Applied scanning probe methods 3. Characterization

NanoScience and Technology

NanoScience and Technology Series Editors: P. Avouris B. Bhushan K. von Klitzing H. Sakaki R. Wiesendanger The series NanoScience and Technology is focused on the fascinating nano-world, mesoscopic physics, analysis with atomic resolution, nano and quantum-effect devices, nanomechanics and atomic-scale processes. All the basic aspects and technology-oriented developments in this emerging discipline are covered by comprehensive and timely books. The series constitutes a survey of the relevant special topics, which are presented by leading experts in the field. These books will appeal to researchers, engineers, and advanced students.

Semiconductor Spintronics and Quantum Computation Editors: D.D. Awschalom, N. Samarth, D. Loss Nano-Optoelectonics Concepts, Physics and Devices Editor: M. Grundmann Noncontact Atomic Force Microscopy Editors: S. Morita, R. Wiesendanger, E. Meyer Nanoelectrodynamics Electrons and Electromagnetic Fields in Nanometer-Scale Structures Editor: H. Nejo Single Organic Nanoparticles Editors: H. Masuhara, H. Nakanishi, K. Sasaki Epitaxy of Nanostructures By V.A. Shchukin, N.N. Ledentsov and D. Bimberg Applied Scanning Probe Methods I Editors: B. Bhushan, H. Fuchs, S. Hosaka Nanostructures Theory and Modeling By C. Delerue and M. Lannoo Nanoscale Characterisation of Ferroelectric Materials Scanning Probe Microscopy Approach Editors: M. Alexe and A. Gruverman

Magnetic Microscopy of Nanostructures Editors: H. Hopster and H.P. Oepen Silicon Quantum Integrated Circuits Silicon-Germanium Heterostructure Devices: Basics and Realisations By E. Kasper, D.J. Paul The Physics of Nanotubes Fundamentals of Theory, Optics and Transport Devices Editors: S.V. Rotkin and S. Subramoney Single Molecule Chemistry and Physics An Introduction By C. Wang, C. Bai Atomic Force Microscopy, Scanning Nearfield Optical Microscopy and Nanoscratching Application to Rough and Natural Surfaces By G. Kaupp Applied Scanning Probe Methods II Scanning Probe Microscopy Techniques Editors: B. Bhushan, H. Fuchs Applied Scanning Probe Methods III Characterization Editors: B. Bhushan, H. Fuchs Applied Scanning Probe Methods IV Industrial Applications Editors: B. Bhushan, H. Fuchs

Bharat Bhushan Harald Fuchs (Eds.)

Applied Scanning Probe Methods III Characterization

With 268 Figures Including 2 Color Figures

123

Editors: Professor Bharat Bhushan Nanotribology Laboratory for Information Storage and MEMS/NEMS (NLIM) 650 Ackerman Road, Suite 255, The Ohio State University Columbus, OH 43202-1107, USA e-mail: [email protected]

Professor Dr. Harald Fuchs Center for Nanotechnology (CeNTech) and Institute of Physics University of Münster, Gievenbecker Weg 11, 48149 Münster, Germany e-mail: [email protected]

Series Editors: Professor Dr. Phaedon Avouris IBM Research Division, Nanometer Scale Science & Technology Thomas J. Watson Research Center, P.O. Box 218 Yorktown Heights, NY 10598, USA

Professor Bharat Bhushan Nanotribology Laboratory for Information Storage and MEMS/NEMS (NLIM) 650 Ackerman Road, Suite 255, The Ohio State University Columbus, OH 43202-1107, USA

Professor Dr., Dres. h. c. Klaus von Klitzing Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1 70569 Stuttgart, Germany

Professor Hiroyuki Sakaki University of Tokyo, Institute of Industrial Science, 4-6-1 Komaba, Meguro-ku Tokyo 153-8505, Japan

Professor Dr. Roland Wiesendanger Institut für Angewandte Physik, Universität Hamburg, Jungiusstrasse 11 20355 Hamburg, Germany DOI 10.1007/b137427 ISSN 1434-4904 ISBN-10 3-540-26909-6 Springer Berlin Heidelberg New York ISBN-13 978-3-540-26909-0 Springer Berlin Heidelberg New York Library of Congress Control Number: 2003059049 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media. springer.com © Springer-Verlag Berlin Heidelberg 2006 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Product liability: The publishers cannot guarantee the accuracy of any information about dosage and application contained in this book. In every individual case the user must check such information by consulting the relevant literature. Typesetting and production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: design & production, Heidelberg Printed on acid-free paper 2/3100/YL - 5 4 3 2 1 0

Foreword

The Nobel Prize of 1986 on Scanning Tunneling Microscopy signaled a new era in imaging. The scanning probes emerged as a new instrument for imaging with a precision sufficient to delineate single atoms. At first there were two – the Scanning Tunneling Microscope, or STM, and the Atomic Force Microscope, or AFM. The STM relies on electrons tunneling between tip and sample whereas the AFM depends on the force acting on the tip when it was placed near the sample. These were quickly followed by the Magnetic Force Microscope, MFM, and the Electrostatic Force Microscope, EFM. The MFM will image a single magnetic bit with features as small as 10 nm. With the EFM one can monitor the charge of a single electron. Prof. Paul Hansma at Santa Barbara opened the door even wider when he was able to image biological objects in aqueous environments. At this point the sluice gates were opened and a multitude of different instruments appeared. There are significant differences between the Scanning Probe Microscopes or SPM, and others such as the Scanning Electron Microscope or SEM. The probe microscopes do not require preparation of the sample and they operate in ambient atmosphere, whereas, the SEM must operate in a vacuum environment and the sample must be cross-sectioned to expose the proper surface. However, the SEM can record 3D image and movies, features that are not available with the scanning probes. The Near Field Optical Microscope or NSOM is also member of this family. At this time the instrument suffers from two limitations; 1) most of the optical energy is lost as it traverses the cut-off region of the tapered fiber and 2) the resolution is insufficient for many purposes. We are confident that NSOM’s with a reasonable optical throughput and a resolution of 10 nm will soon appear. The SNOM will then enter the mainstream of scanning probes.

VI

Foreword

In the Harmonic Force Microscope or HFM, the cantilever is driven at the resonant frequency with the amplitude adjusted so that the tip impacts the sample on each cycle. The forces between tip and sample generate multiple harmonics in the motion of the cantilever. The strength of these harmonics can be used to characterize the physical properties of the surface. It is interesting to note that this technology has spawned devices of a different kind. In one instance, the tip is functionalized in a way that allows the attachment of a single protein. Withdrawing the tip from a surface stretches the attached molecule and measures the elastic properties of single protein molecules. In another the surface tension on the surface of the cantilever is modified with a self-assembled monolayer of molecules such as thiols. The slight bending of the beam is easily detected with the components developed for use in the scanning probes. This system is used to detect the presence not only of the monomolecular layers but also of single molecules attached to the initial self-assembled monolayer. The extensive material in this field means that the variety of topics is larger than can be accommodated in four volumes. The Editors, Profs. Bhushan and Fuchs, must have great powers of persuasion for they have done a remarkable job in collecting this set of paper in a relatively short period of time. The collection will become a milestone in the field of scanning probes. c. f. quate Leland T. Edwards Professor (Research) of Engineering Stanford University Stanford, California Co-inventer of AFM in 1985

Preface

The rapidly increasing activities in nanoscience and nanotechnology supported by sizable national programs has led to a variety of efforts in the development and understanding of scanning probe techniques as well as their applications to industrial and medical environments. Beyond imaging, scanning probe techniques representing the eyes of nanotechnology allows us to investigate surfaces and interfaces close to surfaces at the nanometer scale and below, thus providing information about structure, mechanical, electronic, and magnetic properties. It became apparent during the collection phase of Vol. I in 2003 that many more activities exist which deserve presentation. Therefore, this three volume set was prepared in order to display the wide breadth of this field and also to provide an excellent compendium for recent developments in this area. The response of colleagues and research groups being asked to contribute has been very positive, such that we decided, together with the publisher, to rapidly move on in these areas. It became possible to collect excellent contributions displaying first hand information from leading laboratories worldwide. The present volumes II–IV cover three main areas: scanning probe microscopy (SPM) techniques (Vol. II); characterization (basic aspects, research, Vol. III); and industrial applications (Vol. IV). Volume II includes overviews on sensor technology based on SPM probes, high harmonic dynamic force microscopy, scanning ion conduction microscopy, spin polarized STM, dynamic force microscopy and spectroscopy, quantitative nanomechanical measurements in biology, scanning micro deformation microscopy, electrostatic force and force gradient microscopy and nearfield optical microscopy. This volume also includes a contribution on nearfield probe methods such as the scanning focus ion beam technique which is an extremely valuable tool for nanofabrication including scanning probes. Volume III includes the application of scanning probe methods for the characterization of different materials, mainly in the research stage, such as applications of SPM on living cells at high resolution, macromolecular dynamics, organic supramolecular structures under UHV conditions, STS on organic and inorganic low dimensional systems, and ferroelectric materials, morphological and tribological characterization of rough surfaces, AFM for contact and wear simulation, analysis of fullerene like nanoparticles and applications in the magnetic tape industry. The more relevant industrial applications are described in Vol. IV, which deals with scanning probe lithography for chemical, biological and engineering applications, nanofabrication with self-assembled monolayers by scanned probe lithography, fabrication of nanometer scale structures by local oxidation, template effects of

VIII

Preface

molecular assemblies, microfabricated cantilever arrays, nanothermomechanics and applications of heated atomic force microscope cantilevers. Certainly, the distinction between basic research fields of scanning probe techniques and the applications in industry are not sharp, as becomes apparent in the distribution of the individual articles in the different parts of these volumes. On the other hand, this clearly reflects an extremely active research field which strengthens the cooperation between nanotechnology and nanoscience. The success of the series is solely based on the efforts and the huge amount of work done by the authors. We gratefully acknowledge their excellent contributions in a timely manner which helps to inform scientists in research and industry about latest achievements in scanning probe methods. We also would like to thank Dr. Marion Hertel, Senior Editor Chemistry, and Mrs. Beate Siek of Springer Verlag for their continuous support, without which this volume could never make it efficiently to market. January, 2006

Prof. Bharat Bhushan, USA Prof. Harald Fuchs, Germany

Contents – Volume III

12

Atomic Force Microscopy in Nanomedicine Dessy Nikova, Tobias Lange, Hans Oberleithner, Hermann Schillers, Andreas Ebner, Peter Hinterdorfer . . . . . . .

1

12.1

AFM in Biological Sciences . . . . . . . . . . . . . . . . . . . . .

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12.2 12.2.1 12.2.2 12.2.3 12.2.4 12.2.5

Plasma Membrane Preparation for AFM Imaging . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . Plasma Membrane Preparation . . . . . . . . . . . . . . . Atomic Force Microscopy . . . . . . . . . . . . . . . . . Molecular Volume Measurements of Membrane Proteins . AFM Imaging . . . . . . . . . . . . . . . . . . . . . . . .

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12.3 12.3.1 12.3.2 12.3.3

AFM Imaging of CFTR in Oocyte Membranes Introduction . . . . . . . . . . . . . . . . . . . Does the CFTR Form Functional Assemblies? Two CFTRs are Better Than One . . . . . . . .

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12.4 12.4.1 12.4.2 12.4.3 12.4.4

Single Antibody–CFTR Recognition Imaging . Introduction . . . . . . . . . . . . . . . . . . . Tethering of Antibodies to AFM Tips . . . . . AFM Imaging and Recognition . . . . . . . . . A Single Antibody Sees a Single CFTR . . . .

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12.5 12.5.1 12.5.2 12.5.3

Single Cell Elasticity: Probing for Diseases Introduction . . . . . . . . . . . . . . . . . Force–Mapping AFM . . . . . . . . . . . . Can One Protein Change Cell Elasticity? .

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12.6

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

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Contents – Volume III

Scanning Probe Microscopy: From Living Cells to the Subatomic Range Ille C. Gebeshuber, Manfred Drack, Friedrich Aumayr, Hannspeter Winter, Friedrich Franek . . . . . . . . . . . . . . . . .

27

13.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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13.2 13.2.1 13.2.2

Cells In Vivo as Exemplified by Diatoms . . . . . . . . . . . . . . Introduction to Diatoms . . . . . . . . . . . . . . . . . . . . . . . . SPM of Diatoms . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28 28 30

13.3

Interaction of Large Organic Molecules . . . . . . . . . . . . . . .

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13.4 13.4.1 13.4.2

Nanodefects on Atomically Flat Surfaces . . . . . . . . . . . . . . Ion Bombardment of Highly Oriented Pyrolytic Graphite (HOPG) Bombardment of Single Crystal Insulators with Multicharged Ions

37 38 42

13.5 13.5.1 13.5.2

Subatomic Features . . . . . . . . . . . . . . . . . . . . . . . . . . Atom Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single Electron Spin Detection with AFM and STM . . . . . . . .

45 45 47

13.6

Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . .

50

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51

14

Surface Characterization and Adhesion and Friction Properties of Hydrophobic Leaf Surfaces and Nanopatterned Polymers for Superhydrophobic Surfaces Zachary Burton, Bharat Bhushan . . . . . . . . . . . . . . . . . .

55

14.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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14.2 14.2.1 14.2.2 14.2.3 14.2.4

Experimental Details . . . . . . . . . . . Instrumentation . . . . . . . . . . . . . . Samples . . . . . . . . . . . . . . . . . . Roughness Factor . . . . . . . . . . . . . Test Matrix for Nanopatterned Polymers .

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58 58 59 61 62

14.3 14.3.1 14.3.2

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . Hydrophobic Leaf Surfaces . . . . . . . . . . . . . . . . . . . . . . Nanopatterned Polymers . . . . . . . . . . . . . . . . . . . . . . .

63 64 74

14.4

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Probing Macromolecular Dynamics and the Influence of Finite Size Effects Scott Sills, René M. Overney . . . . . . . . . . . . . . . . . . . . .

83

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

Contents – Volume III

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15.2

The Glass Transition and Molecular Mobility . . . . . . . . . . . .

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15.3 15.3.1 15.3.2 15.3.3 15.3.4 15.3.5 15.3.6

Macromolecular Probing Techniques . . . . . . . . . . . . . Static Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . Modulated Contacts . . . . . . . . . . . . . . . . . . . . . . . Calibration of Lateral Forces in Scanning Probe Microscopy . Shear Modulation Force Microscopy (SM-FM) . . . . . . . . Friction Force Microscopy (FFM) . . . . . . . . . . . . . . . Tribological Models for FFM . . . . . . . . . . . . . . . . . .

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90 90 92 93 97 98 99

15.4 15.4.1 15.4.2 15.4.3

Internal Friction and Dynamics near the Glass Transition . . . . . Molecular Relaxations . . . . . . . . . . . . . . . . . . . . . . . . Structural Heterogeneity and Relaxation near the Glass Transition Cooperative Molecular Motion During the Glass Transition . . . .

103 103 105 107

15.5 15.5.1 15.5.2 15.5.3 15.5.4

Constraints and Structural Modifications near Interfaces Interfacial Plasticization . . . . . . . . . . . . . . . . . . Dewetting Kinetics . . . . . . . . . . . . . . . . . . . . Disentanglement Barriers . . . . . . . . . . . . . . . . . Interfacial Glass Transition Profiles . . . . . . . . . . .

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109 109 110 111 113

15.6 15.6.1 15.6.2 15.6.3

Mechanical Operations in Nanoscopic Polymer Systems Indentation Contact Mechanics . . . . . . . . . . . . . . Rim Formation During Indentation . . . . . . . . . . . . Strain Shielding and Confined Plasticity in Nanoscopic Polymer Systems . . . . . . . . . . . . .

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115 116 120

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122

Closing Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Investigation of Organic Supramolecules by Scanning Probe Microscopy in Ultra-High Vacuum Laurent Nony, Enrico Gnecco, Ernst Meyer . . . . . . . . . . . . .

131

16.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

131

16.2 16.2.1 16.2.2 16.2.3

Methods . . . . . . . . . . . . . . . . . . . Organic Molecular Beam Epitaxy (OMBE) Scanning Tunneling Microscopy (STM) . . Atomic Force Microscopy (AFM) . . . . .

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132 132 134 137

16.3 16.3.1 16.3.2 16.3.3 16.3.4 16.3.5 16.3.6 16.3.7

Molecules . . . . . . . . . . Fullerenes . . . . . . . . . . Porphyrins . . . . . . . . . . Phthalocyanines . . . . . . . Perylene Derivatives . . . . . Lander Molecules . . . . . . PVBA Molecules . . . . . . Decacyclene and Derivatives

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Contents – Volume III

16.4 16.4.1 16.4.2

Molecules on Metals . . . . . . . . . . . . . . . . . . . . . . . . . STM Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . Non-Contact AFM Investigations . . . . . . . . . . . . . . . . . .

145 145 157

16.5 16.5.1 16.5.2

Molecules on Semiconductor Surfaces . . . . . . . . . . . . . . . . STM Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . Non-Contact AFM Investigations . . . . . . . . . . . . . . . . . .

162 162 165

16.6 16.6.1 16.6.2

Molecules on Insulating Surfaces . . . . . . . . . . . . . . . . . . . STM Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . Non-contact AFM Investigations . . . . . . . . . . . . . . . . . . .

167 168 169

16.7 16.7.1 16.7.2

Manipulation of Single Molecules . . . . . . . . . . . . . . . . . . STM Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . Non-contact AFM Investigations . . . . . . . . . . . . . . . . . . .

171 171 175

16.8

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

175

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17

One- and Two-Dimensional Systems: Scanning Tunneling Microscopy and Spectroscopy of Organic and Inorganic Structures Luca Gavioli, Massimo Sancrotti . . . . . . . . . . . . . . . . . . .

183

17.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Basic Principles of STM and STS . . . . . . . . . . . . . . . . . .

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17.3 17.3.1 17.3.2

Inorganic Overlayers . . . . . . . . . . . . . . . . . . . . . . . . . 1D Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2D Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

188 188 196

17.4 17.4.1 17.4.2

Molecular Overlayers . . . . . . . . . . . . . . . . . . . . . . . . . 1D Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2D Overlayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

201 202 208

17.5

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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18

Scanning Probe Microscopy Applied to Ferroelectric Materials Oleg Tikhomirov, Massimiliano Labardi, Maria Allegrini . . . . . .

217

18.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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18.2

Development of Scanning Probe Techniques for Ferroelectrics . .

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18.3 18.3.1 18.3.2 18.3.3

Scanning Force Microscopy Non-Contact Mode . . . . . Contact Mode . . . . . . . . Voltage-Modulated SFM . .

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Contents – Volume III

XIII

18.3.4 18.3.5 18.3.6 18.3.7 18.3.8

Resonance Modes of EFM Lateral Force . . . . . . . . Frontal Force . . . . . . . . Second Harmonic . . . . . Tapping Mode . . . . . . .

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18.4 18.4.1 18.4.2 18.4.3 18.4.4 18.4.5

Scanning Optical Microscopy . . . Pure Optical Microscopy . . . . . . Scanning Electrooptic Microscopy . Near-Field Electrooptic Microscopy Micro-Spectroscopic Techniques . . Second Harmonic Microscopy . . .

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18.5 18.5.1 18.5.2 18.5.3 18.5.4 18.5.5 18.5.6 18.5.7

Applications to Ferroelectrics . . . . . . Imaging of Domains and Domain Walls Writing Patterns . . . . . . . . . . . . . Phase Transitions . . . . . . . . . . . . Morphotropic Phase Boundary . . . . . Relaxors . . . . . . . . . . . . . . . . . Thin Films . . . . . . . . . . . . . . . . Artificial Nanostructures . . . . . . . .

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247 247 248 249 250 251 251 252

18.6

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

253

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

254

19

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Morphological and Tribological Characterization of Rough Surfaces by Atomic Force Microscopy Renato Buzio, Ugo Valbusa . . . . . . . . . . . . . . . . . . . . . .

261

19.1.1 19.1.2 19.1.3

Characterization of Surface Roughness by Atomic Force Microscopy . . . . . . . . . . . . . . . . . . . . . Statistical Methods for Stationary Random Surfaces . . . . . . . . Statistical Methods for Fractal Surfaces . . . . . . . . . . . . . . . Estimation of Morphological Parameters from AFM Topographies

263 264 266 270

19.2 19.2.1 19.2.2 19.2.3

Modeling Contact Mechanics for Rough Surfaces . . Early Phenomenological Contact Theories . . . . . Contact Mechanics Theories for Fractal Roughness . On the Molecular Origins of Amontons’ Law . . . .

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272 273 277 284

19.3 19.3.1

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286

19.3.2 19.3.3

Investigations of Multi-Asperity Contacts by AFM . . . . . AFM Characterization of Surface Roughness for Tribological Purposes . . . . . . . . . . . . . . . . . . . Contact Mechanics Investigations at the Nanometer Scale . Contact Mechanics Investigations on the Micrometer Scale

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286 288 291

19.4

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

293

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

294

19.1

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XIV

20

Contents – Volume III

AFM Applications for Contact and Wear Simulation Nikolai K. Myshkin, Mark I. Petrokovets, Alexander V. Kovalev . .

299

20.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

299

20.2

Scale Factor in Tribology . . . . . . . . . . . . . . . . . . . . . . .

299

20.3 20.3.1 20.3.2 20.3.3 20.3.4 20.3.5

AFM as a Tool of Contact Simulation . . . Contact of Rough Surfaces . . . . . . . . . Rough Contact with Adhesion . . . . . . . Multilevel Contact Models . . . . . . . . . Simulation of Contact Using AFM Images Nanomechanical Probing of Soft Layers . .

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300 300 303 307 309 312

20.4 20.4.1 20.4.2

AFM in Wear Simulation . . . . . . . . . . . . . . . . . . . . . . . Nanoscratching and Nanowear with AFM Tip . . . . . . . . . . . . Wear Simulation in AFM Contact Mode . . . . . . . . . . . . . . .

316 317 320

20.5

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

323

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

324

21

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AFM Applications for Analysis of Fullerene-Like Nanoparticles Lev Rapoport, Armen Verdyan . . . . . . . . . . . . . . . . . . . .

327

21.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

327

21.2 21.2.1 21.2.2

Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . Friction Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . AFM Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . .

328 328 329

21.3

Characterization of Fullerene-Like Solid Lubricant Nanoparticles .

330

21.4

Friction of Solid Lubricant Films . . . . . . . . . . . . . . . . . . .

331

21.5

Friction and Wear of the Surfaces Lubricated with Oil + IF Nanoparticles . . . . . . . . . . . . . . . . . . . . . .

333

21.6

Friction of IF Nanoparticles Under Severe Contact Conditions . .

336

21.7

Mechanisms of Friction of the IF Nanoparticles . . . . . . . . . .

339

21.8

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

341

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

341

22

Scanning Probe Methods in the Magnetic Tape Industry James K. Knudsen . . . . . . . . . . . . . . . . . . . . . . . . . . .

343

22.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

343

22.2

Atomic Force Microscopy . . . . . . . . . . . . . . . . . . . . . .

345

Contents – Volume III

XV

22.2.1 22.2.2 22.2.3

Topographic Characterization of the Magnetic Tape . . . . . . . . Topographic Characterization of Heads . . . . . . . . . . . . . . . Tape Roughness Analysis . . . . . . . . . . . . . . . . . . . . . . .

345 349 351

22.3 22.3.1 22.3.2 22.3.3

Magnetic Force Microscopy . . . . . . . . . . . . Methodology . . . . . . . . . . . . . . . . . . . . . Characterization of the Magnetic Tape with MFM Characterization of Heads with MFM . . . . . . .

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358 358 359 364

22.4

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

367

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

367

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Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

Contents – Volume II

1

Higher Harmonics in Dynamic Atomic Force Microscopy Robert W. Stark, Martin Stark . . . . . . . . . . . . . . . . . . . .

1

1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.2.7 1.2.8

Multimodal Model of the Microcantilever . . . Overview . . . . . . . . . . . . . . . . . . . . . Modal Analysis . . . . . . . . . . . . . . . . . Tip–Sample Interaction . . . . . . . . . . . . . State Space Formulation . . . . . . . . . . . . Dynamics: Linearized Tip–Sample Interaction Poles and Zeros . . . . . . . . . . . . . . . . . Dynamics: Nonlinear Interaction . . . . . . . . Optical Readout . . . . . . . . . . . . . . . . .

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4 4 5 7 9 11 13 16 20

1.3

Higher Harmonic Imaging . . . . . . . . . . . . . . . . . . . . . .

23

1.4 1.4.1 1.4.2 1.4.3

Spectroscopy: Distinguishing Two Polymers Overview . . . . . . . . . . . . . . . . . . . . Experimental Details . . . . . . . . . . . . . Signal Analysis . . . . . . . . . . . . . . . .

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27 27 28 28

1.5

Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

2

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Atomic Force Acoustic Microscopy Ute Rabe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

2.1 2.1.1 2.1.2 2.1.3

Introduction . . . . . . . . . . . . . . . . . . . . . Near-field Acoustic Microscopy . . . . . . . . . . Scanning Probe Techniques and Nanoindentation . Vibration Modes of AFM Cantilevers . . . . . . .

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38 39 40 41

2.2 2.2.1 2.2.2 2.2.3

Linear Contact-resonance Spectroscopy Using Flexural Modes Flexural Vibrations of Clamped-free Beams . . . . . . . . . . . The Point-mass Model . . . . . . . . . . . . . . . . . . . . . . Experiments with Clamped-free Beams . . . . . . . . . . . . .

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42 44 47 48

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XVIII

Contents – Volume II

2.3

Contact Forces as Linear Springs and Dashpots . . . . . . . . . . .

51

2.4 2.4.1 2.4.2 2.4.3

Characteristic Equation of the Surface-coupled Beam Discussion of the Characteristic Equation . . . . . . . Influence of an Additional Mass . . . . . . . . . . . . Roots of the Characteristic Equation with Damping . .

