large values is described in [64, 65, 70].

Theory of FM Mode Including Tip–Sample Forces Now we focus on the solution of (3.1) for the FM mode. In this case, the cantilever is self-oscillated by the feedback loop described in section “Formulation of the Problem and Basic Equation of Motion.” As before, we make the ansatz (3.6) assuming a sinusoidal cantilever oscillation. Consequently, we use the same mathematical

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treatment as in section “Theory of AM Mode Including Tip–Sample Forces” and develop the tip–sample force into a Fourier series. This leads to a set of two coupled trigonometric equations

aexc f2 − f2 cos(2p ft0 ) = 0 2 − I + (d , A) , A f0

(3.24a)

aexc 1 f + I - (d , A) , sin(2p ft0 ) = A Q f0

(3.24b)

which again contain the two integrals already defined in (3.14a) and (3.14b). Both equations can be simplified for the conditions typically found in DFM experiments where the FM mode is applied. First, we assume that the frequency shift ∆f := f − f 0 caused by the tip–sample interaction and the damping is small compared to the resonance frequency of the free cantilever ( Þ f ∕ f0 » 1 and f 2 − f 02 ≈ −2∆ff 0 ). Second, we consider that the phase shift is typically set to 90 ˚ in the FM mode. In this case the terms on the left side are given by cos(2pft0) = 0 and sin(2pft0) = 1. Due to these simplifications, the frequency shift and the driving amplitude can be calculated from

D f (d, A) = −

f0 f0 I+ = − 2 p cz A2 aexc =

d+ A

∫

Fts

d−A

z−d A − ( z − d )2 2

A DE (d , A) + . Q p cz A

dz ,

(3.25a)

(3.25b)

It is worthwhile to note that we got an explicit equation for the frequency shift while we got implicit equations (3.15a) and (3.15b) for the AM mode. Therefore, the frequency shift is continuous and shows no jumps caused by instabilities during approach and retraction. Both equations are valid for every type of interaction as long as the resulting cantilever oscillations are nearly sinusoidal. Equation (3.25a) coincides with the well-known result for the FM mode with constant-oscillation amplitude (see, e.g., [66, 67, 71]), but it is coupled with (3.25b) through the oscillation amplitude. Nonetheless, as shown previously for the AM mode, we can invert (3.25a) using the same mathematical treatment. For the inversion we apply again the “large amplitude approximation” for the integral I+ (3.21) and get

D f ( D, A) ≈ −

D+2 A

f0 2p cz A

3/ 2

∫

D

Fts ( z) z−D

dz .

(3.26)

The inversion now leads to the following formula for the tip–sample interaction potential [67, 72]


Vts ( D ) = − 2

D+2 A

∫

D

cz A( z ′ )3/ 2 D f ( z ′ ) dz′ . f0 z′ − D

87

(3.27)

Consequently, the tip–sample force is given by [67, 72]

Fts ( D) = 2

∂ ∂D

D+2 A

∫

D

Dg ( z ′) z′ − D

dz ′ ,

(3.28)

where we defined the so-called normalized frequency shift [66]

g ( D) :=

cz A3/ 2 D f ( D) , f0

(3.29)

which is independent on the oscillation amplitude, but a function of the nearest tip–sample distance D. In order to recover the tip–sample interaction force from a spectroscopy experiment, we have to measure the frequency shift and the driving amplitude as a function of the tip–sample distance before we calculate the normalized frequency shift. After that, we introduce this data into (3.28). The calculation of the energy dissipation DE is straightforward using (3.25b)

 A2  DE ( A) ≅ p cz  Aaexc −  . Q 

(3.30)

This equation is equivalent to (3.22) and follows also from the conservation of energy [31, 69].

Mapping of Tip–Sample Interactions in Ambient Conditions Experimental Comparison of the AM- and FM mode We realized the set-up presented in Fig. 3.1 by combining a commercial dynamic force microscope (MultiMode AFM with NanoScope IIIa Controller, Veeco Instru ments Inc.) with an additional electronics dedicated for the constant-excitation mode (QFM-Module, nanoAnalytics GmbH). In this way, it is easily possible to switch between AM and FM mode using the same cantilever and sample. Rectangular silicon cantilevers (provided by Nanosensors) were used as sensors. Their spring constants cz were determined via the resonant frequency f0 of the freely oscillating cantilever [73] and their quality factors Q were measured from resonance curves [74].

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To illustrate the main differences between the “conventional” AM mode and the presently much less used FM mode in air, we present two “spectroscopy experiments” in Fig. 3.6, where the oscillating cantilever was approached to and retracted from a mica surface in both modes. The corresponding “spectroscopy curves” are presented in Fig. 3.6a, b. The measured quantities in the AM mode are amplitude and phase shift, whereas the amplitude and frequency shift are recorded in FM mode. The parameters of the cantilever were f0 = 167 224 Hz, cz = 37. 5 N/m, and Q = 465. As highlighted before (see section “Theory of AM Mode Including Tip–Sample Forces”), the amplitude and phase shift curves recorded in AM mode show a significant hysteresis during approach and retraction. At specific positions (marked by arrows in Fig. 3.6a), the oscillation becomes unstable and the cantilever jumps into another stable oscillation state. However, such a hysteresis is not present in the spectroscopy curves measured in the FM mode due to the specific self-oscillation technique [11]. As shown in Fig. 3.6b, the particular amplitude and frequency shift curves are identical within the noise limit for approach and retraction. The amplitude is constant until the tip senses the interaction with the sample surface and decreases continuously during further approach. The frequency shift curves show a decrease and increase of the resonant frequency with a distinct minimum. As detailed in section “Theory of FM Mode Including Tip–Sample Forces” the continuous approach and retraction curves of the frequency modulation mode allow

20 10 0 −10 −20 −30 −40

0

2

4

6

8 10 12 14

piezo movement (nm)

20 19 18 17

approach retraction

16 15 0

0

−20 −40 −60

approach retraction

4

−50 −100 −150 −200

potential (eV)

approach retraction

c

21

force (nN)

b

20 19 18 17 16 15 14 13

frequency shift (Hz) amplitude (nm)

phase (degree)

amplitude (nm)

a

8.5 N/m

2 0 −2 −4 −6

0

2

4

6

8 10 12 14

piezo movement (nm)

−8

-7 nN

0

2

4

6

8

rel. distance (nm)

Fig. 3.6 Examples of “spectroscopy measurements” obtained on mica in ambient conditions. (a) Amplitude and phase vs. distance curves in the tapping mode. The instabilities during approach and retraction cause a hysteresis. (b) Such a behavior is not observed in the constant-excitation mode where the approach and retraction curves of the amplitude and frequency shift are identical within the noise limit. (c) Using the algorithm described in the text, we reconstruct the tip–sample potential and force from the data sets shown in (b). The interaction force decreases until it reaches a minimum of − 7 nN, and increases again with a slope of 8.5 N/m. The origin of all x-axes has been arbitrarily set to the left of the graphs


89

the reconstruction of the tip–sample interaction by an inversion algorithm. An application of this procedure to the spectroscopy data is plotted in Fig. 3.6c and reveals the tip–sample potential and force. Both the tip–sample potential as well as the force show a distinct minimum of − 70 eV and − 7 nN, respectively. The minimum of the force curve is the minimal force needed to retract the tip from the sample surface. Therefore, we denote it as adhesion force in the following. During further approach the tip–sample force increases with a slope of 8.5 N/m as shown by a linear fit (solid line). This linear increase in the tip–sample force is caused by the contact of tip and sample. Justified by the almost linear increase, we use the term contact stiffness for the slope obtained by this linear fitting procedure.

Mapping the Tip–Sample Interactions on Biological Samples The frequency-modulation technique can also be used to record the tip–sample interaction as contour maps perpendicular to the sample surface [75]. In order to examine the possible resolution of this approach under ambient conditions, we recorded sets of spectroscopy curves along predefined scan lines on DPPC (l-adipalmitoyl-phosphatidycholine, Fluka), which frequently serves as a model for membranes [76]. The tip–sample interaction was subsequently calculated from the measured amplitude and frequency shift vs. distance curves with respect to the actual scan position. The obtained curves were then plotted in a color-coded contour map showing the potential of the tip–sample interaction. Monolayers of DPPC were prepared with the Langmuir–Blodgett technique. As shown in the topography image in Fig. 3.7, the monolayers have a lateral structure of alternating stripes and channels. This specific structure is obtained by rapidly withdrawing the mica substrate at a low monolayer surface pressure and constant temperature as described by Gleiche et al. [77]. The stripes consist of DPPC in a liquid condensed phase (LC-phase), whereas the channels between the stripes are filled with DPPC in the liquid expanded phase (LE-phase) [78]. The lateral periodicity of stripes and channels depends on the parameters used during the preparation of the sample. We imaged the sample using the oscillation amplitude as a feedback signal in the FM mode using constant-excitation before we recorded 50 spectroscopy curves along a predefined direction marked in Fig. 3.7a. The parameters of the cantilever were f0 = 170 460 Hz, cz = 39. 6 N/m, and Q = 492. All data sets were than transformed into tip–sample potential curves using the mathematical method described in section “Theory of FM Mode Including Tip–Sample Forces.” Finally, we computed the corresponding contour map as shown in Fig. 3.7. The complete procedure was done by a computer script using IGOR Pro software (Wavemetrics Inc.). The resulting color-coded image reveals the different tip–sample interaction on the stripes (LC-phase) and in the channels (LE-phase). The potential is significantly larger above the stripes ( » − 100 eV) compared to the channels ( » − 150 eV), as it can be seen by the color coding in Fig. 3.7.

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a

12 10

0

8

−50

6

−100

4

−150

potential (eV)

rel. distance (nm)

b

2 0 adhesion force (nN)

c −4 −5

LC phase

−6 −7 LE phase

−8 −9

0

2

4 6 8 10 12 14 scan position (µm)

Fig. 3.7 (a) Surface plot (scan size: 14 × 14 mm2) of the topography of the DPPC film prepared by the Langmuir–Blogdett technique. The monolayer shows alternating stripes and channels which consists of DPPC adsorbed in the LC- and LE-phase, respectively. The white line marks the position where we recorded the frequency shift and amplitude vs. distance curves for the construction of the contour map of the tip–sample interaction potential shown in (b). The graph in (c) displays the corresponding adhesion force obtained from the data shown in (b)

The local stiffness and adhesion force can be determined from the force curves plotted in Fig. 3.8. Here we show amplitude and frequency shift vs. distance curves and the resulting tip–sample potential and force measured at the positions marked in Fig. 3.7. The force curves reveal an adhesion force of − 6 and − 7. 5 nN on the stripes and channels, respectively. However, the local stiffness is about 9 N/m for both positions, and we could not determine a significant difference in the stiffness between the two phases of the DPPC monolayers. We attribute this outcome to the


b

a

150

8 6 4 2 0 −2 −4 −6 −8

100

0

35 force (nN)

34 33 32

LC phase LE phase

31

50

potenial (eV)

amplitude (nm)

36

frequency shift (Hz)

91

0 −50

9 N/m

LC phase LE phase

−6 nN −7.5 nN

−50 −100 −150

−100 0

5

10

15

piezo movement (nm)

20

0

2

4 6 8 10 rel. distance (nm)

12

Fig. 3.8 (a) Spectroscopy curves obtained on the stripes (circles) and the channels (crosses). The tip–sample interaction is calculated from this amplitude and frequency shift vs. distance curves. (b) Using the numerical procedure described in the text we calculated the corresponding tip–sample interaction force and potential. A significant difference between the curves is observed for distances between 2 and 6 nm

fact that the repulsive interaction forces for thin film depend strongly on the actual film thickness. This effect has been already examined by Domke and Radmacher [79] for thin polymer films. They observed that the underlying stiff substrate influences the measured forces for film thicknesses up to hundreds of nanometer. Consequently, it is evident that the contact stiffness measured on the two phases of the DPPC monolayer is dominated by the mica substrate.

Conclusion In this article, we reviewed the theoretical framework of amplitude-modulation and frequency-modulation DFM. First, we clarified the differences between both modes by analyzing their cantilever driving mechanisms. Subsequently, we explicitly included the nonlinear tip–sample forces into our analysis and developed a theory for AM-DFM. We then introduced a spectroscopy method for the measurement of conservative and dissipative tip–sample interactions using the AM mode. In a next step, we used the same mathematical treatment to get a theory describing the FM mode with constant-excitation.

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Finally, we presented some exemplary applications of the introduced methods for ambient conditions. A comparison between spectroscopy curves measured in AM and FM mode demonstrates that FM mode operation avoids instabilities as they are typically present in the amplitude and phase curves in the AM mode. Thus, it is possible to reconstructed the tip–sample interaction over the complete interaction range without jumps. The mapping technique enabling the measurement of two-dimensional “contour maps” of the tip–sample interaction potential was introduced by the example of a DPPC film. Acknowledgments The authors would like to thank X. Chen and L. Chi for the preparation of the sample used in section “Mapping the Tip–Sample Interactions on Biological Samples.” Furthermore, we acknowledge support from and many useful discussions with Boris Anczykowski and Marcus Schäfer (nanoAnalytics GmbH) as well as Daniel Ebeling, André Schirmeisen, and Harald Fuchs (University of Münster). U. S. acknowledges financial support from the National Science Foundation (grant No. MRSEC DMR 0520495).

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Chapter 4

Measuring Mechanical Properties on the Nanoscale with Contact Resonance Force Microscopy Methods* D.C. Hurley

Introduction Nanomechanics, the study of mechanical properties at the nanoscale, provides one of the scientific underpinnings to the rapidly expanding field of nanotechnology. In many systems, the mechanical properties of materials deviate from their macroscopic behavior when relevant length scales reach the nanoscale. Such changes often result from the greatly increased surface-to-volume ratio. As rapidly as materials with novel nanomechanical properties are discovered, they are developed for new products and applications. For example, structural components made with nanocomposites can be lighter, stronger, and tougher; nanostructured coatings possess superior resistance to scratch and abrasion; and ceramic nanomaterials may provide greater flexibility or improved insulating properties than their bulk counterparts. However, shrinking length scales mean that mechanical property information is now needed with nanoscale spatial resolution. For instance, accurate property data enable predictive modeling of complex systems in order to reduce the time and cost of development. In addition, it is increasingly necessary to image or visualize the spatial distribution in properties, rather than relying on a single “average” value. One reason is that new systems frequently involve several disparate materials integrated on the micro- or nanoscale. For these systems, nanoscale information is essential to differentiate the properties of the various components. Furthermore, failure in such heterogeneous systems often occurs due to a localized variation or divergence in properties (void formation, fracture, etc.). Engineering new complex systems therefore requires quantitative nanomechanical imaging to better predict reliability and performance. A variety of techniques to measure small-scale mechanical properties have been demonstrated. Among these are approaches based on indentation [1–3], ultrasonics [4, 5], and other physical phenomena [6, 7]. However, these methods are often not

*

Contribution of NIST, an agency of the US government; not subject to copyright.

D.C. Hurley (*) National Institute of Standards & Technology, 325 Broadway, Boulder, CO 80305, USA e-mail: [email protected] S.V. Kalinin and A. Gruverman (eds.), Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy, DOI 10.1007/978-1-4419-7167-8_4, © Springer Science+Business Media, LLC 2010

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optimal in some way, particularly in their spatial resolution. Other drawbacks to some methods include lack of imaging capability and constraints regarding specimen size or shape. For these reasons, methods based on atomic force microscopy (AFM) present an attractive alternative. AFM was originally invented to measure surface topography with atomic spatial resolution [8], but its utility in other applications was quickly demonstrated. One reason for AFM’s appeal is its ability to provide nanoscale spatial resolution, due to the small radius (~5–50nm) of the cantilever tip. Furthermore, the scanning capabilities of the AFM instrument enable rapid, in situ imaging. Several AFM-based methods have been demonstrated to sense mechanical properties such as elasticity [9–12]. In force modulation microscopy [9], either the tip or the sample is oscillated and the resulting amplitude of the cantilever deflection is detected as the tip is scanned. Because the deflection amplitude depends on the sample’s local modulus, an image of elastic stiffness can be obtained. However, such images are qualitative, indicating only relative stiffness at each position. Methods based on force–displacement curves have also been extensively developed (for a review, see Ref. [13]). Force–displacement techniques work best when the compliance of the cantilever is roughly comparable to that of the test material. They are therefore better suited to very compliant (“soft”) materials, and lose effectiveness as the material stiffness increases. Although force–distance curves can provide quantitative information, the point-by-point nature of this method severely restricts its imaging abilities. The most promising AFM methods for quantitative measurements of relatively stiff materials are dynamic approaches, in which the cantilever is vibrated at or near its resonant frequencies [14]. Such methods often include the words “acoustic” or “ultrasonic” in their name, identifying the frequency of vibration involved (~100kHz to 3MHz). Among these methods are ultrasonic force microscopy (UFM) [15, 16], heterodyne force microscopy [17], ultrasonic atomic force microscopy (UAFM) [18], and atomic force acoustic microscopy (AFAM) [19, 20]. Because AFM was a relatively new field when these techniques were first devised, research focused on exploiting the features of commercial AFM instruments. Very recently, new techniques are emerging that involve customized sensors to replace the standard AFM cantilever [21, 22]. These methods leverage advances made over the last decade both in micromachining and in AFM instrumentation. Of these methods, the AFAM approach has achieved the most progress in quantitative measurements. A general name that encompasses AFAM, UAFM, and related methods is “contact resonance AFM” or simply “contact resonance force microscopy” (CR-FM) [23]. In this chapter, we describe how CR-FM methods can be used for quantitative measurements and imaging of nanoscale mechanical properties. We present the basic physical concepts and explain how they are implemented experimentally. Single-point methods to measure both elastic and viscoelastic properties are described, as well as quantitative imaging techniques to obtain property maps. Results are shown for specific material systems in order to demonstrate the potential of the methods for materials characterization. In this way, we hope to encourage further use of CR-FM as a tool for research and development in nanotechnology.

4 Measuring Mechanical Properties on the Nanoscale

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Single-Point Measurements of Elastic Modulus Basic Concepts Cantilevers used in CR-FM experiments are micromachined from single-crystal silicon (Si) and have a rectangular shape. The long axis of the cantilever is usually oriented in the crystalline direction, and the axis of the tip is -oriented. For measurements on stiff materials (modulus greater than ~50GPa), cantilevers with a spring constant klever of approximately 30–50N/m are typically used. A variety of such cantilevers are available commercially and are usually designated as “noncontact” or “intermittent contact” probes. As described below, experiments are performed with a static force FN applied to the tip. FN is determined through the relation FN = kleverd, where d is the deflection of the cantilever measured by the AFM photodiode. In experiments on stiff materials, FN is typically in the range of several hundred nanonewtons to a few micronewtons. Such forces ensure that the tip–sample contact is predominantly elastic. In recent experiments on more compliant materials such as polymers, we have used more compliant cantilevers with spring constants of approximately 1N/m, with corresponding values of FN less than 100nN. An essential concept of CR-FM methods is that the cantilever can be considered as a microscale beam possessing mechanical or vibrational resonant modes. This idea is illustrated in Fig. 4.1. The resonant modes of the cantilever are excited either by an external actuator, as shown in the figure, or by an actuator attached to the cantilever holder. In Fig. 4.1a, the tip of the cantilever is out of contact with the sample. In this case, the resonant modes of the cantilever occur at the free or natural frequencies that depend on its geometry and material properties. When the tip is placed in contact with a sample, as in Fig. 4.1b, the resonant frequencies increase due to the interaction forces between the tip and the sample. Typically, experiments involve the lowest-order flexural (bending) resonant modes of the cantilever. For cantilevers such as those described above, the frequencies of the flexural modes

b

c

specimen

specimen

piezoelectric actuator

piezoelectric actuator

amplitude

a

2nd free resonance 1stc ontact 1st free resonance resonance

frequenc y

Fig. 4.1 Concepts of contact resonance force microscopy (CR-FM). Resonant modes of the cantilever are excited when the tip is (a) in free space and (b) in contact with a specimen under an applied static force. (c) Resonant spectra. The lowest-order contact resonance occurs at a higher frequency than the first free-space resonance, but is lower than the second free-space resonance

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occur at a few hundred kilohertz for the tip in free space and a few megahertz for the tip in contact. Instead of monitoring the amplitude or phase of the cantilever motion, as in some other AFM methods, CR-FM measurements consist of determining the frequencies at which the free and contact resonances occur. The mechanical properties of the sample are then deduced from the measured frequencies with the help of two models: one for the dynamic motion of the cantilever, and another for the contact mechanics between the tip and the sample. A practical advantage to this approach is that frequency shifts are easier to measure accurately than absolute amplitudes or phase.

Models for Data Analysis In the data analysis, the measured frequencies are first related to the tip–sample interaction force by means of a model for the dynamic motion of the cantilever. Here, we present the basic equations for an analytical model. This model is described in detail in Ref. [20]. Finite-element analysis methods have also been used to describe the cantilever dynamics [24–26]. Figure 4.2 shows several models to describe the cantilever’s vibrations. Note that a distributed-mass model is used; the point-mass (harmonic oscillator) approximation is not accurate under the conditions described here [27, 28]. The cantilever is modeled as an elastically isotropic beam of uniform cross section with length L, width w, thickness t, density r, and Young’s modulus E. The tip is located at a distance L1 3a. This leads to the general guideline that measurements probe to a depth z»3a [29, 84]. For Hertzian contact, a is given by (4.8) and depends on the applied force FN, the tip radius R, and the reduced modulus E* between the tip and the sample. Typical values of these parameters for experiments on stiff materials yield values of z between approximately 10 and 60nm. Such concepts have been exploited experimentally to sense variations in near-surface mechanical properties. For example, reversible displacement of dislocations approximately 10nm beneath the surface in highly oriented pyrolytic graphite was observed with UAFM [68]. UFM methods were used to study cracking during tensile loading at a buried interface approximately 15nm deep between a brittle glass film and a ductile polyethylene terephthalate (PET) substrate [85]. Another subsurface mechanical property of industrial interest is the relative bonding or adhesion between a film and substrate. We have performed CR-FM experiments to investigate variations in adhesion at a buried interface [86]. As shown in Fig. 4.10a, a model system of gold (Au) and titanium (Ti) films on (001) Si was created. A thin Ti interlayer grid with 5mm×5mm holes and a blanket film of Au were deposited with standard microfabrication techniques. This design was intended to contain variations in the adhesion of a buried interface, yet minimize variations in topography and composition at the surface. A very thin Ti topcoat was included merely to prevent contamination of the AFM tip by the soft Au film. A crude scratch test was performed by pulling one end of a tweezer across the sample. Optical micrographs showed that this treatment had removed the film in the scratched regions without the Ti interlayer (square holes) and left the gold intact in the scratched regions containing the Ti interlayer (grid). This result confirmed the

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a

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2 nm Ti

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1 nm

c k/klever

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Fig. 4.10 CR-FM mapping of film/substrate adhesion. (a) Schematic of sample in cross section. (b) Map of the normalized contact stiffness k/klever calculated from contact resonance frequency images. (c) Normalized contact stiffness versus position. The line scan is the average of 40 lines across the center of the image in (b), as indicated by the dotted lines

premise that the film adhesion was much stronger in regions containing the Ti interlayer. Contact resonance frequency images of the two lowest flexural cantilever modes were acquired for this sample. A map of the normalized contact stiffness k/klever calculated from the frequency images is shown in Fig.4.10b. The map clearly reveals that the contact stiffness is lower in the square region with poor adhesion (no Ti interlayer). A line scan of k/klever versus position is shown in Fig.4.10c. The scan represents the average value of k/klever for 40 lines in the map indicated by the dashed lines. Analysis of the entire contact stiffness map gives a mean value for k/klever of 39.1±0.6 in the grid regions and 37.1±0.5 in the square, a difference of 5%. Other contact stiffness images acquired at different sample positions consistently showed a decrease of 4–5% in k/klever for the regions of poor adhesion that lacked a Ti interlayer. With (4.8), we estimate that a=6nm to 8.5nm in this case, sufficient to probe the film interface (z»3a=22–24nm). The observed results are consistent with theoretical predictions for layered systems with disbonds [87]. In that work, an impedanceradiation theory was used to model the disbonded substrate/film interface as a change in boundary conditions (i.e., zero shear stress at the interface). For a disbond in a 20-nm aluminum film on (001) silicon, a reduction of ~4% in the contact stiffness was predicted, very similar to our results. The parameters used for modeling (E*, FN, etc.) differed from those in our experiments, but the overall combination of conditions was sufficiently similar that a comparison between the two results is valid. Therefore, we believe that weak adhesion is responsible for our experimental


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results. These results represent progress toward nanoscale mapping of adhesion, a goal with significant implications for development of thin-film devices in many technological applications. The above contact mechanics arguments imply that typical CR-FM experiments are not sensitive to features deeper than a few tens of nanometers beneath the surface. In contrast, several CR-FM experiments have demonstrated the ability to detect voids several hundred nanometers beneath the surface [88–90]. Simulations and modeling of this behavior indicate that even relatively deep defects can be detected if they are large enough [88, 90–92]. Quantitative values for “large enough” and “relatively deep” depend on the exact experimental configuration. However, studies suggest that as a rough guide, typical CR-FM methods can sense defects buried a few hundred nanometers deep if they are at least a few hundred nanometers in diameter [90]. With this in mind, we have begun CR-FM studies of stress-induced buckling mechanics in thin films [93]. Deposition of thin films can lead to residual stress in the finished film. If the stress is sufficiently large, a variety of stress-relief mechanisms can occur [94–96]. For compressive stress, these include wrinkling, in which the film and the substrate deform together, and buckling or blistering, in which the film delaminates from the substrate. A better understanding of the relationship between the film deposition conditions and the resulting mechanical response of the film is needed. Such information would enable improved modeling of device performance for many applications including flexible electronics and microelectronic interconnect. The sample used for preliminary experiments contained a 300-nm thick gold film on a Kapton polyimide substrate (see footnote 1). Buckling was induced after the film was deposited by clamping the sample. Figure 4.11a shows an optical micrograph of a region of the sample containing “telephone cord” buckles. CR-FM images were acquired for several different regions at the edge of several different buckles. The dotted lines in Fig. 4.11a indicate the approximate scan size and relative location of the images. The frequency images were acquired with a cantilever with nominal spring constant klever=30N/m and an estimated applied static force FN=600nN. The nominal tip radius of curvature was R=30nm when new; little or no wear was observed during scanning. With Hertzian contact mechanics, the estimated contact radius a=5nm, so that the lateral spatial resolution ~3a=15nm. We found that it was sufficient to obtain images of the lowest flexural mode frequency f1 only. In the data analysis, it was important to examine the sample topography and the corresponding CR-FM response simultaneously. An example is given in Fig. 4.11b, which shows the contact resonance frequency f1 as a function of position (solid line) and the corresponding topography (dashed line). Four regions with different behavior are indicated by the vertical dotted lines and the labels A–D. In region A, the height is low, indicating that the tip is located away from the buckle. The contact resonance frequency f1 is high. As mentioned above, higher values of f1 usually imply higher contact stiffness. Therefore, the CR-FM response suggests that the film is adhered to the substrate in this region. In region B, the high height values indicate that the tip is on the side of the buckle. The contact resonance frequency is significantly lower than that in region A. Therefore, the film appears to be delaminated.

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Fig. 4.11 CR-FM results for stress-induced buckling. (a) Optical micrograph of telephone cord buckles in a gold film on a polyimide substrate. The dotted lines indicate the approximate size and relative position at which CR-FM frequency images were acquired. (b) Plot of frequency and topography versus position at the edge of a buckle. The solid line shows the contact resonance frequency f1 of the lowest flexural mode. The dashed line shows the corresponding topography. The topography data have been processed to remove a linear tilt and constant offset from each line. The vertical lines and the labels A–D indicate four regions with different types of behavior, as discussed in the text

The observed behavior in regions A and B is consistent with that expected for a buckle. However, regions C and D exhibit behavior that is less expected. Region C represents a zone at the very edge of the buckle over which the contact resonance frequency f1 is consistently high. This implies that the film is adhered to the substrate at the outermost edge of the buckle. The behavior is consistent with a hybrid wrinkling–buckling mechanism or “meniscus” effect predicted by nonlinear finiteelement analysis for nickel films on polycarbonate substrates [97]. A meniscus effect was observed in all of our experimental images and ranged in width from roughly 1 to 3mm. Finally, region D represents a transition zone several micrometers wide, in which the contact stiffness gradually decreases. This effect represents a decrease in the structural compliance with increasing distance from the clamped edges of the buckles, similar to that observed in suspended nanowires [48]. These results suggest that CR-FM can serve as a nondestructive tool for better understanding the mechanics of thin-film buckling.

Summary and Conclusions In this chapter, we have presented contact resonance force microscopy (CR-FM) measurement methods and their use for materials characterization on the nanoscale. The basic physical principles of CR-FM and the equipment needed to


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implement them experimentally have been discussed. CR-FM experiments involve measuring the resonant frequencies of a vibrating cantilever when its tip is in contact with a material. Models for the cantilever dynamics and for the tip–sample contact mechanics are then used to relate the contact resonance frequencies to the near-surface elastic properties. CR-FM methods to nondestructively measure quantitative elastic properties on the nanoscale were described. Extensions of the original approach that provide further information about mechanical properties were also presented, including the use of torsional modes to measure Poisson’s ratio and a method to determine viscoelastic properties. The use of CR-FM methods for imaging applications was also discussed. In particular, frequency-tracking tools to map the contact resonance frequencies were described. Examples showed how CR-FM frequency-tracking methods provide quantitative images or maps of properties such as elastic modulus and thin-film adhesion at a buried interface. The information provided here is intended to serve merely as an introduction to CR-FM methods. A growing body of work by groups worldwide point to the utility of these methods for a wide range of applications. It is hoped that this discussion stimulates readers to envision further uses in their own research. By providing quantitative nanomechanical information for a variety of material systems, CR-FM techniques will contribute to the rapid growth of nanoscale materials science and will play a significant role in future nanotechnology efforts. Acknowledgements Many current and former NIST coworkers contributed to this work, including R. Geiss, M. Kopycinska-Müller, A. Kos, C. Stafford, and G. Stan. I value interactions with researchers from several institutes, especially J. Turner (University of Nebraska-Lincoln) and W. Arnold, U. Rabe, and S. Hirsekorn (Fraunhofer Institute for Nondestructive Testing IZFP, Germany). The results for viscoelastic properties represent a collaboration with J. Turner and P. Yuya (University of Nebraska-Lincoln). The lyocell-polypropylene composite sample was provided by S. Wang and S. Sudhakaran Nair (University of Tennessee Forest Products Center). The buckling results represent a collaboration with M. Kennedy (Clemson University) and N. Moody (Sandia National Laboratories). I also appreciate interactions with R. Geer (State University of New York at Albany), B. Huey (University of Connecticut-Storrs), and N. Jennett (National Physical Laboratory, UK).

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Chapter 5

Multi-Frequency Atomic Force Microscopy Roger Proksch

The atomic force microscope (AFM) was invented in 1986 [1], a close relative of another instrument, the scanning tunneling microscope (STM), invented in 1981 [2]. Both fall under the umbrella of techniques and instruments referred to as scanning probe microscopes (SPMs), with the common thread being that a sharp probe is scanned in a regular pattern to map some sample characteristic. Unlike the STM, the AFM can readily image insulating surfaces. Combined with the ability to study a wide variety of samples and sample environments – ambient, liquid, and vacuum – has made AFM the technique of choice for many high resolution surface imaging applications, including imaging with atomic resolution. Since those early days, AFM techniques have become the mainstay of nanoscience and nanotechnology by providing the capability for structural imaging and manipulation on the nanometer and atomic scales. Beyond simple topographic imaging, AFMs have found an extremely broad range of applications for probing electrical, magnetic, and mechanical properties – often at the level of several tens of nanometers. One ongoing “holy grail” quest of AFM, since very nearly the beginning [3] has been compositional mapping where materials differences are mapped out with the same nanometer resolution as topographic images. There are many forces acting between an AFM tip and a sample, long-ranged van der Waals, electrostatic and magnetic forces, short-ranged forces stemming from the elasticity of the tip and sample, and dissipative forces associated with adhesion, plasticity, phonon gene ration, and eddy currents, to name a few. Many if not all of these interactions carry compositional information about the sample. However, the forces also depend on the geometry of both the tip and the sample. The sample topography conspires with the tip geometry to make unraveling of the specific contributions to the net forces very difficult. For example, a situation where there is zero net force on the cantilever tip might mean that there are no forces acting on the tip or that there is a very large adhesive (attractive) force being balanced by a very large elastic (repulsive) force. Much of the theoretical and experimental work being done in AFM originates from R. Proksch (*) Asylum Research, Santa Barbara, CA 93117, USA e-mail: [email protected] S.V. Kalinin and A. Gruverman (eds.), Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy, DOI 10.1007/978-1-4419-7167-8_5, © Springer Science+Business Media, LLC 2010

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the desire to separate and understand these different forces and, ultimately, to use them to identify specific materials and material properties at the nanoscale. Multiple frequency techniques, where the cantilever motion is measured (and sometimes driven) at multiple resonant frequencies, have become an active research topic, in part because of their ability to differentiate material properties from the topography of the sample. In this chapter, we will review some of the emerging techniques using AFM cantilevers at multiple frequencies. The scope will be limi ted to techniques where the multiple frequencies are each “active,” or driven, either by the cantilever excitation, as in the case of non-contact and intermittent contact mode techniques, or by a modulated tip–sample interaction, as in the case of electric or piezoresponse force microscopy (PFM). In addition, there is a broad range of “passive” techniques that will not be considered here [4–6], where harmonics of a drive frequency can be monitored and used to glean information regarding the tip–sample interaction [4, 6–8]. Also not reviewed chapter, but included elsewhere in this volume are some very promising techniques where a single frequency is swept, or “chirped” over a range of values to extract more detailed information about the cantilever resonances in contact with the surface [9–13]. A new, related technique called band excitation [14–17] allows rapid acquisition of spectra, was originally developed in the context of PFM but has wide application in a variety of scanning probe techniques and application areas. As we discuss below, simulations and experimental AFM data have shown intriguing contrast on a variety of samples, both in air and liquid, for multifrequency techniques. However, a major challenge that remains in this area – as indeed in any AFM technique that aspires to quantify material properties – is to unambiguously separate compositional differences in the tip–sample forces from geometrical effects, more specifically, tip-shapes. While straightforward in simulations, real samples have topography that is not known a priori, and real tips have a great deal of shape and size variability, especially as the tip size drops below 100nm [18–20]. This has proven to be a thorny problem to solve. Tips are difficult to characterize, requiring either scanning some sort of calibration sample or characterization with some other kind of microscopy, usually high resolution SEM. To confound the problem further, tips are typically not stable creatures that are static over their lifetime. They can both wear and pick up contaminants during the course of imaging. Both issues render initial characterizations moot. For this reason, many of the most robust results end up being relative comparisons of properties over the course of single images rather than quantitative absolute measurements. Despite these quantification difficulties, relative property mapping on length scales of nanometers can be very powerful, intriguing, and useful.