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55 58 61 63

2.5

Forced Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

2.6

Imaging and Contrast Inversion . . . . . . . . . . . . . . . . . . .

70

2.7

Sensitivity of the Flexural Modes . . . . . . . . . . . . . . . . . . .

73

2.8 2.8.1

Quantitative Evaluation . . . . . . . . . . . . . . . . . . . . . . . . Experiments for Quantitative Evaluation . . . . . . . . . . . . . . .

76 78

2.9

Nonlinear Forces . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

2.10

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

A A.1 A.2 A.3

Appendix . . . Definitions . . UAFM-mode . AFAM-mode .

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84 84 85 86

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

3

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Scanning Ion Conductance Microscopy Tilman E. Schäffer, Boris Anczykowski, Harald Fuchs . . . . . . .

91

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

3.2 3.2.1 3.2.2 3.2.3

Fundamental Principles Basic Setup . . . . . . Nanopipettes . . . . . . Electrodes . . . . . . .

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92 92 95 96

3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5

Ion Currents Through Nanopipettes . . Background Theory . . . . . . . . . . . Simple Analytical Model . . . . . . . . Finite Element Modeling . . . . . . . . Experimental Current-Distance Curves Imaging with Ion Current Feedback . .

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97 97 97 99 101 102

3.4 3.4.1 3.4.2

Advanced Techniques . . . . . . . . . . . . . . . . . . . . . . . . . Modulation Methods . . . . . . . . . . . . . . . . . . . . . . . . . Applications in Bioscience . . . . . . . . . . . . . . . . . . . . . .

103 104 106

3.5 3.5.1 3.5.2 3.5.3

Combination with Other Scanning Techniques Combination with Atomic Force Microscopy . Application in Material Science . . . . . . . . Combination with Shear Force Microscopy . .

107 108 108 111

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Contents – Volume II

XIX

3.5.4

Application in Bioscience . . . . . . . . . . . . . . . . . . . . . . .

114

3.6

Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

115

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

116

4

Spin-Polarized Scanning Tunneling Microscopy Wulf Wulfhekel, Uta Schlickum, Jürgen Kirschner . . . . . . . . . .

121

4.1 4.1.1 4.1.2 4.1.3

Introduction . . . . . . . . . . . . . . . . . . . The Resolution Problem in Magnetic Imaging Magnetism and Spin . . . . . . . . . . . . . . . The Tunneling Magnetoresistance Effect . . .

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121 121 122 122

4.2 4.2.1 4.2.2 4.2.3

The Principle of Spin-polarized Scanning Tunneling Microscopy The Constant Current Mode . . . . . . . . . . . . . . . . . . . . The Spectroscopic Mode . . . . . . . . . . . . . . . . . . . . . . Differential Magnetic Imaging Mode . . . . . . . . . . . . . . .

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124 125 125 126

4.3

Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . .

127

4.4 4.4.1 4.4.2

Ferromagnetic Domains and Domain Walls . . . . . . . . . . . . . Ultra-sharp Domain Walls in Co(0001) . . . . . . . . . . . . . . . Asymmetric Néel Caps in Fe(001) . . . . . . . . . . . . . . . . . .

128 129 131

4.5 4.5.1 4.5.2

Antiferromagnets in Contact with Ferromagnets . . . . . . . . . . Mn on Fe(001) and Topologically Induced Frustrations . . . . . . The Layered Antiferromagnet Cr on Fe(001) . . . . . . . . . . . .

133 133 136

4.6 4.6.1 4.6.2

Bulk Versus Surface: Which Electronic States Cause the Spin Contrast? . . . . . . . . . Voltage Dependence of the TMR Effect in Co(0001) . . . . . . . . Voltage Dependence of the TMR Effect in Cr/Fe(001) . . . . . . .

137 137 139

4.7

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

140

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

140

5

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Dynamic Force Microscopy and Spectroscopy Ferry Kienberger, Hermann Gruber, Peter Hinterdorfer . . . . . .

143

5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

144

5.2

Scanning Probe Microscopy . . . . . . . . . . . . . . . . . . . . .

145

5.3

Dynamic Force Microscopy Imaging . . . . . . . . . . . . . . . . .

146

5.4 5.4.1 5.4.2 5.4.3

Force Spectroscopy Principles . . . . . Theory . . . . . . . Applications . . . .

149 149 151 153

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XX

Contents – Volume II

5.5

Combined Imaging and Spectroscopy . . . . . . . . . . . . . . . .

158

5.6

Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . .

161

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

161

6

Sensor Technology for Scanning Probe Microscopy and New Applications Egbert Oesterschulze, Leon Abelmann, Arnout van den Bos, Rainer Kassing, Nicole Lawrence, Gunther Wittstock, Christiane Ziegler . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

6.1

Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . .

165

6.2 6.2.1

Material Aspects of Probe Fabrication . . . . . . . . . . . . . . . . Mechanical Properties of Cantilever Probes . . . . . . . . . . . . .

166 167

6.3 6.3.1 6.3.2

Scanning Near-Field Optical Microscopy . . . . . . . . . . . . . . Principle of Near-Field Optics . . . . . . . . . . . . . . . . . . . . Probes for Scanning Near-Field Optical Microscopy (SNOM) . . .

174 174 175

6.4 6.4.1

Probes for Ultrafast Scanning Probe Microscopy . . . . . . . . . . Improved Sampling Technique . . . . . . . . . . . . . . . . . . . .

179 181

6.5 6.5.1 6.5.2

Functionalized Tips . . . . . . . . . . . . . . . . . . . . . . . . . . Tip Modification . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

182 182 183

6.6 6.6.1 6.6.2

Scanning Electrochemical Microscopy . . . . . . . . . . . . . . . . Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

186 186 189

6.7 6.7.1 6.7.2 6.7.3 6.7.4

Tips for Magnetic Force Microscopy . Ideal Tip Shape . . . . . . . . . . . . Hand-Made Tips . . . . . . . . . . . . Coating AFM Tips . . . . . . . . . . Tip Planes: The CantiClever Concept

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192 192 193 194 195

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

197

7

7.1 7.1.1 7.1.2 7.1.3 7.1.4

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Quantitative Nanomechanical Measurements in Biology Małgorzata Lekka, Andrzej J. Kulik . . . . . . . . . . . . . . . . . Stiffness of Biological Samples . . . . . . . Cell Structure . . . . . . . . . . . . . . . . Determination of Young’s Modulus . . . . Brief Overview of the Application of AFM to Studies of Living Cells . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . .

205

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205 205 208

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217 222

Contents – Volume II

7.2 7.2.1 7.2.2 7.2.3

XXI

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224 225 229 236

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

237

8

Friction Force Microscopy . . . . . . . . Friction and Chemical Force Microscopy Applications of FFM/CFM . . . . . . . . Summary . . . . . . . . . . . . . . . . . .

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Scanning Microdeformation Microscopy: Subsurface Imaging and Measurement of Elastic Constants at Mesoscopic Scale Pascal Vairac, Bernard Cretin . . . . . . . . . . . . . . . . . . . .

241

8.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

241

8.2

Review and Physical Background of Near-Field Acoustic Microscopes . . . . . . . . . . . . . . . . . . . . . . Review of Near-Field Microscopes . . . . . . . . . . . . . . . Physical Basis for Near-Field Acoustics and the Scale Effect Mechanical Approach . . . . . . . . . . . . . . . . . . . . . . Models of Subsurface Sensing Using Acoustic Waves and Surface Bending . . . . . . . . . . . . . . . . . . . . . .

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242 242 244 247

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252

8.3.1 8.3.2 8.3.3

Imaging and Measurement with Scanning Microdeformation Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . Application to Subsurface Imaging . . . . . . . . . . . . . . . Characterization of Local Mechanical Constants . . . . . . .

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254 254 256 259

8.4 8.4.1 8.4.2 8.4.3

Specific Application . . . Thin Film Measurements Shape Memory Alloy . . Viscosimetry . . . . . . .

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260 260 264 267

8.5

Ultimate Metrology: Measurements at the Mechanical Noise Level

274

8.6

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

278

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

279

8.2.1 8.2.2 8.2.3 8.2.4 8.3

9

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Electrostatic Force and Force Gradient Microscopy: Principles, Points of Interest and Application to Characterisation of Semiconductor Materials and Devices Paul Girard, Alexander Nikolaevitch Titkov . . . . . . . . . . . . .

283

9.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

285

9.2 9.2.1 9.2.2

Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . Principles of Surface-voltage Measurements . . . . . . . . . . . .

285 286 287

XXII

9.2.3

Contents – Volume II

9.2.4

Detection of Strong Local Electrical Effect via the “Topographic” Data . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

294 296

9.3 9.3.1 9.3.2 9.3.3 9.3.4 9.3.5

Observation and Interpretation DC Observations . . . . . . . Ω Observations . . . . . . . . 2Ω Observations . . . . . . . Surface Voltage Observations . Guidelines for Interpretation .

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297 299 300 300 302 302

9.4 9.4.1 9.4.2 9.4.3

Future Opportunities . . . . . . . . . . . . . . . Interest in the KFGM Method . . . . . . . . . . Spatially Resolved Observations . . . . . . . . . Another Way to Estimate the Maximum Possible Spatial Resolution . . . . . . . . . . . . . . . . .

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304 304 309

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311

9.5 9.5.1 9.5.2

Some Applications . . . . . . . . . . . . . . . . . . . . . . . . . . Applications Under Ambient Conditions . . . . . . . . . . . . . . Vacuum or UHV Applications . . . . . . . . . . . . . . . . . . . .

313 314 316

9.6

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

316

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

318

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10

Polarization-Modulation Techniques in Near-Field Optical Microscopy for Imaging of Polarization Anisotropy in Photonic Nanostructures Pietro Giuseppe Gucciardi, Ruggero Micheletto, Yoichi Kawakami, Maria Allegrini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

10.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

321

10.2 10.2.1

Polarimetric Imaging . . . . . . . . . . . . . . . . . . . . . . . . . The Jones Formalism . . . . . . . . . . . . . . . . . . . . . . . . .

322 325

10.3

Electromagnetic Field Diffracted by a SNOM Aperture . . . . . .

327

10.4 10.4.1 10.4.2 10.4.3

Experimental Implementations . . . . . . . . . . . . Static Polarization SNOM . . . . . . . . . . . . . . Polarization-Modulation SNOM: Illumination Mode Polarization-Modulation SNOM: Collection Mode .

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333 333 337 342

10.5 10.5.1 10.5.2 10.5.3 10.5.4 10.5.5

Applications of SNOM Polarimetry . . . . . . . . . . . . . Polarization Responses of Photonic Waveguides . . . . . . Measuring Stress-Induced Birefringence . . . . . . . . . . . Polarization Anisotropy in Mesoscale-Structured Materials Polarization Anisotropy in Polymers . . . . . . . . . . . . . Polarization Anisotropy in Photoluminescence Emission . .

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344 345 348 349 351 354

10.6

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

357

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

357

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Contents – Volume II

11

XXIII

Focused Ion Beam as a Scanning Probe: Methods and Applications Vittoria Raffa, Piero Castrataro, Arianna Menciassi, Paolo Dario .

361

11.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

361

11.2 11.2.1 11.2.2 11.2.3 11.2.4

Description of the System . . . . . System Overview . . . . . . . . . Liquid Metal Ion Source (LMIS) . Ion Optics . . . . . . . . . . . . . Dual Beam Systems . . . . . . . .

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362 362 363 364 365

11.3 11.3.1 11.3.2 11.3.3 11.3.4 11.3.5

FIB Processes . . . . . . Imaging . . . . . . . . . Milling . . . . . . . . . . Gas-Assisted Etching . . Gas-Assisted Deposition Ion Beam Lithography .

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367 367 372 376 377 379

11.4 11.4.1 11.4.2 11.4.3

Main Applications . . . . . . . . . . FIB as an Analytical Technique . . FIB in the Semiconductor Industry . Micromachining . . . . . . . . . . .

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380 381 389 401

11.5

Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . .

408

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

409

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Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

Contents – Volume IV

23

Scanning Probe Lithography for Chemical, Biological and Engineering Applications Joseph M. Kinsella, Albena Ivanisevic . . . . . . . . . . . . . . . .

1

23.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

23.2

Modeling of the DPN Process . . . . . . . . . . . . . . . . . . . .

4

23.3 23.3.1 23.3.2 23.3.3 23.3.4

Patterning of Biological and Biologically Active Molecules . DNA Patterning . . . . . . . . . . . . . . . . . . . . . . . . . Protein Patterning . . . . . . . . . . . . . . . . . . . . . . . . Peptide Patterning . . . . . . . . . . . . . . . . . . . . . . . . Patterning of Templates for Biological Bottom-Up Assembly

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7 8 10 13 15

23.4 23.4.1 23.4.2 23.4.3 23.4.4 23.4.5 23.4.6 23.4.7 23.4.8 23.4.9 23.4.10 23.4.11

Chemical Patterning . . . . . . . . . . . . Thiols . . . . . . . . . . . . . . . . . . . ω-Substituted Thiols . . . . . . . . . . . Silanes and Silazanes . . . . . . . . . . . Deposition of Solid Organic Inks . . . . . Polymers . . . . . . . . . . . . . . . . . . Polyelectrolytes . . . . . . . . . . . . . . Dendrimers . . . . . . . . . . . . . . . . Deposition of Supramolecular Materials . Deposition of Metals . . . . . . . . . . . Deposition of Solid-State Materials . . . Deposition of Magnetic Materials . . . .

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17 17 18 19 20 21 23 23 24 25 26 27

23.5

Engineering Applications of DPN . . . . . . . . . . . . . . . . . .

28

23.6

Future Challenges and Applications . . . . . . . . . . . . . . . . .

30

23.7

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

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XXVI

24

Contents – Volume IV

Nanotribological Characterization of Human Hair and Skin Using Atomic Force Microscopy (AFM) Bharat Bhushan, Carmen LaTorre . . . . . . . . . . . . . . . . . .

35

24.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

24.2 24.2.1 24.2.2

Human Hair, Skin, and Hair Care Products . . . . . . . . . . . . . Human Hair and Skin . . . . . . . . . . . . . . . . . . . . . . . . . Hair Care: Cleaning and Conditioning Treatments, and Damaging Processes . . . . . . . . . . . . . . . . . . . . . . .

39 39

24.3 24.3.1 24.3.2

Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . Hair and Skin Samples . . . . . . . . . . . . . . . . . . . . . . . .

51 53 57

24.4 24.4.1

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78

24.4.5

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . Surface Roughness, Friction, and Adhesion for Various Ethnicities of Hair . . . . . . . . . . . . . . . . . . Surface Roughness, Friction, and Adhesion for Virgin and Chemically Damaged Caucasian Hair (with and without Commercial Conditioner Treatment) . . . . . Surface Roughness, Friction, and Adhesion for Hair Treated with Various Combinations of Conditioner Ingredients Investigation of Directionality Dependence and Scale Effects on Friction and Adhesion of Hair . . . . . . . . . . . . . . . . . Surface Roughness and Friction of Skin . . . . . . . . . . . . .

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85 98

24.5

Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

103

24.4.2

24.4.3 24.4.4

25

46

Nanofabrication with Self-Assembled Monolayers by Scanning Probe Lithography Jayne C. Garno, James D. Batteas . . . . . . . . . . . . . . . . . .

105

25.1 25.1.1 25.1.2 25.1.3 25.1.4

SPM-Based Methods of Lithography . . Bias-Induced Nanofabrication . . . . . . Force-Induced Nanofabrication of SAMs Dip-Pen Nanolithography (DPN) . . . . . Automated Scanning Probe Lithography .

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105 107 108 110 111

25.2 25.2.1 25.2.2 25.2.3

Patterning with Self-Assembled Monolayers . . . . . . . . . . . . Structure of SAMs . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples of SAM Nanopatterns Generated by Force-Induced SPL Nanofabrication of SAMs by DPN and Bias-Induced SPL . . . . .

112 112 114 118

25.3

Directed Fabrication of Polymeric Structures . . . . . . . . . . . .

120

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Contents – Volume IV

XXVII

25.4

Fabrication of Metallic Structures . . . . . . . . . . . . . . . . . .

122

25.5 25.5.1 25.5.2 25.5.3

Nanoscale Patterning of Proteins . . . . . . . . . . . . Protein Arrays Generated by DPN . . . . . . . . . . . Applying Bias-Induced SPL for Protein Nanopatterns Protein Immobilization on SAMs Generated by Force-Induced SPL . . . . . . . . . . .

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126 127 128

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129

Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . .

130

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

131

25.6

26

Fabrication of Nanometer-Scale Structures by Local Oxidation Nanolithography Marta Tello, Fernando García, Ricardo García . . . . . . . . . . .

137

26.1

Introduction to AFM Nanolithographies . . . . . . . . . . . . . . .

137

26.2

Basic Local Oxidation Aspects . . . . . . . . . . . . . . . . . . . .

138

26.3

Mechanism and Kinetics . . . . . . . . . . . . . . . . . . . . . . .

141

26.4

Feature Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

143

26.5

Applications I: Patterning, Data Storage and Template Growth . .

146

26.6

Applications II: Nanoelectronic Devices . . . . . . . . . . . . . . .

151

26.7

Parallel Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . .

154

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

155

27

Template Effects of Molecular Assemblies Studied by Scanning Tunneling Microscopy (STM) Chen Wang, Chunli Bai . . . . . . . . . . . . . . . . . . . . . . . .

159

27.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

159

27.2

27.2.2 27.2.3 27.2.4

Single Guest Molecule Immobilization with Assembled Molecular Networks . . . . . Hydrogen Bonded Supramolecular Networks and Single Molecule Inclusions . . . . . . . . Van der Waals Interaction Stabilized Networks Metal-Organic Coordination Networks . . . . Covalently Bonded Molecular Grids . . . . . .

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160

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160 163 165 166

27.3 27.3.1 27.3.2

Intralayer Heterogeneous Molecular Arrays . . . . . . . . . . . . . Hydrogen Bond Stabilized Heterogeneous Lamellae . . . . . . . . Van der Waals Interaction Stabilized Intralayer Arrays . . . . . . .

166 167 168

27.4 27.4.1

Interlayer Effect on Molecular Adsorption and Assemblies . . . . Site Selective Adsorption . . . . . . . . . . . . . . . . . . . . . . .

171 172

27.2.1

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XXVIII

Contents – Volume IV

27.4.2 27.4.3

Molecular Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . Directional Assembly of Nanoparticle Arrays . . . . . . . . . . . .

176 177

27.5

Future Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . .

179

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

179

28

Microfabricated Cantilever Array Sensors for (Bio-)Chemical Detection Hans Peter Lang, Martin Hegner, Christoph Gerber . . . . . . . .

183

28.1 28.1.1 28.1.2 28.1.3 28.1.4

Introduction . . . . . . . . . Sensors . . . . . . . . . . . . Cantilevers . . . . . . . . . . Cantilever Operating Modes Cantilever Arrays . . . . . .

. . . . .

183 183 184 186 192

28.2 28.2.1 28.2.2

Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement Chamber . . . . . . . . . . . . . . . . . . . . . . . . Cantilever Functionalization . . . . . . . . . . . . . . . . . . . . .

196 196 198

28.3 28.3.1 28.3.2

Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Artificial Nose for Detection of Perfume Essences . . . . . . . . . Label-Free DNA Hybridization Detection . . . . . . . . . . . . . .

203 204 206

28.4

Applications and Outlook . . . . . . . . . . . . . . . . . . . . . . .

209

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

210

29

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Nano-Thermomechanics: Fundamentals and Application in Data Storage Devices B. Gotsmann, U. Dürig . . . . . . . . . . . . . . . . . . . . . . . .

215

29.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

215

29.2 29.2.1 29.2.2 29.2.3 29.2.4

Heat Transfer Mechanisms . . . . . . . . . . . . . . Heat Generation in Microcantilevers . . . . . . . . . Heat Transfer Through Air and Silicon . . . . . . . Heat Transfer Through Radiation . . . . . . . . . . . Heat Transfer Through a Tip-Surface Point Contact

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215 216 217 222 224

29.3

Momentum Transfer Through Air . . . . . . . . . . . . . . . . . .

227

29.4 29.4.1 29.4.2 29.4.3 29.4.4 29.4.5 29.4.6 29.4.7

Thermomechanical Nanoindentation of Polymers . . . General Considerations . . . . . . . . . . . . . . . . . Indentation Experiments . . . . . . . . . . . . . . . . Interlude: Carbon Nanotube Tips . . . . . . . . . . . . Interlude: Thermal Force and Indentation Formation . Interlude: Rim Formation on Polymer Samples . . . . Indentation Kinetics and the Indentation Mechanism . Interlude: Thermo-Nano-Mechanics Without a Heater

229 229 230 232 234 234 236 239

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Contents – Volume IV

XXIX

29.5

Thermomechanical Nanowear Testing . . . . . . . . . . . . . . . .

241

29.6 29.6.1 29.6.2

Application to Data-Storage Devices . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scaling Challenges for Nanoindentation of Polymers . . . . . . . .

243 243 245

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

248

30

Applications of Heated Atomic Force Microscope Cantilevers Brent A. Nelson, William P. King . . . . . . . . . . . . . . . . . . .

251

30.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

251

30.2 30.2.1 30.2.2 30.2.3

Physical and Environmental Sensing . . . . . . . . . . . . Pressure Sensing . . . . . . . . . . . . . . . . . . . . . . . Thermal Conductivity Mapping and Subsurface Imaging . Topographical Detection . . . . . . . . . . . . . . . . . .

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252 252 253 258

30.3 30.3.1 30.3.2 30.3.3 30.3.4

Chemical Sensing Applications . . . . . . . Calorimetry . . . . . . . . . . . . . . . . . Mass Detection . . . . . . . . . . . . . . . Time-of-Flight Scanning Force Microscopy Explosives Detection . . . . . . . . . . . .

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261 261 262 263 264

30.4 30.4.1 30.4.2

Data Storage and Lithography . . . . . . . . . . . . . . . . . . . . Data Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

264 265 269

30.5

Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . .

272

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

272

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Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

Contents – Volume I

Part I

Scanning Probe Microscopy

1

Dynamic Force Microscopy André Schirmeisen, Boris Anczykowski, Harald Fuchs . . . . . . .

3

Interfacial Force Microscopy: Selected Applications Jack E. Houston . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

Atomic Force Microscopy with Lateral Modulation Volker Scherer, Michael Reinstädtler, Walter Arnold . . . . . . . .

75

Sensor Technology for Scanning Probe Microscopy Egbert Oesterschulze, Rainer Kassing . . . . . . . . . . . . . . . .

117

Tip Characterization for Dimensional Nanometrology John S. Villarrubia . . . . . . . . . . . . . . . . . . . . . . . . . .

147

2 3 4 5

Part II

Characterization

6

Micro/Nanotribology Studies Using Scanning Probe Microscopy Bharat Bhushan . . . . . . . . . . . . . . . . . . . . . . . . . . . .

171

Visualization of Polymer Structures with Atomic Force Microscopy Sergei Magonov . . . . . . . . . . . . . . . . . . . . . . . . . . . .

207

Displacement and Strain Field Measurements from SPM Images Jürgen Keller, Dietmar Vogel, Andreas Schubert, Bernd Michel . .

253

7 8 9

AFM Characterization of Semiconductor Line Edge Roughness Ndubuisi G. Orji, Martha I. Sanchez, Jay Raja, Theodore V. Vorburger . . . . . . . . . . . . . . . . . . . . . . . . . 277

10

Mechanical Properties of Self-Assembled Organic Monolayers: Experimental Techniques and Modeling Approaches Redhouane Henda . . . . . . . . . . . . . . . . . . . . . . . . . . .

303

XXXII

11 12

Contents – Volume I

Micro-Nano Scale Thermal Imaging Using Scanning Probe Microscopy Li Shi, Arun Majumdar . . . . . . . . . . . . . . . . . . . . . . . .

327

The Science of Beauty on a Small Scale. Nanotechnologies Applied to Cosmetic Science Gustavo Luengo, Frédéric Leroy . . . . . . . . . . . . . . . . . . .

363

Part III Industrial Applications 13 14 15

16

SPM Manipulation and Modifications and Their Storage Applications Sumio Hosaka . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

389

Super Density Optical Data Storage by Near-Field Optics Jun Tominaga . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

429

Capacitance Storage Using a Ferroelectric Medium and a Scanning Capacitance Microscope (SCM) Ryoichi Yamamoto . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Room-Temperature Single-Electron Devices formed by AFM Nano-Oxidation Process Kazuhiko Matsumoto . . . . . . . . . . . . . . . . . . . . . . . . .