Multi-Frequency Motivation Using higher modes can be motivated by a number of physical arguments. In pioneering early work in non-contact microscopy, Rodriguez and Garcia pointed out that the second resonant mode oscillations are sensitive to weak, long-ranged van der Waals

5 Multi-Frequency Atomic Force Microscopy

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interactions due to the nonlinear coupling of the two oscillating modes (coupled through the tip–surface interactions) combined with their higher Q-factors [21]. In addition, while operating the distance control feedback on the first mode necessarily constrains it to the “set-point,” the second mode is then free to explore a larger part of phase space [22]. In contact mechanical measurements, the dependence of contact resonance frequencies on the contact stiffness for various modes is shown in Fig. 5.2 [23]. This dynamic stiffness of successively higher modes makes them sensitive to greater tip–sample stiffness. Finally, and perhaps one of the greatest motivations for multiple frequency methods, is the large number of unknown parameters in even the simplest models of AFM tip–sample interactions [17]. Conventional single frequency AFM measurements typically produce two measured quantities at each point in space – the amplitude and phase. Even the simple harmonic oscillator (SHO) model contains more than two parameters. The resonance frequency, quality factor, drive amplitude, and drive phase are all required to unambiguously calculate the response. In some cases, separate measurements of the drive sensitivity of the excitation piezo can be made, allowing quantification of the SHO response, including quantities such as the power dissipated between the tip and the sample [24]. However, as discussed in greater detail below, this assumption can break down if the transfer function of the cantilever drive mechanism is not well understood. In addition, applications such as PFM [17, 25], the drive amplitude and phase originate from the sample being measured and are inherently unknown. In this particular case, the SHO model necessarily includes four unknown parameters (resonant frequency, quality factor, drive amplitude, and drive phase), implying that single frequency measurements returning only two independent parameters will always leave the SHO model under-determined. Finally, there are many examples where the SHO model is clearly insufficient to extract details of the nonlinear tip– surface interactions, requiring even more parameters in any model to describe the dynamics [26].

Cantilever Resonant Modes and Boundary Conditions All of the results presented here, and indeed in AFM in general, were made possible by the batch fabrication of disposable, reliable mechanical probes, typically in the form of cantilevers with sharp tips on the end. Because cantilevers are extended mechanical objects, they have many different flexural resonant modes. Historically, atomic force microscopes have typically excited one of those modes, usually the lowest frequency, or “fundamental” mode, and then used the amplitude or frequency of that mode as the input for a feedback system that controls the tip–sample separation. When the amplitude of the fundamental motion is used, the term “amplitude modulated AFM” (AM-AFM) has been employed [27]. Included under this umbrella are labels such as “tapping,” “intermittent contact” and “AC” modes.

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Fig. 5.1 Theoretical resonant frequencies of diving board shaped cantilevers in terms of the f undamental, f1 as well as actual resonant frequencies for the Olympus AC240 and Bio-Levers. In these cases, the theoretical predictions typically agree with the measured results to well within 10%

Fig. 5.2 Calculated local vibration amplitudes along a cantilever with rectangular cross section for modes 1–3 (from left to right) and for different values of k*/kc (increasing from top to bottom). Because of space, in the second column, the spring was drawn with its fixed end on top. The springs are always in their un-deflected rest positions when the end of the cantilever is at zero. (a) In the clamped-free case the maximum of the vibration amplitudes is at the free end. (b, c) show the effect of a spring with increasing stiffness. (d) For an infinitely stiff contact, the end of the cantilever is pinned but free to rotate. At this end, the vibration amplitude of the cantilever becomes zero. From [23]


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Because of their shape, the relationship between the resonant modes is somewhat more complicated than most “Physics 101” treatments of resonant or normal modes where the normal modes are also harmonics of the fundamental. For example, a plucked guitar string has higher flexural resonances that are harmonic, meaning that if the fundamental mode is at a frequency f1, the next resonance is at 2f1, the next is at 3f1, and so on. However, for all but a few very specialized types, cantilever resonant frequencies are non-harmonic. Figure 5.1 gives the theoretical resonant frequencies for diving board-shaped cantilevers for the first few resonant frequencies. The measured resonant frequencies for two representative cantilevers are also shown: a 240-µm long Si cantilever primarily used for imaging in air (AC-240, Olympus), and a 60-µm long SiN cantilever primarily used for imaging in fluid (BioLever, Olympus). There are a large variety of dynamic techniques where the probe is essentially in continuous contact with the surface while it is oscillated, subject to the tip–sample boundary condition. Generally, these techniques are especially useful for samples where the stiffness is larger than the cantilever spring constant, a condition that makes conventional AFM-based force curve measurements more difficult. Of these techniques, the most promising one make use of one or more of the contact resonance frequencies. These techniques include so-called acoustic and ultrasonic force microscopies [28]. These same techniques are also relevant to techniques such as PFM where the contact resonance is very useful for amplifying the small displacements from the piezoelectric properties of a sample (typically of order 2–500pm of displacement for a volt of applied potential). Figure 5.2 shows a simplified view of the changes in the cantilever boundary conditions as it comes into contact with a surface. This causes the resonances to shift in a manner strongly dependent on the contact mechanics [23]. The general idea of these contact resonances is shown in Fig. 5.2, where the tip of a cantilever is placed in contact with a sample surface. Resonant vibrational modes of the cantilever are excited by an external actuator attached either to the sample (dubbed atomic force acoustic microscopy [AFAM]) [23] or to the AFM cantilever holder (ultrasonic force microscopy [UFM]) [29–32]. Oscillations can also be induced by other means, as in PFM [33, 34] where localized motion of the sample is induced by an oscillating tip potential, or as in a variation of localized thermal analysis where motion is induced by localized heating of the sample [35, 36]. Whatever the drive mechanism, the tip–sample interactions can be sensitively probed by measuring the contact resonance frequency. When the cantilever approaches the surface and the tip changes from free to contact, the boundary conditions alter the normal cantilever flexural modes. Generally, the frequencies of the resonant modes increase, and are strongly dependent on the tip–sample interactions. CR AFM involves measuring the frequencies at which the free and contact resonances occur. The mechanical properties of the sample are then deduced from these frequencies with the help of appropriate models, as is discussed in detail in several review articles [10, 13, 37]. A complication with this picture is that most surfaces have some roughness at the length scales of nanometers. This roughness will affect the contact area of a tip

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as it scans over the surface. To explore this effect, consider a simplified Hertz model consisting of two spheres having radii Rt and Rs, the tip and sample radii, respectively, in contact with each other and loaded by a force Fn. They will have a contact area given by [38] 1/3

 Fn Rt Rs  a=  E (R + R )  t s  

(5.1)

In this expression, the elastic modulus of the two spheres, E is assumed to be the same for the two materials, as is the Poisson ratio v = 0.3. The stiffness of this contact is given by kts=aE and the resulting resonance frequency of the cantilever in contact with the surface, including the first linear term then becomes

 k  f res = 1 − 5.8 c  f res,bound k ts  

(5.2)

Here, fres,bound is the resonance frequency of the cantilever pressed into an infinitely stiff sample material and kc is the spring constant of the cantilever. This equation can be used to model the dynamics of a spherical tip as it scans along a rough surface. The results of such a simulation are shown in Fig. 5.3. The phase and amplitude curves in Fig. 5.3 show the results of a cantilever scanning in contact across a rough, bit otherwise homogeneous surface. Despite the intrinsic parameters (Young’s modulus, dissipation) remaining constant over the

Fig. 5.3 The phase (a) and amplitude (b) of a modeled cantilever in contact with a rough surface (c) is plotted as a function of lateral position. The cantilever response is calculated assuming that the resonance frequency is dependent on only the contact area, a quantity estimated from the localized curvature of the surface near the tip. The resonance frequency drops when the tip is on top of a sharp feature because the contact area is small (highlighted in blue), causing the amplitude (blue curve in (e)) to drop as the peak moves away from the drive frequency. The phase increases at the drive frequency (blue curve in (f)). Similarly, the resonance frequency increases when the tip is in a valley and the contact area is large (red highlight and curves), and is intermediate over a flat part of the sample (green highlight and curves)


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surface, the amplitude, and phase show a great deal of contrast. This contrast results since the single drive frequency was chosen to be close to the contact resonance. As the tip scans over the surface, the contact resonance frequency varies, resulting in large, difficult to interpret changes in the cantilever amplitude and phase.

Methods The most direct method for using higher modes is to simply drive the cantilever at a single frequency in the vicinity of the higher mode resonance. This can be accomplished using the same experimental setup used for imaging at the fundamental mode. As with imaging using the first resonant frequency, the amplitude of the cantilever measured at the drive frequency is used as the error signal in a feedback loop. There have been a number of groups who have reported enhanced phase contrast when operating at a higher resonance mode and who have reported contrast presumably associated with variations in sample elasticity, adhesion or dissipation [4, 6, 39]. A major issue with operating at a higher mode is the imaging stability. Operating at a higher mode is not as stable as imaging at the fundamental. This has limited the applications of single frequency higher mode imaging.

Attractive and Repulsive Mode During a single AM-AFM oscillation cycle, the tip typically samples a range of forces, from the long-range attractive to the short-range repulsive. These forces in turn affect the dynamics of the cantilever, specifically the amplitude and phase shift of the cantilever oscillation relative to the driving force [27]. If the time-averaged phase shift of the cantilever interacting with the surface is positive relative to the phase well above the surface, it is customary to refer to the imaging mode as “net attractive” or simply “attractive.” If the phase shift is negative, the mode is referred to as “net-repulsive” or simply “repulsive.” In simulations of attractive mode operation, the phase of the second mode has a strong dependence on the Hamaker constant of the material being imaged, implying that this technique can be used to extract compositional information about the surface. Note that since the van der Waal’s interaction is usually attractive and relatively long-range, attractive mode imaging is likely to be more non-invasive and gentle than imaging in repulsive mode. Figure 5.4 shows the basic idea of bimodal imaging mode using two (non-harmonic) resonant frequencies of a cantilever. The cantilever is driven with a linear combination of sinusoidal voltages at or near two resonant frequencies, f1 and f2. This signal is used to drive the base of a cantilever with a piezo shaking the base of the cantilever. Similar results can be obtained with magnetically activated cantilever with similar results. It is expected that other actuation methods where two drive

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Fig. 5.4 In bimodal dual AC, the cantilever is both driven and measured at two (or more) frequencies. The sinusoidal “shake” voltage is the sum of voltages at frequencies f1and f2. The cantilever deflection then contains information at both of those frequencies, as shown in the red curve. The amplitude and phase at the two frequencies are then separated again by the two lock-ins and passed on to the controller. The controller can use one or both of the resonant frequencies to operate a feedback loop

waveforms can be summed will prove as effective. The resulting motion of the cantilever is measured with the standard position-sensitive detector. This signal in turn is used as the input for two lock-in amplifiers, where the sinusoidal drive at f1 is used as a reference for one lock-in and f2 is used as a reference for the other. The output of the lock-in amplifiers, including the Cartesian in-phase and quadrature pairs (x1, y1, x2, y2) and polar amplitude and phase (A1, j1, A2, j2) representations of the cantilever motion at the two or more frequencies, can then be passed on to the controller where they can be displayed, saved, combined with other signals, and used in feedback loops [40].

Feedback As with conventional AC imaging, the amplitude of the cantilever is used as the feedback error signal. There is a difference here, however, since there are two amplitudes – one at each drive frequency, either of which could be used as a feedback signal. The initial results we present use the amplitude of the fundamental frequency A1 as the feedback error signal and the fundamental phase ϕ1 , the second resonant frequency amplitude A2, and phase ϕ2 as “carry-along” signals. Reversing this and using the higher resonant frequency amplitude as a feedback, and carrying the fundamental amplitude and phase along, can also yield interesting results. The sum of all of the amplitudes as the error signal also allows stable imaging.


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An interesting feature of this measurement is that the signal processing can be performed on the same cantilever deflection data stream for each flexural mode. With a digital lock-in implementation, for example, this implies that the same position-sensitive detector and analog-to-digital converter (as long as it has sufficient bandwidth for the higher mode) can be used to extract information regarding the various distinct resonant frequencies.

Intermittent- and Non-contact Bimodal Experimental Results Figure 5.5 shows a 30-µm image of a highly oriented pyrolitic graphite (HOPG Graphite, SPI Incorporated, West Chester, PA, USA) surface. The cantilever was a silicon AC-240 driven at the fundamental frequency (f1~69.5kHz, A1~8nm) and second resonant frequency (f2~405kHz, A2~8nm). The Z-feedback loop was operated using the fundamental amplitude A1 as the error signal. The topography (a) shows the expected terraces separated by single or multiple atomic steps. The first mode amplitude (b) channel resembles a high-pass filtered image of the topography, typical for the error signal in AFM. The fundamental phase image (c) shows an average phase lag of ~34° and very little variation (£1° standard deviation), implying that the cantilever was consistently in repulsive mode. Again, there is very little contrast in the fundamental phase image. However, the second mode amplitude image (d) has significant contrast, with broad patches showing regions where A2, the second mode amplitude, was reduced by tip–sample interactions. A threedimensional rendering of the surface topography (a) with the second resonant frequency amplitude (d) “painted” onto the rendered surface (e) allows the high contrast second mode data to be correlated with the topography. Although (e)

Fig. 5.5 (a) Topography, (b) fundamental amplitude, (c) fundamental phase, and (d) bimodal second mode amplitude of HOPG, 30 µm scan. (e) Second mode amplitude data overlaid on rendered AFM topography. From [22]

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makes it clear there is a high degree of correlation, there are also boundaries in the second mode amplitude that seem to have no connection to topographical features. As another example, the second resonance mode phase of an epoxied natural rubber and polybutadiene rubber blend with embedded Si particles is shown in Fig. 5.6a. In this case, bimodal imaging allows the three components of the polymer blend to be clearly identified. To verify this interpretation, more conventional force–distance or “force” curves were performed over different regions. Colorcoded force curves made over three circled regions in Fig. 5.6a are shown in Fig. 5.6b. The curves were each offset along the vertical axis for visibility. In general, the slope of the deflection curve versus piezo extension provides a measure of the sample stiffness while the area enclosed by the loop provides a measure of the energy dissipated during an approach–retraction cycle. From the force curve data, the black dots (the most repulsive phase regions) can be identified as likely belonging to the embedded Si particles since the force curve (red) shows the steepest slope and the smallest dissipation. Similarly, the relatively stiff epoxied natural rubber ENR component is identified with the intermediate stiffness (blue), appearing as dark purple patches in Fig. 5.6a, while the softest polybutadiene rubber BR component (green) is associated with the yellow regions. Bimodal imaging can also be successfully applied for AM-AFM imaging in fluids. A high-density lambda-digest deoxyribonucleic acid (DNA Sigma 50µg/ml, imaged in 40mM HEPES, 5mM NiCl2 with a pH of 6.6–6.8) sample was prepared in a dense mat on freshly cleaved mica. Figure 5.7 shows the response of a 60-µm long Olympus Bio-Lever in fluid being driven at its fundamental resonance (f1~8.5kHz, A1~8nm) and at its second mode (f2~55kHz, A2~5nm) in the DNA buffer solution. The topography in Fig. 5.7a shows a dense mat of material on the surface with no clear strands of DNA visible. Similarly, the fundamental amplitude in Fig. 5.7b, the channel used for the feedback error signal, shows no particular structure. The fundamental phase channel

Fig. 5.6 (a) Second resonance mode phase of epoxied natural rubber (ENR) and polybutadiene rubber (BR) blend with embedded Si particles, 3 µm scan. (b) A series of force curves made over the color-coded locations on the sample, shown in (a) as circles. Sample courtesy of S. Cook, TARRC, UK


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Fig. 5.7 (a) Topography, (b) fundamental amplitude, (c) fundamental phase, (d) bimodal second mode amplitude of DNA, 750 nm scan. (e) Second mode amplitude data overlaid on rendered AFM topography. From [22]

(Fig. 5.7c) shows subtle contrast between the background and a structure that shows hints of being strands of DNA molecules. The second mode amplitude (Fig. 5.7d) shows clear, high contrast images of the same DNA strands. The strands appear dark, corresponding to an increased dissipation. This is consistent with the DNA strands being slightly less bound to the sample and thus able to absorb some of the second resonant frequency energy. Again, rendering the topography in three dimensions and painting the second mode amplitude on top in Fig. 5.7e allowed the topography and second mode amplitude to be spatially correlated.

The Energy Viewpoint Energy analysis is a useful way to look at bimodal imaging. The power dissipated by the ith resonant mode of the cantilever, Pi is given by the expression

Pi =

πkA2 f Q

 QAdrive sin ϕ f  −   A f0  

(5.3)

where the cantilever spring constant k, the piezo drive amplitude Ad, the cantilever quality factor Q, and the resonant frequency fn are all measured at a reference position above the sample surface (i.e., where the dissipative interactions are assumed absent). The amplitude A and phase j are used in (5.3) to yield the dissipated power relative to the reference position. Note that depending on the reference point, the dissipated power can be positive or negative. If the power dissipated by the tip due to the tip–surface interactions is zero, (5.3) can be solved to give a characteristic relationship between the amplitude and the phase of the cantilever,

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A−

ω 0 QAdrive sin ϕ w

(5.4)

This characteristic arcsine behavior of the phase on the amplitude is illustrated by the red curves in Fig. 5.10. During typical imaging, a feedback loop constrains the amplitude of the first mode to be constant. In this case, (5.3) implies that any phase contrast requires dissipative interactions between the tip and the sample. Purely conservative forces will not change the phase, they will only change apparent height of the sample. This is a significant limitation on compositional contrast using single frequency AM-AFM. However, if a second resonance is also excited, without a feedback loop, there is no such constraint on the dynamics. The second mode amplitude and phase are able to freely evolve in response to both conservative and dissipative forces. An example of this is shown in Fig. 5.8, where we imaged collagen fibers extracted from a rat tail tendon. The tail was mechanically dissected in PBS buffer. The extracted collagen fibers were torn apart and deposited on a mica surface. After rinsing with de-ionized water, the fibers were imaged. An AC240 cantilever (Olympus) was bimodally driven. The first resonance was at 72.1kHz and the amplitude set-point was ~60nm. The second resonance was at 437.5kHz and the amplitude was nominally ~6nm. The topographic data show the very typical 67nm banding pattern. Note that the fundamental resonance amplitude signal is relatively

Fig. 5.8 (a) Topography, (b) fundamental amplitude, (c) fundamental phase, (d) second mode amplitude and (e) second mode phase, 750 nm scan. Clear contrast differences between the background glass substrate, the collagen fibers and various contaminants are visible in the second mode phase channel (e)


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featureless as might be expected – this was the feedback error channel. The fundamental phase in Fig. 5.8c shows contrast at the edges of features, becoming more positive at these points. This is consistent with the overall interaction becoming more attractive at the edges. The second mode amplitude (Fig. 5.8d shows a similar contrast. The second mode phase (Fig. 5.8e) clearly differentiates the glass substrate, the fibers, and contaminants. In addition, the second mode phase is reduced over lengths of fibers that are suspended. Figure 5.9a shows image (Fig. 5.8e) with blue ovals indicate suspended fibers that appear dark in the second mode phase. In a manner similar to that discussed for Fig. 5.6, force curves were performed over the glass substrate (red) and on a suspended fiber (black). The adhesive portions of the curves are quite similar while the contact portions show distinctly different slopes, indicative of different stiffness values. In particular, the smaller slope indicates, not surprisingly, that the suspended fiber is significantly softer than the glass substrate. This in turn is clear evidence that the second mode phase is sensitive to variations in the sample stiffness. Figure 5.10 show two-dimensional histograms of the amplitude and phase values for the images shown in Fig. 5.8. In Fig. 5.10a, the fundamental phase and amplitude are plotted, showing the effects of the feedback loop. The amplitude is maintained at a more or less constant value of ~65nm with a narrow distribution of a few nanometers. The phase shows a wider distribution, with dissipation causing phase excursions towards 90°, as described by (5.3). Figure 5.10b shows very different behavior, with the second mode dynamics ranging over a much larger range of values. Since there is no feedback loop constraining the dynamics, the second mode is able to sample a wide range of both conservative and dissipative interactions as it scans over the surface.

Fig. 5.9 (a) Second mode phase image from Fig. 5.9. Two suspended fibers are indicated with blue ovals where the second mode phase shows a clear localized decrease. (b) Shows force– distance curves made over a supported (red) and a suspended (black) part of a collagen fiber. The adhesion over the two regions is quite similar while the slope of the contact portions of the curves are quite different, suggesting that the difference between the tip–sample interactions in the two areas is primarily elastic

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Fig. 5.10 Two-dimensional histograms constructed from the collagen data shown in Fig. 5.9. (a) Shows the distribution of the fundamental phase and amplitudes while (b) shows the distribution for the second resonance amplitude and phase. The red curves in each figure are the zero dissipation phase versus amplitude curves calculated from (5.4)

High Resolution, Low Force Bimodal Imaging One significant benefit of bimodal attractive mode imaging is that the forces between the tip and the sample are extremely small, allowing clear and nondestructive differentiation of composition, even on soft biological samples. As an example, type I collagen molecules form tensile-bearing structural fibers that are very common in connective tissue and the extracellular matrix. The fibril packing structure of collagen has been debated for some time. The most commonly accepted structure of the fibers corresponds to the model where the molecules of collagen are


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arranged in a staggered manner, leading to a typical 68nm pattern [41]. However this staggered arrangement has never been clearly demonstrated, and other models have been proposed. More recently AFM has been used to image collagen fibers, and additional models have been proposed [42]. A few AFM studies have also followed the assembly of molecules dynamically, but no insight was given on the molecular level. In Fig. 5.11, bimodal imaging was used to probe the ultra-structure of the same collagen sample shown in Fig. 5.8. In this case, we are imaging at very small amplitudes, keeping the cantilever in a net-attractive state. The first resonance was at 73.4 kHz and the set-point was 5nm. The second resonance was at 444.7 kHz and the amplitude was nominally ~1nm. The topographic data show the typical 67nm banding pattern, while the second mode amplitude shows detailed features at the surface of the fibers on the nanometer scale. Note that the fundamental resonance phase signal is relatively featureless. The small elongated structures visible in the second mode amplitude channel are on a length scale consistent with individual molecules inside the fibers. The round features could correspond to the terminal parts of the molecules forming the top layer of the fiber.

Fig. 5.11 Bimodal images (300 nm scan) of the (a) topography obtained from feeding back on the first mode amplitude, (b) first mode phase and (c) second mode amplitude of a collagen fiber. Image (d) shows a zoom into a region of the second mode amplitude image and (e) shows a section taken along the red line. The first mode phase is relatively featureless. The second mode amplitude shows a fine structure with a resolution of 2–3 nm. The white bar in images (a) and (d) is 50 nm long

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Separating Long- and Short-Range Forces: Bimodal Magnetic Force Microscopy Magnetic samples provide a nearly ideal situation for examining the relative role of short- and long-ranged forces because the long-range magnetic forces can change sign while other sample properties that affect short-ranged forces remain the same. Furthermore, the interaction length scales are set by the size of the domains or recorded bits, and more of the sample volume participates in the interaction than in the case of van der Waals forces. This means the long-range magnetic forces are much more independent of topographic effects like surface roughness. This allows single-pass imaging of the topography and magnetic forces between the tip and sample at high spatial resolution. Furthermore, magnetic samples are ideal test cases for determining contrast mechanisms in bimodal imaging theory (Fig. 5.12). In the above examples, the second cantilever mode was driven with the same excitation piezo. It is also possible to drive different modes with different mechanisms, including the tip–sample interaction, in cases where this interaction can be modulated. One example is the electrical force between the tip and the sample [44]. In a manner similar to the MFM results above, this allows the short-range topographic interactions to be separated from the long range, in this case, electrical interactions. Rodriguez et al. have recently shown that the second resonance can be used to image the ferroelectric domain structure in a number of samples in fluid [45]. Finally, bimodal drive techniques can also be used for contact resonance measurements, where the tip is pressed into the surface with a preset load and the resonances of two modes are excited [46].

Multiple Frequencies at the Same Resonance Peak Revisiting Past Assumptions: More Than Two Independent Variables As mentioned in the introduction, a common and useful approximation for the dynamics of a cantilever is the single simple harmonic oscillator. If we explicitly include the drive amplitude Adrive and phase j drive along with the cantilever resonance frequency w 0 and quality factor Q as unknown parameters in the steady-state amplitude can be written as [47]:

A (w ) =

Adrivew 02 (w 02 − w 2 ) 2 − (w 0w / Q )

2

,

(5.5)


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Fig. 5.12 A bimodally driven cantilever was used to image and then locally probe a hard disk sample, shown in (a) and (b). An attractive and a repulsive region were individually probed as indicated by the circular and triangular markers. Separate plots of phase corresponding to the first (c) and second modes (d) are shown as functions of Z position as the tip approaches the surface. The marker used in each plot also corresponds to the location where that particular data was acquired. After the point indicated by the dashed line when the short-range forces begin to dominate the tip–sample interaction, there is no longer any difference in the first mode phase signals. In contrast, there still remains a distinct difference in the second mode phase signals. From [43]

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and the steady-state phase as

  w 0w + j drive (w ). j (w ) = j cant (w ) + j drive (w ) = tan −1  2 2   Q(w 0 − w ) 

(5.6)

For a given imaging technique, these quantities carry different information about the tip–sample interactions. In the case of PFM for example, Adrive can be linked to the local piezo coefficient of the sample, jdrive depends on the polarization orientation and is assumed to be frequency independent, w0 depends on the contact stiffness which in turn depends on the contact mechanics and elastic moduli or the tip and sample, and variations in Q give information about the localized damping. This damping can be related to contact mechanics or polarization-lattice dissipation. In conventional single frequency measurements, information on two of the above quantities can be extracted based around the assumption that the other two quantities remain constant during the measurement. One example of this is dissipation imaging [24, 48]. In this formalism, the dissipated power Ptip is related to the phase shift and other cantilever parameters through the expression

Ptip =

πkA2 f  QAdrive sin (j − j drive ) f  −   Qref  A f0 

(5.7)

In this expression, we have included an unknown variable drive phase jdrive, which Cleveland et al. assumed to be zero. The spring constant of the cantilever k, the drive amplitude Adrive (usually provided by a vibrating piezo element) and the quality factor Qref are usually only calibrated once, before or after the dissipation and at a reference position. They are then assumed to remain constant over the duration of the dissipation measurements. For applications where the drive is supplied by a separate piezo or other actuator and, most importantly, the drive frequency is kept constant, the assumption is likely reasonably valid. If it does change, it is unlikely to correlate with other image or measurement features, allowing the artifact to be diagnosed. However, this is manifestly not the case for frequency tracking measurements of the type discussed here. In this case, we expect the transfer function to introduce artifacts into the measurement.

Frequency Tracking There are many examples of frequency tracking applications in scanning probe microscopy, most of which originate from the seminal frequency-modulated AFM (FM-AFM) work of Albrecht et al. [49]. This technique has garnered a great deal of attention because of its high spatial resolution in air, vacuum, and even fluid [50–55]. Of the many successes of FM-AFM, a few of note include single atomic defect resolution [56] and even sub-atomic resolution, allowing individual chemical


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bonds between surface atoms to be imaged [57] and used to directly measure the force as a single atom was moved across a surface [58]. FM-AFMs typically use phase-locked loops (PLLs) to maintain the drive frequency of the oscillator at the cantilever resonance. Briefly, PLLs involve circuitry or logic that utilizes the measured phase lag between excitation and response signals as the error signal for a feedback loop that maintains the cantilever phase at a constant value (typically 90°, the resonance point of the oscillator) by adjusting the frequency of the cantilever drive oscillator. In addition to the non-contact applications, PLLs can also be used to track contact resonance frequencies [59, 60].

Dual AC Resonance Tracking In the last several years, measuring dissipation has attracted increasing interest as it provides information on energy losses and hysteretic phenomena associated with magnetic, electrical, and structural transformations at the tip–surface junction. Traditional heterodyne detection schemes for the amplitude and phase dispersion in the cantilever drive can change the quantitative and even the qualitative dissipation [61]. Multiple frequency measurement including bimodal [25] and band- excitation [17, 62] techniques offer the possibility of independent correction of transfer function dispersion. Dual AC resonance tracking [25] (DART) technique provides much higher sensitivity to mechanical changes at the tip–sample junction than does the cantilever deflection. In addition to tracking the resonant frequency, this technique allows the additional model parameters such as the tip–sample dissipation to be measured. Figure 5.13 shows the basic idea behind DART. The cantilever is driven with a linear combination of sinusoidal voltages, one above (f2) and one below (f1) the resonant frequency f0. This dual frequency signal is used to modulate the tip–sample interaction. This modulation could be of the tip–sample distance as in UFM and AFAM or the tip potential as in PFM or even the tip–sample temperature if a heated cantilever is used. The resulting motion of the cantilever is measured with the standard position-sensitive detector. This signal in turn is used as the input for two lock-in amplifiers, where the sinusoidal drive at f1 and f2 is used as references for each lock-in. The output of the lock-in amplifiers consists of the two amplitude and phase pairs measured at each frequency A1, j1, A2, j2. To implement resonance tracking, the difference between the two amplitudes, A2–A1, is used as the error signal for frequency feedback. As noted above, since there are four independent measured quantities in DART, we can solve for four model parameters. By measuring the amplitudes and phases at the two drive frequencies, one can solve for the unknown model parameters Adrive, jdrive, w0 and Q as described below [63]. From (5.5) and noticing that A1»A2 we have

(ω 02 − ω12 )2 + (ω 0 ω1 / Q)2 = (ω 02 − ω 22 )2 + (ω 0 ω 2 / Q)2

(5.8)

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Fig. 5.13 In dual AC resonance tracking (DART), the cantilever is both driven and measured at a frequency below and a frequency above resonance. The total drive voltage is the sum of voltages at frequencies f1 (blue) and f2 (red). The cantilever deflection then contains information at both of those frequencies (purple). The amplitude and phase at the two frequencies are then separated again by the two lock-ins and passed on to the controller. Resonance tracking uses the difference of the two amplitude measurements as the error signal input for a frequency feedback loop

which, on simplification results in

ω 02 =

ω 22 + ω12 2(1 − 1 / 2Q 2 )

(5.9)

The parameters Q, w0 and jdrive can be solved iteratively using the following relations in addition to (5.3)

Q−

ω 0 ω 2 / (ω 02 ω 22 ) tan (ϕ '2 − ϕ drive )

ω ω /Q ϕ drive = ϕ '1 − tan −1  02 1 2  ω 0 − ω1

(5.10)

 . 

(5.11)

An example of the results of this process is shown in Fig. 5.14 where the topography, contact resonance and Q are plotted on a sample from a section of a


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Fig. 5.14 (a) Topography, (b) contact resonance frequency, and (c) quality factor for a section of a printed circuit board at the border between the copper conductive layer and polymer support. The polymer support shows both a greatly reduced stiffness and increased dissipation (decreased cantilever quality factor, Q) compared with the Cu. Sample courtesy of Junhee Hahn, Korea Research Institute of Standards and Science (KRISS), South Korea

printed circuit board at the border between the copper conductive layer and polymer support. The topography image in Fig. 5.14a shows some increased roughness on the right side over the polymer. The derived contact resonance (b) shows a distinct drop over the polymer (roughly 100 kHz) and the quality factor

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(c) shows a significant lowering, consistent with increased dissipation over the polymer region.