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Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

List of Contributors – Volume III

Maria Allegrini INFM and Dipartimento di Fisica “Enrico Fermi”, Università di Pisa Largo Bruno Pontecorvo 3, 56127 Pisa, Italy e-mail: [email protected] Friedrich Aumayr Institut für Allgemeine Physik, Technische Universität Wien Wiedner Hauptstraße 8-10/134, A 1040 Wien, Austria e-mail: [email protected] Bharat Bhushan Nanotribology Laboratory for Information Storage and MEMS/NEMS (NLIM) 650 Ackerman Road, Suite 255, The Ohio State University Columbus, OH 43202-1107, USA e-mail: [email protected] Zachary Burton Shell Global Solutions (US) Inc. 3333 Highway 6 South, Houston, TX 77082-3101, USA e-mail: [email protected] Renato Buzio National Institute for Physics of Matter INFM Via Dodecaneso 33, 16146 Genova, Italy e-mail: buzio@fisica.unige.it Manfred Drack GrAT Center for Appropriate Technology, Technische Universität Wien Wiedner Hauptstraße 8-10/965, A 1040 Wien, Austria e-mail: [email protected] Andreas Ebner Institute for Biophysics, J. Kepler University Altenbergerstr. 69, A-4040 Linz, Austria e-mail: [email protected]

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List of Contributors – Volume III

Friedrich Franek Austrian Center of Competence for Tribology Viktor Kaplan-Straße 2, A 2700 Wiener Neustadt, Austria Institut für Sensor- und Aktuatorsysteme, Technische Universität Wien Floragasse 7/2, A 1040 Wien, Austria e-mail: [email protected] Luca Gavioli INFM and Dipartimento di Matematica e Fisica Università Cattolica del Sacro Cuore via dei Musei 41, I-25121 Brescia, Italy e-mail: [email protected] Ille C. Gebeshuber Austrian Center of Competence for Tribology Viktor Kaplan-Straße 2, A 2700 Wiener Neustadt, Austria Institut für Allgemeine Physik, Technische Universität Wien Wiedner Hauptstraße 8-10/134, A 1040 Wien, Austria e-mail: [email protected] Enrico Gnecco National Center of Competence in Research in Nanoscale Science University of Basel 4056 Basel, Switzerland e-mail: [email protected] Peter Hinterdorfer Institute for Biophysics, J. Kepler University Altenbergerstr. 69, A-4040 Linz, Austria e-mail: [email protected] James K. Knudsen 3328 York Bay, Woodbury, MN 55125 e-mail: [email protected] Alexander V. Kovalev Tribology Department Metal-Polymer Research Institute of Belarus National Academy of Sciences Kirov st. 32A, Gomel, 246652, Belarus e-mail: [email protected] Massimiliano Labardi INFM, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy e-mail: [email protected] Tobias Lange Institute of Physiology II Robert-Koch Str. 27b, 48149 Muenster, Germany e-mail: [email protected]

List of Contributors – Volume III

Ernst Meyer National Center of Competence in Research in Nanoscale Science University of Basel 4056 Basel, Switzerland e-mail: [email protected] Nikolai K. Myshkin Tribology Department Metal-Polymer Research Institute of Belarus National Academy of Sciences Kirov st. 32A, Gomel, 246652, Belarus e-mail address: [email protected] Dessy Nikova Institute of Physiology II Robert-Koch Str. 27b, 48149 Muenster, Germany e-mail: [email protected] Laurent Nony L2MP, Equipe Nanostructuration, Faculté des Sciences de Saint-Jérôme 13397 Marseille, France e-mail: [email protected] Hans Oberleithner Institute of Physiology II Robert-Koch Str. 27b, 48149 Muenster, Germany e-mail: [email protected] René M. Overney Department of Chemical Engineering, University of Washington Box 351750, Seattle, WA 98195-1750, USA e-mail: [email protected] Mark I. Petrokovets Tribology Department Metal-Polymer Research Institute of Belarus National Academy of Sciences Kirov st. 32A, Gomel, 246652, Belarus e-mail: [email protected] Lev Rapoport Department of Science, Holon Academic Institute of Technology 52 Golomb St., Holon 58102, Israel e-mail: [email protected] Massimo Sancrotti INFM and Dipartimento di Matematica e Fisica Università Cattolica del Sacro Cuore via dei Musei 41, I-25121 Brescia, Italy Laboratorio TASC-INFM Strada Statale 14, km. 163.5, Basovizza, I-34012 Trieste, Italy e-mail: [email protected]

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Hermann Schillers Institute of Physiology II Robert-Koch Str. 27b, 48149 Muenster, Germany e-mail: [email protected] Scott Sills Department of Chemical Engineering, University of Washington Box 351750, Seattle, WA 98195-1750, USA e-mail: [email protected] Oleg Tikhomirov Institute of Solid State Physics, Chernogolovka 142432, Russia INFM, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy e-mail: [email protected] Ugo Valbusa National Institute for Physics of Matter INFM and Dipartimento di Fisica dell’Università degli Studi di Genova Via Dodecaneso 33, 16146 Genova, Italy e-mail: valbusa@fisica.unige.it Armen Verdyan Department of Science, Holon Academic Institute of Technology 52 Golomb St., Holon 58102, Israel e-mail: [email protected] Hannspeter Winter Institut für Allgemeine Physik, Technische Universität Wien Wiedner Hauptstraße 8-10/134, A 1040 Wien, Austria e-mail: [email protected]

List of Contributors – Volume II

Leon Abelmann Systems and Materials for Information storage group MESA + Research Institute P.O. Box 217, 7500 AE Enschede, The Netherlands e-mail: [email protected] Maria Allegrini INFM and Dipartimento di Fisica “Entrico Fermi”, Università di Pisa Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy e-mail: [email protected] Boris Anczykowski nanoAnalytics GmbH, Gievenbecker Weg 11, 48149 Münster, Germany e-mail: [email protected] Piero Castrataro Scuola Superiore Sant’Anna, Polo Sant’Anna Valdera – CRIM Lab Viale Rinaldo Piaggio, 34, 56025 Pontedera (PI), Italy e-mail: [email protected] Bernard Cretin Department LPMO, FEMTO-ST Institute, UMR CNRS 6174 32 avenue de l’Observatoire, 25044 Besançon Cedex, France e-mail: [email protected] Paolo Dario Scuola Superiore Sant’Anna, Polo Sant’Anna Valdera – CRIM Lab Viale Rinaldo Piaggio, 34, 56025 Pontedera (PI), Italy e-mail: [email protected] Harald Fuchs Center for Nanotechnology (CeNTech) and Institute of Physics University of Münster, Gievenbecker Weg 11, 48149 Münster, Germany e-mail: [email protected] Paul Girard LAIN, UMR CNRS 5011, CC 082, Université de Montpellier II Place E. Bataillon, 34095 Montpellier Cedex 5, France e-mail: [email protected]

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List of Contributors – Volume II

Hermann Gruber Institute for Biophysics, J. Kepler University Altenbergerstr. 69, A-4040 Linz, Austria e-mail: [email protected] Pietro Giuseppe Gucciardi CNR-Istituto per i Processi Chimico-Fisici Via La Farina 237, I-98123 Messina, Italy e-mail: [email protected] Peter Hinterdorfer Institute for Biophysics, J. Kepler University Altenbergerstrasse 69, A-4040 Linz, Austria e-mail: [email protected] Rainer Kassing University of Kassel Institute for Microstructure Technologies and Analytics, IMA Technological Physics Heinrich-Plett-Str. 40, D-34132 Kassel, Germany e-mail: [email protected] Yoichi Kawakami Department of Electronic Science, Graduate School of Engineering Kyoto University, Nishikyo-ku, Katsura, 615-8510 Kyoto, Japan e-mail: [email protected] Ferry Kienberger Institute for Biophysics, J. Kepler University Altenbergerstr. 69, A-4040 Linz, Austria e-mail: [email protected] Jürgen Kirschner Max-Planck-Institut für Mikrostrukturphysik Weinberg 2, 06120 Halle, Germany e-mail: [email protected] Andrzej J. Kulik Ecole Polytechnique Fédérale de Lausanne EPFL – IPMC – NN 1015 Lausanne, Switzerland e-mail: Andrzej.Kulik@epfl.ch Nicole Lawrence (geb. Schwendler) Technische Universität Kaiserslautern Erwin-Schrödinger Strasse, 67663 Kaiserslautern, Germany e-mail: [email protected]

List of Contributors – Volume II

Małgorzata Lekka The Henryk Niewodniczañski Institute of Nuclear Physics Polish Academy of Sciences Radzikowskiego 152, 31-342 Kraków, Poland e-mail: [email protected] Arianna Menciassi Scuola Superiore Sant’Anna, Polo Sant’Anna Valdera – CRIM Lab Viale Rinaldo Piaggio, 34, 56025 Pontedera (PI), Italy e-mail: [email protected] Ruggero Micheletto Department of Electronic Science, Graduate School of Engineering Kyoto University, Nishikyo-ku, Katsura, 615-8510 Kyoto, Japan e-mail: [email protected] Egbert Oesterschulze Universität Kaiserslautern, Fachbereich Physik Physik und Technologie der Nanostrukturen Erwin-Schrödinger Straße, 67653 Kaiserslautern, Germany e-mail: [email protected] Ute Rabe Fraunhofer Institute for Nondestructive Testing, IZFP, Bldg. 37 D-66123 Saarbrücken, Germany e-mail: [email protected] Vittoria Raffa Scuola Superiore Sant’Anna, Polo Sant’Anna Valdera – CRIM Lab Viale Rinaldo Piaggio, 34, 56025 Pontedera (PI), Italy e-mail: [email protected] Tilman E. Schäffer Center for Nanotechnology (CeNTech) and Institute of Physics University of Münster, Gievenbecker Weg 11, 48149 Münster, Germany e-mail: [email protected] Uta Schlickum Max-Planck-Institut für Mikrostrukturphysik Weinberg 2, 06120 Halle, Germany e-mail: uta.schlickum@epfl.ch Martin Stark Ecole Polytechnique Fédérale de Lausanne Institut des Sciences et Ingénierie Chimiques Laboratory of Ultrafast Laser Spectroscopy 1015 Lausanne, Switzerland e-mail: Martin.Stark@epfl.ch

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Robert W. Stark Ludwig-Maximilians-Universität München and Center for NanoScience (CeNS) Dept. Earth and Environmental Sciences, Section Crystallography Theresienstr. 41, 80333 München, Germany e-mail: [email protected] Alexander N. Titkov Ioffe Physico-Technical Institute, 26 Polytecknicheskaya 194021 St Petersburg, Russia e-mail: [email protected] Pascal Vairac Department LPMO, FEMTO-ST Institute, UMR CNRS 6174 32 avenue de l’Observatoire, 25044 Besançon Cedex, France e-mail: [email protected] Arnout van den Bos Systems and Materials for Information storage group MESA + Research Institute P.O. Box 217, 7500 AE Enschede, The Netherlands e-mail: [email protected] Gunther Wittstock Carl von Ossietzky Universität Oldenburg Carl von Ossietzky Str. 9–11, 26129 Oldenburg, Germany e-mail: [email protected] Wulf Wulfhekel Max-Planck-Institut für Mikrostrukturphysik Weinberg 2, 06120 Halle, Germany e-mail: [email protected] Christiane Ziegler Technische Universität Kaiserslautern Erwin-Schrödinger Strasse, 67663 Kaiserslautern, Germany e-mail: [email protected]

List of Contributors – Volume IV

Chunli Bai National Center for Nanoscience and Technology Beijing 100080, P.R. China e-mail: [email protected] James D. Batteas National Institute of Standards and Technology Surface and Microanalysis Science Division 100 Bureau Drive, Stop 8372, Gaithersburg, MD 20899 e-mail: [email protected] Bharat Bhushan Nanotribology Laboratory for Information Storage and MEMS/NEMS (NLIM) Ohio State University, Columbus, OH 43210, USA e-mail: [email protected] U. Dürig IBM Research GmbH, Zurich Research Laboratory Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland e-mail: [email protected] Fernando García Instituto de Microelectrónica de Madrid, CSIC C/ Isaac Newton 8, 28760, Tres Cantos, Madrid, Spain e-mail: [email protected] Ricardo García Instituto de Microelectrónica de Madrid, CSIC C/ Isaac Newton 8, 28760, Tres Cantos, Madrid, Spain e-mail: [email protected] Jayne C. Garno Department of Chemistry, Louisiana State University 232 Choppin Hall, Baton Rouge, LA 70803 e-mail: [email protected]

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Christoph Gerber National Competence Center of Research in Nanoscale Science, Basel Klingelbergstrasse 82, CH-4056 Basel, Switzerland e-mail: [email protected] B. Gotsmann IBM Research GmbH, Zurich Research Laboratory Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland e-mail: [email protected] Martin Hegner National Competence Center of Research in Nanoscale Science, Basel Klingelbergstrasse 82, CH-4056 Basel, Switzerland e-mail: [email protected] Albena Ivanisevic Purdue University, Weldon School of Biomedical Engineering 500 Central Drive, West Lafayette, Indiana 47907-2022 e-mail: [email protected] Joseph M. Kinsella Purdue University, Department of Biomedical Engineering 500 Central Drive, West Lafayette, Indiana 47907-2022 e-mail: [email protected] Hans Peter Lang National Competence Center of Research in Nanoscale Science, Basel Klingelbergstrasse 82, CH-4056 Basel, Switzerland IBM Zurich Research Laboratory, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland e-mail: [email protected] Carmen LaTorre Owens Corning, Insulating Systems Business 2790 Columbus Road, Route 16 (Bldg 20-1), Granville, OH 43023, USA e-mail: [email protected] William P. King Woodruff School of Mechanical Engineering, Georgia Institute of Technology 771 Ferst Drive N.W., Atlanta, GA 30332-0405 e-mail: [email protected] Brent A. Nelson Woodruff School of Mechanical Engineering, Georgia Institute of Technology 771 Ferst Drive N.W., Atlanta, GA 30332-0405 e-mail: [email protected]

List of Contributors – Volume IV

Marta Tello Instituto de Microelectrónica de Madrid, CSIC C/ Isaac Newton 8, 28760, Tres Cantos, Madrid, Spain e-mail: [email protected] Chen Wang National Center for Nanoscience and Technology Beijing 100080, P.R. China e-mail: [email protected]

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12 Atomic Force Microscopy in Nanomedicine Dessy Nikova · Tobias Lange · Hans Oberleithner · Hermann Schillers · Andreas Ebner · Peter Hinterdorfer

12.1 AFM in Biological Sciences Advances in our understanding of molecular and cellular biology were and still are dictated by the development of new techniques, allowing the structural and functional study of living material. This started with van Leeuwenhoek’s “craving after knowledge” leading to the discovery of the first microscope in the 17th century, which made the visualization of individual cells possible. His powerful magnifying glasses have laid the foundations for many revolutions in biology. Since then the development of new microscopes have allowed us to observe smaller and smaller structures, ranging from sub-cellular components to individual molecules. Undoubtedly, elucidating the three dimensional structures of proteins, nucleic acids and assemblies of these macromolecules at a molecular level is critical to gain insight into their biological function. Using techniques such as X-ray diffraction, nuclear magnetic resonance (NMR) and electron microscopy (EM), a wealth of information on the structure and function of individual biomolecules has been gathered. However, those standard structural tools also have limitations, e.g. (i) difficulties in crystallization of multimeric membrane proteins may limit the general use of X-ray diffraction; (ii) solution NMR studies of macromolecular structure and dynamics have size restriction that limits the studied structures; and (iii) the contrast is low in biological EM, thus additional sample preparation is required. It thus seems clear that future progress in revealing the complex machinery of the cell will depend in part on additional and perhaps ground-breaking developments in structural biology techniques. In this regard, recently considerable attention has focused upon the biological and biomedical applications of the atomic force microscopy (AFM), and in particular on its ability to directly “look at” both the biomolecule structure and dynamics at the single molecule level with outstanding signal-to-noise ratio. Initially designed as a technique for the solid-state material sciences [1], nowadays AFM has completely crossed the limits of its traditional areas of application and it is routinely used as a diagnostic probe of biomaterials. The breakthrough came with the development of the liquid cell, which permits the observation of samples in buffer solutions [2]. However, the first images of DNA molecules obtained with contact mode AFM were encouraging, but often very irreproducible as a result of the movement of the molecules under the tip. In contact mode, the tip is scanned over the surface, maintaining a constant deflection (i.e. force). The created large lateral forces can easily sweep away or deform the fragile biomolecules encountered. This problem was greatly reduced upon the invention of the tapping-mode in liquid [3].

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Since the tip is oscillating, it only probes (or touches) the sample for a very short time, reducing lateral forces on the molecules enormously. Therefore, this mode allows imaging of very delicate biological samples. The unique potentials of AFM to image biological substrates with molecular or even sub-molecular resolution under physiological conditions in a non-damaging manner, where the native structure and function of the biomolecules under investigation are preserved, make this technique very attractive to biologists. To this end, AFM has been used in a broad scope of biological investigations, ranging from high-resolution of the arrangement of membrane proteins within two-dimensional arrays [4] and, e.g. Fig. 12.1, to determination of the structure of protein–DNA complexes such as nucleosomes [5]; also from molecular manipulation [6] to real-time visualization of DNA degradation [7] and, e.g. Fig. 12.2; or from pulling of nucleic acids [8] to imaging of cells [9] and force mapping to measure properties such as the cell elasticity [10]. The cell, the basic unit of life, is considered as one of the building blocks in all organisms. Early biologists saw cells as simple membranous sacs containing fluid and a few floating particles. It is known today that cells are infinitely more complex than this. There are many different types, sizes, and shapes of cells, each possessing unique functions in the body. Just, e.g. the cell membrane itself, by which every cell is enclosed, is a multifunctional dynamic organization of lipid bilayers and proteins (Fig. 12.3). The role of the membrane is not only to maintain the integrity of the cell but to perform a variety of physiologically important functions as well. The plasma membrane with its embedded membrane proteins is the locus of all communications of the cell with its environment. It acts as receptor sites, controls the transport of molecules into and out of the cell and maintains signal transfer between cells, e.g. of the nervous system by membrane potential. However, if dysfunctional, those membrane proteins could be the cause of many diseases. The misfolding of the protein three-dimensional macromolecule structure, e.g. is recognized as such a factor in cystic fibrosis (CF) [11], and Parkinson’s and Alzheimer’s disease [12]. CF is a lethal genetic disease affecting approximately one in 3200 people. CF is mainly the result of an incorrectly folded membrane protein called the cystic fibrosis transmembrane regulator (CFTR). In a healthy organism, CFTR functions as

Fig. 12.1. High-resolution AFM image of light harvesting complexes LH2 from photosynthetic purple bacterium assembled in two-dimensional arrays

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Fig. 12.2. An enzymatic degradation of plasmid DNA. (a–f) Consecutive AFM images in buffer solution with a time interval of 30 s, revealing the action of DNase I (indicated by arrows). Bar 100 nm, z-range = 6 nm

Fig. 12.3. Schematic of a cell membrane composed of a lipid bilayer and proteins

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a chloride channel and it controls several other membrane proteins by still unknown mechanisms. CFTR is known to play a crucial role in maintaining the salt and water balance on the epithelium and to regulate processes such as cell volume regulation. A mutation in the gene encoding the protein causes the deletion of the amino acid phenylalanine at position 508 (∆F508). The resulting protein (∆F508 CFTR) is misfolded and this leads to an impaired trafficking to the plasma membrane. In most of the cases when misfolded, the protein cannot be inserted into the cell membrane. The loss of CFTR functions on the surface of airway epithelial cells causing enormous obstructive airway problems and hypoxia. CFTR dysfunction is also a problem in the gastrointestinal system, where it is responsible for pancreas insufficiency and malabsorption. This chapter describes the utilization of AFM for studying cells and particularly cell microelasticity in relation to CF, and the identification of CFTR within the cell membrane at a single molecule level. Such measurement can provide considerable advantages, as it removes the data-averaging drawback inherent in the conventional techniques that record measurements over large ensembles of molecules. With the single molecule approach, the differences between individual molecules are clearly observed. Moreover, elucidating the distribution of single proteins and their organization within the cell membrane becomes feasible. Slowly but surely, we are beginning to learn that the world is a very different place when looked at one molecule at a time.

12.2 Plasma Membrane Preparation for AFM Imaging Membrane proteins are important components of the cellular machinery and are involved in many cellular processes. To study membrane proteins in their native environment they must be embedded in lipid membranes, which is a great limitation factor for several techniques including X-ray crystallography. Atomic Force Microscopy (AFM) is a good alternative for determining the structure and the arrangement of single ion channels, such as the CFTR proteins, in their physiological cell membranes with nanometer resolution. Since the main part of the CFTR protrudes from the inner surface of the plasma membrane into the cytoplasm, we have developed a method for inside–out membrane isolation, such that the cytoplasmic surface of plasma membrane is accessible for the scanning tip. The resulting membranes exhibit a typical height of ∼ 5 nm corresponding to an intact lipid bilayer and a great number of clearly detectable membrane proteins with heights of 5 to 20 nm. The method sets the basis for identifying single proteins within their plasma membranes. 12.2.1 Introduction In living cells, plasma membranes separate the cell interior from the extracellular space by using a lipid bilayer, ∼ 5 nm in thickness, for isolation and membrane proteins as selective barrier molecules for transmembrane signaling. Over the years, AFM has been applied to biological membranes [13] artificial bilayers [14], 2D and 3D protein crystals [15], isolated membranes [16], nuclear envelopes [17], and

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also to living cells [18]. AFM has permitted an unprecedented level of exploration of different biomolecules because of the ease with which samples are prepared compared to electron microscopy and also because of the freedom to image under solution. However, the flatness of the studied specimen and the supporting surface is a prerequisite for a high-resolution imaging. Spreading a plasma membrane patch on a flat solid support is currently the method of choice for identifying individual protein structures at the cell membrane, since it overcomes the softness and the height variations of living cells and allows single molecule resolution. 12.2.2 Plasma Membrane Preparation The cells are attached to a poly-L-lysine (PLL) coated mica or glass surface and then depending on the cell type, different approaches for the membrane isolation are applied: (i) Xenopus Laevis oocytes serve as a well-established expression system for membrane proteins in molecular cell biology. Before attaching the cell to a surface, the vitelline membrane, a protein meshwork, has to be removed. The oocyte, a cell with a diameter of more than 1 mm, can be easily brought in contact with the coated glass for a minute and then rolled off with the help of a pipette [19] (Fig. 12.4). The plasma membrane patches remain on the glass exposing their cytoplasmic side. (ii) Nearly all cells need a surface to grow on. Some of these adherent cells are polarized, which means that they express specific proteins either on the basolateral or apical membrane, such as MDCK or Calu-3 cells. In order to isolate inside out oriented membranes of these cells, we let them grow on a PLL coated mica surface to a certain degree of confluence. Then, another PLL-mica is pressed on top, creating a “sandwich” of cells placed between two mica surfaces. The “sandwich” is rapidly frozen in liquid nitrogen. Then the two mica surfaces are fractured apart while still frozen, resulting in clearly separated apical and basolateral membrane patches attached to the top and base surfaces, respectively (Fig. 12.5). (iii) Red blood cells (RBC) are cells that exist in suspension and they are too small to be manipulated by a pipette. Therefore, we used a method developed by Swiheard et al. [20] to isolate membrane patches. RBC were attached to PLL coated glass and sheared open by exposing to a jet stream of isotonic phosphate buffered saline (PBS with 0.2 mM EGTA) (Fig. 12.6). The upper membrane is washed away and a membrane patch remains attached to the glass surface.

Fig. 12.4. Schematic of the oocyte membrane isolation

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Fig. 12.5. Schematic of membrane isolation from polarized cells. The cells are sandwiched between two mica surfaces. Then the “sandwich” is rapidly frozen in liquid nitrogen. Finally, the two mica surfaces are fractured apart while frozen

Fig. 12.6. (a) Schematics of the RBC membrane preparation. RBCs are exposed to fluid flowimposed shear stress and as a result the cells are open, exposing their cytoplasmic side of the membrane. AFM images of (b) RBCs attached to poly-L-lysine coated glass, (c) inside out oriented RBC membrane patches, spread on the glass surface, after shear stress (to be published)

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Thus prepared inside–out oriented RBC membrane patches, spread on glass or a mica surface are gently shaken in low salt buffer (0.3 mM NaPi, 0.2 mM EGTA) at 37 ◦ C for 20 min in order to remove cell organelles, remnant cytoskeletal proteins or hemoglobin. Finally, the membranes are fixed with 4% paraformaldehyde in PBS for 35 min at room temperature. Subsequently, the membranes are washed with PBS and used for AFM imaging. 12.2.3 Atomic Force Microscopy AFM was performed in contact mode using a Nanoscope III Multimode-AFM (Digital Instruments, Santa Babara, California, USA) unless specified. V-shaped oxide sharpened cantilevers with spring constants of 0.06 N/m (Digital Instruments) were used for scanning in air. Images (512 × 512 pixels) were captured with scan sizes between 1 and 25 m2 at a scan rate of up to12 Hz (12 scan lines/s). Images were processed using the Nanoscope III software (Digital Instruments). Particle counting and 3D presentation were performed with the software SPIP (Scanning probe image processor, Image Metrology, Lyngby, Denmark). 12.2.4 Molecular Volume Measurements of Membrane Proteins In order to estimate the molecular mass (M0 ) of individual membrane proteins, we used a model published by Larmer et al. [21]. The calculation is based on a simplified model imaging a membrane protein as a sphere embedded in the lipid bilayer. The volume of a single protein (VProt ) was calculated using the sphere’s volume equation (V = 4/3πr 3 ), with the protein radius, r, given by the half height of the protein. The molecular mass M0 can then be calculated: M0 = NA /(V1 + dV2 ) × VProt .