Intermodulation AFM As discussed above, nonlinearities in the tip–sample interaction can complicate the dynamics and interpretation of the cantilever response. A technique that makes direct use of this is dubbed Intermodulation AFM (IMAFM) [64]. IMAFM uses two pure harmonic drive tones at frequencies f1 and f2 to excite the cantilever. The nonlinear tip–surface force will cause a mixing of these drive tones, so that response is generated at frequencies called intermodulation products, fIMP=nf1+mf2, where n and m are integers (see Fig. 5.15). The response at each intermodulation frequency contains both amplitude and phase, each carrying information about the cantilever dynamics. The technique allows much information to be gathered in the spectral

Fig. 5.15 (a) The amplitude of the response of a free cantilever, far away from the surface, when driven with two pure harmonic tones, f1 and f2, both placed near resonance. (b) When the cantilever engages the surface, the nonlinear tip–surface force causes intermodulation response of odd order near resonance (e.g., 3H = 2f2 - f1, 3L = 2f1 - f2, 5H = 3f2 - 2f1, 5L = 3f1 - 2f2, etc.)


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Fig. 5.16 The amplitude of intermodulation response at frequencies 3L, 5L, 7L, and 9L, plotted as a function of the approach distance. The zero of approach distance is taken to be the start of the approach ramp, and the cantilever begins to engage the surface at about 2 nm. The intermodulation amplitudes are plotted on a log scale, where the curves 3L, 5L, and 7L have been offset by 1.0, 0.4, and 0.2 nm, respectively, for clarity

response near resonance, which is highly advantageous because the sensitivity of the oscillating cantilever as a force transducer is largest near resonance. With intermodulation AFM one can generate response of high order, l = |m|+|n|, efficiently using the system bandwidth in comparison to measuring harmonics. Harmonics requires a second torsional oscillator to get an appreciable transfer gain, and a system bandwidth of l times the resonant frequency to acquire the lth harmonic. Each intermodulation product shows a unique and complex dependence on approach distance (see Fig. 5.16), and detailed images can be constructed by recording the amplitude and phase at each intermodulation frequency while scanning. Research is underway on inversion algorithms to extract the tip–surface force from the measured intermodulation spectrum at one distance, thus enabling determination of the force curve at each measurement point.

Conclusions, Future Challenges and Opportunities There have been many promising developments in multi-frequency nano-scale measurements. In the case of non- and intermittent-contact imaging applications, the signals at higher resonance modes provides higher compositional contrast and higher spatial resolution while at the same time maintaining very low-force, gentle

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imaging conditions. For contact resonance measurements, multiple measurement frequencies opens up many opportunities to better constrain various tip–sample interaction model parameters. Compositional mapping using the AFM still has many challenges. Qualitatively, the methods described here and others in the literature have been quite successful in mapping relative differences between various regions of a multi-component sample. True quantitative mapping is a much more serious challenge that can also be viewed as opportunities for future work. These barriers include at least the following: (1) quantifying the forces depends on quantifying spring constants, detector sensitivities, effective masses, and damping of the various cantilever resonant modes; (2) interpreting and controlling the sometimes complex dynamics of the multi-modal cantilever interacting with the highly nonlinear and dissipative sample surface, and perhaps most significantly (3) ill-defined contact mechanics that strongly depend on the shape of the cantilever probe. The last issue may be the most difficult to overcome because the relevant length scale of the mechanical contact is extremely small (this is where the high resolution of AFM comes from after all) and even if a tip is well characterized before and/or after making measurements, tips clearly wear and pick up contaminants over time, making those shape measurements only of transient relevance.

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Chapter 6

Dynamic Nanomechanical Characterization Using Multiple-Frequency Method Ozgur Sahin

Abstract Macroscopic behavior of materials, whether synthetic or biological, depends on the morphology and characteristics of their microscopic constituents. Improving the performance of engineered materials and understanding the design principles of biomaterials demand tools that can characterize material properties with nanoscale resolution. What is the spatial arrangement of the components of a heterogeneous material? Are the material properties of those components different from their respective bulk properties? How do material properties change near the interfaces? What is the influence of temperature, electric or magnetic fields, or solvents? Answering these questions is of critical importance to the rational design of advanced materials and to the analysis of biological materials. In this chapter, we focus on the recent advances in the measurement and characterization of dynamic nanomechanical properties with high spatial resolution using specially designed atomic force microscope cantilevers. We will first describe the basic operation principles of this method and present results to judge its performance on various material systems. Functional materials generally consist of multiple components with different material properties and feature dimensions. The level of complexity in these materials demands sophisticated characterization tools. Before going into details of the nanomechanical measurements, we list some of the desired attributes of a good nanomechanical characterization instrument below: Spatial resolution. A characterization tool should be able to provide a spatial resolution better than the smallest feature size of the sample, which approximately corresponds to 1–10 nm. In addition, the material properties should be mapped across a surface area wide enough to capture the properties of different components. The scan area can range between 100 nm and 100 µm or even more. Sensitivity and dynamic range. The properties of different components of a material can vary by several orders of magnitude and in some cases they can vary only slightly. The characterization tool should be able to differentiate both small and large variations in the properties being mapped. O. Sahin (*) The Rowland Institute at Harvard, Cambridge, MA, USA e-mail: [email protected] S.V. Kalinin and A. Gruverman (eds.), Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy, DOI 10.1007/978-1-4419-7167-8_6, © Springer Science+Business Media, LLC 2010

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Measurement speed. In research and development of functional materials, the characterization step should be ideally faster than the preparation of the samples so that it does not become a bottleneck in the development process. While faster measurements offer practical advantages, it should be noted that mechanical properties of materials are frequency dependent, i.e., faster measurements will necessarily reflect high frequency mechanical response. Non-destructive measurements. Mechanical interactions can damage the sample under test as well as the probe, such as a sharp indenting tip. Non-destructive measurements permit repeated analysis of the same sample region and also permit additional analysis with other methods. In some cases, non-destructive measurements enable characterization of the sample while it is functioning. In order to measure mechanical properties of samples with high spatial resolution, one has to bring a sharp object, such as an atomic force microscope tip, in contact with the sample surface. If the sharp tip is pressed against the surface, the sample will deform under the influence of localized interaction forces. The amount of stored or dissipated energy in this process, then, allows to measure local mechanical properties. In principle, larger forces provide better sensitivity and measurement speed. However, larger forces also result in increased contact areas that compromise spatial resolution and potentially damage the sample or the probe tip. In these respects, the attributes of a good nanomechanical characterization instrument, as listed above, have contradicting requirements on the forces involved in the mechanical measurements. Non-destructive operation and high spatial resolution demand lower forces, whereas sensitivity, dynamic range, and measurement speed demand higher forces. In general, spatial resolution and non-destructive operation are given higher priorities over measurement speed and dynamic range; therefore, researchers often spend more time characterizing their samples and they also use different probes or instruments to extend the dynamic range of the measurements. In this chapter, we will describe a non-destructive nanomechanical measurement technique that promises high spatial resolution and high speed characterization of materials with large dynamic range. This method is based on tapping-mode atomic force microscopy, where an oscillating cantilever periodically and intermittently interacts with the sample. A special geometrical design of the tapping cantilever turns this widely used nanoimaging method into a quantitative material analysis tool. We will first describe the technical details of this approach, which will allow us to judge its limitations and potential. Subsequently, we will give examples of measurements obtained on a wide range of material systems that illustrate the speed, spatial resolution, and dynamic range of this technique. Finally, an application of this technique in observing the glass transition of polymer blends with sub-micron domains will be presented.

Measurement Basics Measurement of mechanical properties of materials primarily relies on the observation of the deformation of a sample under a known external load. Two physical quantities, position and force, have to be determined. For example, in the case of a

6 Dynamic Nanomechanical Characterization Using Multiple-Frequency Method

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Hookian spring, the ratio of force and displacement corresponds to the spring constant that fully characterizes the mechanical properties of the spring. When a sharp object is indenting a sample, such as nanoindenters or atomic force microscopes, the forces and displacements do not necessarily follow a linear relationship. This is not because the sample has a non-linear mechanical behavior, but it is merely a consequence of non-linear evolution of the contact geometry as the sharp object indents the sample. In this more general case, measurement of a force– distance curve is needed to account for the geometrical effects and fully characterize the mechanical properties of the sample. To obtain high spatial resolution in mechanical measurements, one has to keep the size of the contact region small. Sharper probes and lower interaction forces are the two important factors in improving spatial resolution. As a result of lower interaction forces, the deformation of the sample also gets smaller. Note that the magnitudes of the two quantities necessary for mechanical characterization have to be reduced in order to improve spatial resolution. Therefore, the sensitivity and accuracy of the displacement and force measurements become even more critical in high spatial resolution mechanical measurements. In this section, we will review the displacement and forces in tapping-mode AFM. We will show that a specially designed cantilever can perform accurate displacement and force measurements while the tip is intermittently striking and deforming the sample.

The Tapping Cantilever Moves in a Sinusoidal Trajectory In tapping-mode AFM, the force probe, a flexible cantilever beam with a sharp tip, is vibrated at its resonance frequency near the surface [1]. The amplitude of the vibrations is sufficiently large so that the sharp tip interacts with the sample only at the bottom of its trajectory and does not stick to the surface. The amplitude of the vibrations is held constant by a feedback mechanism that adjusts the vertical position of the cantilever base with respect to the sample. When the cantilever is scanned across the sample, the feedback signal corresponds to the surface topography. The intermittent contact of the tip minimizes lateral interactions and prevents damage to the sample and the tip. The resonant operation minimizes the vertical forces because on resonance it takes much less force to generate or dampen the motion of the cantilever. The reduction in forces is mainly determined by the qualityfactor of the cantilever and it is on the order of 100 in ambient conditions. The resonant operation has another important advantage in mechanical measurements – the tip moves in a sinusoidal trajectory. By measuring the vibration amplitude and phase, one can accurately determine the position of the tip with respect to time. The reason why the tip is moving in a sinusoidal trajectory can be understood by considering the speed of the response of the cantilever to rapid changes in external forces on the tip. When the external forces change at rates below the resonance frequency of the cantilever, the cantilever can respond to the forces.

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If the forces change at rates beyond the resonance frequency, however, the cantilever cannot respond to the forces effectively. In the special case of tappingmode operation, the cantilever is driven at the resonance frequency, so the changes in forces due to the intermittently striking tip are at much higher rates than the resonance frequency. Therefore, the sinusoidal motion of the cantilever remains largely unaffected by the intermittent force pulses acting on the tip. As a result, the resonant excitation in the tapping-mode allows accurate determination of the tip position in time. Mechanical measurements require determination of both forces and displacements. As discussed above, the tapping cantilever provides a good way of determining the tip position in time. If one can also determine the temporal variation of forces acting on the tip, one can extract force–distance relationships and characterize mechanical properties of the samples. In principle, forces acting on the tip can be detected from the bending or vibrations of the cantilever. Unfortunately, the very reason that moves the cantilever in a sinusoidal trajectory makes it insensitive to the tip–sample interaction forces, because the forces are changing faster than the resonance frequency of the cantilever and their effect on the cantilever motion is negligible. This dilemma can be resolved by using special cantilevers that allow access to multiple mechanical modes with different resonance frequencies. In this scheme, the mechanical mode with the lower resonance frequency can be used to determine position by using the tapping-mode principles described above and the mode with the higher resonance frequency can be used to determine temporal variation of interaction forces. Surprisingly, the twisting and bending modes of rectangular AFM cantilevers provide the mechanical resonances with low and high resonance frequencies. To gain better insight on the dilemma of making simultaneous displacement and force measurements and how it is resolved by specially designed cantilevers, we are going to investigate cantilever motion and tip–sample interaction forces in tapping-mode AFM.

Information About the Mechanical Properties Are Contained in Higher Harmonic Forces The vibrating cantilever in tapping-mode AFM can be modeled with a damped harmonic oscillator driven by the external excitation force and the tip–sample forces. Both of these force components are time depended, and so does the cantilever motion. The equation of motion for the cantilever depends on its spring constant, quality factor (a measure of damping), resonance frequency, and the external forces. Under typical imaging conditions, it is observed that the cantilever motion is mainly sinusoidal, i.e., single frequency. This has been justified by the qualitative arguments in the previous section and by the numerical simulations of the cantilever dynamics reported extensively in the literature. Here, we will summarize the results of numerical simulations to the extent they relate to the measurement of the mechanical properties of the sample.


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Our analysis of the tip–sample interaction forces begins by modeling the mechanicsof the tip–sample contact. We use the Derjaguin–Muller–Toporov model [2], which predicts the forces between a spherical tip and a flat surface as follows:

4 Ftip - sample = E * R (d - d 0 )3/ 2 + Fadhesion . 3

(6.1)

Here Ftip-sample is the interaction force between the tip and the sample, E* is the reduced elastic modulus of the tip–sample ensemble, R is the radius of the tip, d0 is the rest position of the surface, d-d0 is the depth of indentation, and Fadhesion is a constant attractive adhesion force between the tip and the sample that is present during the contact. The conclusions that will be derived in this section are independent from the specific functional form of (6.1). The key attribute of the contact mechanics that we intend to capture is the increase in the forces with higher elastic modulus or with larger indentations. Nevertheless, experimental measurements of mechanical properties that will be presented later in this chapter suggest that (6.1) provides a good description of the tip–sample forces. We have carried out numerical simulations [3] of the equation of motion for a cantilever tapping on samples with three different elastic modulus values: 1GPa, 100MPa, and 10MPa. The cantilever’s spring constant and quality factor are assumed to be 2N/m and 50, respectively. The amplitude set-point is assumed to be 30 nm and the driving force is selected such that the free vibration amplitude of the cantilever is equal to 40 nm. In addition, the adhesion force Fadhesion is set to 1.5 nN. Figure 6.1 presents the spatial, temporal, and frequency domain characteristics of tip–sample interaction. Each row of graphs belongs to a different elastic modulus value for the sample. The force–distance relationships given in the left column extends 60 nm, twice the set-point amplitude. The rest position of the surface is set to 0nm in each plot. The slopes of the forces in the interaction region (negative distances) are proportional to the elastic modus of the sample as determined by (6.1). Note that the peak forces and indentation depths are different for each sample. While the indentation depths increase toward the more compliant samples, the peak forces reduce. The reason why peak forces and indentation depths vary with the elastic modulus is better understood by analyzing the temporal characteristics of the tip–sample forces. During the vertical oscillations of the cantilever, the position of the tip remains in a sinusoidal orbit. So the force–distance relationships on the left column in Fig. 6.1 can be plotted against time to obtain force–time waveforms seen in the middle column. In addition to the observed reduction in peak forces toward the more compliant samples, these force–time waveforms show that the duration of contact is also increasing with decreased elastic modulus. This behavior is predicted by the analytical solutions derived to relate cantilever vibration amplitude and phase to the driving force and the mechanical properties of the sample. It is found that under the same driving force and set-point amplitude, the time-average forces remain approximately constant regardless of the elastic modulus of the sample. So with larger peak forces, the duration of contact gets smaller.

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Fig. 6.1 Simulated tip–sample forces in tapping-mode AFM. Three samples with different elastic modulus values are used: (a) 1 GPa, (b) 100 MPa, and (c) 10 MPa. Force–distance, force–time, and force–frequency relationships calculated on each sample are given in separate columns (cf. [3])

In the above analysis of the temporal characteristics of the interaction forces, we see that despite large variations in the tip–sample force waveform, the time-average forces remain approximately constant on samples with different elastic modulus values. Unfortunately, the two measured quantities in the tapping mode, vibration amplitude and phase, tell us only about the average forces. Therefore, much of the information about the elastic properties of the sample is lost. The following analysis of the frequency domain characteristics of the tip–sample forces will explain where the lost information is and what is needed to recover it back. The cantilever vibrations and the tip–sample forces are periodic in time. The force–time waveforms given in the middle column of Fig. 6.1, therefore, represent single cycles of the periodic tip–sample forces. Each of these waveforms can be seen as a superposition of forces at different frequencies, which corresponds to the Fourier transform of these waveforms [4]. In the specific case of periodic waveforms of the tapping mode, the force components are at exact integer multiples of the fundamental frequency, i.e., the driving frequency. These force components are referred as harmonic forces. Their magnitudes are plotted with respect to frequency on the rightmost column in Fig. 6.1. When we compare the spectrum of harmonics on each sample, we see that the magnitudes of the first few harmonics are approximately the same at different elastic modulus values. The differences between the samples are mainly at higher order harmonics. This tells us that the information regarding the elastic properties of the samples is at the higher harmonics. Moreover,


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it is seen that the magnitudes of the higher harmonics are larger on the stiffer samples. The harmonic index where the first local minimum of the spectrum is a bigger number for stiffer samples compared to the compliant samples. This is a consequence of the Fourier transform, in which temporally narrower pulses lead to wider frequency spectra. From the analysis of the higher harmonics of the tip–sample forces, we learn that measuring high frequency force components is necessary to reconstruct tip–sample force waveforms. If recovered, this waveform is sufficient to obtain the force– distance relationship for a given sample, because the position of the tip is known to be a sinusoid in time. Then, by assuming a contact mechanics model, such as (6.1), one can estimate material properties like elastic modulus. The spectra of higher harmonics in Fig. 6.1 illustrate the challenge of measuring the mechanical properties of samples in tapping-mode AFM. The two experimentally accessible parameters, vibration amplitude and phase, are measured at the driving frequency, i.e., the first harmonic. The high frequency force components of the tip–sample interactions are not accessed by the conventional amplitude and phase measurements; hence the information about the elastic properties of the sample is lost. Just like the tip–sample force waveforms, the vibrations of the cantilever also contain frequency components. Therefore, in principle, the high frequency vibrations can be used to recover the high frequency force components [5]. However, the amplitude of those vibrations is small and therefore difficult to detect. Indeed, the statement that the cantilever motion is mainly a sinusoid is equivalent to the statement that the higher harmonic vibrations have small amplitudes. This brings us to the conclusion that accessing higher harmonic forces, and therefore the mechanical properties, demands improved performance of the force-sensing cantilever at higher frequencies without perturbing the tapping-mode operation.

There Are Multiple Force Sensors in a Single Cantilever The vibrations of the AFM cantilever are governed by continuum mechanics. The cantilever base is fixed to a supporting chip and the sharp tip is near the free end. This configuration leads to multiple vibration modes whose resonance frequencies lay near the frequencies of the higher harmonics forces discussed in the previous section [6]. The response of a given vibration mode to the forces acting on the tip can be represented with an effective spring constant, resonance frequency, and quality factor. In principle, any of these modes can be actuated to displace the tip or more importantly they can be used as independent force sensors. In AFM cantilevers the fundamental mode, i.e., the mode with the lowest resonance frequency, has an effective spring constant more than an order of magnitude smaller than any of the higher order modes. In the special case of tapping-mode AFM, the cantilever is driven at the resonance frequency of the fundamental mode where the displacement response of this mode is further enhanced by the sharp resonance. As a result,

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the response of the fundamental mode dominates the response of the vibrating cantilever in the tapping mode. For practical purposes, a single mode description of the cantilever is sufficient to predict the vibration amplitude and phase response of the tapping cantilever. However, for the measurement of higher harmonic forces the response of those vibration modes whose resonance frequencies fall within the ranges of harmonic frequencies of interest should be considered. The tapping cantilever is subject to tip–sample forces whose pulse-shaped temporal characteristics are depicted in Fig. 6.1. The width and the height of the pulses depend on the mechanical properties of the sample [7]. The overall motion of the cantilever is a superposition of the response of each mode to these forces. Unfortunately, this superposition makes it difficult to access the individual responses of these modes. The motion of the cantilever is detected by a laser beam reflected from the cantilever falling onto a position-sensitive photo detector. The signal at the detector is proportional to the slope of the cantilever at the region where the laser spot is focused [8]. Because the slope of the cantilever results from a summation of the slopes originated in each mode, one cannot determine the contribution of each mode separately. However, there is one important exception, and that enables accessing the temporal characteristics of the tip–sample force waveform. The photo detectors used in AFM instruments are split into four quadrants to detect lateral and vertical motion of the laser spot simultaneously. This allows distinguishing flexural (bending) and torsional (twisting) motion of the cantilever; since flexural deflections result in vertical motion of the laser spot and torsional deflections result in lateral motion. In typical AFM cantilevers, the tip–sample forces do not excite torsional vibrations of the cantilever because the sharp tip is conventionally placed at the center of the cantilever so that no torque is generated around the symmetry axis of the cantilever. However, if the sharp tip is placed offcentered, the interaction forces will twist the cantilever. It turns out that the mechanical properties of the first torsional mode make it suitable for measuring the tip–sample forces. This configuration is illustrated in Fig. 6.2. The T-shaped cantilever in Fig. 6.2 is named as the torsional harmonic cantilever, since it allows the measurement of higher harmonic forces through the torsional oscillations of the cantilever [9, 10]. When this cantilever is oscillated vertically as in conventional tapping-mode AFM, the tip–sample forces generate a twisting motion that can be independently detected by the quadrant photo detector. The twisting motion has much smaller amplitude compared to the vertical oscillations of the cantilever and even compared to the typical indentation depths of samples; therefore its effect on the overall tapping-mode operation is negligible. On the other hand, the first torsional mode has a much higher resonance frequency compared to the fundamental flexural resonance frequency so that it can follow the rapidly changing tip–sample forces. In addition, the sensitivity of the torsional modes is geometrically enhanced by the short torsion arm, i.e., the tip offset distance, because smaller tip displacements resulting from a twist in the cantilever produce larger slopes compared to flexural modes. Figure 6.3 shows calculated frequency responses of flexural and torsional vibration modes of a torsional harmonic cantilever and experimentally recorded vibration spectra


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Fig. 6.2 Diagram of the torsional harmonic cantilever operation. The T-shaped cantilever with an offset tip is vibrated near the surface vertically at its resonance frequency. The cantilever is twisted by the interaction forces. The resulting torsional motion is used to generate high-speed force– distance curves (cf. [10])

of a torsional harmonic cantilever tapping on a polystyrene sample. The frequency response calculations are performed for rectangular cantilever geometry, 30 µm wide and 300 µm long, with a tip 15 µm offset from the longitudinal symmetry axis of the cantilever. The response curves are plotted for frequencies up to 20 times the fundamental flexural resonance frequency. In this frequency range we see three resonance peaks in the flexural response and one resonance peak in the torsional response, which has a frequency comparable to the third flexural resonance. Furthermore, the response of the torsional mode is larger than the flexural modes at higher frequencies. This means the torsional mode combines high bandwidth and sensitivity, which is essential for sensitive and accurate measurements of tip–sample forces. The higher harmonic force components of the tip–sample interactions drive flexural and torsional vibrations in proportion to their response at each harmonic frequency. The vibration spectra shown in Fig. 6.3b, c show the measured amplitudes of the flexural and torsional vibrations at each frequency. The peaks in these spectra correspond to the harmonics, i.e., integer multiples of the drive frequency. The peak with the largest amplitude is in the flexural vibrations and it is exactly at the drive frequency. All other peaks in flexural and torsional vibrations have amplitudes that are orders of magnitude smaller than the large peak at the drive frequency. This means, for practical purposes, the cantilever motion can be considered to be sinusoidal in time at the drive frequency. Other peaks, while good for mechanical property measurements, do not have significant effects on the tip position.

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Fig. 6.3 Frequency response (a) and vibration spectra (b, c) of a torsional harmonic cantilever. The frequency axis is normalized to the first flexural resonance frequency. Flexural (b) and torsional (c) vibration spectra is recorded on a polystyrene sample. The torsional peaks show enhanced signal levels at higher frequencies (cf. [9])

The spectrum of torsional vibrations does not attenuate up to frequencies 20 times as much as the driving frequency. Therefore, it recovers the information in the higher harmonic tip–sample forces. However, the relationship between the forces and torsional vibrations is not trivial. The harmonic forces that are closer to the torsional resonance frequency are translated into larger vibrations compared to the harmonics that are away from the torsional resonance. This feature of the torsional response is evident in the torsional vibration spectrum in Fig. 6.3b as peaks around the 16th harmonic exhibit larger magnitudes compared to the other peaks. The effect of the torsional resonance can be approximated by the frequency response of a simple damped harmonic oscillator that matches the resonance frequency and


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q uality factor of the first torsional vibration mode. Then, one can numerically correct the torsional resonance effects. Given the periodic motion of the tapping cantilever, it is easier to carry out these numerical calculations in frequency domain where the frequency response of the torsional mode can be approximated as:

H T (w ) =

1 . w - w + iww T / Q 2 T

2

(6.2)

Here w is the angular frequency, wT is the torsional resonance frequency, and Q is the quality factor of the torsional resonance. Note that HT is a complex number. This is because there is a time delay between the higher harmonic forces and the response of the cantilever to those forces, which translates to a phase shift in the frequency domain. In practical implementations, the numerical calculations are carried out with a computer in a semi-automatic fashion. The user needs to input calibration parameters like the force sensitivity of the torsional mode and photo-detector sensitivity to tip displacements. Then, the computer program transforms the torsional vibrations into the frequency domain by taking its Fourier transform and then corrects for the torsional resonance effects by dividing it to (6.2). The resulting signal is transformed back to the time domain, by taking its inverse Fourier transform, so that a tip–sample force waveform is obtained. Figure 6.4 depicts detector signals and calculated tip–sample forces recorded on a highly oriented pyrolytic graphite sample. The cantilever used in this experiment is driven at its flexural resonance frequency at 47.4 kHz. The periodic vibration signals in both vertical and lateral deflection signals are averaged over 12 consecutive oscillation cycles to reduce noise. The resulting waveforms are given in Fig. 6.4a. Note that the flexural response is mainly a sinusoid; however, the torsional response is complicated. The most important component of the torsional response is marked with an orange arrow. This is where the tip hits the surface at the lowest point in its trajectory. As a result of the impact, the cantilever twists, and the peak at the arrow is generated. After this impulse, the torsional mode exhibits oscillatory response that is natural to weakly damped harmonic oscillators. Because the tip swings away and hits back to the surface in the following oscillation cycle, the high frequency torsional oscillations do not decay completely. Another feature of the torsional vibration signal is the crosstalk from the large vertical oscillation signal. It is seen that the impact at the arrow and the oscillatory response are superimposed on a low frequency sinusoid. That low frequency signal is exactly at the drive frequency and it is mainly due to a crosstalk originating from misalignments in the cantilever and photo detector alignment. Even a small angular misalignment can result in considerable crosstalk because vertical oscillation has much larger signal amplitude compared to the torsional vibrations. The effects of the torsional resonance can be corrected numerically by using (6.2). However, this procedure will not eliminate the crosstalk-related sinusoidal component. The crosstalk component can be eliminated by subtracting a sinusoid such that the value of the resulting waveform is zero when the tip is away from the surface, i.e., outside the pulse marked with the arrow in Fig. 6.4a. The amplitude

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Fig. 6.4 Reconstructing the tip–sample force waveform. (a) Oscilloscope traces of the periodic flexural (blue) and torsional (orange) vibration signals at the position-sensitive detector, obtained on graphite. (b) Time-resolved tip–sample force measurements calculated on graphite. (c) The same data as in (b), plotted against tip–sample distance. Negative distances mean that the sample is indented. Arrows indicate the direction of motion. The solid part of the curve marks the points between the largest sample indentation and breaking of the contact on the retraction portion of the curve (cf. [9])

and phase of the sinusoid to be subtracted is determined by linear curve fitting. Note that the complete numerical procedure takes about 10 µs for a typical desktop computer (2008). This is sufficient to carry out real-time calculations for a cantilever tapping at 100 kHz. Figure 6.4b shows the resulting tip–sample force waveform after calculations. The pulse-shaped force waveform and attractive and repulsive force components are visible in this waveform. Once the tip–sample force waveform is recovered, it can be plotted against the tip–sample distance to obtain the force–distance relationship. The tip sample distance


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can be obtained from the vertical signals in Fig. 6.4a; however that waveform does not directly correspond to tip position. Instead, we use a computer-generated sinusoid that has the same amplitude with the cantilever vibrations. This change also eliminates the noise in instantaneous position measurements. Figure 6.4c plots the resulting force–distance relationship on a graphite sample. The origin of the position is arbitrarily referenced to the lowest force measurement. This point approximately corresponds to the rest position of the surface. Note that there are two force values recorded for a given position of the tip; one for the approach and one for the retraction. The differences between the approach and retraction become more prominent at the first 2nm above the rest position of the surface. The resulting hysteresis dissipates energy at each cycle of the oscillating cantilever. The force–distance relationship also displays increasing forces at positions below the rest position of the surface. As the tip pushes into the sample, mechanical restoration forces rise up. For spherical tip geometry, the relationship between the forces and indentations are approximately given by (6.1). With the knowledge of tip size, one can estimate the elastic modulus of the sample by analyzing the measured force–distance curve. To demonstrate the effects of sample elastic modulus on the tip–sample force waveform and force–distance curves, we present measurements on samples with different stiffness. The force–time and force–distance relationships given in Fig. 6.5a, b belong to high- and low-density polyethylene samples. These samples are

Fig. 6.5 Experimental measurements of force–time and force–distance relationships on (a) highand (b) low-density polyethylene samples under identical tapping-mode feedback conditions. The shapes of the curves are determined by the mechanical properties of each sample (cf. [3])

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known to have distinct mechanical properties with typical elastic modulus values of 750 and 50 MPa, respectively. The tip–sample force waveform recorded on highdensity polyethylene shows larger peak force and smaller pulse duration compared to the waveform recorded on low-density polyethylene. As previously discussed, this leads to constant time-average forces in tapping mode. The force waveforms also exhibit non-zero values during the times when the tip is away from the surface. Therefore, these forces reflect the noise in force measurements. The respective force–distance curves in Fig. 6.5 reveal the differences in the samples more clearly. The slopes of the curves in the region where the tip is pushing into the sample are largely different. The tip radius for the cantilever used in this experiment is approximately 7 nm. When we use this number with (6.1) and perform a curve fitting to the force–distance data, we estimate the reduced elastic modulus values as 588 MPa for the high-density polyethylene and 56 MPa for the low-density polyethylene. These numbers are fairly close to the typical values for these samples. Note that unlike the theoretical models, the exact position of the sample surface is not well known. This poses a challenge while fitting (6.1) to the force–distance curves. Instead of assuming a fixed position for the surface, the fitting process finds the surface position that provides the best fit together with the elastic modulus value of the sample.

High-Speed and High Spatial Resolution Nanomechanical Analysis with Large Dynamic Range At the beginning of this chapter, we have listed a number of key aspects of nanomechanical sensors: spatial-resolution, sensitivity and dynamic range, measurement speed, and non-destructiveness. In this section, we will present experimental results that demonstrate the performance of the torsional harmonic technique according to the listed measures. We will first investigate the accuracy, sensitivity, and dynamic range of the measurements. Second, we will provide mechanical property maps of heterogeneous materials with feature sizes ranging from 1 to 500 nm. Lastly, we will present an application of this technique in characterizing the phase transition behavior of a polymer blend with sub-micron features.