(12.1)

In this equation, NA is the Avogadro constant (6.022 × 1023 mol−1 ), V1 is the partial specific volume of the protein (0.74 cm3 /g), V2 is the specific volume of water (1 cm3 /g) and d is a factor describing the extent of hydration for air-dried proteins (0.4 mol H2 O/mol protein). 12.2.5 AFM Imaging AFM imaging of thus prepared samples revealed single cell membrane patches with diameters of up to 30 m. Figure 12.7 depicts a typical image of an oocyte plasma membrane fragment spread on a glass surface, revealing a great number of protruding membrane proteins. This area showing the outline of the membrane was chosen so that the total height of the plasma membrane and its structures could be determined. Three different height levels are clearly detectable. The first level has a value of ∼ 1.5 nm and it is associated with the PLL coating. The second level corresponds to

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Fig. 12.7. (a) AFM image of a membrane fragment attached to a PLL coated glass (3D representation). The image is color-coded: the glass is shown in blue, the lipid bilayer membrane is shown in turquoise and the membrane proteins are shown in brown. The inset shows a detail from the right part of this image (marked with a black rectangle) at higher magnification. (b) A height profile taken along the broken line in (a). In the lower part of the figure, the first height level is ∼ 1.5 nm corresponding to PLL coating. The second level corresponds to the 5 nm-height of the lipid bilayer. The third level indicates the height of the proteins (up to ∼ 15 nm) protruding from the inner surface of the plasma membrane. The figure is adopted from [19]

the 5 nm-height of the lipid bilayer. Finally, the third level indicates the height of the proteins (up to 15 nm) protruding from the inner surface of the plasma membrane. The proteins appear with different heights and shapes. Some proteins are located so close to each other that they overlap or merge into one structure (inset). Similar membrane fragments and membrane structures are observed when the other two methods for membrane isolation from Calu-3 cells and RBCs are applied. In Fig. 12.8 an image of the apical membrane of a Calu-3 cell is shown. The border of the membrane and the proteins emerging from the lipid bilayer are clearly visible. The RBC membrane patches prepared by the shear stress exhibit circular shapes with a diameter of ∼ 10 m (Fig. 12.6c, Fig. 12.9). The high-resolution image reveals proteins in an extremely high density. Even if they are positioned close to one another, single proteins or groups of proteins are easily distinguishable. It should be noted here that the apparent shape of the proteins is usually found to be conical, which is most likely due to the fact that lateral dimensions of the base of individual proteins are overestimated as a result of AFM-tip geometry. Please notice that the height measurement of proteins is still precise. The height measurements

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Fig. 12.8. AFM image of the apical membrane isolated using the freeze–fracture method from the Calu-3 cell, inside out oriented. The image is gray-level coded: from dark (0 nm) to white (∼ 20 nm). Scan size: 4 µm

(data not shown) of the plasma membranes and the proteins from the Calu-3 and RBCs reveal comparable values to those taken from the oocyte membranes. Clearly, using either of these approaches of isolation results in membranes with similar characteristics and this be further applied for identification of single proteins. Furthermore, in order to verify whether the structures emerging from the oocyte lipid membrane towards the cytoplasmic space are proteins, the membranes were incubated with the enzyme trypsin. About 5 min after incubation with 0.05% trypsin protruding structures are dramatically decreased in height. Before trypsin treatment, the structures have a wide range of different heights with peak values of ∼ 11 nm. After trypsin treatment, a strong shift to the left with a sharp peak appearing at ∼ 6 nm is observed (Fig. 12.10). The data indicate that the protrusions are indeed proteins sensitive to trypsin digestion. Modeling plasma membrane proteins as spherical structures protruding from the lipid bilayer allowed an estimation of their possible

Fig. 12.9. (a) AFM image of an inside-out oriented RBC membrane, isolated using shear stress. (b) Higher resolution image of the area indicated with a white rectangle in (a). Gray-level code: dark (0 nm), white (∼ 20 nm)

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Fig. 12.10. Histogram of the plasma membrane protein distribution (intracellular side) in relation to measured protein heights and calculated molecular weights before and after incubation with trypsin. Molecular weights were calculated from the respective volume measurements. The figure is modified from [19]

molecular weights. From the calculated molecular weights it is assumed that single proteins assemble into multimers or clusters. In conclusion, the techniques for membrane isolation described here may serve as a suitable method for imaging the inner surface of the plasma membrane from different cell types. Quantification such as determining the number and distribution of membrane proteins within their physiological environment, as well as their height and molecular weight becomes possible. Undoubtedly, this is a valuable step in identifying specific proteins imbedded in native membranes.

12.3 AFM Imaging of CFTR in Oocyte Membranes Xenopus Laevis Oocytes are a widely used expression system, which means that these cells express a specific protein after injection of the corresponding mRNA. AFM has been applied to study the protein incorporation into plasma membranes of CFTRexpressing oocytes upon cAMP stimulation. Quantification of the protein distribution has revealed two peak values of 10 and 14 nm of protein height corresponding to 275 kDa and 750 kDa, respectively. The results suggest that CFTR causes clustering of plasma membrane proteins after stimulation. In addition, immuno-gold labeling of CFTR in combination with AFM has been used to specifically identify CFTR

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among the proteins present in the plasma membrane at a single molecule resolution. The frequently observed ring-like structure in the vicinity of a gold particle and the proposed model imply a tail-to-tail dimerization of the CFTR associated with a functional channel. 12.3.1 Introduction Raising intracellular cAMP concentration stimulates, among other things, CFTR insertion into the plasma membrane and activates CFTR via protein kinase A (PKA) [22]. It is discussed that stimulation of CFTR by cAMP raising agents also initiates several types of protein–protein interactions that might result in a formation of clusters. Clusters are structural and functional units of proteins, which has been shown for numerous plasma membrane proteins, e.g. a potassium channel with members of the ATP-binding cassette (ABC) transporter family [23]. The CFTR, as a member of the ABC-transporter family, is assumed to form clusters with different proteins, such as sodium channels [24], potassium and chloride channels, as well as purinergic receptors [25], in order to perform autocrine cell regulation. Although activation of CFTR has been elegantly examined by electrophysiological and fluorescence microscopy techniques [26,27], little is known about the spatial distribution and organization of this protein within the plasma membrane. Since imaging with AFM has been beneficial in protein counting and protein height measurements essential for the determination of individual molecular masses and protein distribution on the cell surface, this technique would be relevant to the identification of CFTR and its assemblies within the cell membrane. 12.3.2 Does the CFTR Form Functional Assemblies? In order to visualize CFTR molecules in their natural environment AFM has been employed to inside-out oriented plasma membrane patches of CFTR-expressing oocytes in relation to cAMP stimulation [28]. The AFM topography shown in Fig. 12.11a represents a typical image of a non-stimulated oocyte membrane with regularly distributed proteins. After stimulation (Fig. 12.11b), the density of protein increases clearly. Quantification of protein distribution (Fig. 12.12) reveals a mean density of 200 proteins per µm2 in a non-stimulated CFTR-expressing oocyte membrane while in the stimulated ones, the number of proteins increased to 400 per µm2 . The data obtained indicate that the protein covered area increases dramatically in response to cAMP by ∼ 110%. This observation strongly suggests protein insertion into the plasma membrane. Furthermore, the accurate height determination of the non-stimulated oocytes showed distribution with a peak value of 12 nm, corresponding to a molecular mass of 475 kDa (hatched area in Fig. 12.12). In contrast, the height of the proteins from the stimulated membranes exhibited a two-peak distribution with values of 9 nm and 14 nm corresponding to molecular masses of 275 kDa and 750 kDa, respectively.

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Fig. 12.11. Membrane patches of CFTR-positive oocytes. The membrane patch shown in (a) was isolated before cAMP stimulation, the membrane shown in (b) was isolated after cAMP stimulation. In this gray-level coded image the plasma membrane, 5 nm in height, is shown in “dark”. Proteins are shown with a gray-level gradient from dark to white, corresponding to heights from 6 nm to 20 nm. The figure is modified from [28]

Fig. 12.12. Protein distribution of a CFTR-expressing plasma membrane (mean ± s.e.m., n = 12; 4 oocytes, 3 patches per oocyte). The gray line represents the protein height distribution of stimulated oocytes, while the hatched areas represent the respective height distributions of non-stimulated oocytes. Molecular weights were calculated from the respective volume measurements (see Sect. 12.2). The figure is modified from [28]

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Considering the molecular mass of 200 kDa for a CFTR monomer, the peak at 275 kDa and 750 kDa could be multimeric CFTR or CFTR forming clusters with other proteins. It should be noted here that in a control experiment, CFTR negative (native, not CFTR expressing) oocytes do not exhibit any clustering upon cAMP stimulation. Evidently, using AFM imaging makes it possible to show complex protein– protein interactions within native membranes upon stimulation. These measurements clearly reveal that, at least in the examined cell type, cAMP induces both CFTR insertion into the plasma membrane and leads to the formation of protein clusters with yet unknown stoichiometry. However, these data are consistent with the concept that the physiological function of CFTR involves interactions with other proteins or with itself. 12.3.3 Two CFTRs are Better Than One The long-standing dilemma of whether the functional CFTR is a monomer or a dimer has not been solved yet. Although recent publications have provided evidence that two CFTR molecules interact together to form a single conductance pore for chloride ions [29,30], structural details of CFTR in native membranes are still unknown. The predicted model of an individual CFTR molecule exhibits two hydrophobic core regions, each with six transmembrane spanning domains (TMs), and two nucleotide binding folds (NBD’s). A large cytoplasmic regulatory domain (R-domain) connects the two halves of the CFTR molecule [31] (Fig. 12.13). CFTR-related structures that protrude from the inner side of the membrane towards the cytoplasm are expected to be in the range of only a few nanometers. Structures with such dimensions cannot be detected with more conventional methods. As we have seen in the section above, AFM is a suitable method to detect proteins within native membranes, since scanning can be performed with a vertical resolution (resolution in height) in the sub-nanometer range. However, it is important now to be able to distinguish and pinpoint a specific single protein, such as the CFTR, among the vast diversity of proteins present in the membrane. In order to identify

Fig. 12.13. Schematic of the predicted organization of CFTR within the plasma membrane (the crystal structure has not been solved yet). The intracellular domains (R domain, NBD1 and NBD2) are known to be involved in channel gating, while the transmembrane segments (TMs) are presumed to form the anion-conducting pore

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CFTR, a novel method of staining CFTR with gold-labeled antibodies was applied and AFM was used for high-resolution single molecule imaging [32]. Figure 12.14 shows a 1 µm2 patch of plasma membrane excised from a cAMPstimulated, CFTR-expressing oocyte. The light structures on the surface correspond to the individual gold labels. The height of the gold particles is in the range of 10 to 15 nm, while the respective width is sometimes more than 50 nm. The latter number is an overestimate due to the AFM tip geometry. About 100 gold particles per µm2 of plasma membrane were detected. Gold particles appear, uniform in height and size, as the most prominent structures on the membrane. Although the density of proteins in the plasma membrane is high and the shape of proteins varies considerably, frequently distinct circular structures in close vicinity to individual gold labels were detected (see inset of Fig. 12.14). Higher resolution images of such ring-like structures (Fig. 12.15) reveal globular subunits correlated with the ring and craterlike structure with a central aperture and a surrounding fringe exhibiting bipartite symmetry. A single CFTR is expected to have three intracellular substructures: one regulatory subunit (R domain) and two nucleotide binding domains (NBD1 and NBD2). However, the AFM images demonstrate up to 6 subunits associated with one pore. On the basis of the substructures a model was developed representing the CFTR as a dimer with a tail-to-tail configuration and a central pore (Fig. 12.16). The C-termini form a tail-to-tail outlet to which the primary antibody is bound. Then, the secondary antibody spans the short distance to the gold label. Starting from the C-terminus, the NBD2 is the first structure detectable as a tiny protrusion. Then, the R-domain and the NBD1 follow. In between coiled hydrophilic parts of the CFTR molecule are expected. The tail-to-tail arrangement indicates a mirror-like

Fig. 12.14. AFM image of inside-out plasma membrane patch excised 5 minutes after cAMP stimulation from CFTR expressing Xenopus laevis oocyte. Light particles (height = 10 to 15 nm) correspond to the gold labels of the secondary antibodies directed against CFTR primary antibodies. Gold particles are frequently found associated with ring-like structures (see inset). The figure is modified from [32]

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Fig. 12.15. (a) AFM images of four different ring-like structures supposed to be the cytoplasmic morphological correlate of CFTR. The structures are found in close vicinity to gold particles. Heights (given as “z” in the images) are gray-level coded from dark to light. (b) High-resolution AFM image of a CFTR ring. The arrow indicates the cytoplasmic aperture of the central pore. Intracellular substructures of possible nucleotide binding domains (NBD1 and NBD2) and regulatory domains (R domain) are fairly distinguishable. Gray-level code: from dark to light. The figure is modified from [32]

dimerization of two CFTR molecules. Two such molecules form a CFTR dimer as indicated in Fig. 12.16. Analysis of several ABC-transporters report homodimeric structures in which monomers interact within the transmembrane domains. They form a central pore or internal chamber open to the inner or outer leaflet between the two subunits constituting the homodimer [33–39]. The findings are consistent with electron microscopy [40] and electrophysiology [41–43] studies showing that CFTR forms a homodimer in plasma membrane. However, no structural data exist that directly

Fig. 12.16. Model of a CFTR dimer in tail-to-tail configuration (a) superimposed on the AFM image of a CFTR ring (b). The length of the extramembrane loops are drawn to scale. The transmembrane helices (TM) are numbered in the inset. The model assumes that the N-terminus interacts with the R domain and may be flexible enough to interfer with ion channel gating at the pore entrance. The C-termini form parallel structures at one end of the dimer interacting with the primary monoclonal antibody. The figure is modified from [32]

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show the orientation of CFTR (e.g. head-to-tail or tail-to-tail arrangements) and the substructural components of the proposed CFTR-dimer in plasma membrane. The assessment of the AFM images suggests a mirror-image-like two-fold symmetry of CFTR. This is supported by functional studies in which tail-to-tail dimerization is associated with highest chloride channel conductance. Tandem linkage of two CFTR molecules (i.e. head-to-tail dimerization) as proposed in other functional studies [42, 44] seems less likely, at least in CFTR expressing oocytes, since AFM images show mirror-image-like dimeric structures. In conclusion, the study shows the advantage of the AFM technique for imaging fully functional CFTR in its native environment without the limitations of artificial systems (e.g. isolated proteins). Since intramolecular domains can be identified by AFM, it should be possible to address the structure–function relationship of the CFTR chloride channel. Imaging CFTR mutations like ∆F508 could be one of the next exciting goals to be addressed in the future.