Torsional Harmonics Provide a Large Dynamic Range in Mechanical Measurements Any measurement instrument or sensor has upper and lower limits on the magnitude of the quantity that it can measure. Beyond a certain value of the measured signal, the output of the sensor will saturate and below a certain value of the measured signal, the output will display noise. The range of values in between these two limits is the dynamic range of the sensor. In the case of elastic modulus measurements, there is a lower and an upper limit of elastic modulus. To measure


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a sample that has an elastic modulus value that falls outside its dynamic range, one has to change the sensor device, i.e., the cantilever in AFMs. In some cases, using different settings for the sensor device can also shift the measurement range slightly. To assess the dynamic range of the measurements with the torsional harmonics, it is therefore important to carry out the measurements with the same cantilever and under identical feedback conditions. These circumstances also reflect the imaging conditions. Furthermore, the measurements bandwidth has to be constant and it should be equal to the bandwidth that is relevant to the experimental timescale. For typical tapping-mode imaging conditions, a bandwidth of 1kHz is sufficient to generate high resolution mechanical maps in less than 10 min. Therefore, in the following analysis of the dynamic range of the torsional harmonic measurements, the bandwidth was set to 1kHz. Figure 6.6 presents histograms of measurements on ten different samples with elastic modulus values ranging from 1 MPa to 50 GPa. This analysis will not only determine the dynamic range of the measurements, but it will also demonstrate the sensitivity and accuracy of the measurements. These samples are chosen because of their availability and knowledge about their approximate elastic modulus. On a given sample, 5,000 consecutive measurements of the tip–sample force waveform are performed and the resulting values are plotted in a histogram given in Fig. 6.6a. The spread of these histograms reflect the measurement noise. The width of the histograms gets narrower toward samples with increasing elastic modulus. Note that the histograms are plotted on a logarithmic scale. This means that the relative errors reduce toward stiffer samples. At lower elastic modulus, around 1MPa, the relative error reaches to 50%. This is approximately where the signal-to-noise ratio of the measurement becomes unity. Measurements below this level of elastic modulus will be dominated by noise. The origin of noise in elastic modulus measurements can be best understood by analyzing the tip–sample force waveforms in Fig. 6.5. We see that the measured forces outside the duration of contact are non-zero due to the noise in the detection of cantilever deflections. As the sample elastic modulus reduces, the peak forces drop and contact durations increase. At a certain level of peak forces, the interactions will become difficult to distinguish from the noisy background forces, therefore the elastic modulus estimate based on the waveform will reflect the force noise. Toward increased elastic modulus values, the histograms point out another mechanism of measurement error besides noise. The measured values on Mica underestimate the elastic modulus of this material. As we discussed in the “Measurement Basics” section, the contact duration becomes narrower and peak forces larger toward stiffer samples. Beyond a certain level of stiffness, the bandwidth of the torsional mode becomes insufficient to follow the rapidly changing forces. As a result, the contact duration in the measured force waveform appears wider than the actual interactions. The elastic modulus estimate based on the measured waveform, therefore, reflects a lower value than the actual elastic modulus of the sample. So, this phenomenon presents a saturation mechanism for the mechanicalmeasurements with torsional harmonics. The analysis of measurement noise and saturation based on the histograms in Fig. 6.6a tells that the lower limit of measurements is around 1MPa and the upper

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Fig. 6.6 Nanomechanical measurements on different materials. (a) Histograms of elastic modulus values calculated from the tip–sample forces. The histograms represent 5,000 consecutive measurements, 1 ms per data point. (b) Mean values and standard deviations of the histograms are plotted against nominal elastic modulus values of the samples (cf. [10])


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limit of measurement is around 10 GPa. A dynamic range of four orders of magnitudecan be especially helpful when analyzing heterogeneous materials with largely different components. Furthermore, in principle, this range can be shifted toward larger or lower values of elastic modulus by using cantilevers with different spring constants. The histograms in Fig. 6.6a also allow judging the accuracy of the measurements. In Fig. 6.6b, the mean values of elastic modulus measurements are plotted against the expected elastic modulus of each sample. The widths of the histograms in Fig. 6.6a are also shown as error bars. A perfect agreement would bring all the data points onto the dashed diagonal line. However, due to deviations between the bulk and surface values of elastic modulus and unknown thermal history, cross-linking density, frequency dependence of mechanical properties, and anisotropic mechanical response of the samples, a perfect agreement is not expected. While there is a fair degree of agreement between the measured values and the expected ones, the deviations could also be attributed to the inaccurate modeling of the contact mechanics. In this analysis, (6.1) is used to estimate the elastic modulus values, however on more compliant samples, around 1–10 MPa, adhesive forces have a larger contribution to the contact geometry and the contact mechanics model becomes more complicated. In addition, viscosity of the samples can also play a larger role in contact mechanics.

High Resolution Maps of Stiffness, Adhesion, and Dissipation Can Be Obtained in a Single Tapping-Mode Scan The analysis of the range of elastic modulus values that can be measured by the torsional harmonics showed that an elastic modulus value can be obtain in 1ms with good sensitivity and dynamic range. This speed is sufficient to generate images of elastic modulus of the samples by scanning the tapping cantilever across the sample surface. In addition to the stiffness of the sample, tip–sample force waveforms also allow to characterize adhesive properties of the sample. The peak attractive force observed during the retraction of the tip provides a measure of adhesion. This value can also be mapped simultaneously with the elastic modulus measurements. Furthermore, the tapping-mode operation readily provides conventional topography and phase image, the latter of the two is a map of energy dissipation [11]. So, in a single scan one can obtain four different and complementary images of the surface. In this section, we will present images on two samples: thermoplastic vulcanizate (TPV) and a triblock copolymer (polymethylmethacrylate-polyisobutylenepolymethylmethacrylate, PMMA-PIB-PMMA). These samples contain stiff and compliant regions, however their morphological organization is different. TPV is composed of micron-sized rubbery domains of ethylene-propylene-diene monomer elastomer (EPDM) and a stiff polypropylene matrix (PP). The triblock copolymer exhibits lamellar phase-separated morphology. Figure 6.7a shows the reduced elastic modulus map of TPV across a 20-µm-sized region. The image shows the rubbery domains of EPDM and the stiffer PP matrix.

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Fig. 6.7 High resolution nanomechanical mapping. Images of thermoplastic vulcanizate (left column) and PMMA-PIB-PMMA block-copolymer film (right column) are obtained in the tapping mode by using torsional harmonic cantilevers. Calculated local elastic modulus are given in (a) and (b).


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The image is colored according to the logarithm of the elastic modulus values and brighter colors correspond to larger values. The numerical values of elastic modulus across a section indicated by the dashed line are plotted right below the elastic modulus map. We see that the EPDM regions are measured to be 5–10 MPa and the PP regions are about 2 GPa. These values are close to the bulk values reported in Fig. 6.6. Note that there is more than two orders of magnitude difference between the two components. The large dynamic range in measurements allowed us to characterize the two components with the same cantilever under imaging conditions. Figure 6.7b shows the map of reduced elastic modulus recorded on a 1-µm-wide region across the triblock-copolymer sample. The two chemical blocks are differentiated by their elastic modulus. The numeric values of elastic modulus across the dashed line given below the image shows that the stiffer region is approximately 1.5 GPa and the compliant region is about 0.5 GPa. While the stiffer component has a value that is close to the bulk value recorded on PP, the value of the compliant region is much higher than that of rubbery materials. The frequency-dependent mechanical response of rubbery materials can account for an increase in the values measured by this technique; however geometrical confinement can be another mechanism that is particularly important in the design of materials with nanoscale feature sizes. Geometrical confinement can enhance molecular or supramolecular ordering. It can also increase the roles of surface tension and surface stress. Therefore, the effects of confinement on the mechanical properties of materials can be dramatic. A high resolution mechanical analysis technique is therefore invaluable for the analysis of confinement effects. Simultaneously with the elastic modulus measurements on each of the two samples, the peak attractive forces are recorded as a measure of adhesion. The resulting images are presented in Fig. 6.7c, d. The respective cross section of the numerical values of peak attractive forces across the same dashed lines shown in Fig. 6.7a, b are given below each image. The images are colored such that attractive forces with larger magnitudes are represented with brighter colors. The image in Fig. 6.7c shows that the stiff PP regions are more adhesive compared to the rubbery EPDM regions. On the contrary, the image in Fig. 6.7d shows that the stiffer PMMA blocks show lower adhesive forces. The noise in force measurements is approximately 0.25 nN rms. However, the cross section data on the TPV sample shows much larger fluctuation on the PP regions. A closer look at the image data reveals that the fluctuations are not due to noise, but there is substantial local variation in adhesive forces. A possible reason for this variation might be the surface roughness. The preparation of the TPV sample for imaging involves cutting process that can introduce surface roughness. Figure 6.7e, f show the phase image recorded on each of the two polymer samples. Phase contrast reflects the energy dissipated at the tip–sample interaction. A lower value of phase corresponds to a larger amount of energy dissipated. There are

Fig. 6.7 (continued) Peak adhesion forces at each location are mapped in (c) and (d). Conventional phase images are given in (e) and (f). Numeric values of each data type across the sections indicated by the dashed lines in (a) and (b) are given below their respective images. Scale bars are (a) 2 mm, (b) 100 nm. Images in (a) and (b) are colored according to logarithms of elastic moduli (cf. [10])

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several physical mechanisms that contribute to the tip–sample energy dissipation. Hysteresis in adhesive forces, capillary forces [12], and viscosity of the sample are among the major contributors. The amount of energy dissipation is also influenced indirectly by the elastic modulus of the sample. For example, during the retraction of the tip, the attractive forces can pull the surface and locally raise it above its equilibrium level. Once the contact is broken the energy stored in the sample is dissipated. In this mechanism, samples with lower elastic modulus and larger adhesion force will dissipate more energy. According to the elastic modulus maps given in Fig. 6.7a, b, there is a larger stiffness contrast on the TPV sample, which would favor increased energy dissipation contrast on this sample. However, the adhesion force maps in Fig. 6.7c, d show an inverted contrast, i.e., on the TPV sample the stiffer component is more adhesive and on the triblock-copolymer sample the compliant component is more adhesive. Therefore, the inversion in adhesive force contrast would increase the dissipation contrast on the triblock-copolymer sample and decrease the contrast on the TPV sample. Hence, the larger elastic modulus contrast on the TPV sample is balanced by the inverted adhesion force contrast so that the contrast in energy dissipation maps on each sample may end up being similar. The numerical values of phase recorded across the same section indicated by the dashed lines in Fig. 6.7a, b supports this hypothesis. The data show that there is approximately 40° of phase difference on the two material components of both samples. The images obtained on the two polymer samples illustrate the ability of torsional harmonic measurements to generate high resolution maps of elastic modulus and adhesion at the typical imaging speed of the tapping mode. The spatial resolutions of these maps are also comparable to that of the typical resolution obtained in the tapping mode, i.e., ~10 nm. In addition, the images exhibit a large dynamic range in elastic modulus measurements, both small and large variations can be mapped.

Sub-molecular Resolution Mechanical Measurements with Ultra Sharp Tips and Lower Forces The level of spatial resolution observed in Fig. 6.7a–d is sufficient to analyze a wide range of samples. However by carefully adjusting imaging forces and using ultra sharp tips, one can improve the spatial resolution further. Figure 6.8a shows transmission electron microscope image of carbon spikes grown on top of the silicon tip of a torsional harmonic cantilever [13]. These carbon spike tips provide tip apex radii of ~1nm. While this improvement is helping to achieve better spatial resolution, the reduction in contact area leads to substantial increases in contact pressure. If one employs the imaging forces used for mechanical analysis in Fig. 6.7, the resulting

Fig. 6.8 (continued) An example of tip–sample force waveforms recorded with this tip during the experiments is given to the right. Scale bar in (a) is 100 nm. Topography (b), elastic modulus (c), and phase images (d) are given with section plots on the right of respective images. Scale bar in (b) 10 nm. All images are recorded simultaneously (cf. [10])


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Fig. 6.8 Sub-molecular resolution mechanical mapping. Images across the molecular self-assembly of C36H74 alkane layers on graphite are obtained using a torsional harmonic cantilever with an ultra sharp carbon spike grown on its tip. (a) TEM picture of the carbon spikes grown on the THC.

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pressure will damage the carbon spike. Therefore, the forces have to be kept as small as possible. Figure 6.8b shows a tip–sample force waveform with a peak tapping force less than 1nN obtained with the carbon spike tip. Under these conditions, images of the surface formed by self-assembling ultra-thin layers of C36H74 alkane chains on highly oriented pyrolytic graphite were obtained. These molecules assemble into lamellar ribbons with a periodicity of 4.7 nm, close to the fully extended conformation of the alkane chain. The topography image in Fig. 6.8c reproduces the ribbon pattern. Scanning tunneling microscope studies on this molecular system showed that the carbon backbone of the alkanes are aligned parallel to the substrate and perpendicular to the ribbon edges [14]. The height profile across the dashed line shows that there is approximately 3 Å of height variation across the ribbons. The simultaneously recorded elastic modulus map of the ribbons shows that topographically lower regions also exhibit lower elastic modulus. The regions with lower stiffness are likely to be near the –CH3 end groups because they are covalently connected to the carbon backbone only on one side and therefore they are more flexible. The numerical values of elastic modulus show that the reduced elastic modulus values vary between 200 and 450 MPa. These values are calculated based on (6.1) and further assuming a tip radius of 1nm. However, that formula is derived for the contact of macroscopic objects. Therefore, the numerical values provide a measure of stiffness, but they do not correspond to true elastic modulus values. The phase image recorded on the self-assembled alkanes is given in Fig. 6.8e together with its cross section data. The ribbon structure is also visible in the phase image; however, the contrast is about 0.5°. This is much smaller than typical phase contrasts observed in tapping mode. Smaller peak forces and contact also reduce the energy that can be dissipated in the contact region. The analysis on the self-assembled alkane chains with the ultra sharp carbon spike tips demonstrates the possibility to obtain sub-molecular resolution in mechanical measurements. These kinds of measurements can be helpful in the analysis of intermolecular interactions and changes in material properties across abrupt interfaces.

High Resolution Thermo-Mechanical Characterization of Polymer Blends In this section, we will conclude our discussions on the dynamic nanomechanical analysis with torsional harmonic cantilevers with an investigation on the thermal behavior of polymer blends with sub-micron segregation features. If the components of blended polymer have different glass transition temperatures, it becomes difficult to understand the thermal behavior of the blend via bulk mechanical measurements. Here, we present high resolution mechanical analysis of a binary polymer film near the glass transition temperatures of its components; polystyrene (PS) and polymethylmethacrylate (PMMA). The thickness of the film is approximately 50 nm and the two polymer components form sub-micron domains in the film.


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Below the glass transition temperatures, these polymers are in a stiff glassy state and above the glass transition temperature they are in a rubbery phase. PS has a glass transition temperature of around 100°C and PMMA has a glass transition temperature around 130°C. As a result, there is a temperature range where one component is in the rubbery phase and the other one is in a glassy phase. Mechanical measurements can differentiate the two components in that temperature range. To study the mechanical response of the binary polymer film, topography and higher harmonic images (magnitude of the tenth harmonic of torsional vibrations) were recorded at temperatures between 85 and 215°C. These measurements had been performed before the real-time calculations of tip–sample force waveforms were possible. A lock-in amplifier was used to determine the amplitude of the tenth harmonic as a qualitative measure of stiffness. Torsional vibration signals were also recorded during the image process and calculations of the tip–sample force waveforms on each component were carried out offline. Those results will be presented later. First, we will discuss the topography and harmonic images presented in Fig. 6.9. Images recorded at different temperatures in Fig. 6.9 belong to approximately the same region on the sample surface. The topography images show that there are height variations between the two components. Especially at low temperatures, the boundaries are clear. PMMA forms the round features within the PS matrix. At elevated temperatures, the rubbery material forms round, droplet-like, features on the surface. Note that the height ranges of the images are larger at higher temperatures. When the polymers go through glass transition, they acquire a liquid-like mobility so that they can flow and rearrange themselves. As a result topographical variations are also getting smoother at higher temperatures. The qualitative stiffness maps in Fig. 6.9 show that the domains of PS and PMMA have different stiffness even at 85°C. However, the contrast between the two regions increases at 160 and 175°C, mainly because of a reduction in the harmonic amplitude on the PS regions. The contrast between the two regions reduces around 190°C and almost completely disappears at 215°C. Beyond 190°C, the amplitudes of the tenth harmonic are small, because both materials are in rubbery phase. The increased contrast around 160 and 175°C suggests that this is the temperature range where one material is in the glassy phase and the other is in the rubbery phase. The changes in the mechanical behavior of the two polymer components can be better understood by analyzing the tip–sample force waveforms recorded during the imaging process. Figure 6.10a, b shows the unloading portions of the tip–sample force–distance relationships on the two regions at each temperature including the room temperature. It is seen that the slopes of the curves gradually reduce with temperature. According to (6.1), this indicates a lowering of stiffness. After fitting (6.1) to the recorded curves, the reduced elastic modulus values are obtained. Figure 6.10c plots the resulting values against temperature. The values of PS and PMMA at room temperature, 2.3 and 3.7 GPa, are in the range of typical bulk values for these materials. The stiffness of both components reduce by two orders of magnitude at high temperatures, however, the transitions are located at different temperatures for the two materials. The stiffness of PS reduces around 160°C and the

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Fig. 6.9 Observing the glass transition of a polymer blend through nanomechanical measurements. A thin polymer film composed of PS and PMMA is investigated. Topography and tenth-harmonic images are recorded at different temperatures. The circular features are PMMA, and the matrix is PS.


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Fig. 6.10 Indentation forces measured as a function of temperature in a polymer blend. Time-varying force measurements are plotted against the depth of indentation in the sample for polystyrene (a) and PMMA (b). Corresponding effective reduced elastic modulus values are plotted in (c) (cf. [9])

Fig. 6.9 (continued) The scan area is 2.5 × 5 µm. The color bar represents different height ranges at each temperature where the range is given in the top left corner of each panel. The color bar represents a 10-V lock-in output signal at all temperatures for the harmonic images. Note that height contrast increases with temperature, however the contrast in the harmonic image is first increasing and then decreasing (cf. [9])

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stiffness of PMMA reduces around 180°C. This range approximately corresponds to the temperature range where the harmonic images in Fig. 6.9 exhibit the largest contrast. Note that the apparent transition temperatures are approximately 60°C higher than the typical transition temperatures for PS and PMMA. The glass transition temperatures are expected to rise by 5–10°C for an order of magnitude increase in the measurement frequency [15]. The tapping cantilever interacts with the sample at the drive frequency, which is around 50 kHz. This is several orders of magnitude faster than the frequencies of conventional dynamic nanomechanical measurements. Therefore, the observed increase in the glass transition temperatures in high-speed nanomechanical measurements is an expected consequence of the frequency dependence of glass transition.

References 1. R. Garcia and R. Perez, “Dynamic atomic force microscopy methods,” Surf. Sci. Rep. 47 197–301 (2002). 2. J. Israelachvili, Intermolecular and Surface Forces. (Academic Press, London, 2003). 3. O. Sahin, “Accessing time-varying forces on the vibrating tip of the dynamic atomic force microscope to map material composition,” Israel J. Chem. 48 55–63 (2008). 4. R. W. Stark and W. M. Heckl, “Fourier transformed atomic force microscopy: tapping mode atomic force microscopy beyond the Hookian approximation,” Surf. Sci. 457 219–228 (2000). 5. M. Stark, R. W. Stark, W. M. Heckl et al., “Inverting dynamic force microscopy: From signals to time-resolved interaction forces,” Proc. Natl. Acad. Sci. U.S.A. 99 8473–8478 (2002). 6. U. Rabe, K. Janser, and W. Arnold, “Vibrations of free and surface-coupled atomic force microscope cantilevers: Theory and experiment,” Rev. Sci. Instrum. 67 3281–3293 (1996). 7. J. Tamayo and R. Garcia, “Deformation, contact time, and phase contrast in tapping mode scanning force microscopy,” Langmuir 12 4430–4435 (1996). 8. R. W. Stark, “Optical lever detection in higher eigenmode dynamic atomic force microscopy,” Rev. Sci. Instrum. 75 5053–5055 (2004). 9. O. Sahin, S. Magonov, C. Su et al., “An atomic force microscope tip designed to measure time-varying nanomechanical forces,” Nat. Nanotechnol. 2 507–514 (2007). 10. O. Sahin and N. Erina, “High-resolution and large dynamic range nanomechanical mapping in tapping-mode atomic force microscopy,” Nanotechnology 19 445717 9 (2008). 11. J. P. Cleveland, B. Anczykowski, A. E. Schmid et al., “Energy dissipation in tapping-mode atomic force microscopy,” Appl. Phys. Lett. 72 2613–2615 (1998). 12. L. Zitzler, S. Herminghaus, and F. Mugele, “Capillary forces in tapping mode atomic force microscopy,” Phys. Rev. B 66 155436 8 (2002). 13. D. Klinov and S. Magonov, “True molecular resolution in tapping-mode atomic force microscopy with high-resolution probes,” Appl. Phys. Lett. 84 2697–2699 (2004). 14. S. De Feyter and F. C. De Schryver, “Two-dimensional supramolecular self-assembly probed by scanning tunneling microscopy,” Chem. Soc. Rev. 32 139–150 (2003). 15. I. M. Ward, An Introduction to the Mechanical Properties of Solid Polymers. (Wiley, Chichester, UK, 2004).

Part III

Thermal Characterization by SPM

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Chapter 7

Toward Nanoscale Chemical Imaging: The Intersection of Scanning Probe Microscopy and Mass Spectrometry Olga S. Ovchinnikova

Introduction There exists a clear need to extend the limits of our understanding of chemical and physical phenomena of materials and biosystems to the nanoscale. Chemical analysis on the nanometer scale has become necessary in the fields of biology, medicine, and material science. Understanding the processes such as signal transduction in a single cell [1, 2], elemental distribution in single cells and organelles [3], characterization of nanoelectronics to trace impurities [4], and the study of pharmaceuticals [5] requires nanometer-resolved chemical analysis. The chemical analysis of compounds in complex mixtures or specimens such as biological tissue requires highly specific and sensitive analytical methods that require little or no sample preparation and can be studied in vivo. Analyzing with an ability to chemically image fragile biological systems at atmospheric pressure (AP) is a growing field of interest because preparation of biological samples for analysis in vacuum is often difficult, time-consuming, and even at times not possible. An analytical tool with high sensitivity that can provide detailed molecular information with high spatial resolution has been the goal behind the development of different chemical imaging techniques. In mass spectrometry, the desorption and ablation of material from surfaces in vacuum is a well-established field. Techniques like secondary ion mass spectrometry (SIMS) [6] and matrix-assisted laser desorption ionization (MALDI) [7, 8] have become common tools for surface sampling and imaging. Each approach has advantages and disadvantages depending on the particular application. In SIMS, surface species are desorbed by keV particle bombardment [9] while the ionization of the particles occurs during their desorption by intrinsic processes. SIMS can yield images with lateral resolution on the order of 100nm [10]. Laser-based desorption systems like MALDI are capable of routinely achieving 20mm spatial resolution and have the advantage of not fragmenting the molecules of O.S. Ovchinnikova (*) Department of Physics and Astronomy, University of Tennessee, Knoxville 401 Nielsen Physics Building, 1408 Circle Drive, Knoxville, TN 37996-1200 e-mail: [email protected] S.V. Kalinin and A. Gruverman (eds.), Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy, DOI 10.1007/978-1-4419-7167-8_7, © Springer Science+Business Media, LLC 2010

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interest [3]. However, both of these imaging techniques have the drawback that the imaging has to be carried out in vacuum, which limits the type of sample that can be studied because of the constraints of placing the sample into a vacuum system. Atmospheric pressure mass spectrometry (MS) is especially suited for this with its high degree of chemical specificity and its minimal or no sample preparation. The ability to carry out AP-MS experiments largely depends on the desorption and ionization mechanisms. Techniques such as atmospheric pressure chemical ionization (APCI) [11], electrospray ionization (ESI) [12] and inductively coupled plasma ionization (ICP) [13] that have the ability to ionize samples at atmospheric or reduced pressures in combination with highly localized sample desorption techniques such as near-field laser desorption [14] and micro-thermal desorption [15] are opening the door for mass spectrometry to carry out nanometer scale chemical imaging at AP. Combining AFM and mass spectrometry has been approached from two directions: using laser desorption/ablation as the means to sample the surface [16] and using AFM heated probes to thermally desorb the sample [15]. The initial laser desorption/ablation work developed by Zenobi et al. in 2001 used a 355-nm Nd:YAG laser with up to 250mJ of energy per pulse coupled into the back of an NSOM fiber with a 170-nm diameter aperture to create laser ablation craters 200 by 20-nm [16] in size on an anthracene crystal surface. This volume of material ablated corresponds to a quantity of 1.7amol of material desorbed from each individual crater. Using a heated stainless steel capillary, the ablated material was then directed at an electron impact ionizer (EI) source of a quadruple mass spectrometer. A quadruple mass spectrometer was used in the experiment because it allows for material from several laser shots to be accumulated in the trap to allow for better signal to noise. It should also be noted that EI requires a vacuum environment to operate and is only capable of producing singly charged negative ions, thereby drastically limiting the samples that can be studied. After ablation of the surface, the NSOM tip was used in a force feedback arrangement to scan the surface to acquire a topographic image. More recently in 2008 Zenobi et al. modified their experiment to operate using a combined quadruple/time-of-flight (TOF) mass spectrometer to increase the detection sensitivity [17] as well increased the NSOM tip size to be in the range of 500–800nm in order to produce a larger ablation area. Using the ability of a quadruple to accumulate ions with the sensitivity afforded by a time-of-flight mass spectrometer Zenobi et al. were able to acquire mass spectra from ~1.7mm wide × 0.8mm deep craters in anthracene and 2,5-dihydrobenoic acid (DHB) [17]. This set-up allowed them to acquire multiple laser shots in the quadruple trap prior to analysis with the time-offlight. This experiment demonstrated the feasibility of extracting chemically specific information as well as topographic information in tandem using an AFM/MS set-up. Work has also been done by Goeringer et al. toward AP apertureless near-field laser ablation mass spectrometry [18]. Here a frequency doubled 532nm Nd:YAG laser was focused at the tip of a gold-coated AFM probe that was positioned ~10nm from the surface to create ~50nm craters in a rhodamine 6G thin film. More recently Goeringer et al. used a quadruple trap mass spectrometer and a focused laser beam to create 1-mm spatially resolved chemical images with corresponding AFM topographic images (Fig. 7.1) [19]. These works demonstrated a clear application of combined AFM/MS technique for chemical imaging.

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Fig. 7.1 Combined AFM and MS chemical imaging of an “X” etched out from a rhodamine 6G thin film surface (used with permission from [19])

Another laser desorption technique that shows promise for its application to the set of techniques already incorporating AFM and MS is laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). Becker et al. have shown the possibility of using LA-ICP-MS to perform elemental analysis of Cu, Zn, Au, Si, and U from ~200nm craters using near-field enhancement from a frequency doubled 532-nm Nd:YAG laser focused on the end of a sharp silver needle that is positioned 200nm above the surface [20, 21]. Their experiment demonstrated the possibility of nano-local analysis by near-field (NF) laser ablation ICP-MS, and opens the door for coupling NF-ICP-MS with current AFM techniques for an apertureless NF-ICP-MS experiment using AFM probes as the source for the near-field enhancement. The details and applicability of the ICP-MS technique are described in more detail later on in this chapter. The other successful avenue for coupling AFM imaging with MS identification was developed using thermal desorption via micro-thermal (micro-TA) AFM probes coupled to an electron impact (EI) gas chromatogram mass spectrometer (GC-MS) [22]. In this work Wollaston wire micro-TA AFM probes were used to desorb craters with ~6mm diameter in feverfew leaves. The evolved gas was extracted via a heated capillary packed with a suitable sorbent such as Tenax and sent to an EI GC-MS where the camphor molecule extracted from the leaf by means of thermal desorption was monitored on the GC-MS. The same micro-TA/GC-MS analysis technique has also been applied to the study of pharmaceuticals [23] where the precise distribution of chemicals can be correlated to an AFM topographic image. Recently, the use of thermal desorption combined with AFM as a means of studying samples at the nanoscale has become possible with the invention of silicon-based heated AFM probes that have a 50-nm radius of curvature and are able to rapidly heat and cool up to 400°C. Using these new nano-TA AFM probes for thermal desorption combined with mass spectrometry opens up a new avenue for analyzing samples. This technique alleviates tedious experimental set-up that is associated with near-field laser desorption/AFM experiments. Using thermal desorption also minimizes the tip-to-tip fluctuation in enhancement that is found when using near-field tip enhancement technique.

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The goal of true nanoscale chemical imaging is now becoming a reality due to recent advances in both mass-spectrometry and scanning probe microscopy. The availability of commercial mass spectrometers that are able to efficiently detect an attomole of material transferred from AP as well as the development of online AP secondary ionization techniques have increased sensitivity to the point needed for nanoscale sampling. Closed loop stages that reduce drift making long dwell times needed for spectroscopy possible and the development of new AFM probe technology that makes thermal desorption possible on the nanoscale have brought about the successfully marrying of AFM and MS for nanoscale chemical imaging. In this chapter the AP MS methods that are most appropriate for coupling with scanning probe systems are described in detail.

Atmospheric Pressure Mass Spectrometry Techniques Thermal Desorption with Secondary Ionization Mass Spectrometry Ambient surface sampling techniques remove the constraints that are associated with vacuum-based sampling/imaging techniques. Using ambient techniques allows for the study of living samples, wet samples, large samples, and allows for fast and easy interchange of samples and often removes the need for extensive sample preparation. Literature reports suggest that scanning probe techniques using atmospheric pressure thermal desorption (AP-TD) might be an alternative means to achieve nanometer-scale surface sampling resolution for mass spectrometry. Atmospheric pressure thermal desorption (AP-TD) is a well-established surface sampling technique in mass spectrometry. In this approach to surface sampling, heat is used to liberate the sample intact from the condensed phase to the vapor phase. Typically, this heating is accomplished through the use of a heated gas passingover the sample and/or a resistively heated sample surface. Given the nature of the desorption process, this approach is limited to relatively low mass species (ca. 2,000Da or less) that can be liberated intact into the gas phase by heat; thermally labile, highly polar, and high molecular-mass species are typically not amenable to vaporization by heating. Once in the gas phase, the sample can be ionized by any number of ion/molecule chemistries. An example of an emerging AP-TD/MS technique is atmospheric pressure chemical ionization (DAPCI) [24]. As defined and used by Cooks’ group [25], DAPCI consists of a capillary with a taper-tip stainless-steel electrode aimed at the surface. An inert sheath gas, into which a solvent vapor is in some cases introduced, is supplied to the capillary and flows through the emitter at high velocity. A highvoltage power supply is used to apply a voltage (typically ±3–6kV) to the electrode; this induces a corona discharge at the tip of the electrode, ionizing the introduced solvent vapor. The sheath gas in some cases may be heated. Ionization mechanisms


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in DAPCI are similar to other APCI ionization sources. As in all APCI systems, the reagent ion species formed can be influenced by means of initiating the reagent ion plasma, and by the particular solvent vapor and sheath gas used [26]. The desorption mechanisms in DAPCI are in some cases unclear. When the sheath gas is heated, TD is certainly a dominant process. In other cases, the high velocity gas might actually liberate minute particles from the surface that can then be ionized in the gas phase. Desorption atmospheric pressure photoionization (DAPPI) [27] is similar to DAPCI except that the reagent ion population is initiated by a photoionization process utilizing a UV lamp rather than a corona discharge. Currently, there are several commercially available AP-TD with secondary ionization sources for mass spectrometry (AP-TD/SI-MS) [28]. Direct analysis in real time (DART) [29] is one of the best known. In DART, He gas flowing through a probe is subjected to a discharge at a needle electrode, producing ions, electrons, and metastable species. Perforated electrodes downstream act to remove ions from the gas stream, while neutral metastable species are carried by the gas through a heated chamber, passing though a grid electrode before entering the ambient atmosphere. The grid electrode prevents ion–ion and ion–electron recombination, and also acts as a source of electrons, either through Penning ionization of a neutral species or through surface Penning ionization [30]. The exiting gas flow is directed at the entrance of the mass spectrometer and the sample surface to be analyzed is placed between the two. The ionization process in DART is a variation of APCI in which the reagent ion population originates from the gas phase reactions of the metastable He atoms (He* (1s2s3S1) produced in the discharge. Another commercially available device is atmospheric-pressure solids analysis probe (ASAP) [31, 32]. Here analyte deposited on the glass meltingpoint capillary is thermally desorbed by a hot gas, ionized by APCI, and analyzed by mass spectrometry (Fig. 7.2). This technique has similar merit to DART, allowing for fast analysis of individual samples. None of the above-mentioned AP-TD/SI-MS techniques have shown to be useful for chemical imaging of surfaces. Moreover, they are fundamentally limited in their ability to carry out chemical imaging because they sample from a relatively large area (many mm to cm scale). In order to overcome the limitation of available thermal desorption techniques for chemical imaging Reading et al. used a Wollaston wire AFM tip to carry out local thermal desorption in order to analyze the desorbed material using gaschromatography mass spectrometry (GC/MS) [23]. With their set-up they were able to desorb material from a PMMA surface by heating to 600°C the Wollaston probe in contact with the surface. The heated probe created craters that were on the order of 7mm wide by 2mm deep. Using a syringe co-located with the Wollaston probe they were able to suction out the desorbed vapor and analyze it with GC/MS. The sample was imaged afterward in an AFM to confirm the presence of ablation craters. Reading et al. [15] applied this technique for examination of polymers as well as small molecules found in pharmaceuticals [5]. Reading’s work demonstrates the potential for a nanometer spatially resolved TD-based mass spectrometry chemical imaging technique.

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Fig. 7.2 Cross-sectional drawing of an atmospheric pressure LC/MS ion source modified for ASAP analysis (used with permission from [23])

Laser Desorption (Ablation) Ionization Mass Spectrometry Laser desorption/ablation experiments that couple laser ionization with a mass spectrometer were introduced in the 1960s. In some of the first laser ionization experiments, Vastola et al. [33] used a 694.3nm ruby laser to ionize organic salts in vacuum. These early laser desorption experiments provided a new technique for desorbing material that decomposed from direct heating, like organic salts. Although, direct laser desorption ionization has been used to examine larger molecules like peptides, it is much better suited for small molecule analysis like organic dyes, porphyrins, organic salts, and UV-light absorbing synthetic polymers [34]. However, laser desorption produces a greater number neutrals over ions, and therefore can be successfully coupled with many different secondary ionization sources. For laser desorption and ionization at AP these techniques include: inductively coupled plasma (ICP), and various forms of APCI, ESI, as well as AP-MALDI.


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Introduced by Alan Gray [13] in 1985, Laser Ablation Inductively Coupled Plasma (LA-ICP) is one of the most established AP laser ablation techniques. In the LA-ICP-MS technique material is ablated from the surface by a laser; and then atomized and ionized in the high-temperature plasma (Fig. 7.3). In LA-ICP-MS experiments, the sample is placed in a closed ablation chamber which is flushed with argon or helium as a carrier gas and the laser beam is focused on the sample surface through a cell window [35]. When the laser irradiance is high enough the material is ablated and carried in the carrier gas to the plasma of the ICP-MS. The ICP is a separate excitation source where laser-generated particles are vaporized, atomized, and ionized. The ions are then extracted by a vacuum interface and guided into a mass analyzer. The advantages of LD-ICP-MS analysis are high sensitivity, large dynamic range, and simple spectra. The LA-ICP-MS technique’s biggest merit is its sensitivity, achieving a sub-ng/g detection limit for spot sizes that are above 100mm [20]. Combining high spatial resolution that is achieved with laser ablation with the high sensitivity in the ICP allow for trace-element determination at a micron scale. This makes the LA-ICP-MS a tool that is widely used in geology for the detection of trace elements in minerals, as a screening tool in geochemical studies of (U/Th/Pb), and for the elemental analysis of fluid inclusions for studies of ore-formation processes [36]. Forensics is another area where the LA-ICP-MS is heavily used; within this field fingerprinting of gemstones seems to be the fastest growing areas of LA-ICP-MS [20]. The LA-ICP technique has also recently been used by Becker et al. to image elements in thin cross section of human brain samples [37–39]. The tissue samples were ~20 mm thick, and an ablation of the sample was preformed with a 266-nm frequency quadrupled Nd:YAG laser. The ablated material was carried by argon gas into the inductively coupled plasma. Laboratory standards were created by spiking the brain tissue with known solutions of the selected elements such as Cu. The signal was then maximized to the maximum ion intensity of 63Cu+ using the laboratory standards.

Fig. 7.3 Schematic of LA-ICP-MS set-up (used with permission from [20])

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Using this LA-ICP-MS technique Becker et al. [22] were able to do a 50 line scan of a section of tissue in 6h. Chemical imaging of a human brain sample done using LA-ICP-MS by Becker et al. [22] can be seen in Fig. 7.4. Quantitative analysis on the amount of element in interest was performed only on the elements for which suitable standard solution could be created. This therefore creates a limitation on the ions that can be quantified in a mapping scan. The LA-ICP-MS is a therefore rather slow compared to other biological surface mapping techniques such as MALDI and DESI. As a tool for analytical application to biology, the LA-ICP-MS has been used for a variety of applications such as tissue imaging as discussed earlier as well as for proteomics with protein quantification by the detection of trace elements in proteins by means of polyacrylamide gels [40, 41]. Laser Desorption Atmospheric Pressure Chemical Ionization (LD-APCI) is another technique that uses laser desorption to produce a plume of neutrals that then undergo secondary ionization. AP chemical ionization uses an IR-laser to desorb neutral molecules from a surface and then uses a corona discharge to carry out the secondary ionization. The corona discharge is used as an electron emitter to ionize neutral molecules in the gas phase. The neutral molecules are created by laser desorption from a target that is near to the discharge. The ionized molecules are

Fig. 7.4 Cu images in part of (top, right) and the whole (bottom, right) human hemisphere measured by LA-ICP-MS compared with the light photograph of the thin tissue section (used with permission from [22])


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then sucked into a heated capillary into mass spectrometer. The LD-APCI apparatus schematic can be seen in Fig. 7.5. Currently Harrison et al. [42, 43] are developing LD-APCI as tool for detection small organic molecules. Harrison et al. use a focused IR 10.6-mm pulsed CO2 laser to desorb neutral molecules at AP followed by ionization in the gas phase with a corona discharge [44]. By separating out the laser desorption signal from the ionization by corona discharge Harrison et al. were able to increase their ion signal 150-fold [29]. To demonstrate an increase in the signal by carrying out secondary ionization of the laser desorbed molecules, Harrison et al. toggled the corona discharge on and off while the laser desorption was continuously running [29]. Using this method they were able to show that the 150-fold reduction of sepirerone still yielded a signal using the LD-APCI method and no signal where only direct laser desorption was used. Also, despite the 150-fold decrease in the amount of seiperone present in the sample, the ion signal only dropped by a one quarter of the original signal in the LD-APCI. In later work Harrison et al. [28] were able to use the LD-APCI to detect desorbed gas-phase neutral peptide molecules at AP. Using the LD-APCI technique provides benefits over using direct AP-MALDI for detecting peptides because in LD-APCI the matrix containing analyte does not need to assist in the ionization, this allows for the opportunity for examining analyte matrixes that include biological solutions, tissue, polyacrylamide gels [27, 45], and thin layer chromatography plates. Work has also been done with UV laser sources for the LD-APCI [46], in these experiments a 337-nm nitrogen laser was used to desorb the molecules from a sample. Using a nitrogen laser for desorption rather that an IR laser produced a larger number of neutral molecules, and therefore gave a better signal in the mass spectrometer.

Fig. 7.5 Schematic representation of LD-APCI source (used with permission from [28])

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Laser Desorption Electrospray Ionization (LD-ESI) was introduced by Shiea et al. [47] under the acronym ELDI, electrospray-assisted laser desorption/ionization. The LD-ESI technique works on the principle that a solid substrate is first desorbed by a pulsed nitrogen laser at AP, followed by secondary ionization of the desorbed material with an electrospray ionization source (ESI) [48] (Fig. 7.6). Combining laser desorption with the ESI technique allowed Shiea et al. to demonstrate the possibility of detecting intact protein spectra without the use of a matrix compound. The ELDI technique is able to overcome the low mass limit imposed by direct laser desorption by using an ESI source to post-ionize neutral molecules generated by laser desorption [32]. The ELDI set-up consists of a 337-nm nitrogen laser operating at 20 mJ per pulse and a focused laser spot size of 100 mm×150 mm. The incident angle of the laser beam in Shiea’s work is fixed at 45°[32]. The sample is placed on a translation stage so as to produce a continuous ion signal. The laser ablated material is then ionized by electrospraying. Using this technique Shiea et al. were able to perform direct characterization of chemical compounds like amines on thin layer chromatographic plates and detect intact proteins in dried biological fluids such as blood, tears, saliva, and serum. They were also able to estimate their detection limit using cytochrome c to be from 10-4 to 10-9M. With their laser desorption area ranging between 100. and 200 mm they were able to detect 50amol of protein molecules per each ELDI spectrum. Very similar to the ELDI technique that uses a UV laser source, Vertes et al. [49, 50] have developed the LAESI technique, laser ablation with electrospray ionization, which uses an infrared laser source instead of a UV source. Using a mid-infrared laser source instead of a UV laser source, Vertes et al. [35] were able to look at biological samples that have resonant frequencies in the infrared versus the near-UV. Vertes et al. used an infrared laser source because of the water that is

Fig. 7.6 Detailed schematic of ELDI set-up, (A) sampling skimmer, (B) laser beam, (C) electrospray capillary, (D) sample plate, (E) focusing lens, (F) reflecting lens, (G) syringe pump (used with permission from [33])


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intrinsic to biological samples has a resonance frequency in the infrared. Vertes’ approach allows for direct analysis of biological samples without any prior sample preparation such as drying. The LAESI technique depends on samples high water content and therefore it works very well in water-rich tissue, but is limited in analysis of tissues like bone, nail, or dry skin which has a low water concentration. Atmospheric Pressure Matrix Assisted Laser Desorption Ionization (AP-MALDI) was introduced by Dorshenko et al. in 2002 as an alternative to vacuum MALDI for carrying out MALDI experiments in situ [36]. AP-MALDI operates on the same principle as vacuum MALDI, where a low melting point substrate, the matrix, which is doped with the analyte is desorbed by laser irradiation. In most cases this is accomplished with a UV-laser source; however, IR lasers have also been used due to the strong absorption of water molecules in the IR region. In the AP-MALDI system, ions are transferred from the AP into vacuum via a heated capillary into a differential pressure region (Fig. 7.7). While ion loss is inevitable during the transfer, the total ion yield in the AP-MALDI is usually higher than in vacuum MALDI due to fast thermal stabilization at atmospheric conditions. The AP-MALDI introduces the possibility of direct coupling separation techniques like liquid chromatography (HPLC) with MS,

Fig. 7.7 Schematic of AP-MALDI set-up (used with permission from [36])

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which is not possible with vacuum MALDI where the samples have to be dried prior to analysis. The AP-MALDI has also demonstrated large tolerances to laser fluence variations and minimal fragmentation of molecular ions [51]. There are different AP-MALDI systems that use different laser sources, the most common laser is the 337nm UV nitrogen laser. The nitrogen laser is used in the AP-MALDI set-up because of the strong interaction of the matrix compounds in the UV regions. Doroshenko et al. [36] found the AP-MALDI source to be extremely practical for studies of small molecules because the AP-MALDI allows for low detection limits, and the limitation of mass range was mostly affected by the limits imposed by the mass spectrometer in question and not the AP-MALDI. Doroshenko et al. also reported that the AP-MALDI system allowed for softer ionization than vacuum MALDI because the analyte could also become thermally ionized in the air, subsequently requiring lower laser power for ionization and allowing more fragile samples can be examined. Recent work by Vertes et al. [35] has shown that 2,940-nm IR laser can also be used for carrying out AP-MALDI experiments. Using a wavelength that is in the IR region allows for sampling tissue in situ and using the water in the sample as an inherent matrix. Vertes et al. have demonstrated this technique on tissue samples of different fruit such as bananas and strawberries [34]. In Vertes’ experiments the sample plate sits on an x and y stage controller allowing for rapid analysis of sequential spots as well as opening the door for in situ surface sampling of tissue. The AP-MALDI has been successfully used by Vertes et al. to image sections of fruit [35] and plants [52] as well as for detecting peptides [35]. When it comes to imaging mass spectrometry spatial resolution plays a significant role in the ability to precisely map chemical distributions, therefore, the ability to lower the spatial resolution of in chemical imaging will provide more accurate determination of compounds in samples such as plant tissue, human, and animal tissues as well in materials. Currently for laser desorption experiments the spatial resolution is determined by first the laser spot size and the scanning spot size. Vertes et al. used a 250-mm laser spot size which they used to image an electron microscope grid with bar spacing of 92 mm [50]. Moving their stage in 40-mm increments they were able to generate a chemical image through over sampling where the resolution was determined by the spot size of the stage. The obtained chemical image can be seen in Fig. 7.8. Vertes’ work demonstrates the ability to create chemical images at micron resolutions, but at the same time leaves lots of room for improvement and generation of competing techniques. Advances in technology are required to push the limit of what we are able to study and examine. The push toward studying materials and systems on the nanoscale range creates the opportunity for new discoveries. However, the currently available techniques that allow nanometer resolution studies are limited in the amount of chemical information provided. Techniques such as electron microscopy and scanning probe microscopy (SPM) that allow for spatial imaging resolution of 1nm or better provide almost no chemical information about sample. In contrast, techniques such as mass spectrometry and RAMAN and IR imaging provide a vast supply of chemical information about a sample on the molecular level but are not


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Fig. 7.8 (a) Electron microscope grid. (b) Chemical image of toluidine blue O obtained through over sampling (used with permission from [50])

capable of imaging at a submicron resolution. Therefore, it seems that the coupling of two techniques like SPM and mass spectrometry would be the next stage in scientific progress toward the development of new methods for studying systems that require low spatial resolution as well as high chemical information such as cell walls, membrane proteins, material junctions, etc. In recent years Zenobi et al. have attempted to couple mass spectrometry with near field scanning optical microscopy (NSOM) in order provide chemical information at the nanometer spatial resolution [16] Zenobi’s technique relied on using tip-enchanced laser ablation to create submicron-sized ablation craters in a material and then sample the chemical composition of the material using mass spectrometry. Zenobi’s experiments showed promise for the technique but were limited in what type of systems they could study because the experiments were carried out under vacuum. More recently Zenobi et al. have carried out similar tip-enchanted NSOM experiments at AP [16]. This experimental set-up for coupling a mass spectrometer with an SNOM system in AP can be seen in Fig. 7.9. Their experiments show the feasibility of acquiring mass spectrometric data from nanometer-sized craters at AP as well as obtaining structural information about a surface through NSOM imaging. Aperture based near field optical microscopy works by overcoming the diffraction limit also known as the Abbe criterion

∆x = 0.61λ / NA

(7.1)

where Dx is the spatial resolution, l is the wavelength of the interacting radiation, and NA=n sina is the numerical aperture of the objective lens. In near-field optical microscopy, the resolution Dx no longer depends on l but on a characteristic length d, the aperture diameter or tip diameter, of a local probe (Fig. 7.10) [16]. NSOM relies on a confined photon flux between a local probe and a sample surface.

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Fig. 7.9 Instrument set-up for SNOM-MS [10]

Fig. 7.10 Comparison of diffraction-limited optical microscopy and near-field optical microscopy. (a) Schematic representation of the diffraction limit showing the minimum detectable separation of two light sources. (b) Schematic of aperture scanning near-field microscopy [7]


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The probe is scanned over a surface and an x–y detector acquires the position and optical information. This idea for overcoming the diffraction limit by confining light to an aperture smaller than to the wavelength of light was first proposed by Edward Synge in his paper in 1928 [16]. However, because of a lack of a coherent light source like a laser that would produce a sufficient photon flux as well as necessary electronic and detection equipment, Synge’s idea was not realized until the 1980 when researchers at the IBM Research Laboratory in Switzerland where able to produce the first near-field optical measurements. In the most common NSOM light is sent down a tapered optical fiber which is uniformly coated in a metal such as aluminum. The fiber is chemically etched to an aperture diameter of around 50 nm. Companies like Nanonics use this technique to create hybrid SNOM/AFM scanning probe equipment to image at the nanometer resolution. Zenobi’s technique relied on using tip-enchanced laser ablation to create submicronsized ablation craters in a material, sampling the ablated material into an electron ionization (EI) source of a mass spectrometer for ionization and detection. Zenobi’s experiments demonstrated proof of principle, but were limited in the types of systems they could study because the experiments were carried out under vacuum and because EI creates only singly charged positive ions as well as fragments of the original molecules. More recently, Zenobi et al. [17] have carried out similar tip-enchanced NSOM experiments at AP. Their experiments show the feasibility of acquiring mass spectrometric data from nanometer-sized craters at AP as well as obtaining structural surface information through NSOM imaging. Discussed in this chapter is research toward a novel set of techniques, using AP hybrid proximal probe topography chemical imaging, where a mass spectrometer is coupled with a state-of-the-art atomic force microscope (AFM). These techniques use AFM probes to desorb material from a surface and then analyze the desorbed gas phase material with a mass spectrometer. These techniques have broad application for studying systems such as cell walls, material junctions, etc. where enhanced or high spatial resolution chemical information is required. Laser desorption/ablation and thermal desorption with a secondary ionization are the two main routes for analyzing surfaces with mass-based chemical imaging that also allow for simultaneous topographical imaging.

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Chapter 8

Dynamic SPM Methods for Local Analysis of Thermo-Mechanical Properties M.P. Nikiforov and Roger Proksch

The Need for Localized Mechanical Analysis: Industrial and Basic Science Perspective Thermo-mechanical properties of materials determine whether they will be useful or not. Measurement techniques for bulk mechanical parameters (Young’s modulus, loss modulus, Poisson ratio, etc.) are well established and regulated by ASTM standards [1–4]. As length scales shrink, Nanoindentation (NI) and Atomic Force Microscopy (AFM) techniques allow sub-1,000nm spatial resolution thermo-mechanical properties measurements. These techniques started becoming available less than two decades ago [5] and are evolving rapidly. Examples of nanoscale property measurements include subsurface delamination in thin films [6], the structure of the cytoskeleton of a single cell [7] and composition of polymer blends [8]. As the spatial resolution increases, the variability in the measurements also increases. Part of this increase in variability is real in the sense that as one approaches characteristic length scales of a material, one begins to sample domains with very different thermal and mechanical properties. Another reason for increased uncertainty comes from experimental noise associated with measuring small forces and displacements and uncertainties and instabilities in the contact areas of the probe interacting with the sample. Despite signal to noise and calibration issues associated with measuring small forces and distances, NI- and AFM-based techniques allow researchers to answer the questions which cannot be addressed with conventional bulk techniques. For example, measurements of the kinetics of the polymerization of automotive clear-coats was not possible with conventional dynamic mechanical analysis (DMA) because of the softness of the material in the first several hours after deposition and the small thickness of the film [9]. From the basic science point of view the change in thermo-mechanical properties of polymers is closely related to phase transitions. AFM/scanning probe-based techniques can ultimately provide 10-nm resolution or better for the measurements of mechanical parameters – changes

M.P. Nikiforov (*) Oak Ridge National Laboratory (ORNL), Oak Ridge, TN 37831, USA e-mail: [email protected] S.V. Kalinin and A. Gruverman (eds.), Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy, DOI 10.1007/978-1-4419-7167-8_8, © Springer Science+Business Media, LLC 2010

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in which are intimately associated with phase transitions. In many cases, this resolution is approaching the length scale at which phase transformations occur. In polymeric materials this length scale corresponds to the length of the Kuhn’s segment (0.1–2 nm) [10–12]. Thus, studying temperature dependencies of the mechanical properties allows phase transformation in polymers to be understood at a physically relevant length scale. In this chapter the basic NI models and mechanical analysis with AFM are briefly introduced; however, this is not the main focus. Most attention is paid to experimental techniques which allow mapping of the thermo-mechanical properties at different temperatures. More details on NI and mechanical analysis with AFM at room temperature can be found in several excellent reviews [13–16].

Mechanical Characterization of the Materials with High Spatial Resolution: Lessons from Nanoindentation Mechanical properties measurement using indentation is a well-established technique for the characterization of hard surfaces [5]. This technique involves a rigid probe with a well-defined geometry that is pressed into the flat surface of a test sample. This forces the material to undergo elastic and usually plastic deformation at the probe location. Mechanical properties are determined from the values of indentation force for a measured indentation depth and other parameters. The methods developed for macroscopic indentation can be applied for tests at micron and sub-micron length scales on hard materials such as metals, ceramics, plastics, calcified biological tissues, composites etc. [17–21]. Because of their relevance in everyday life, among the most interesting objects for thermo-mechanical characterization are polymeric materials and biological samples including cells [22, 23] and various biological molecules [24]. When the indentation methodology is applied to soft materials, the physics of the indentation process is inherently more complex because soft materials undergo purely elastic deformations even at large indentation depths. This results in the following experimental issues: • Data analysis usually requires complicated models, which take into account contributions from interactive forces. This happens because tip–sample interactions (e.g., adhesion) are stronger in compliant samples. • The point of contact is difficult to identify, because applied forces for a given indentation depth are much smaller in soft materials than in hard ones. • The transition from linear to nonlinear stress–strain behavior may be ambiguous, because of the large elastic deformation range. During the last two decades the accuracy of NI measurements has been constantly improving. Models have been created to address the issues raised in the list above [25–30]. The main theoretical models of tip–surface contacts and experimental protocols used for data fitting based on these models are presented below. Theoretical models can be divided into three main classes based on the tip–surface

8 Dynamic SPM Methods for Local Analysis of Thermo-Mechanical Properties

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interactions: (1) elastic indentation of an infinite half sphere without adhesion, (2) elastic indentation of an infinite half sphere with adhesion, and (3) repulsive tip–surface interactions (electrostatic forces, when indentation is performed in solution; electrosteric interactions). The Hertz model is the prototypical contact model. This model is based on the following assumptions: • The strains are small, i.e., rcont⪌R (and d⪌R), where rcont is the contact radius, R is the radius of the sphere, d is the indentation depth. • The indented solid is a linear elastic, infinite half space. • The surfaces are frictionless. In the simplest case of indentation with a sphere of radius R the force F=ER1/2d3/2, where E is Young’s modulus, and d is indentation depth. More complicated geometries are reviewed in [31]. Since the seminal paper by Hertz in 1881, it has become obvious that attractive interactions between indenter and surface cannot be neglected in many real world systems. In 1971 Johnson–Kendall–Roberts (JKR) [32] suggested a model where Hertz theory was modified by introducing an apparent Hertz load, or the equivalent load in the absence of adhesion. In the JKR model, the contact radius is typically increased compared to the Hertz model. Later, in 1975 Derjaguin–Muller–Toporov (DMT) [33] proposed a theory in which the adhesion forces are taken into account, but the profile is assumed to be Hertzian, neglecting the contribution of adhesion forces to the surface deformation profile. In 1976, Tabor identified the applicability of the two theories for a range of sample compliances and adhesive forces. The JKR theory was found to be valid for the indentation of relatively compliant materials with probes of relatively large radii and strong adhesive forces. In contrast, the DMT theory applies under conditions of stiff materials, small probe radii, and weak adhesive forces. In 1992 Maugis suggested a universal model, which more realistically describes adhesion between spheres and has both the JKR and DMT solutions as limiting cases [34]. When a probe approaches a surface, attractive interactions typically prevail. However, repulsive interactions between probe and surface can also be observed when the probe comes in the close proximity with the surface [35]. Those interactions are mainly of electrostatic nature. Various theories, such as Derjaguin– Landau–Verway–Overbeek (DLVO) [36, 37] and theories based on electrosteric and electrostatic interactions [38–40], were used to explain data on indentation obtained with AFMs. In soft materials and large deformations, the small strain approximation – one of the assumptions of the Hertz model – is no longer valid. The contact mechanics beyond the Hertzian regime is an interesting part of applied mathematics and it is well reviewed by Lin and Horkay [31]. Here we will discuss only one model which treats slight deviations from rubber–elastic behavior of materials. This model was proposed by Lin et al. [27] where the nonlinear force–indentation relationship was derived from an approximate equation based on the Mooney–Rivlin strain energy function [41]. Several groups used the theoretical models described above for determination of materials properties such as Young’s modulus from force distance curves measured

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Table 8.1 Comparison of the applicability ranges for different models Small force Mooney – NonRivlin interactive, Herzian Adhesive Repulsive elastic Lin et al. [27]     Jaasma et al. [44]     Guo and    Akhremitchev [43] Crick and Yin [42]    Oliver and Pharr   [5, 46–50] Sun et al. [45]

Large force JKR – DMT JKR transition DMT   





with AFM. The main challenges for the correct determination of Young’s modulus were tip shape, the determination of contact point, thermal (Brownian) fluctuations, and instrumental noise. Using elaborate data processing techniques and data acquisition protocols, six main models for the extraction of mechanical properties from NI and AFM data were proposed: Crick and Yin (AFM) [42], Guo and Akhremitchev (AFM) [43], Jaasma et al. (AFM) [44], Lin et al. (AFM) [27], Oliver and Pharr (NI) [16], Sun et al. (AFM) [45]. Table 8.1 shows what types of interactions are treated in each of the models. The model developed by Lin et al. provides the biggest versatility, albeit at a price of using multiple triggers to differentiate between different tip–surface interactions. Each of the methods presented in Table 8.1 is accompanied by a specific protocol for the analysis of force–distance data (see original articles for details).

Principles of Thermo-Mechanical Analysis Using AFM Platform: Examples of Thermo-Mechanical Properties Mapping The models and data analysis protocols discussed in the previous section provide a framework for the conversion of the data obtained in the experiments (force–distance curves) into mechanical properties of the materials. AFM is a common tool for obtaining force–distance curves with high spatial resolution, making it an excellent platform for high-resolution mechanical analysis of the materials. Extensions of this technique to measure temperature dependence of mechanical properties with high resolution provides an exciting opportunity to study phase transformations in polymeric materials. An AFM platform allows two implementations for this concept: variation of the entire sample temperature using a “bulk” heater, and high resolution variation of the sample temperature using a localized heater built into the AFM tip. Bulk variation of the sample temperature allows significantly more stable and precise temperature control while local heating achieves much faster heating rates of the material. Recently, several groups have implemented thermo-mechanical analysis


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using AFM platforms [51–53]. Thermo-mechanical analysis was implemented on various AFMs operated in contact mode (where the tip stays in contact with the surface all the time and applies constant force on the surface). The brief description of operational principles and hardware for each of the techniques is given below as well as examples of the results of mapping thermo-mechanical properties of the materials.

Transition Temperature Microscopy Transition Temperature Microscopy (TTM) uses the probe deflection as a function of the tip temperature to measure localized thermal expansion. When these probes are heated, the region under the tip usually expands, causing the cantilever to deflect upwards (Fig. 8.1a). When the material under the tip warms enough to soften, this process can begin to reverse as the tip penetrates the softer, but still expanding, material. In TTM the temperature of the transition is determined as the temperature maximum on the probe deflection versus temperature curve. Figure 8.1b shows a map of the glass transition temperature with 2.5-mm point-to-point resolution on a poly-styrene/poly(methyl metacrilate) sample [54, 55].

Fig. 8.1 (a) The red curve shows the cantilever deflection as a function of the heater sensor. Initially, the thermal expansion of the PET sample under the tip causes the deflection to increase. As the sample starts to soften under the tip, the deflection levels off and then decreases. To minimize damage to the tip and sample, the tip was manually pulled off the surface at the asterisk. The transition temperature can be estimated from the crossover between the expansion and melting portions of the curve. The inset image shows the topography of the indent created by this measurement. (b) Transition Temperature Microscopy (TTM) image of a polymer blend sample of Polystyrene and Poly(methyl methacrylate) taken with a scan size of 100 × 100 mm. These two materials are immiscible and so phase separated into micron size domains. The two materials can be easily differentiated by their different Tg values and TTM resolves the polystyrene domains as the blue roughly circular features (image is courtesy of Anasys Instruments, http://www.anasysinstruments.com)

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One complication of the variable deflection approach is that the load on the cantilever varies as the sample expands and then starts to soften or melt. This increasing and then decreasing load can in turn cause variations in the mechanical behavior of the tip–sample junction, as well as variations in the thermal coupling between the tip and the sample. For example, increasing the load will typically lower the measured transition temperature, while increasing the contact area will typically increase the heat transfer between the tip and the sample. Finally, the load can change the measured transition temperature. Multiple frequency techniques discussed in Section “Multiple Frequency Methods for ThermoMechanical Mapping (BE-NanoTA and Z-Therm)” solve some of the problems mentioned above by utilizing more sensitive oscillatory techniques for the detection changes of the mechanical properties of the sample as a function of temperature. As suggested by Nelson and King, one way to simplify these variations is to instead use a feedback loop to keep the deflection constant by varying the z-position of the base of the cantilever [56]. In the absence of thermally induced bending of the cantilever (discussed below), this approach provides much the same signal as simply measuring the deflection, with the advantage that the load on the sample is constant. Nelson and King reported better reproducibility using this technique. Not surprisingly, this allows smaller volumes of material to be probed. An example is shown in Fig. 8.2 below, where the indentations made into the sample were significantly smaller when deflection feedback was enabled. Note that this method is more quantitative when the signal from an independent position sensor on the z-axis is plotted rather than just the z-piezo drive voltage. Piezo motion is susceptible to hysteresis and creep, introducing significant error in the plotted position when the piezo drive voltage is used. Repeatability of the thermal curves of the type shown in Fig. 8.2 can be improved with automatic, high speed triggering of the pull-off. In both cases of varying deflection or deflection feedback, using a defined trigger point results in more repeatable melting curves. An example is shown in Fig. 8.2 where melting curves on a polyethylene-terephthalate (PET) surface were made using both variable cantilever deflection (open loop) and closed loop (feedback) methods, each with a nominal 50nm trigger pull-off. This trigger condition continuously monitors the signal and stores the maximum value. If the measured signal drops a specified amount below the recorded maximum value, the z-piezo is instructed to pull the cantilever away from the surface while it is still at a high temperature. Figure 8.2a shows four deflection curves made at different positions on a PET surface while Fig. 8.2b shows similar curves of the z-sensor output made with the deflection feedback enabled. Perhaps not surprisingly, there is a significant difference between the position of the maxima for the curves in (a) and (b). This is consistent with a higher loading force causing an earlier melting onset. Figure 8.2c shows an image taken after the melting curve measurements, with the resulting pits visible. The pit depths for the two methods are virtually identical. However, there are systematic pile-ups next to the open-loop pits. This may originate from the lateral motion of the tip as the load, and therefore the distance, between the base of the cantilever and the sample surface changes.


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Fig. 8.2 (a) Four deflection curves made at different positions on a PET surface. The pull-off trigger was set to nominally 50 nm below the maximum recorded value, based on the cantilever sensitivity calibration. (b) Similar curves of the z-sensor output made with the deflection feedback enabled. As with (a), the trigger value was chosen to be 50 nm below the maximum value. Notably, there is a significant difference between the position of the maxima for the curves in (a) and (b). This is consistent with a higher loading force causing an earlier melting onset. (c) An image taken after the melting curve measurements. The top four pits, circled in red correspond to the variable deflection measurements. In these any almost all other variable deflection measurements we observe a small pile-up besides the melted pits. This is consistent with the cantilever tip sliding laterally as it heats and is deflected by the expanding material. The bottom four pits, circled in blue, show the feedback enabled results. The depth of the different techniques using this rather large trigger value was not statistically different

One of the natural questions that arises with these measurements is what is the fundamental limit on the volume of probed material? To probe smaller volumes, there are some requirements. The first is to operate at smaller forces to minimize the contact area of the tip. Second, as the material starts to undergo a melting transition, we need to avoid having the cantilever tip rapidly plunge into the melted material. We can avoid this by having a low pull-off trigger threshold. Figure 8.3 shows the results of a short study where the two methods were tested using small trigger values. Respectively, the trigger values were 25, 10, and 5 nm

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Fig. 8.3 Cross sections of pits created with trigger values of (a) 25 nm, (b) 10 nm and (c) 5 nm. The solid curves were taken using the open-loop (variable deflection) method while the dashed lines show the results of the closed-loop technique. The color of the section curves are coded to the location on the image (d). Consistent with the load increasing because of the variable cantilever deflection, the width of the open-loop measurements systematically increases compared to the closed-loop pits. The arrow shows the location of an attempted 1 nm trigger value that resulted in an early pull-off for both techniques. The open loop deflection increased enough to leave an indentation in the sample

for the red, blue, and green color coded results. Probably due to the increasing load, the depth and width of the open-loop measurements systematically increases compared to the closed-loop pits. The arrow shows the location of an attempted 1nm trigger value that resulted in an early pull-off for both techniques. This is close to the thermal noise limit of the deflection detector in the AFM measurement and likely represents a fundamental limit on the trigger value. If this is indeed the case, the limit for this particular cantilever using the open-loop technique is a pit roughly 100 nm in diameter and 100 nm deep, while for the closed-loop technique, the limit is roughly 75 nm in diameter and 50 nm deep.

Scanning Thermal Expansion Microscopy One of the first measurements of thermo-mechanical properties with AFM was reported by Varesi and Majumdar [57] in 1998. These authors measured thermal expansion of Au wires on an SiO2/Si substrate during AC heating. The difference


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in thermal expansion for Au wires and SiO2 is clearly seen in Fig. 8.4b despite some topographical crosstalk (Fig. 8.4a). The amplitude of thermal expansion for Au wires was determined to be 24 pm. The sample was heated using AC current with a frequency on the order of tens of kilohertz. The fixture for the resistive heating of the sample was the add-on module used in this experiment. Periodic heating of the sample resulted in periodic expansion of the material, which was detected as displacement of the AFM tip. The amplitude of the tip oscillations in this case is proportional to the thermal expansion of the material. This method is quite simple in implementation and does not impose any special requirements on the AFM tip. However, the requirements for high electrical conductivity and large thermal expansion coefficient of the sample material significantly limited the applicability

Fig. 8.4 Thermal expansion maps of the Au stripes deposited on Si substrate (b) and PET/resin (d). The map (b) was acquired using AC heating of Au wires. AC heating of the tip was used for creation of map (d). Images (a, b) are courtesy of J. Varesi and A. Majumdar. Reproduced with permission from Appl. Phys. Lett. 72(1), 37 (1998). Images (c, d) are courtesy of A. Hammiche et al. Reproduced with permission from J. Microsc.-Oxf. 199, 180 (2000)

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of this method. Furthermore, this implementation of Scanning Thermal Expansion Microscopy (SThEM) provides accurate relative information about the sample’s mechanical properties. Unfortunately, quantification of the results is virtually impossible, because of the unknown temperature profile. In 2000, Hammiche et al. [51] used a similar approach to create a thermal expansion map of the material (Fig. 8.4c, d), but instead of periodic heating of the sample, he used periodic heating of the tip with AC current. This approach eliminates the sample’s electrical conductivity restriction and opens the pathway to measuring mechanical properties of non-conductive materials, such as polymers (PET/resin). The other benefit of localized heating of the tip is better lateral resolution demonstrated for this method compared to that demonstrated by the Varesi and Majumdar implementation of the SThEM technique. In Hammiche’s version of SThEM a specialized AFM tip (Wollastone probe or micro-machined probe) was used. Heating of the probe allowed researchers to heat the sample and also to know the precise temperature at the probe end. Quantification of the results and conversion of the thermal expansion amplitude to the thermal expansion coefficient of the material is possible with careful calibration of tip–surface contact properties, photodetector sensitivities, and other instrumental parameters. Without the calibration data Fig. 8.4c, d clearly show that the thermal expansion coefficient of PET is smaller than that of the resin, because the thermal expansion amplitude measured on PET is smaller than that measured on the resin.

Thermally Assisted Atomic Force Acoustic Microscopy Concurrently with SThEM development, Thermally Assisted Atomic Force Acoustic Microscopy (TA-AFAM) method was being developed by Oulevey and co-workers [58]. In this method, the stiffness of the sample was measured as a function of temperature using the same principle used in AFAM. They used a piezooscillator on top of the heater for the single frequency modulation of the normal force. PVC/PB polymer samples were measured. Several years later Oulevey, in collaboration with researchers from the UK, improved the resolution of this method and used TA-AFAM to determine softening transition of a PS/PMMA blend spincoated on a glass substrate. The softening transition temperature was determined by measuring stiffness maps at different temperatures. At 98°C, below the softening point of PS, the stiffness map has almost no contrast (Fig. 8.5b). At 103°C, above softening point of PS, some domain structure starts to appear (Fig. 8.5d). The dark domains in this figure were interpreted as the PS phase because of the lower stiffness of those domains at higher temperature [52]. In this experiment the contact area is not known and has not been controlled, thus, quantitative interpretation of the data is impossible. The TA-AFAM technique appears in publications under different names, such as variable temperature scanning local acceleration microscopy (T-SLAM) [52, 58] and dynamic mechano-thermal analysis by scanning microscopy (D-MASM). Since there is variation in the acronyms in the literature and the


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Fig. 8.5 The left-hand images (a, c) are topography of PS/PMMA on glass; the right-hand ones are simultaneously acquired DLT-MA amplitude (elasticity) images (b, d). The top set (a, b) were taken at 98°C, and the bottom at 103°C (c, d). Because of thermal drift, the three sets of images represent similar, but not the same, locations. The image is courtesy of Oulevey et al. Reproduced with permission and adapted from Polymer 41(8), 3081 (2000)

working principle of the technique is similar to Atomic Force Acoustic Microscopy AFAM [59], we will refer to this method as TA-AFAM. This method provides qualitative measurements of stiffness with sub-100nm spatial resolution [52]. Quantification of the results is possible in principle, however, the unknown properties of the tip–surface contact and cantilever stiffness makes this process quite challenging. Regular AFM probes are required for this technique.

Multiple Frequency Methods for Thermo-Mechanical Mapping (BE-NanoTA and Z-Therm) Both SThEM and TA-AFAM use single frequency detection techniques. In the case of SThEM, periodic heating of the sample is done at a single frequency and thermal

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expansion of the material is detected at the same frequency. In TA-AFAM, the transducer is excited with a single frequency and tip displacement is measured at the same frequency. In SThEM and TA-AFAM experiments, two oscillation parameters (amplitude and phase) are measured. The single frequency measurement approach for characterization of tip–sample contact does not provide all information about the tip–sample contact, because even the simplest model of tip–surface contact (Simple Harmonic Oscillator) has four independent fitting parameters (amplitude, resonance frequency, quality factor, and phase). In order to avoid this shortcoming multi-frequency measurement techniques are required. Contact mechanics can be probed with extremely high resolution by measuring the resonant frequency and quality factor rather than the DC deflection or feedback signal. That resonant frequency–domain measurements are more sensitive to tip–sample interactions is not news to the AFM community. AC methods were used by Binnig, Quate, and Gerber in their first AFM [60] to improve the sensitivity and noise rejection of the microscope over DC contact techniques. Recently, Band Excitation (BE) [61] techniques have been used on polymer samples to demonstrate the high sensitivity of the contact resonance and dissipation to thermal transitions [53]. Similarly, using the Dual AC Resonance Tracking [62] (DART™) technique provides much higher sensitivity to thermo-mechanical changes at the tip–sample junction than does the cantilever deflection (see Chaps. 5 and 17 for more details on DART technique). In addition to tracking the resonant frequency, this technique allows the tip–sample dissipation to be measured, a quantity that shows very strong temperature dependence in a wide variety of samples. In the examples (Figs. 8.6–8.8) shown here, we measure changes in the contact resonance behavior as a function of tip heating. To do this, we limit ourselves to the following experimental conditions: • The sample position is modulated at two frequencies, one above and one below the resonance to enable the resonance tracking (DART). • The temperature of the tip is ramped at a frequency significantly below the DART contact resonance modulation frequencies. PVDF and its copolymers are the most well-known polymer ferroelectrics with a wealth of potential applications in piezoelectric and pyroelectric devices, such as pyroelectric infrared sensors, shock sensors, energy conversion systems, etc. Although magnitudes of these effects in PVDF are much lower than those of ferroelectric ceramics, other factors make these materials very desirable for many applications. The PVDF polymers have low permittivity, low acoustic impedance and low thermal conductivity and are available in flexible large area sheets at a relatively low cost. Investigation of thermomechanic and thermoelectric responses in nanoscale PVDF structures is important from the viewpoint of their integration in nanoelectronic devices, as well as for advancing the fundamental understanding of the thermodynamics of phase transitions in ferroelectric polymers, where only rudimentary attempts at using SPM techniques have been undertaken so far. In the experiments below, PET samples were cut from a commercially available water bottle and glued to the top surface of the piezoelectric transducer. These


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Fig. 8.6 The effects of heating curves on PVDF sample. A 6 × 3 array of locations were heated to ~80°C while the tip was pressed into the sample with a preload of ~5 nN. (a) A topographic scan before the probing. (b) The same location afterwards. Selected heating curves were plotted in (c), color-coded by location in the images (a), (b), (d) and (e). Locations red, violet and dark blue were on the sample substrate and show large resonance frequencies that are independent of the heating. Locations green, yellow and light blue were made on the PVDF and show both lowered resonance frequencies because of the reduced modulus of the material and also clear temperature-dependent changes. The black location is a place where the localized heating resulted in a relatively large change in the sample topography. The black curve in (c) indicates that this change happened during the first heating cycle, where the resonance frequency initially increased significantly and then leveled out to behavior intermediate between the substrate and the on-PVDF curves. (d, e) Zooms before and after. In these images, the sample change at the black location is easy to see. (Sample courtesy of Alexei Gruverman, University of Nebraska–Lincoln)

samples were probed and imaged using silicon heated probes (see Section “Silicon Heater” below for more details). The probes were used in AC mode to produce high resolution topographic and phase images of the surfaces before and after thermal probing. The same probes were used in DART mode to locally probe the surface deformation, contact resonance and dissipation during thermal cycling [63].

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Fig. 8.7 Demonstration of mapping capabilities of Ztherm™. Thermo-mechanical properties of tip–surface junctions (resonance frequency, amplitude as a function of temperature) were measured on 6 × 3 grid on PET. Topography (a–d) and phase images ((a¢–d¢)) of PET sample after probing with decreasing peak heating voltages show that the decrease in peak probing voltage results in the decrease of sample damage. The temperature response curves are shown in (e), with each curve color-coded to the appropriate topographic and phase image. (f) The associated frequency shifts, (g) the associated local deformation of the sample surface and (h) the amplitude (related to the dissipation) of the cantilever during each cycle. The frequency (f) and amplitude (h) curves were each given arbitrary offsets to make them visible

PET, (C10H8O4)n), is a common thermoplastic polymer resin material used in a variety of products. The bulk Young’s modulus is ~3 GPa. The glass transition temperature is ~75°C while the melting temperature is ~260°C. As with most thermoplastics, PET has poor thermal conductivity (~0.24W/mK) and a large coefficient of thermal expansion (cte ~7×10-5/K). The above capabilities [64] allow us to take this technique to its logical conclusion – repeatable thermal probing of volumes of material so small that surface alterations are undetectable by normal AFM imaging (Fig. 8.7). Moreover, the improvements enable observations of significant and repeatable changes in the contact mechanics as a function of temperature – while afterwards being unable to locate the sites of these probed volumes with high resolution AC mode (tapping) images. Thermomechanical analyses of the amyloid fibrils were done using the Ztherm technique; tapping mode topography images before (Fig. 8.8a) and after (Fig. 8.8b) analysis show the degradation of the fibril after the measurements. Temperature dependencies of resonance frequency, amplitude and probe displacement were recorded. Figure 8.8c shows that temperature dependence of probe displacement shows a monotonic increase, while resonance frequency shows a significant jump, which probably corresponds to the transformation of the fibril. This observation proves that resonance frequency detection is much more sensitive than probe displacement to the change in mechanical properties of the sample. The Band Excitation-NanoTA method is the most versatile technique for contact characterization of all the techniques presented above. It allows direct determination


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Fig. 8.8 (a) An AC mode image of insulin fibers deposited on a mica surface. After imaging, a series of thermal bending compensated, low-temperature thermal cycles were performed in a 12 × 6 array of points. A small selection of those locations are indicated by the colored markers in both (a) and (b). (b) An AC image of the same region after the thermal cycling was completed. There are numerous gaps in the fibers where thermomechanical decomposition has occurred. (c) The local thermal expansion (top plots) and resonant frequency shifts (bottom plots) associated with the thermal cycles, color coded by location. Note the clear signal putatively associated with thermal decomposition of the fibers visible in the frequency shift curves. The deflection curves show no significant response at the same temperature. Some tip broadening has occurred during the thermal cycling that reduces the resolution between (a) and (b). Because the heating cycles were made at constant load, compensated for the thermally induced bending of the lever, the resonant shifts can be associated primarily with thermal decomposition, rather than a simple mechanical effect

of the mechanical properties of the tip–surface junction as a function of temperature by measuring mechanical response in the band of frequencies and comparing it with the excitation signal spanning the same band of frequencies. There are two implementations for this method. The first one is the modification of the atomic force acoustic microscopy (AFAM) [59, 65] technique by mechanical excitation and oscillation detection over a broad frequency range (band excitation (BE) technique) [66], and by using the heated tip probe [53] (BE-AFAM). The second one is the use of the heated tip and thermal expansion of the material combined in conjunction with the BE technique (BE-SThEM) [67]. The BE technique used in the BE-NanoTA method provides direct measurement of the four parameters of system resonance (resonance amplitude, resonance frequency, quality factor and phase) [67]. Furthermore, a protocol that maintains a constant tip/surface pressure and reproducible contact area during a temperature sweep has been reported, effectively extending the Oliver– Pharr method for NI to local thermal analysis [16, 53]. This method also provides measurements of mechanical properties as well as glass transition temperatures with sub-100 nm resolution. Specialized probes with a heater at the end are required for both implementations of this technique. The AFAM-based implementation of the method requires the use of the transducer to induce mechanical oscillations of the sample.

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Fig. 8.9 (a) Contact resonance frequency of tip–surface contact as a function of temperature. Red curve corresponds to the PMMA-rich region and extracted from the position (1) on the Tg map (b). Black curve corresponds to SAN-rich region and corresponds to the position (2) on the Tg map. (b) Spatial distribution of glass transition temperatures (Tg) determined as a temperature of maximum on contact resonance frequency curve. The point-to-point resolution is 50 nm. The image size is 3.75 × 3.75 mm. The image is courtesy of M.P. Nikiforov (unpublished)

Recently, Nikiforov, Jesse, and Kalinin mapped the glass transition temperature of SAN/PMMA phase separated polymers based on the measurement of the thermo-mechanical properties of this polymer mixture (Fig. 8.9b) [68]. The BE-SThEM technique was used. The point-to-point resolution of the glass transition temperature map was 50nm, which makes this technique applicable for the analysis of the internal structure of the polymeric materials. The glass transition temperature can be determined either as a temperature maximum on the resonance frequency versus temperature curve or as a temperature at which the quality factor falls below a certain value. Figure 8.9a shows the typical dependence of resonance frequency as a function of temperature. The initial increase in resonance frequency (region A) comes from the increase of the tip–surface contact area associated with initial sinking of the probe into the surface. The decrease of the contact resonance frequency (region B) as a function of temperature occurs because of the sharp decreases in the Young’s modulus of the sample after the polymer undergoes glass transition. Thus, the temperature maximum on the contact resonance frequency curve is a good measure of the glass transition temperature. To measure the Young’s modulus as a function of temperature, the “freeze-in” protocol was developed [53]. This protocol is similar to the Oliver–Pharr method used for NI when on the first temperature cycle, the AFM tip sinks into the surface and materials properties are measured on the subsequent cycles. This protocol allows maintaining contact area constant during the experiment and quantitative determination of Young’s modulus maps at different temperatures. Young’s modulus of PET as a function of temperature was measured using this technique. Temperature, resonance frequency, and quality factor as a function of time are presented in Fig. 8.10a. Using the mechanical model (Fig. 8.10c) and the Young’s modulus of


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Fig. 8.10 Resonant frequency and quality factor of the tip–surface system as a function of time (a) and as a function of temperature (b). (c) Equivalent model for tip–surface contact. (d) The local Young’s modulus and damping coefficient for PET sample as a function of temperature. The image is courtesy of S. Jesse et al. Reproduced with permission and adapted from Appl. Phys. Lett. 93(7), 073104 (2008)

PET at room temperature, Young’s modulus of PET as a function of temperature can be calculated [53, 67]. The main characteristics of each of the techniques discussed above are listed in Table 8.2. Table 8.2 also shows that most of the work on local thermo-mechanical characterization was done on polymeric samples. The reasons for such behavior are discussed below. The small size of the heated probes limits the output heating power these probes can supply to the junction. This imposes restrictions on the thermal conductivity of the samples analyzed with those techniques. For example, the high thermal conductivity of metallic samples does not allow measurement of mechanical properties as a function of temperature. Samples with small thermal conductivity or small heat capacity are the most suitable for SThEM, TA-AFAM, Z-Therm, and BE-NanoTA. Thus, these methods are well positioned for the study of thermomechanical properties of polymeric materials. The samples with relatively small surface roughness (below 10–20nm RMS on the area 10×10µm2) provide the best measurements of the thermo-mechanical properties because of the minimization of the cross-talk between topography and mechanical measurements.

Table 8.2 The comparison of experimental implementations for TTM, SThEM, TA-AFAM, Z-Therm, BE-NanoTA TTM SThEM TA-AFAM Z-Therm Detection of Detection of Detection of thermal Working principle Detection of the changes the changes expansion in out-ofthe onset in contact in contact plane direction of material stiffness stiffness softening Spatially resolved Spatially resolved thermal Spatially resolved Measured sample Spatially resolved contact stiffness expansion map contact stiffness property glass transition map at constant map at constant maps temperature; temperature glass transition and softening temperature Samples PS/PMMA blend Au stripes on SiO2, Au PVC/PB blend PET, PVDF stripes coated with PMMA, ITO resistor Conditions Ambient Ambient Ambient Ambient Time of the Tens of minutes Tens of minutes Tens of minutes Tens of minutes experiment

Ambient Several hours

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BE-NanoTA Detection of changes in contact resonance characteristics as a function of temperature Spatially resolved elastic and viscous properties; glass transition and softening temperature

216 M.P. Nikiforov and R. Proksch


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Types of Probes Used for Thermo-Mechanical Analysis The cantilever probe is a crucial component of every AFM-based technique. In the previous section we saw that two types of probes were mainly used for local thermal analysis using AFM: regular cantilevers and cantilevers with miniature heaters at the end. The description and specifications of various regular AFM cantilevers can be found on the web-sites of major AFM tip manufacturers, such as MikroMash [69], Nanosensors [70], and Olympus [71], as well as major AFM manufacturers (Agilent [72], Asylum Reseach [73], NT-MDT [74], Veeco [75], etc.). In this section we focus on the progress made in the manufacturing of thermally active probes. The development of thermally active probes, started in 1986 by Wickramasinghe et al. [76] continues today [77]. The main goal of this development is to manufacture the probe whose temperature can be independently measured and controlled. In the course of the probe development, several constraints need to be balanced: the fast heating/cooling rate necessary for fast probing; the heater power that determines which materials can be studied and what heating electronics hardware can be used; and the size of the contact area of the heater which determines spatial resolution of the mechanical properties mapping, etc. Multiple designs have been explored over the past two decades [78–85]. Nowadays, there are two widely accepted designs, which are described in detail below. Both designs utilize resistive heating of the probe. As a result of the efforts in tip development, the spatial resolution of the measurements has reached tens of nanometers and the temperature resolution has reached a few degrees Kelvin [86]. The outstanding problem is the batch processing and reproducibility of the properties of the thermal probes.

Wollaston Probe Resistive probes have one great advantage in applications requiring more than topographic and thermal imaging: they may be used in active mode, thereby acting as a self-contained device for the supply of heat as well as temperature measurement. Consequently, they may be used for localized thermal analysis as well as AFM and Scanning Thermal Microscopy. The type of sensing element often used in nearfield resistance thermometry consists of the apex of a fine V-shaped wire, known as the Wollaston probe after the type of silver-sheathed noble metal wire from which they are made (Fig. 8.11) [87]. The resistive probe is capable of performing three functions: it exerts a force on the sample surface; it acts as a highly localized heat source; and it measures heat flow. Probes can be used in either of two operating modes [88, 89]: • Constant temperature mode and variable temperature mode, where the probe acts as local heater. • Constant current mode – where a small current is passed through the probe which then acts as a thermometer.

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Fig. 8.11 Scanning electron microscopy image of the Wollaston probe. Image is courtesy of H.M. Pollock and A. Hammiche. Reprinted with permission from J. Phys. D: Appl. Phys 34 (2001) R23–R53

Constant temperature mode: The thermal element can be used as a resistive heater and forms part of a Wheatstone bridge circuit. When the probe contacts successive regions of the sample surface that may differ in their thermal properties, varying amounts of heat will flow from the probe to the sample. However, the probe heating circuit uses a feedback loop to adjust the current through the probe to keep the probe resistance, and hence the temperature, constant. The required feedback voltage is used to create contrast in the thermal image. The power involved may be calculated from the bridge output voltage and is affected by several factors including the probe/sample contact area, the temperature difference between probe and sample, and variations in the local thermal conductivity of the near-surface regions of the sample. For the samples with low thermal conductivity, such as polymeric samples, the constant power approach can be used. Tip temperature in contact with surface can be calibrated using the melting temperature of the polymer as a reference point. The calibration of the input voltage as a function of tip temperature works well for materials with similar thermal conductivities. The spatial resolution of Wollaston probes is on the order of 10µm [90]. Variable temperature mode: Similar hardware (Wheatstone bridge circuit) is used for both variable temperature mode and constant temperature mode. Variable temperature mode is used to measure local thermal expansion of the material under the tip, when amplitude (and phase) of the oscillations in the displacement is measured at the frequency of local heating [51]. Local thermal conductivity of the material can also be measured when the amplitude (and phase) of the oscillations in tip–surface temperature is measured at the third harmonic of the frequency of local heating [91, 92].


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Silicon Heater In 2006 King et al. developed and patented a process for manufacturing silicon heaters [93]. The SEM photograph of the silicon heater is presented in Fig. 8.12. The end of the probe is heated by passing current through the resistor (low doped Si region) located at the end of a degenerately doped U-shaped silicon cantilever. The functionality and performance of these heater probes, such as tip temperature as a function of sourced electrical power [86], mechanical behavior of the cantilever as function of time [94], etc. [90, 94] were extensively characterized. High heating rates (up to 25×106K/s) [94] achievable by these cantilevers make them suitable for imaging mechanical properties at high frequencies (up to 5MHz). The extremely sharp tip (~20nm radius) located at the end of the cantilever allows imaging of the mechanical properties with sub-100nm spatial resolution. Precise temperature calibration of these tips remains the main issue for these cantilevers. For free-standing cantilevers, various methods are available such as Stokes Raman peak shift [95], IR-thermometry [86], and others. However, when the tip is brought into contact with the surface, the temperature of the tip–surface junction changes depending on the thermal conductivity and heat capacity of the surface material. One of the possible solutions for this issue is the use of melting standards to calibrate the tip–surface temperature. The input voltage required to melt the tip into the polymer surface was measured for the polymers with different melting temperatures, providing a calibration for tip–surface contact temperature as a function of input voltage [67].

Fig. 8.12 Scanning electron microscopy image (left) and infrared microscope (right) of the heated AFM cantilevers. The image is courtesy of B.A. Nelson and W.P. King. Reproduced with permission from Sensors and Actuators A 140 (2007) 51–59

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Mathematical Models for Understanding Thermo-Mechanical Results Mathematical models for tip–surface heat transfer, mechanical response of the material to temperature gradients, and tip–surface contact mechanics are necessary for quantitative interpretation of the data obtained using the experimental techniques described above. Each of the topics listed above is broad and important enough to be a topic of a review paper, thus, only the basic concepts necessary to understand the techniques discussed above, will be presented here. Excellent papers and books have been written on the topics of tip–surface heat transfer [96–98], mechanical response of the material to temperature gradients [99], and tip–surface contact mechanics [100], and readers are encouraged to read those for better coverage of the specific topic. Several processes are happening at the same time when the heated probe is located in close proximity to the surface: • • • •

Radiative heat transfer according to the Stephan–Boltzmann law. Diffusive heat transfer. Heat transfer through solid–solid contact. Heat transfer through the water meniscus between probe and the surface.

Xu et al. determined [101] that under ambient conditions diffusive heat transfer by air is several orders of magnitude larger than radiative heat transfer. For probesurface distances smaller 100nm, heat flux transferred by air is ~4W/(Kcm2), while radiative heat flux transferred by irradiation is ~0.1W/(Kcm2) [101]. After that a group of researchers led by Majumdar started to investigate other mechanisms of heat transfer. The authors found that heat transfer rate does not depend on the indentation force and ruled out heat transfer through solid–solid contact as a possible mechanism [102]. However, the other group of researchers [103] found that for the warm Wollaston probe in contact with copper and Duralium, heat transfer through solid–solid contact is the main mechanism for heat transfer. The other hypothesis to be checked was a diffusive heat transfer, Majumdar et al. [102] varied the gas atmosphere during the experiments and found no significant change in heat transfer rate, despite the fact that the gases chosen had several orders of magnitude difference in thermal conductivity. Recently, Shen et al. found that heat transfer coefficients at nanoscale gaps (tens of nanometers) are three orders of magnitude larger than that of the blackbody radiation limit [104], which indicates the surface phonon polaritons dramatically enhance energy transfer between two surfaces at small gaps. The widely accepted model of heat transfer between probe and surface is transfer through the water meniscus. It is well known that when a sharp probe approaches the surface the water from air condenses around the contact area. The calculated heat resistance of such contact corresponds pretty well with the value measured by Majumdar et al. [102]. This leaves two main mechanisms for heat transfer: heat transfer through water meniscus and via solid–solid contact. Both of these mechanisms allow for high resolution imaging of thermo-mechanical properties, because the heating region is confined to the contact area in both cases.


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Contact Mechanics Model of Elastic Media in the Presence of a Heat Transfer Understanding of a material’s response to a temperature gradient requires knowledge about the temperature dependent contact mechanics of the tip–surface junction. From simple dimensionality arguments, the thermal response of a material, dl , is linear and related to temperature variation, dT, through the thermal expansion coefficient, a, and the characteristic tip–surface contact radius, R0, i.e., dl=adTR0. To establish the contact mechanics model, Morozovska et al. has used the decoupled approximation originally developed for Piezoresponse Force Microscopy (i.e., bias-induced phenomena), i.e., the equations of state for an isotropic elastic medium in the presence of a heat transfer. The mechanical stress tensor sij and elastic strain uij are linked as dij adT + sijkl s kl = uij , where dij is the Kroneker delta, and sijkl is the tensor of elastic compliances [105, 106]. The general equation of mechanical equilibrium, ¶s ij / ¶x j = 0, leads to the equation for the mechanical displacement vector, ui, as:

cijkl

¶ 2 uk ¶dT - cijkk a = 0. ¶x j ¶xl ¶x j

(8.1)

Here, we introduce the boundary conditions of the free surface S:

æ ö ¶uk - cijkk adT ÷ n j ç cijkl ¶xl è ø

= 0.

(8.2)

S

where cijkl is the tensor of elastic stiffness, and nj are the normal components. The maximal surface displacement (corresponding to the point x=0) below the tip is

u3 (0, t ) = -

x3 adT (ξ , t ) 1+ n dx1dx 2 dx3 . òòò p x3 > 0 (x 2 + x 2 + x2 )3/ 2 1

2

(8.3)

3

where Gijs is the appropriate tensorial Green function [105–107]. Temperature distribution is found as a solution of Laplace’s equation k 2 Ñ 2 dT (x, t ) = 0 , where the k 2 = c / cr is the thermal diffusivity of the media, c is thermal conductivity [W/(mK)], and c is the specific heat [J/(kgK)], and r is density [kg/m3] [108]. After integration, we derive

ui (0) » - (1 + n )adTR0

(8.4)

While the numerical prefactor in (8.4) depends on the choice of boundary conditions (zero temperature, zero flux, or mixed) on the free surface, the overall functional form is universal as dictated by dimensionality considerations. Physically, there are two limiting cases for boundary conditions: zero temperature outside of the contact (provides smallest values of strain) and zero flux outside of the contact (provides largest values of strain), which give the prefactors in (8.4) of 1 and p/2, respectively.

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For all other boundary conditions, the prefactors in (8.4) will lie in the 1-p/2 range. If the mean value of the prefactor range is chosen, the model error will not exceed 30%, which is comparable to the experimental error of ~10% (especially given the uncertainty in contact radius). The choice of a static (zero frequency) regime is justified by the fact that the temperature drops exponentially with distance from the contact [109]

T (r ) = T0

æ æ æ rcont w ö w öö exp çç - (r - rcont ) ÷÷ exp çç i çç wt - (r - rcont ) ÷ ÷ (8.5) r 2k ø 2k ø÷ ø÷ è è è

The characteristic thermal length is determined to be either d = 2k / w or the contact radius (whichever is smaller), where w is the frequency of incoming heat waves. For the typical polymer material (e.g., PET), the characteristic length at experimental frequencies (~500kHz) is about 500nm, much larger than the contact radius of the tip (~10–100nm). Thus, the major temperature drop happens at the distances between one and two contact radii from the center of the tip and the imaging is essentially near-field for thermal strain waves within the material. Hence, the measured thermo-mechanical response is directly related to contact radius which, in turn, is determined by the indentation force and Young’s modulus.

Contact Mechanical Model for Deconvolution of the Mechanical Properties of Samples from Parameters of Tip–Surface Contact Resonance Young’s and loss moduli as a function of temperature can be determined from temperature dependencies of quality factor and resonance frequency of the tip–surface junction [53]. The decrease in quality factor and resonance amplitude of the tip– surface junction is an indicative of polymer softening and subsequent melting. When the polymer melts, the Q factor for mechanical resonance decreases due to viscous damping in the molten polymer (Fig. 8.10a, b). A simplified model of the tip–surface junction is presented in Fig. 8.6c. The spring constant, k1 is the stiffness of free cantilever, m is the effective mass of the cantilever, k2 is the tip–surface contact stiffness, and c is the viscosity of the polymer. The change in resonant frequency can be attributed to either changes in the effective dissipation [110] or effective material properties. For a damped oscillator, the resonant frequency decreases with the decrease of Q as

fres = f0 1 - 1 / Q 2

(8.6)

Equation (8.6) predicts a 0.3% decrease in the resonant frequency during the heating cycle (taking Q values from Fig. 8.6b), as compared to the experimentally observed


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10% decrease in resonant frequency. Therefore, the decrease in resonant frequency is ascribed to a decrease in the contact resonance stiffness only. Using the approximate formulae [111, 112], different contact resonances can be used to calculate contact stiffness as a function of frequency:

æ k ö f resi @ ç1 - bi 1 ÷ f 0BOUND k2 ø è

(8.7)

where fres is the resonance frequency of tip–surface contact, i is the order of the resonance, f0BOUND is the resonance frequency of the tip in contact with an infinitely stiff surface (this parameter depends only on the cantilever), k1 is the spring constant of the cantilever, and k2 is contact stiffness. The coefficients for the first five contact resonances are calculated (b1=7.7, b2=36.5, b3=80.4, b4=144.9, b5=230.8, …) based on the numerical analysis of contact resonance developed by Mirman [113]. Estimating a constant area between the tip and surface (with the radius a=50nm) and taking the Young’s modulus for PET at room temperature as E=3GPa and k2=2aE, we extract the relative change of the contact stiffness for the tip–polymer contact as a function of temperature, as shown in Fig. 8.10d. In this analysis the assumption was that the spring constant of the cantilever was temperature independent. Notably, this assumption holds within 20% error, as shown by Lee and King [114] who performed a thermal actuation of the silicon heated cantilever and found that the resonant frequency of the oscillations changes 1):

c@

m(k1 + k2 ) æ 3ö ç2 - ÷ Q Q è ø

(8.8)

Figure 8.10d shows the dependence of c as a function of temperature assuming tip mass m=2.2×10-9kg (re-calculated from w0BOUND ) and k1=1N/m. The two transitions at ~80°C and 250°C that are seen after the first heat/cool cycle are presumably associated with the re-crystallization and melting which occurs after first heating. Thus, temperature dependencies of Young’s modulus and the damping coefficient can be used for determination of local glass transition and melting temperatures of the polymeric materials.

Technique Development Prospects and Limitations In order to understand the positioning of the local thermal analysis technique within the group of techniques used for mechanical analysis, we compared the spatial resolution and sensitivity of the displacement measurements provided by various techniques

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used in mechanical analysis (local thermal analysis (LTA) with Wollason probe [51], silicon heater [90]; local thermal analysis with silicon heater and band excitation detection (NanoTA, current work); dynamic mechanical analysis (DMA) [115]) with the resolution and sensitivity required for the solution of practical problems in different industrial applications, such as analysis of pharmaceuticals, organic layers in OLEDS, lithography masks, and mechanical properties of surfaces (auto, optics, etc.), as well as for the understanding of basic scientific problems such as thermomechanical motion of single molecules (Fig. 8.13). The spatial resolution and sensitivity of the technique discussed in this paper are estimated below. Recently, it was shown [67] that the spatial resolution for the local thermo-mechanical measurements in general and Tg measurement in particular is limited by the tip–surface contact radius, which is usually ~10nm. The vertical sensitivity level in static AFM (e.g., contact mode) is estimated as ~0.1nm (experimental noise limit for conventional photodetectors). For ac-detection methods based on amplitude or frequency

Fig. 8.13 Comparison map for precision in displacement measurements achievable with different techniques of thermal analysis as a function of spatial resolution overlaid with precision in displacement measurements and spatial resolution desired by different industries. Precision in displacement measurements is often limited by thermal noise, thus, low temperature (4 K) diagram draws the limits for ultimate resolution of the local thermal analysis techniques


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detection, the vertical sensitivity as limited by the thermo-mechanical noise [116] is dltm » 2 kBTB / kw r , where kB – Boltzman constant, T is the temperature, B is the measurement bandwidth, K is the cantilever spring constant, and wr is the cantilever resonant frequency. This yields the relationship between resolution and sensitivity as

dl » - (1 + n )adT . For a typical polymer linear expansion coefficient (a) 5×10-4/K, R0 Poisson’s ratio is about 0.34. For the typical cantilever parameters, k~1N/m, wr ~ 2p 300kHz (contact resonance frequency), and B~1kHz (typical experimental bandwidth). At room temperature (300K), the thermo-mechanical noise will be on the order of 3pm, lowering temperature to 4K results in an order of magnitude decrease of thermo-mechanical noise (dl~0.3pm). We have reviewed several techniques for high spatial resolution analysis of the mechanical properties of samples as a function of temperature, with the main area of applications being the thermo-mechanical analysis of polymeric materials. Clearly, significant opportunities and challenges for development of the technology must be met before the field reaches maturity and widespread adoption. On the data analysis side, better mathematical models are required for modeling thermal expansion response to local heating, specifically frequency dependencies of thermal expansion for different indenters, better understanding of the heat transfer mechanism between tip and surface etc. On the experimental side, heated probes with better mechanical stability and better reproducibility of the mechanical properties would be highly desired. The probes currently available have significant drift in the mechanical properties during thermal cycling. Extension of thermo-mechanical measurements towards calorimetric measurements seems to be a logical direction for technique development. However, in ambient air, the main heat transfer mechanism between probe and the surface is heat transfer through the surface liquid film, which precludes these experiments being performed quantitatively in air. The shape and properties of the liquid meniscus forming between the tip and surface depend on many external conditions such as temperature and humidity, which are often difficult to control. This makes the contact thermal properties extremely irreproducible. Thus, under ambient conditions, scanning calorimetry is very tricky; however, in low vacuum, where the liquid meniscus between tip and surface is eliminated, scanning calorimetry might work. Finally, the resolution of thermo-mechanical techniques is limited to the tip size, which is about 10nm. This resolution allows scientist to study fundamental processes of phase transitions in polymers (glass transitions, melting transitions) at physically relevant length scales in the polymeric materials, i.e., the size of Kuhn’s segment. Acknowledgements Research at Oak Ridge National Laboratory’s Center for Nanophase Materials Sciences was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy.

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Part IV

Electrical and Electromechanical SPM

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Chapter 9

Advancing Characterization of Materials with Atomic Force Microscopy-Based Electric Techniques Sergei Magonov, John Alexander, and Shijie Wu

Scanning Probe Microscopy in its Development Modern materials science is focused on development of novel materials and functional structures for a number of fast progressing industries (semiconductors, data storage, biomaterials, health care, and others) where miniaturization plays the dominant role. This tendency influences not only synthesis of materials and technology of structure fabrication but also a development of analytical methods applied for materials characterization at small scales. In recent years an increasing number of analytical methods have been introduced for comprehensive analysis at the micron and nanometer dimensions. Of particular interest is scanning probe microscopy (SPM) – a family of methods allowing visualization of surface structures and examination of their mechanical, electromagnetic, optical, and other properties at such scales. The invention of scanning tunneling microscope in 1981 [1] was the starting point of SPM, which attracted many researchers by fascinating capabilities of visualization surface structures from the macroscopic down to the atomic-scale. The history of SPM is curious in itself. The revolutionary move was to use prior known technologies, such as profiler [2] and topographiner [3] in studies at the atomic scale in STM and its offspring – atomic force microscope [4]. The core of SPM is the measurement and control of current and force interactions between a minute probe and a sample surface. Actually, atomic force microscopy (AFM), which is based on the probe–sample force detection and is not limited by sample conductivity, became the leading SPM method. The exciting features of these methods are their applicability to a broad range of materials and operation in different environments: vacuum, air, gases, liquids, and at different temperatures. The introduction of AFM was accompanied by several important developments such as the use of optical deflection detection [5, 6], and oscillatory modes [7, 8], especially allowing the imaging of soft materials in air [9]. The batch fabrication of AFM probes made of Si3N4 and Si [10, 11] was also the important step in establishing this technique as a routine characterization tool. The progress of SPM S. Magonov (*) Agilent Technologies, 4330 W. Chandler Blvd, Chandler, AZ 85226, USA e-mail: [email protected] S.V. Kalinin and A. Gruverman (eds.), Scanning Probe Microscopy of Functional Materials: Nanoscale Imaging and Spectroscopy, DOI 10.1007/978-1-4419-7167-8_9, © Springer Science+Business Media, LLC 2010

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instrumentation and enthusiastic motivation of many researchers who joined this field have stimulated the broadening of AFM applications and its fast spread from academic labs to industrial environment. Through practical applications it became clear that true AFM value extends far beyond its basic capability of high-resolution visualization of surface structures. The AFM probe, which is a microfabricated cantilever with the sharp tip at its end, is actually a highly sensitive detector of mechanical, electromagnetic and other tip–sample interactions. The probe responds differently at sample locations or components with dissimilar properties (mechanical, electromagnetic, etc.) that provides the basis of AFM compositional mapping of heterogeneous and multicomponent materials. For many complex polymer materials the AFM phase images obtained in oscillatory amplitude modulation (AM) mode provide the best contrast differentiating individual components. Naturally, the probe sensitivity to different materials’ properties raises a question about its possible use for local quantitative measurements of these properties. This refers not only to the examination of local mechanical properties (e.g., by making AFM-based nanoindentation measurements), but also to the studies of various electric and magnetic properties. There is a large amount of data illustrating the AFM sensitivity to these properties, yet the rigorous approaches towards reliable quantitative measurements have not been fully developed. It happened that for a number of years the development of SPM instrumentation was in relative stagnation and the growth of practical applications was not adequately supported by instrumental innovations. Nowadays this trend is changing and the progress is noticeable in several areas. The ongoing improvement of noise characteristics of AFM electronics, the microscope overall performance (e.g., by minimizing thermal drift), and manufacturing of sharper probes will enhance the capabilities of high-resolution imaging in different environments. Particularly, the improved home-built microscope allows extending the frequency modulation (FM) mode, which is commonly used for atomic-scale imaging in UHV [12, 13], to measurements in air and under liquid, where imaging with molecular and atomic resolution was demonstrated [14]. Similar efforts are needed to make molecular-scale measurements in air and liquid the routine features of the commercial microscopes. When these capabilities become available to a large number of researchers we might expect a better understanding of the true atomic-resolution imaging in AFM. In the probing of local mechanical and electric properties, the multifrequency measurements offer new capabilities of characterization of materials in the broad frequency range and, particularly, for quantitative analysis of these properties. AFMbased mechanical studies are traditionally performed in the quasistatic regime when a probe is positioned at one location and is moved towards and into the sample. In this procedure, the cantilever deflects in response to elastic, plastic or viscoelastic tip–sample interactions [15] and such deflection-versus-distance (DvZ) curves – the analog of stress–strain dependences are used for the extraction of quantitative mechanical properties of the sample. The tip indentation is usually performed in the rate of 0.1–10 Hz. This measurement can be performed on many locations, and the resulted map of the mechanical response might have the nanometer spatial

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resolution if thermal drift of the instrument is low. Latest progress showed that reliable quantitative data can be obtained in this way [16] yet such measurements are relatively slow and cover only a relatively low frequency range. The expansion of mechanical measurements to higher frequencies has been recently demonstrated by fast detection of the DvZ curve practically during every cycle of the probe oscillation in the AM mode. This can be done either through the reconstruction of the probe response at large number of harmonics (multiples of the main cantilever resonance) [17] or directly by using the grating-type probes [18]. Therefore, the way for quantitative nanomechanical measurements in the broad frequency range (up to 100kHz) is demonstrated and the practical results are accumulating. Besides local mechanical measurements, AFM has excellent capabilities for measurements of electric and magnetic properties of samples and their mapping with high spatial resolution. The response of the AFM probe to the electrostatic tip–sample forces was examined shortly after the introduction of this technique [19]. The main issue of the sensing of the electrostatic forces by the probe is related to the fact that during AFM imaging the probe behavior is influenced by mechanical and electrostatic forces simultaneously. Therefore efficient separation of these effects is essential for reliable measurements of the local electric response. For this purpose the use of different frequencies was suggested long time ago and this operation was performed in the non-contact mode that limits the spatial resolution of such electrostatic measurements. When the electrostatic force and mechanical tip–sample interactions are detected at single frequency then the lift method [20] was suggested for the separation of their responses. The main limitation of this approach is a remote position of the probe while recording the electrostatic force response. As a result the spatial resolution of these measurements is rather restricted. With development of the multifrequency SPM, novel approaches in probing of local electric properties can be suggested and verified. Recent results obtained in the electric force microscopy (EFM), Kelvin force microscopy (KFM), and piezoresponse force microscopy (PFM) with a commercial microscope equipped with three lock-in amplifiers that allows simultaneous measurements at different frequencies are presented in this Chapter. Novel schemes of these techniques will be described below. The value of these methods will be illustrated by experimental results obtained on different samples. Such direct interplay between the instrumental developments and their practical evaluation is indispensable for AFM advancement. The chapter consists of three parts. The first deals with different AFM approaches in measurements of electrostatic and electromechanical surface properties, overview of EFM and KFM applications, and discussion of the outstanding issues of these techniques. In the second part a practical implementation of EFM and KFM measurements will be described and novel approaches to electrostatic measurements will be introduced. The use of PFM for examination of electromechanical sample properties will be described shortly. Several issues regarding experimental procedures and choice of the probes will be also discussed. The third part presents a number of recent results obtained with EFM, KFM, and PFM on semiconductor materials, metal surfaces, and organic adsorbates on different substrates.

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Electrostatic and Electromechanical Interactions in Atomic Force Microscopy Tip–sample force interactions are the basis of AFM and related modes, which are used for the examination of surface topography as well as local mechanical, electromagnetic, and other properties. These forces of different origin cause displacements of the same microfabricated AFM probe in quasistatic (contact) and dynamic modes applied in this method. The dynamic modes are more applicable to a broad range of materials including soft polymer and biological specimen. Studies of electric properties are performed using both types of techniques. The quasistatic or contact mode is preferable for measurements of electromechanical response of piezo-materials known as PFM, which will be discussed later. The contact mode and consequently, PFM is limited in applications to soft materials due to excessive lateral forces common to the tip scanning in a permanent contact with the sample. This drawback is overcome in the oscillatory techniques, which are also employed for studies of electrostatic tip–sample force interactions in EFM and KFM. In addition to the mentioned AFM-based modes, which are discussed in this chapter, there are also scanning capacitance microscopy, scanning current sensing microscopy and scanning microwave microscopy – all operating in the contact mode. The oscillatory techniques in AFM are implemented as the amplitude modulation (AM) [3] and frequency modulation (FM) [4] modes, which complement each other in study of samples in various environments. In AM the probe is brought into oscillation near or at its resonance frequency and the damping of amplitude, which is measured as difference between the probe oscillation A0 (before it interacts with a sample) and the set-point amplitude Asp is used for sensing the surface topography. Initially, this mode was implemented at small damping caused primarily by the attractive part of van der Waals tip–sample force interactions – often described as a non-contact operation. The breakthrough in AFM applications was made with the introduction of AM imaging in the intermittent contact [9], which is characterized by a steep decline of amplitude-versus-separation (AvZ) curves. Although the AM operation at set-point amplitudes (Asp) along the steep part of the AvZ curve, which is also known as the tapping mode, is characterized by higher tip–sample forces compared to the non-contact mode, this operation allows a non-destructing and high-resolution imaging of soft materials in ambient conditions. Furthermore, a reduction of Asp leads to stronger tip–sample forces and local sample deformation and energy dissipation. These effects, which depend on mechanical properties of surface locations, allow compositional mapping of heterogeneous samples best revealed in phase images [21]. Theoretical description of the probe behavior in dynamic modes was based on first principles and mechanical setting of the AFM [22, 23]. The probe motion was described by Euler–Bernoulli’s type of equation, and a relationship between the empirical “effective” parameters of mass–spring models and the properties of cantilever and mechanical characteristics of the AFM was formulated. Krylov– Bogoliubov–Mitropolsky (KBM) averaging method [24] was used to derive asymptotic dynamics with amplitude and phase as the state variables.


sin q =

cos q = −

1 p A  ∫ [Fa − Fr ](ZC + A cos y ) sin ydy +  A0  2 N  2g   0 1+    w1  1

1

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(9.1)

1 p 2g A   ∫ [Fa − Fr ](ZC + A cos y ) cos ydy +  (9.2) w1 A0  2 N   0

 2g 1+    w1 

where N = πA0w12 m and A0 is the amplitude of the non-interacting probe, w1is the initial (usually resonant) frequency of the probe, and mis the mass of the probe. In these equations there are four unknowns: A is the amplitude during tip–sample interaction, q is the phase of the probe, g = (w − w1 ) / e = Q1 (w − w1 ) is the frequency shift, and Z C is the vertical position of the probe. Other parameters are either known or those that can be measured separated or reasonably approximated, e.g., Fa and Fr are the functions defining tip–sample interaction forces during the probe approach to the sample surface and its removal, respectively. The latter depend on the particular surface locations and can be approximated using different models such as van der Waals, Hertz, JKR or DMT. Keeping two of four unknown variables constant (and re-solving other two by the equations for steady state) determines six potential dynamic AFM modes, of which four are widely used. They are AM and FM with force spectroscopy and imaging operations. In AM mode, frequency shift g = Q1 (w − w1 ) is kept constant (usually 0) and the force spectroscopy curves AvZ and qvZ are calculated for solving the above equations for each surface location. In the imaging operation one should take into account that the tip–sample force interactions ( Fa and Fr ) might change in every surface location (XY). Therefore, the images in AM mode, which reflect the changes of Z (topography or height image) and the changes of q (phase images) at XY positions, are obtained by solving the equations for amplitude A fixed at the set-point level (Asp). In FM mode, the phase q is kept constant (usually as p/2) and the force spectroscopy curves AvZ and wvZ can be calculated by solving the equations for each surface location. The images in this mode (Z versus XY – topography image and A versus XY – amplitude image) are calculated for constant frequency shift dw = w − w1 . This theoretical consideration shows that the AM and FM modes are close to each other and they bring similar information about the sample. Actually, the presented approach is further applied in the AFM simulator that is very helpful for practitioners in verifying their experimental results by computer modeling of the images of structures with probes of different stiffness and various apex size [25]. Furthermore, the addition of the electrostatic tip–sample interactions can increase the value of this simulator. Parallel to the development and practical applications of the intermittent-contact AM mode at ambient conditions, its companion – FM mode [8] has been broadly

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applied in AFM studies in UHV and, particularly, for imaging of atomically smooth crystalline surfaces. Monitoring of the frequency shift caused by tip–sample forces is the winning procedure in UHV, where extremely high quality factor of the probe limits AM capabilities. FM imaging is usually performed in the overall attractive force range by keeping the frequency shifts below the resonant frequency of the non-interacting probe. The fine control of tip–sample interactions in FM mode helps reaching atomic-scale imaging with the “lattice-plus-defect” observations of crystalline surfaces [12, 13]. Later the similar observations were reported in FM studies in air and under liquid [14, 26] as well as in ambient AM measurements [27], yet the question regarding true atomic-resolution in AFM is still open [28].

Detection of Electrostatic Responses in AFM Already in the first AFM applications, AM was applied for detection of electrostatic tip–sample interactions, which are enhanced when a conducting probe is used [19]. A scheme of detection of electrostatic forces includes a conducting probe which is biased with respect to a back electrode or substrate carrying a sample on top, Fig. 9.1. U = U DC + U AC sin (wt )

(9.3)

In a simplified form of the capacitor-like set-up the contribution of electrostatic force is proportional to j 2 and ∂C / ∂Z, where j is the potential difference, C is the capacitance, and Z is the probe–sample separation. Felec (Z ) =

1 ∂C 2 j 2 ∂Z

(9.4)

When DC (UDC) voltage and AC (UAC) voltage at frequency w, are applied to the probe then the electrostatic force can be expressed as 2 1 ∂C (9.5) (j − U DC − U AC sin(w t )) 2 ∂Z  where j is the surface potential or contact potential difference between the probe and the sample. This equation can be separated into three components definingthe DC and frequency responses:

Felec (Z ) =

Fig. 9.1 A set-up for measurements of electrostatic forces in atomic force microscopy


FDC (Z ) = Fw (Z ) = −

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1 ∂C 1 2 (j − UDC )2 + 2 UAC 2 ∂Z

(9.6)

∂C  (j − U DC )U AC sin(w t )   ∂Z 

(9.7)

1 ∂C 2 U cos (2w t ) 4 ∂Z AC

(9.8)

(

F2w (Z ) = −

)

In the attempt to record surface topography and electrostatic forces simultaneously and independently the AFM measurements were performed at two different frequencies [19]. The AM detection at the probe resonant frequency (wmech) was employed for topography imaging. At the same time, an AC voltage was applied to the probe at welec, which was chosen well below wmech, and the cantilever deflections at this frequency were used for detection of the electrostatic tip–sample interactions. Additionally, the force variations were observed at 2welec. The experiments showed that the probe responses at welec and 2welec were in-line with a model representing the probe–sample geometry as a capacitor. In general, any of the probe responses (amplitude, frequency or phase) at welec can be measured in EFM and used for mapping of the electrostatic force variations. A quantitative analysis of EFM data in terms of individual electric properties (such as surface potential, capacitor gradient, charge, dielectric constant) is the very complex problem [29]. It can be simplified when surface potential is of the prime interest. In KFM, the electrostatic tip–sample forces are nullified by applying an appropriate voltage to the probe [30, 31]. This voltage equals to a difference of surface potentials of the tip and a nearby sample location. Though surface potential is usually used in studies of semiconductors and metals, a charge deposited on dielectric sample or presence of dipoles also influence surface potential of organic compounds, polymers, etc. Therefore, KFM is applicable to a broad range of materials. The value of EFM and KFM has been proved in measurements of surface potential, dielectric constants, and local surface charges [31–34]. Such measurements were conducted in non-contact FM mode in UHV, and the first flexural mode was applied for tracking a sample topography, whereas the second flexural mode [35] or a frequency much lower than wmech was used for KFM feedback [36]. There is also another possibility to map electrically different sample locations using an intermediate of EFM and KFM. Instead of nullifying the electrostatic force by applying the voltage that equals to surface potential, the feedback can be used to maintain the electrostatic force at some constant level. In this case, according to the (9.4), the map of UDC reflects spatial changes of j and ∂C / ∂Z . When surface potential does not change over the examined area then the UDC map represents the ∂C / ∂Z variations, see the example below. In the alternative case the subtraction of the surface potential data (obtained in the KFM operation) from the −1 UDC map will be proportional to the (∂C / ∂Z ) variations. Studies of the electrostatic force effects should not be limited by KFM, and they can be diversified by using the 2welec response for the feedback mechanism [37–39]. In such a way one can get information regarding local dielectric constant and its

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high-frequency dispersion [37]. Simultaneous measurements of sample topography (wmech=70kHz), surface potential (welec) and dielectric or polarization response (2welec) were performed while the probe was scanning ~30nm above the sample surface [39]. Important questions regarding a way of detection of the electrostatic forces, a choice of mapping procedure, and a cross-talk between electrostatic response and sample topography were raised already in first AFM-based electric studies. There was also a strong intention to use the non-contact regime where the probe response to electrostatic forces is not disturbed by tip–sample mechanical interactions [19]. Since 1993 the intermittent contact regime in AM in air became very popular due to highresolution imaging of soft samples. This operation, however, imposes definite limitations for simultaneous and independent measurements of surface topography and electrostatic responses, especially, when the measurements are performed at the same frequency. An easy solution of this problem was provided by the two-pass technique or lift mode [20], which was originally introduced to tackle the similar problem in magnetic force microscopy. In this approach, for each scan line, the height profile is recorded during the first pass with probe oscillating at wmech. At the end of the first pass the probe is lifted typically 5–50nm above the surface. After that the AM feedback is switched off, and the probe is moved along the just-learned profile but at the constant lift above the surface. During this second pass, the DC bias voltage is applied to the probe oscillating at wmech. The changes of the probe frequency or phase, which are caused by electrostatic probe–sample forces, are monitored and mapped in EFM. In KFM these changes are nullified to obtain surface potential images. Though the lift operation has been routinely applied for local electric measurements [40], a more strict consideration of this operation reveals several problems. Imaging of surface topography in the first scan even with a non-biased and a non-metallic probe can be already “contaminated” due to electrostatic interactions between the sample locations and Si probes, which are electrically conducting to some level. The use of the same wmech for detection of mechanical and electrostatic tip–sample interactions demands a finding of an appropriate lift height to avoid the cross-talk between topography and electrostatic force variations, especially for corrugated surfaces. The moving the probe away from the surface in the second pass reduces sensitivity and resolution of the electrostatic detection. The use of the two-pass approach not only increases the experiment time but also limits studies of dynamic processes related to electrostatic forces.

KFM Applications Despite a number of open questions in AFM-based electric modes, their applications have been fast developed and they include studies of semiconductor structures and devices, quantum nanodots, organic layers and biological objects. Visualization of doped pn-structures covered by 2-nm Si oxide layer [41] is instructing for KFM imaging of semiconductor structures. In measurements performed at 54% humidity the surface potential of p-regions was 18mV higher than that of n-regions. Yet this difference depends strongly on hydrophobicity of the oxide surface because


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of potential shielding by the surface water layer. In addition to this effect, a possible sample contamination during imaging in air influences quantitative surface potential measurements, which are more reliable in UHV studies or in the properly controlled environment. KFM studies of the carbon nanotube/Au junction in different environments showed that the interfacial dipole layer changes direction when measurements were transferred from ambient air to vacuum or oxygen-free media [42]. Highresolution surface potential images of individual quantum dots (QD) with spatial dimensions in the 22–46nm range were obtained in UHV [43]. The surface potential of QD with smaller height was larger than that of higher ones. This finding was interpreted in terms of the quantum size effect by which the amount of charges is determined through the confinement energy levels in the QD. KFM studies of organic thin-film transistors in different configurations led to mapping of surface potential in the accumulation layer [44]. Particularly, it was shown that the potential changes take place at the film interfaces between source and drain elements [45]. A correlation between surface photovoltage and polymer blend morphology has been examined in polyfluorene-based photodiodes [46]. In the bilayer geometry, two polymers, which serve as holes-rich and electrons-rich reservoirs, adopt a complex morphology with domains of different charges. These domains were observed with KFM images under illumination and in dark that indicates on steric hindrances to the charge recombination and lower photodiode efficiency. In further KFM approach to photovoltaic materials, this method was applied to the 100-nm film of an organic blend consisting of soluble fullerene derivative (acceptor) and paraphenylene-vinylene (PPV)-based polymer [47]. The 100-nm thick films of this blend, which were prepared by spin-casting of its solutions on ITO substrate, have been examined in dark and illuminated states. The differences of surface morphology and surface potential maps were found in the films cast from toluene and chlorobenzene solutions. A smooth morphology was found in the chlorobenzene-cast film and its surface potential decreases from 4.55 ± 0.06V to 4.22 ± 0.06V. The toluene-cast film was rougher with well-defined hills and valleys, whose surface potentials were 4.51 ± 0.04V and 4.43 ± 0.04V, respectively. There was a minor population of the hills with lower potential of 4.39 ± 0.05V. In response to illumination, these hills did not change their potential, whereas the surface potentials of other hills and valleys increased to 4.66 ± 0.05V and 4.46 ± 0.05V. The obtained results together with TEM findings indicate that the hills are composed of PCBM-rich material and the surrounding matrix consists of both components were useful for understanding the photovoltaic behavior of the films prepared from different solvents. Conducting polymers, which are important materials for molecular electronics and solar cells, are attractive objects for KFM studies. A correlation between surface potential and sample morphology has been examined at various doping levels of poly-3-methylthiophene [48]. The surface potential images of similar semicrystalline polymer – poly(3-octylthiophene) revealed different contrast not only between amorphous and crystalline components but also between sectors of crystallites [49]. The potential variations in the segments are in the 40–60mV range and, most likely, they reflect different molecular dipole orientation in these crystalline domains.

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In KFM studies of organic films and layers on various substrates one can observe surface locations with different surface potential, which are interpreted in terms of layer architecture and molecular dipole arrangement within the layers. KFM studies of fluoroalkanes, alkylthiols, and organosilanes are most relevant to our results presented below. Study of a mixed monolayer of perfluorodecanoic acid (FC) and arachidic acid (HC) polyion, which formed a complex with (poly(4-methylvinyl pyridinium)) iodide, revealed that the phase-separation in this system led to the “islands” and “sea” morphology with different surface potential in these locations [50]. The KFM contrast was assigned to differences of surface dipoles of Cd+–Fb- and C–H bonds of the FC and HC components. The same morphology was observed in molecular layers of C19H39COOH and C9F19COOH mixture on Si substrate [51]. For this system, the difference between surface potentials of the “islands” and “sea” was 0.057 V that is substantially smaller than surface potential (~0.5V) of the layers made of the individual components. Therefore, the presence of a low surface potential capping layer was suggested. Surface potential of 0.007V, 0.17V, and 0.25V was measured respectively for single, double, and triple bilayers in Langmuir–Blodgett layers of arachidic acid (AA) on hydrophobic Si surface. In these measurements surface potential of the substrate (~-0.98V) versus Au-coated probe was taken into account. The same measurement for an oxidized Si gave the value of -0.76V. Surface potential of the single, double and triple bilayers of AA on the oxidized Si surface was -0.17V, -0.16V, and -0.11V, respectively. In the convention used by the authors, a negative surface potential is consistent with dipole orientation having negative charge closer to the surface. Dissimilar types of the AA layers’ organization on hydrophobic and oxidized Si substrates were suggested on the base of the KFM data [52]. A micro-printed pattern with alternative domains of alkylsilane [H3C(CH2)17Si(OCH3)3] – ODS and fluoroalkylsilane [F3C(CF2)7(CH2)2Si(OCH3)3] – FAS on Si has been prepared as a test structure for KFM [53]. The highest-contrast surface potential images, which differentiate fluorinated material (DV=171mV), were obtained when high AC voltage (15V) at 25Hz was applied for electrostatic force detection and when recording was made at slow scanning rates (down to 0.1Hz). The origin of the surface potential difference between alkylsilane and fluoroalkylsilane domains was discussed in terms of dipole moments of the QDC and FAS molecules estimated from the molecular orbital calculations. An estimate of the surface potentials of the layers based on the dipoles of individual molecules (OD – 1.18D, FAS – 1.47D) and their orientation gives a much stronger DV compared to the measured one. Therefore, several other factors such as intermolecular interactions, screening, and depolarization effects should be considered for the rational interplay between the experimental and theoretical results. A condensation of dipalmitoylphosphatidylcholine (DPPC) monolayer on water sub-phase in Langmuir–Blodgett trough from an expanded state to a mixture of liquid expanded (LE) and liquid condensed (LC) phases and to solid condensed (SC) state was monitored with KFM [54]. The single layers, which were transferred to Al-coated glass substrate, exhibit surface potential which is 270mV higher than that of bare Al. Surface potential of the layers increases 50–100mV on transition from LE to LC phase and 300mV on transition from LC to the SC state. The increase of molecular


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density was adequate for explanation of the changes of LE and LC potentials whereas the steep potential raise in the SC phase resulted from a compression-induced change of the effective dipole near the polar head group of lipid molecules. Several research groups have examined surface potential of molecular layers of alkanethiols and their various derivatives and its dependence on length of molecular chain. With respect to Au-coated probe surface single layers of hexadecanethiol HS-(CH2)15-CH3 and mercaptohexadecanecanoic acid HS-(CH2)15-COOH chemisorbed on gold substrate exhibit potential of ~0.181V and 0.392V, respectively [55]. Variations in the chain length of both compounds (n=11-22) led to the potential increase of 14.1±3.1mV per (-CH2-) unit. These findings were further confirmed for alkanethiol couples C8/C12, C10/C12, and C12/C14 [56]. Furthermore, a sample of octadecanethiol monolayer partially covering a gold substrate was used for comparison of force- and frequency-based detection of tip– sample electrostatic interactions. Pt-coated Si probes were used in this study [57]. The frequency-based spectroscopy (d2C/dz2 versus piezo displacement) and surface potential images were more sensitive and clearly revealed the difference of surface potentials of the C18 layer (-680±10 mV) and the gold substrate (-540±10 mV). The correlation between the molecular structure and distribution of electron density leading to charge and dipole formation on one hand and the experimentally determined surface potential, dielectric properties, etc. – on other hand is the principal question determining the KFM value. Only initial efforts are made in this direction. Self-assembled molecular layers of various aromatic thiols on gold were examined with KFM and compared with calculated dipole moments of these molecules. Even these simplified estimates (without considering molecular packing and Au–S bonding) help to understand the surface potential data. First of all, the layers formed by aromatic thiols with symmetric molecular structure exhibit very small potential (few tens of millivolts) compared to that (150–240 mV) of the layers of non-symmetric molecules. This is consistent with difference of dipoles for these molecules (0 Debye for symmetric molecules and 0.9–1.0 for non-symmetric). Second, the fit between the experimental and theoretical data implies that Au–S bonding does not cause strong charge rearrangement in the attached molecules. Finally, an addition of electron acceptor to the layer formed by symmetric aromatic thiols induced strong negative potential due to a formation of charge–transfer complex.

Challenges and Solutions Despite the obvious progress in electrostatic AFM modes, the issues regarding the practical implementation of EFM and KFM, spatial resolution of these modes, sensitivity and reliability of surface potential studies are under intense scrutiny. As already mentioned the separation of the probe responses to mechanical and electrostatic interactions is the main problem of AFM-based electric modes and the measurements and control of these forces can be performed in different ways. We will follow the notation introduced in [58] where experimental KFM approaches were

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named according to the modes applied for detection of the mechanical and electrostatic responses. For example, the AM–AM approach means that both force responses were recorded using amplitude modulation mode. Actually, this approach, in which the mechanical interactions are recorded at (or near) the resonant frequency of the probe and the electrostatic forces, at lower frequency, is the most common in the applications discussed above. These measurements are typically conducted in the non-contact mode, and they efficiently separate the mechanical and electrostatic effects. However, the detection of electrostatic force on a non-resonant frequency is not very sensitive. The use of the second Eigen mode, which is ~6.3 times higher in frequency than the main flexural mode, might improve this instance. The situation is different in the single-frequency measurements that are performed in combination with the lift mode. The detection of the electrostatic response in the second pass is performed by monitoring the frequency or phase changes at the probe resonant frequency and this mode can be described as AM–FM. Yet the remote position of the probe from a sample during the electrostatic measurements is the serious drawback of this approach limiting its spatial resolution [59]. In the non-contact AFM, which was originally applied mostly in UHV, the topography control is performed in FM mode and the FM–AM and FM–FM approaches can be used for KFM studies. In the FM–AM mode, the use of the second Eigen mode for electrostatic measurements is preferable. In FM–FM method the electrostatic force is stimulated at a non-resonant frequency but in the bandwidth of FM detection. Therefore the electrostatic response is detected as a modulation of the resonant frequency. It is worth noting that KFM measurements in UHV on clean crystalline surface demonstrated the contrast variations at the atomic-scale [60] that is way better than the spatial resolution of tens of nanometers common for ambient studies. A thorough consideration of the imaging procedures, optimization of probe, and data interpretation in AFM-based electrostatic measurements was given in [61]. The authors estimated the contributions of a cantilever, tip cone, and tip apex to the electrostatic probe–sample force and force gradient and came to conclusion that high spatial resolution can be achieved when the tip–apex contribution will be dominating. This condition can be realized by using probes with special geometry (the probes with long and sharp tips) or by employment of the force gradient detection. The other possibility – the imaging at tip–sample distances 20 nm can be reliably detected [71]. Ferroelectric materials have potential application in ultrahigh-density rewritable data storage systems. A data storage system based on a thin film of ferroelectric single-crystal lithium tantalite has been demonstrated at a data density above 10.1Tbit/in.2 with 500ps domain switching speed [72]. The high spatial resolution of PFM provides a unique opportunity to study the fundamental process of domain switching, including the thermodynamics and kinetics of domain nucleation, growth, and relaxation [70]. PFM has also been used to study the switching dynamics of ferroelectric capacitors. The fast domain switching kinetics using a step-by-step switching approach was investigated in [73]. PFM visualization of the domain switching process revealed that for larger capacitors, two distinct stages of polarization reversal can be observed: a fast switching stage (1ms) via lateral domain wall motion; while for small capacitors the process is dominated by domain wall motion. Consequently, large capacitors switch faster in low-field while small capacitors switch faster in high field. By analyzing local hysteresis loop measured by PFM, important information about the piezoelectric properties of small ferroelectric domains can be obtained, including coercive voltages, nucleation voltages, forward and reverse saturation and permanent responses, as well as the effective work of switching defined by the area included in the hysteresis loop. Simultaneously recorded VPFM and LPFM nanoscale hysteresis loops were used to differentiate 90° domain switching from 180° domain switching [74]. Furthermore, the dependence of PFM on crystallographic orientations has been examined in [75], and a novel approach for nanoscale imaging and characterization of the orientation dependence of electromechanical properties – vector piezoresponse force microscopy (Vector PFM) was introduced. The vertical and lateral electromechanical responses are analyzed to give a complete threedimensional (3D) reconstruction of the electromechanical response vector as functions of position. The approach can be applied to crystallographic orientation imaging in piezoelectric materials with a spatial resolution better than 10 nm.


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Similar to the force volume measurement in AFM, the spatial information about the local switching behavior of ferroelectric materials, particularly nanoscale domains and particles, can be obtained by performing switching spectroscopy at predefined locations that form the M×M point mesh on the scanned surface area [76, 77]. This approach, switching spectroscopy PFM (SS-PFM), has been applied for 2D mapping of the positive and negative coercive bias, imprint voltage, saturation response, and the work of switching. The spatial variations of these parameters reflect the change of local switching behavior of the surface location and nanostructures. Despite the wide application of PFM in the research of piezoelectric and ferroelectric materials, the imaging mechanism, particular the quantitative interpretation of PFM is yet to be fully understood. In the detailed analysis [78, 79] the additive contributions of the long-range electrostatic and the electromechanical interactions to the total PFM response have been considered as follows:

A = Ael + Apiezo + Anl ,

(9.14)

where A is the total PFM amplitude, and Ael, Apiezo and Anl are the amplitudes of electrostatic, electroelastic, cantilever-surface capacitive contributions, respectively. The presence of Anl results in a constant background to the measured piezoresponse, and it can be minimized by using tall and high aspect-ratio tips. High qualitypiezoresponse data requires the maximization of the electroelastic contribution and the minimization of electrostatic contribution. The electroelastic contribution depends strongly on the contact interface between the tip and the surface, the shape, size, and material of the tip itself. The presence of a “dielectric gap” between the tip and the surface below, particularly in the case of “week indentation” with a soft cantilever, can cause screening of the electric field introduced by the tip, and consequently reducing the piezoresponse amplitude. Therefore, the use of metalcoated, stiff cantilever with large force (strong indentation) is most desirable for PFM imaging. However, sample modification and other effects such as stressinduced suppression of piezoelectricity [80] may occur under high mechanical force due to the “contact” nature of PFM. Another concern for quantitative PFM measurement is the calibration of the PFM system. The general procedure is to calibrate the instrument with each cantilever mounted against a piezoelectric sample of known piezoelectric coefficient (PC) [70]. For example, the commercially available a-quartz has a precisely known PC of d11=2.3±0.05pm/V, and is often used as a standard for PFM calibration. The system coefficient is thus calibrated from the PFM signal (Pac), measured at a specific frequency and voltage, against the displacement calculated from the known PC, x=d11Vac /Pac. However, this process could be complicated by the presence of a frequency dependent background which is unique for the particular instrumental setup used for the measurement. Consequently, extra efforts that might be needed for accurate calibration and measurement of quantitative piezoelectric constants were proposed in [81, 82]. Furthermore, one should realize that PFM deals with the

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piezoresponse of a local, confined volume, which is effected by the tip–sample field. This response might be different from that of the same volume when it is subjected to a large field when both macroscopic surfaces of the sample serve as the electrodes.

Implementation of EFM, KFM and PFM AFM-based electric measurements summarized in this Chapter were performed with the commercial scanning probe microscope 5500 (Agilent Technologies) equipped with the MACIII accessory, which is designed for multifrequency measurements. The MACIII has three dual phase lock-in amplifiers (LIA) converting the AC inputs to amplitude and phase. These digitally controlled analog LIA have a broad bandwidth (up to 6 MHz) that covers the operation bandwidth of the photodetector employed in the microscope. The auxiliary inputs and drive outputs are accessible through the MACIII signal access box. The software, which is flexible in routing signals back to the controller, supports two servo systems related to these LIA. One LIA is used for AM tracking of sample topography with the probe peakto-peak amplitude or its X-, Y-vector components used for feedback. The other servo can be applied for electric or mechanical measurements. The third LIA can be used for tuning the operation parameters or for recording of various signals (lateral response, torsional signal, harmonics, etc.) during measurements. Voltages up to 20 V in DC or in different pulse regimes can be applied to the probe–sample junction as an external stimulus for lithography or other applications.

Electric Force Microscopy and Kelvin Force Microscopy: AM–AM approach The set-up for EFM and KFM measurements in the AM–AM mode is shown in Fig. 9.3. A sample on a microscope stage is grounded (or biased) and an electric signal is applied to a conducting probe. The probe oscillation, which is excited at or near its resonance wmech, is influenced by the tip–sample forces and it is monitored by a positional four-quadrant photodetector. The photodetector output carrying the AC probe amplitude is sensed in parallel by LIA-1 and LIA-2. The first LIA is tuned to w1=wmech, and it delivers the error amplitude signal (Ai-Asp, where Ai is measured amplitude in a new surface location) to the servo that controls the vertical tip–sample separation. This servo loop is used for topography imaging. The second LIA is tuned to w2=welec and from the input signal the X-component of amplitude at welec is selected for KFM servo, i.e., for finding the tip bias voltage that nullifies the incoming signal related to the electrostatic force. In preparation for KFM imaging the phase of the second LIA is tuned to maximize the X-component signal. The operation of the electric servo loop can be monitored and controlled with the


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Fig. 9.3 A scheme illustrating the general set-up and signal wiring of the AM–AM approach of KFM

third LIA, which can determine the magnitude of the electrostatically induced oscillation by sweeping the frequency around welec. Typical sweep curves in the “on” and “off” states of the electric servo loop are shown in Fig. 9.4a, b, where the scale is ~10× smaller in b. The detection of the amplitude signal at welec=10 kHz in the “off” state helps to choose the level of AC voltage applied to the probe in the second loop. The MACIII accessory can provide a voltage up to ±10 V, however the voltage should be chosen as small as possible to minimize its influence on the sample’s electronic states. We are mostly operating with the voltages in the 1–5 V range. In the “on” state one should minimize the remainder of the amplitude signal at welec=10 kHz (the error signal in the feedback operation documented in Fig. 9.4b) by optimizing the servo gain parameters. The experimental protocol for KFM also includes a compensation of the occasional contribution to surface potential from the probe and/or sample surroundings; which causes a dependence of surface potential on the probe–sample separation. This dependence is eliminated by finding the proper setpoint voltage for the KFM servo loop. The optimization procedures for KFM measurements are described in more detail elsewhere [83]. Here it is appropriate to mention about the relationship between the EFM and KFM operations. The electrostatic probe response is generally measured in EFM and its spatial variations are presented in the related image. In the capacitor-like set-up the electrostatic force depends on the tip–sample surface potential difference and capacitance vertical gradient [(9.7) and (9.8)] and its sensitive detection relies on dynamic (resonant and non-resonant) approaches. In the AM–AM approach one can use the amplitude response at 10kHz in the “off” servo state and use it in the EFM image.

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Fig. 9.4 (a, b) The amplitude-versus-frequency curves showing the electrostatic-force induced oscillation in the “off” and “on” state of the KFM servo in the AM–AM mode

The latter might bring a better contrast in studies of samples with electric heterogeneities but add more complexity in quantitative assignment of these changes to particular material property. This contrast will disappear on switching the servo to the “on” state and KFM contrast will outline only surface potential ( j ) variations leaving aside those of ∂C / ∂Z . Therefore, the relationship between EFM and KFM mode is not simple, because the contract of the first depends on more surface properties than the contrast of the second. In the AM–AM experiment there is a choice of frequencies for wmech and welec. A mechanical drive of the probe is typically done at wmech chosen near the first flexural resonance of the cantilever, whereas the electric servo loop is set either at much lower frequency (10kHz as was suggested above) or at the second or even third flexural mode. The following arguments are usually considered in the choice of welec. The electrostatic probe response is higher at the various resonant frequencies, yet this also increases the possibility of cross-talk between different force interactions. The cross-talk is less probable when welec= 2 p −1 ∫ N S SdS / ∫ N S dS

(12.4)

estimated from the NS(S) distributions decreases with increasing x (see inset to Fig. 12.4a). The domain size distributions follow power laws with exponential cutoff [74],

12 Polar Structures in Relaxors by Piezoresponse Force Microscopy

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Fig. 12.4 (a) Domain-size distributions measured at room temperature on single crystals of SBN40 (1), SBN61 (2), and SBN75 (3). The broken lines are best fits to (12.3). The inset shows the dependence of the mean domain size on the Sr concentration x. (b) Domain perimeter (L) vs. area (S) for the determination of the Hausdorff dimension (DH) of the domain boundaries for the PFM images taken on SBN40 (1) and SBN75 (2) single crystals. The inset shows the concentration dependence, DH vs. x (from [73])

N S ∼ S − δ exp (− S / S0 ),

(12.5)

where S0 corresponds to a cutoff size, above which domains become rare. It was found that on increasing of Sr/Ba ratio d increases continuously from the value 1.2 in SBN40 to d=1.6 in SBN75, while S0 drops down from 1.1 to 0.05mm2, respectively. Similar behavior of NS(S) was also reported for a Ce-doped SBN61 single crystal [74]. It is worth comparing the obtained experimental data with theoretical predictions for the RFIM systems. In particular, it was shown that the domain-size distributions are described by a power law with exponential cutoff in the case of two-dimensional RFIM systems [75, 76]. While in our case the domain structure is in reality a threedimensional system, PFM probes a projection of this three-dimensional domain pattern on a sample surface. This projection is actually a two-dimensional object and may be described by two-dimensional RFIM statistics. In the two-dimensional model both parameters, S0 and d, depend on the strength of RFs [75, 76]. Namely, S0 decreases with increasing RFs, while the exponent d approaches the value 1.55 in the limit of strong RFs. A similar tendency is observed for the experimental domain size distributions with increasing Sr/Ba ratio. It points out that the effect of RFs becomes stronger in the composition with higher Sr content, i.e., in compositions showing more pronounced relaxor behavior. It is worth mentioning that the exponent d has approximately the same value for SBN75 [73] and for SBN61 doped with only 1.1% of Ce [74]. This conforms to a substantially stronger effect of heterovalent substitution on relaxor properties, which is probably due to the different RF activities of hetero- and isovalent doping. The shape of the domains reminds of fractal-like objects similar to those found in Monte Carlo simulations of the RFIM systems [77]. Quantitatively, the shape of the domain walls may be analyzed by determining their fractal dimension. The PFM images show cross-sections of two-dimensional domain walls within the sample surface.

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These cross-sections, which we call domain boundaries, are topologically one-dimensional objects. The area of an individual domain, S, is related to its perimeter, L, as

L1/ DH S −1/ 2 = const ,

(12.6)

where DH is the Hausdorff (or fractal) dimension of domain boundaries [78]. In the case of an “irregular” domain structure, DH deviates significantly from the topological dimension D=1. Figure 12.4b shows the experimental dependences, L vs. S, which follows power laws according to (12.6) quite satisfactorily. The x dependence of the best-fitted values of DH is shown in the inset of Fig. 12.4b. One can see that the fractal dimension of domain walls increases with increasing Sr content. Theoretically, previously determined fractal dimensions for the two-dimensional RFIM have been reported to be DH=1.18 using Monte Carlo simulations [77] and DH=1.96 from the exact solution for the ground state [76]. The large difference between these two theoretical values is partly due to the fact that Monte Carlo simulations are far from thermal equilibrium. In addition, their small DH value refers to rather weak RFs and to finite temperatures [77], both parameters favoring weak domain wall roughness, since local pinning can easily be overcome by thermal fluctuations. The experimental values obtained from analysis of the PFM images DH(0.4)=1.23, DH(0.5)=1.29, DH(0.61)=1.48, and DH(0.75)=1.60 lie between the two above theoretical values. The increase of DH indicates that “irregularity” of domain structures caused by polar disorder, becomes increasingly pronounced with increasing Sr content. A substantial deviation of the Hausdorff dimension from the topological one is observed even in ferroelectric SBN40, where 180° domains have an “irregular” shape in comparison to those typical of conventional uniaxial ferroelectrics, e.g., “ovals” or “lenses” in triglycine sulphate [79, 80]. It is important to note that the total fractal dimension of the domain surfaces in SBN crystals finally comes out to be Dtot=D⊥+D||=2.23–2.6, if we accept an additional longitudinal dimension D||=1 along the polar c direction. Indeed, a strong anisotropy of 180° domains is typical of SBN single crystal [73, 81] giving rise, e.g., to a huge anisotropy of the second harmonic light scattering as reported recently for SBN61 by Betzler et al. [82]. It can be illustrated by comparison of vertical (VPFM) image for the c-cut and lateral PFM (LPFM) image for the a-cut (with polarization in-plane) of the SBN40 single crystals (Fig. 12.5) [73]. In the plane perpendicular to the polar axis a complex maze-type domain pattern is seen, as it was discussed above. Contrastingly, on the a-cut sample stripe domains extended along the polar axis were observed. The size of domains along the polar axis is several tens of microns, which is about two orders of magnitude larger than that perpendicular to the polar axis. A simple explanation of this shape anisotropy can be found under the assumption of a corresponding anisotropy of the inter- and intralayer interactions, Jc and Ja, acting between the ferroelectric O–Nb–O “spin” chains along the c- and a(b)-axes, respectively. Within the framework of an anisotropic Ising model, the excess of the free energy for RF-induced domains [33] can be considered in a first approximation as [73]


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Fig. 12.5 The PFM images of a SBN40 single crystal observed on a c-cut sample in the vertical mode (a) and on an ab cut in the lateral mode (b). The blue and red colors correspond to domains with the spontaneous polarization oriented up and down relative to the figure plane (vertical PFM) and left and right in the figure plane (lateral PFM), respectively. Regions with negligible piezoresponse are shown in yellow adapted from [73]

W = 2 L2a J c + 4 La Lc J a − hLa Lc .

(12.7)

Here a square column-shaped domain has length Lc (in lattice units) and cross-section La2, h is the average RF acting on the statistical excess N = L2a Lc of up (or down) “spins.” Minimization of the free energy with respect to both La and Lc yields the relationship La / Lc = J a / J c . Hence, La of SBN61 (from [73])

where D(x, y) is the value of the piezoresponse signal. Positive or negative values of the autocorrelation function correspond to probabilities to find a region with parallel or antiparallel direction of the polarization after a shift by (r1, r2) from an arbitrary point in the original PFM image. Typically, a peak arises in the center of the autocorrelation images. For the paraelectric state, in the absence of piezoactive regions (PRs), the width of the “central” peak is determined by the resolution of the PFM image as well as by scan parameters (scanning velocity, probing frequency, and time constant of the lock-in amplifier). The condition that the width of the central peak in the autocorrelation image becomes larger than the minimal size related to noise was used as a criterion of appearance of a region of correlated polarization. Both in SBN61 and SBN75 quasi-static PRs were resolved approximately 15K above the corresponding transition temperature (Fig. 12.7a, curve 2). The width of the central peak is a measure of the size of PRs. To describe correlations of the piezoresponse signal (polarization) inside individual PNRs, the autocorrelation function can be presented as

2h < C (r ) >= σ 2 exp  − (r / < x > )  ,  

(12.9)

where r is the distance from the central maximum [86]. A similar expression has been used for the analysis of rough surfaces [87]. Here is the autocorrelation function averaged over all in-plane directions, <x> is the average correlation radius and the exponent h (0 < h < 1) describes the “roughness” of a polarization interface [87]. Figure 12.7b shows the temperature dependence of <x> for SBN61. It appears above the resolution limit at T»TC+15K, and increases on cooling when approaching TC. Below TC the PRs continue to grow, but less abruptly. Such regions of correlated polarization observed above TC were attributed to relatively large “mesoscale” PNRs. The existence of PNRs in SBN61 at temperatures well above TC was evidenced by the measurements of the optic index of refraction [88], birefringence [88, 89], second harmonic generation [90], dynamic

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[91], and inelastic Brillouin [92] light scattering. The estimated TD is about 750K [89, 92]. On cooling the PNRs grow and in the vicinity of the transition temperature some of them becomes “frozen” (immobilized) on the experimental timescale due to their large size. Their polarity is controlled by fluctuations of RFs. These “frozen” PNRs are surrounded by non-PRs, which consist of still dynamic PNRs and probably on smaller static PNRs not resolved in the PFM experiment. The occurrence of quasi-static PNRs above the transition temperature provides an additional evidence of the transition from the high-temperature ER state into the low-temperature one (long-range ferroelectric state in the case of SBN). It points out that the transition does not takes place at a fixed temperature, but there is a certain temperature range above TC where the system contains both small dynamic and large quasi-static PNRs. The latter ones are precursors of domains in the lowtemperature ferroelectric state. The intermediate state has a non-ergodic character, which was verified for the studied single crystal by observation of aging (as indicated by an isothermal decay of the dielectric permittivity) in the same temperature range above TC, where frozen PNRs were visualized [83, 84]. This aging is related to isothermal growth of quastistatic PNRs at the expense of the dynamic ones. Another macroscopic manifestation of the existence of quasi-static PNRs is the appearance of a particular relaxation mode in the dielectric spectra of SBN single crystal, which was related to a “breathing” motion of the boundaries of “frozen” PNRs [85]. It has to be mentioned that the appearance of frozen PNRs in the close vicinity above TC may explain a long time disputed controversy between the experimentally observed critical behavior in 3D-RFIM systems and theoretical predictions [84, 93, 94]. Namely, the values of critical exponents found in experiments are close to those theoretically predicted for the two-dimensional Ising model, but deviate strongly from those of the 3D-RFIM systems. Kleemann et al. suggested that the appearance of quasi-stable PNRs excludes true equilibrium criticality when approaching TC [84]. While these large PNRs are frozen on a finite timescale, the unfrozen interfaces can be considered as regions with very short-ranged correlation of RFs, which are not able to select sizable polar clusters via field energy gain. In these essentially two-dimensional regions, forming a percolating network through the sample, a phase transition may take place under the constraint of a weakly disordered quasi-staggered field. At the same time, two-dimensional Ising model criticality of interface system is preserved [84]. Even below TC the domains in SBN are metastable and the system needs an extremely large time to reach its equilibrium state. Figure 12.8 shows PFM images acquired on a Ce-doped SBN61 single crystal, Sr0.61–xCexBa0.39Nb2O6 (x=0.0113), at different times after cooling from the paraelectric state to room temperature [95]. For this composition, TC is about 320K. The domains observed immediately after the cooling procedure (Fig. 12.8a) are relatively small and their borders are strongly jagged. Between the domains large areas show gray contrast corresponding to vanishing piezoresponse. In the course of time significant changes of the images take place: the domains are coarsening and become more compact with smoother borders. The growth of the domains occurs at the expense of both


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Fig. 12.8 Piezoresponse images of a SBN61:Ce single crystal acquired at room temperature after cooling down from the paraelectric state: (a) after 1 h, (b) after 72 h. (c) Dependence of the mean domain size, R, in a SBN61:Ce single crystal cooled down from the paraelectric state to room temperature as a function of the waiting time. The logarithmic growth law, (12.10), is best fitted (broken line) to the data points

embedded small “patches” of opposite polarity and gray areas. After 72h (Fig. 12.8b) the “white” and “black” domains occupy the major part of the scanned area, the mean domain size is nearly two times larger than in the initial situation. Nevertheless, the domains are still very irregular. Their size varies in a wide range from tens of nanometers to several microns. Some of the large nanodomains still contain small “patches” of opposite polarity. Continuous growth of domains is observed even 1 month (720h) after the sample cooling. Figure 12.8c shows the temporal dependence of the mean domain size estimated from the domain size distribution, NS(S), according to (12.4). The temporal evolution of domains clearly indicates the metastability of the domain state in SBN:Ce, which is in accordance with theoretical predictions [96, 97] for the RFIM systems. If the system is cooled down from the paraelectric state, the domains emerging in the vicinity of TC are closely related to the fluctuations of RFs, where the smallest domain size corresponds to the largest attainable correlation length of the ferroelectric order parameter at T>TC. The size of the domains is a function of temperature (it increases on cooling) and depends on the relation between the strength of RFs (i.e., their average magnitude) and domain wall energy. The domain growth occurs via absorption of smaller domains of opposite sign both in the interior part and near to the borders. These smaller domains are stabilized by RFs of appropriate orientation, therefore a potential barrier has to be overcome to absorb them. The waiting time being necessary to overcome this barrier is related to its height by the Arrhenius law, t=texp(U/kT), where t is a microscopic attempt time. On the other hand, the height of the potential barrier, U, is proportional to the size of absorbing domain [96]. Thus, whereas the small domains may be absorbed relatively fast, the larger ones are long lived providing that transformation into equilibrium long-range ordered state needs time, which – in principle – may largely exceed the experimental scale. Villain [96] has shown that the typical radius of the domains, R, is related to the waiting time, t, as

R = AT ln(t / t ),

(12.10)

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where A is a constant, which depends on the strength of RF, domain wall energy, and value of the order parameter. The experimental dependence of the mean domain size on the waiting time (Fig. 12.8c) is in good agreement with this theoretical prediction.

Piezoresponse Force Microscopy Studies of Cubic Relaxors Pb(Mg1/3Nb2/3)O3–PbTiO3 Single Crystals To the largest group of the relaxors belong “cubic” relaxors with the perovskite structure ABO3. In this case the relaxor behavior is closely related to charge disorder, which is caused by cations of different valency randomly occupying equivalent crystallographic positions, i.e., Pb2+ and La3+ on A sites of (Pb1–xLax)(Zr1–yTiy)O3 (PLZT) or Mg2+ and Nb5+ on B-sites of PMN. Pure PMN exhibits a transition into a cluster glass state with random orientation of the local polarization [52]. The introduction of ferroelectrically active Ti4+ ions in (1–x)PMN–xPT solid solutions enhances the interactions between PNRs leading to a breaking of the macroscopic cubic symmetry at x > 0.27 [98]. In compositions with 0.05 (squares) and the fractal dimension of the “polarization interface” d = 3–h (circles). The lines are drawn to guide the eye (from [86])

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the domains observed at lower temperatures [103]. The size of individual PRs at high temperatures is larger than in PMN–PT10, <x>»110nm at TC+45K. As in the case of the uniaxial SBN system quasi-static mesoscale PRs were found in cubic relaxors PMN–PT above TC. By analogy, we can attribute them to large PNRs “frozen” on the experimental timescale in the vicinity of the transition temperature. Nevertheless, it is worth noting that they are observed in a much wider temperature range above TC in PMN–PT than in SBN. Another particular feature is that these PRs are not fully random, but exhibit some regularity, in particular, a preferential orientation of the PR boundaries along directions. This feature becomes more pronounced in compositions with higher titanium content. It was suggested that it is related to an effect of mechanical strains resulting from the rhombohedral distortion of unit cell in cubic relaxors [103, 105]. There are three main factors influencing the polar structure in relaxors: (a) minimization of the depolarization field energy, which controls formation of 180° domains; (b) the influence of RFs which break domains into smaller entities; (c) minimization of mechanical stress, which is achieved by formation of ferroelastic domains (twins). Obviously, in uniaxial SBN only the first and the second factors are acting. On the other hand, the stress accommodation factor is important for PMN–PT resulting in a preferential orientation of domain walls parallel to {110} habit planes, which are invariant for systems with rhombohedral symmetry. It is supposed that large domains in compositions with high Ti4+ content are self-assembled agglomerates of smaller nanosized domains [105]. The driving force for such self-organization may be due to stress relief, i.e., minimization of the free energy related to mechanical deformation. The RFs may essentially modify the energy balance resulting in diffused domain patterns in composition with less Ti4+. Nevertheless, self-assembly of the nanodomains still persists in PMN–PT10 on a small scale. Furthermore, one can assume that this tendency to self-organization may stimulate the formation of relatively large agglomerates of PNRs already at high enough temperatures above the nominal TC. The observed regions of correlated piezoresponse [86, 103] probably correspond to such agglomerates. It should also be taken into account that PMN–PT relaxors are spatially inhomogeneous materials. As it was mentioned in Sect.114 3 ferroelectric transition occurs in these compounds not homogeneously, but only in the outer layer, several tens of microns thick. The nature of this phenomenon is unclear. In particular, a large compressive strain was found in the near-surface layer in PMN single crystals [14]. Such strain may stabilize the ferroelectric state shifting the phase transition to higher temperatures. The effect may be similar to one observed in ferroelectric thin films, where the Curie temperature depends on a misfit strain, um, between the film and the substrate [115, 116]:

TC = TC0 + 2Ce 0

2Q12 um , s11 + s12

(12.12)

where TC0 is the Curie temperature for the free-standing film, Q12 the electrostriction coefficient, s11, s12 the components of the elastic compliance tensor, C the Curie–Weiss constant, and e0 the dielectric permittivity of vacuum. Moreover, it


367

was recently found that the misfit strain may induce a ferroelectric state in nominally relaxor thin films of PLZT [117]. Suggesting that in PMN–PT a gradient of the strain across the outer layer might exist, then the shift of the Curie temperature will be also nonuniform and the transition point in a very thin subsurface layer, which gives the main contribution to the PFM signal, may be considerably higher than the average (nominal) Curie temperature estimated from X-ray measurements. Similar arguments may be applied, if we assume that the existence of the outer layer in PMN–PT single crystals is due to a gradient of the composition, e.g., the Ti content, in the vicinity of the sample surface.

PbZn1/3Nb2/3O3–PbTiO3 Single Crystals The domain structure and electromechanical properties of relaxor single crystals of solid solutions (1–x)PbZn1/3Nb2/3O3–xPbTiO3 (PZN–PT) have been intensively investigated during the last few years. The attracting feature of this system is the extremely high piezoelectric effect (piezoelectric coefficients up to 2,500pm/V) and electrically induced strain (up to 1.7%) measured for (001)-cut faces of rhombohedral crystals of the composition close to the morphotropic phase boundary (MPB) with tetragonal phase (x~0.08–0.10) [118]. It was also observed that the corresponding coupling coefficients are very high (~95%) making these crystals a promising material for piezoelectric transducers for medical imaging, active vibration damping, and underwater sensing [119, 120]. It was clearly shown [121] that the unusually high strain in these crystals is somehow related to the phase transition from rhombohedral to tetragonal phase under high electric field applied along the pseudocubic directions. For compositions close to the MPB a new monoclinic phase (intermediate between rhombohedral and tetragonal phases) has been observed by both X-ray diffraction and direct domain study [122, 123]. This phase provides the possibility of domain rotation between rhombohedral and tetragonal phases and was suggested as a reason for the extraordinarily large electromechanical response of PZN–PT under an applied electric field [124]. Several domain studies have been performed on PZN–PT crystals that revealed the existence of ferroelastic twins that exist even in poled specimens [107, 125, 126]. In another study, a peculiar dendritic domain pattern formed under pulsed poling conditions has been documented making domain structure very complicated [127]. The disadvantage of these investigations is that they have been performed mainly using optical techniques with a resolution limited to the wavelength of the light. However, submicron-size domains can exist in such materials and contribute to their final electromechanical performance. Indeed, using PFM technique it was possible to visualize irregular micron-size domains in PZN–PT single crystals with compositions both at the MPB [107] and far from MPB [108]. Figure 12.13 shows domain images of the PZN–4.5% PT crystals at four different scales: 100, 15, 5, and 2mm taken on (001) and (111) faces. The contrast is

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Fig. 12.13 Piezoresponse images of Pb(Zn1/3Nb2/3)O3–4.5% PbTiO3 single crystal: (a, c, e, g) – (100)-oriented sample, (b, d, f, h) – (111)-oriented sample. The inset to Fig. 12.13b shows the central part of self-correlation image. The inset to Fig. 12.13f is the variation of piezoresponse signal along the marked cross-section (1, 3 – signal from domains with polarization tilted to crystal surface, 2, 4 – signal from domains with polarization normal to crystal surface)

determined by the out-of-plane component of polarization (P⊥), where dark and bright areas correspond to the opposite directions of P⊥. Inset to Fig. 12.13b demonstrates the image of the self-correlation function calculated according to (12.8) from the corresponding domain picture. It illustrates that, along certain directions, there exist spatial correlations of seemingly irregular domains. These directions should coincide with the intersections of allowed domain walls with the crystal surface. It is clearly seen that the self-correlation image of the (111) surface reveals the symmetry of the rhombohedral phase (3m), where domain walls are preferably aligned parallel to ;110= and ;100= planes. In contrast, no clear correlation for the domain wall directions has been observed for the (001)-oriented surface. The rhombohedral ferroelectric phase allows for the existence of eight equivalent domain states and the contrast for a (111)-oriented crystal should be made up of four different signal levels corresponding to all possible values of the polarization projections on the [111] axis. The cross-section in Fig. 12.13f demonstrates these levels corresponding to different angles between polarization direction and [111] direction. The domain boundaries often appear L-shaped. (Fig. 12.13d). It has previously been shown that such boundary should comprise both charged and uncharged domain walls [125]. It can be noticed that domains in (001)-oriented crystals are much finer than in (111) samples. In a larger magnification (Fig. 12.13e, g) it is clearly seen that the micron-size domains on (001)-oriented surface actually consist of much finer irregular structures of the size down to 20nm (limited by PFM resolution). Seemingly “dark” areas are actually split into numerous “bright” inclusions and vice versa. The statistical


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Fig. 12.14 Nanodomains size distribution for (001)-oriented Pb(Zn1/3Nb2/3)O3–4.5% PbTiO3 single crystal

distribution of the domain area inside a micron-size domain is shown in Fig. 12.14. The average size of fine domains is ~ 65nm, but it is the upper limit because of the limited resolution. No nanodomains have been observed in (111)-oriented crystals. The complex domain structures seen on a (001)-cut are similar to those observed in PMN–PT single crystals with Ti content 0.20 £ x £ 0.35 [103, 105]. All these compositions exhibit an “intermediate” behavior between canonical relaxor and ferroelectric ones. While the PbTiO3 addition favors the long-range ferroelectric order, relaxor features still remain in zero-field-cooled crystals. So, the existence of short-range order manifested in the formation of nanoscale polar region (polar clusters) is the principal feature of the relaxor state [128]. For example, frozen PNRs with an average size of about 10nm were found in PZN–4.5% PT at room temperature by neutron scattering [129]. Appearing far above TC the PNRs grow in size when cooled in zero field. At the same time the presence of the highly polarizable Ti4+ ions promotes interaction between PNRs, which thus can reorient and merge into micron-size domains upon cooling. The nanoscale inclusions embedded into these domains may represent regions where RFs were especially strong to prevent reorientation and growth of PNRs. As was shown by Viehland and Li [130], such locations can serve as heterogeneous nucleation centers for polarization switching in “soft” ferroelectrics. In this context, it is worth noting that the macroscopic coercive field is much smaller for the (001) cut than for the (111) one [131]. This may be a consequence of the peculiar domain structure shown in Fig. 12.13. The average size of nanodomains observed in the PFM experiment is significantly larger than estimated by neutron scattering experiments (65nm vs. ~10nm). This can result from the natural difference in the two techniques and from the fact that the PFM method is only sensitive to the surface of the crystal (see the arguments for explaining the

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Fig. 12.15 Local piezoresponse hysteresis loops of PZN–4.5% PT crystals: (a) (100)-oriented crystal. (b) (111)-oriented crystal

PMN–PT results). The growth and coalescence of PNRs may apparently differ near the surface and in the crystal’s bulk. The natural question arises why no nanodomains are observed on a (111) surface. Results of diffuse neutron scattering on PZN–5% PT [129] indicate that, even though the polarization in the nanodomains is oriented along [111] direction, their easy growth direction is along the axes. This results in a larger correlation length and, as a consequence, in a higher piezoelectric signal measured by PFM on the (001) cut. If the piezoelectric signal is lower than the vertical resolution of PFM it may not be observed on a (111) cut. An attempt was made to measure nanoscale hysteresis loops in both crystallographic directions in order to verify the ability of the PFM tip to induce a phase transition in the tetragonal phase and, therefore, creating a high piezoelectric signal in the vicinity of the PFM tip. The results are shown in Fig. 12.15. The sequence of the measurements was as follows: first the crystal was prepoled by pulses of variable height and then the piezoelectric response was measured at the same location in the absence of an electric field. Since the electric field is highly nonuniformly distributed under the surface [4], even small voltages applied by the PFM tip are expected to induce the phase transition. However, no evidence of such transition has been observed for the (001)-oriented crystals (see Fig. 12.15). The loops are very similar for both interfaces. In macroscopic measurements, the difference in respective piezoelectric coefficients for (001) and (111) cuts is more than an order of magnitude [118]. Thus, our observation contradicts the macroscopic data and underlines the importance of nanoscale measurements performed on the scale comparable with the domain size.


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Fig. 12.16 The PFM images of a PMN–PT14 ceramics (TC = 330 K) at 360 K (a), 315 K (b), 295 K (c). Grain contours are indicated by solid lines

Fig. 12.17 Temperature dependence of the remanent polarization of PMN–PT14 ceramics

Polycrystalline Materials (Ceramics) Temperature Evolution of Domains in the PMN–PT Ceramics The investigation of polar structures of polycrystalline relaxors is of special interest. In this case the microstructure of the samples, namely grain size effect and grain boundaries, may play an important role thus giving PFM unique possibilities to study these effects via the domain structure. Figure 12.16 shows the PFM images taken on the PMN–PT ceramics with 14% of titanium (PMN–PT14) on cooling from high temperatures (420K). This temperature is well above the Curie temperature for this sample (TC~330K), which may be estimated from the temperature dependence of the remanent polarization, Pr (Fig. 12.17). Like in the case of single crystals, quasi-static PRs of several hundred nanometers in size appear already above the nominal TC. It is important that they are concentrated near grain boundaries, especially near “triple points,” where several

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Fig. 12.18 Temperature evolution of the poled area in PMN–PT14 ceramics. (a) initial state; (b–e) after the area 3 × 3 mm2 was scanned under -30 V: at 295 K (b), 330 K (c), 350 K (d), and 360 K (e). (f) – temperature dependence of the piezoactive (polar) area relative to initially poled one

grains are joining. Obviously, in these places mechanical stresses are accumulated, which promote coarsening of PNRs and stimulate their agglomeration into bigger entities, as it was discussed above. Both the growth of already existing domains and the appearance of new ones take place on cooling. Even below TC the domain pattern remains metastable and an isothermal growth of domains with time was observed. The transition from the ferroelectric into the ER state is often associated with a macroscopic depolarization of the sample, for example, in a field cooling-zero field heating cycle [3]. To simulate such conditions in a PFM experiment, a square area 3×3mm2 was scanned under bias voltage Udc=-30V at RT. As a result this area was almost uniformly polarized in one direction (Fig. 12.18b). The created polarization is stable, no decay of the polarized area was observed during 24h. Then the sample was heated, and piezoresponse images of the poled area were acquired at different temperatures (Fig. 12.18c–e). From the analysis of the distributions of the piezoresponse signal inside the poled square, a relative amount of polar (piezoactive) phase (polarized area) was estimated as a function of the temperature (Fig. 12.18f). It was found that the artificial domain disappears abruptly in the narrow temperature range 330–340K, which agrees well with the temperature dependence of the remanent polarization (Fig. 12.17). Thus, the Curie temperature indeed corresponds to the decay of polar ordering on a macroscopic (micron-size) scale. It is worth noting that during the decay of the artificial domain not only areas of zero-piezoresponse, but also regions with opposite polarity appear. Such polar regions of both polarities are still present at higher temperatures on a mesoscale (100nm

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