12.4 Single Antibody–CFTR Recognition Imaging A novel AFM mode that can visualize specific antigen–antibody interactions while simultaneously recording high-resolution topographical images using “MacMode” dynamic force microscopy was employed. An antibody-modified AFM tip was used to specifically recognize CFTR molecules within red blood cell membranes. The images revealed recognition patterns that were assigned to the topography of single and/or clustered CFTR proteins. 12.4.1 Introduction As we discussed in the previous sections, due to AFM high-resolution spatial imaging capabilities, a wealth of structural information on DNA-protein complexes, membranes and cells has been gathered. However, AFM has long been criticized because of its inability to provide chemical/biochemical specificity of the imaged structures. This was realized by combining molecular recognition with dynamic force microscopy [45], which led to the development of TREC imaging (topography and recognition; the principles of TREC will be discussed in greater detail in Vol. II, Chap. 5). The method vastly improves the ability of the AFM to visualize the chemical composition of a sample while mapping its topographic structure at sub-molecular resolution. For example, investigating both the interactions of single molecules with their specific receptors and their localization becomes feasible. In order to provide a specific recognition a ligand such as antibody is covalently bound to the scanning AFM tip. The AFM tip approaches the surface that contains cognate antigen and an antibody–antigen bond is formed. During a subsequent retraction of the tip, the bond will cause a tension and with the increased force will eventually break, allowing the estimation of affinity constants [46]. Importantly, the specificity of recognition can be tested by blocking either the antibody on the tip or the antigen on the sample, resulting in a complete abolishment of the recognition

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signals. TREC imaging has been used to study single lysozyme molecules showing ∼ 70% recognition efficiency [47] and to recognize histone H3 within a complex chromatin fiber by an antihistone H3 functionalized tip. Moreover, the authors were able to follow an ATP-dependent nucleosome remodeling process [48]. Here the TREC imaging was used as an alternative method to directly map CFTR sites on RBC membranes as a result of the molecular recognition of the antigen by a CFTR-antibody tethered to an AFM tip. 12.4.2 Tethering of Antibodies to AFM Tips MacLevers tips (Molecular Imaging Corp., Tempe/AZ, USA) were activated with ethanolamine HCl and subsequently coupled to a heterobifunctional tether of ∼ 8 nm length of polyethylene glycol (PEG) derivative as described [49]. A mouse monoclonal antibody against a C-terminal epitope of CFTR (MAB25031 (21-4), R&D Systems Inc., Minneapolis, MN) was then bound to the reactive end of the PEG tether. The flexible linker gives the possibility for the antibody to freely orient, achieving unconstrained binding to its cognate site. The antibody density is adjusted to a value where only one antibody on the tip is expected to have access to the receptor on the surface. 12.4.3 AFM Imaging and Recognition Magnetized cantilevers are driven by a small solenoid using a MacMode dynamic force microscope (Molecular Imaging). The tip is oscillated by an alternating magnetic field while being scanned across the surface. By passing the raw deflection signal from the AFM-scanning head to a PicoTREC signal-processing system, the oscillation is split into lower and upper parts, resulting in simultaneously acquired topography and recognition images. MacLever cantilevers had a spring constant of 0.1 N/m. Measurements were performed in PBS buffer with 5 nm free tip oscillation amplitude at 5 kHz driving frequency and 20% amplitude reduction. The lateral scanning frequency was of 1 Hz. 12.4.4 A Single Antibody Sees a Single CFTR In this study of TREC, an anti-CFTR antibody functionalized tip was used to map single CFTR molecules at the cytoplasmic side of RBC membranes (Fig. 12.17). The topographical image of a part of an RBC membrane together with the map of recognition sites was recorded with nm-resolution. The identification of CFTR molecules at the single molecule level was achieved without compromising its topographic imaging performance, despite the fact that the tip was carrying the tethered antibody (Fig. 12.18). Figure 12.18a revealed structures protruding out of the membrane with 10–15 nm in height, representing the membrane proteins at the cytoplasmic site of the membrane. The observed structures were comparable

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Fig. 12.17. Schematic of recognition imaging. When the tip-tethered antibody binds to its antigen in the sample being scanned, there is a transient reduction in the oscillation amplitude. This reduction, corresponding to the recognition event, is then presented in an image as a dark spot at its defined position on which it occurred. The figure is modified from Molecular Imaging Corp., Tempe/AZ, USA

Fig. 12.18. TREC imaging (a) topography of an area of a non-CF RBC membrane showing the protruding proteins of the lipid bilayer; (b) the same area as in (a) but representing the specific interaction between the modified tip (i.e. anti-CFTR antibody tip) and the CFTR at the membrane, identified as darker spots (to be published)

to the topography of membrane proteins obtained with the standard AFM. The simultaneously acquired recognition image showed darker spots, corresponding to the specific interaction between the antibody on the tip and the surface CFTR molecules (Fig. 12.18b). When the tethered antibody binds to an antigen on the surface, the upward extent of the cantilever swing is restricted by the PEG tether. This reduction of the oscillation amplitude on binding is compensated for by the microscope servo. The servo pulls the probe away from the surface to restore the amplitude to its previous value, but now the peak signal is displaced downward by the amount of the amplitude reduction. Thus, the locations of the antibody-binding events are shown as dark patches [50]. Interestingly, the observed recognition patterns here do not appear to be uniform in size and distribution across the membrane surface. This finding supports the hypothesis that CFTR forms functional clusters (as discussed in Sect. 12.3) to fulfill its regulatory functions within the cell membrane. The specificity of the antibody– CFTR recognition process can be tested by blocking the antibody attached to the

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tip with an antigenic peptide. After blocking, the specific interactions disappear. Clearly, the TREC has an advantage over the labeling methods where the direct visualization of the molecule is not possible since gold dots hinder it. Moreover, with further advances in the TREC methodology (increasing spatial resolution, improving sample preparation), this technique will provide more detailed information on issues such as clustering. In conclusion, by using TREC it was possible to recognize CFTR molecules in heterogeneous RBC membranes and carry out epitope mapping on a nanometer scale.

12.5 Single Cell Elasticity: Probing for Diseases As discussed above, the lack of CFTR in human RBC might contribute to the development of pulmonary hypertension and hemolytic anemia in CF patients. In this respect, it was hypothesized that a reason for those symptoms might be altered cell elasticity. In this study, AFM was used to directly quantify the local stiffness of individual CF and non-CF RBCs. According to this method, a very low force (in the order of pico Newtons) was applied via an AFM cantilever to non-fixed RBCs and as a result an indentation with a controlled depth was generated by the AFM tip. The obtained force–distance relations were used to assess the Young’s modulus, a measure of the matter’s elasticity. Comparison of the Young’s moduli of CF and non-CF RBCs revealed a two-fold increase in stiffness for RBCs from patients with CF. 12.5.1 Introduction Mechanical properties of living cells are very important for a proper physiological functioning, and yet our knowledge in this regard is rather limited. For instance, it is not fully understood how a cell responds structurally and mechanically to external stress or what role the micromechanistics of the cell may play in various physiological or pathological conditions; or how the elasticity of a certain type of cells will be altered in diseased compared to healthy organisms. The red blood cell (RBC) is known for its ability to withstand great deformations when it passes through small capillaries. Because cell cytosol is only composed of a viscous fluid (solution of hemoglobin), the resistance to stress is mainly attributed to the elastic properties of its membrane. The RBC membrane, made of a lipid bilayer and membrane proteins, is reinforced on its inner side by a flexible two-dimensional cytoskeleton. The cytoskeleton elasticity is determined by the association/dissociation of the spectrin and actin filaments, its integral components. It is obvious that an abnormal RBC deformability will affect the ability of the cell to transit in the small blood vessels, resulting in blood circulation disturbances. Interestingly, CF patients have been diagnosed with pulmonary hypertension or hemolytic anemia. Clearly, decreased cell deformability might be a factor contributing to those symptoms in CF patients. In addition, it has been demonstrated that CFTR associated deformation-induced ATP release of RBCs from patients with CF is abolished [51]. This RBC associated

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ATP plays a crucial role in stimulating endothelial cells of the blood vessels, leading, ultimately, to an increase in vascular caliber and thus regulating the vascular resistance. In turn, is not unreasonable to think, that this ATP might act on the RBC itself, initiating different signaling pathways. For example, studies have shown that ATP induces changes in the cell cytoskeleton leading to alteration of the membrane elasticity [52, 53]. In the present work, we investigated the hypothesis that the lack of CFTR in RBC membranes may alter their mechanical properties. As we have seen in the previous sections, AFM provides detailed surface topography at nm-scale by raster scanning a cantilever tip over the sample. In addition, due to the technique’s force detection sensitivity, it has given us the possibility of measuring forces in the pico Newton range. The force felt by the tip as it approaches and retracts from a point on the sample surface is presented as force–distance curves. Thus, local elastic properties of biological matter, in terms of the Young’s modulus or elastic modulus, can be quantitatively derived from the force–distance curves obtained at a point of contact on the surface. Furthermore, a two-dimensional spectroscopic matrix of force–distance curves can be collected simultaneously with the topographical data. In this way, elastic properties of the sample can be mapped and correlated with the topographic image. The capability of AFM to provide valuable information on the mechanical properties of living cells has been gaining increasing attention [54–56]. Therefore, we employed AFM as well as a force sensor to quantify the local elasticity of individual RBCs in relation to CF. 12.5.2 Force–Mapping AFM RBCs were attached to poly-L-lysine coated glass coverslips. AFM measurements were performed in force–mapping mode in PBS buffer using a Nanoscope III Multimode-AFM (Digital Instruments, Santa Babara, CA, USA). We used soft silicon nitride cantilevers with spring constant of 0.01 N/m and pyramidal tip with an opening angle of 35 (Veeco Instruments, USA). Force–mapping was performed with the following parameters: scan sizes of 10 µm2 , scan rate of 14 Hz, samples/line 256, number of samples 64, force/line 64, in relative trigger mode. To calculate Young’s modulus from the force curves, the data were fit with the Hertz model [57] for an indentation of a completely elastic soft sample by a stiff cone. The relation between the indentation, δ (for our calculations we used a value of ∼ 100 nm), and the loading force, F, is given by the following: ∆F = δ2 × (2/π) × (E/[1 − ν2 ]) × tan(α) ,

(12.2)

where ν is the Poisson ratio (for incompressible materials it is 0.5), E is the elastic modulus (or Young’s modulus), and α is the half opening angle of the AFM tip (for Veeco Instruments is 35◦ ). Data were analyzed with self-written macros for the software IGOR PRO (WaveMetrics).

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12.5.3 Can One Protein Change Cell Elasticity? The adhesion of the cells to the support surface is very critical for obtaining reliable data. Poly-L-lysine (PLL) is a polycation commonly adsorbed to surfaces for strong attachment to the negatively charged molecules such as the glycocalyx of RBCs.

Fig.12.19.Low force contact mode AFM imaging in PBS buffer: (a) topography image of a spread RBC, demonstrating compression of the disc shape due to strong adhesion to the glass surface; (b) immobilization at reduced adhesion shows regularly shaped RBCs. Scan size: 12 µm

Fig.12.20.Comparison of typical force curves on soft and stiff samples. The black trace represents an approach curve taken on a glass substrate, on CF and non-CF RBCs, respectively. This slope can be used for the determination of the sensitivity of the photodetector. On the stiff sample the force curve shows a sharp bend (the contact point is at the 0 z position of the piezo). In contrast, the approach on the cell surface shows a shallow transition

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At 1 mg/ml concentrations of PLL preadsorbed to a coverslip, erythrocytes adhere firmly to the substrate but a drastic change of the shape occurs due to the strong adhesion (Fig. 12.19a). With a 10-fold-diluted PLL solution (0.1 mg/ml), erythrocyte immobilization is accompanied without alteration of their shape (Fig. 12.19b). For our force mapping measurements only intact RBCs exhibiting disc shape, which were not under tension due to spreading, were used. Local micromechanical properties of single non-fixed CF and non-CF RBCs were quantitatively characterized using force–mapping AFM. In this mode force

Fig. 12.21. Force map of a non-fixed RBC measured in PBS buffer. (a) A typical topography image of an RBC, higher areas are depicted in lighter color; (b) corresponding elasticity map, softer areas are shown in gray; (c) a force–distance curve during approach to RBC membrane taken at the point of the RBC indicated with a cross on (a). The analysis of the Young’s modulus is made for an indentation of ∼ 100 nm (gray line). Scan size: 10 µm

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curves (Fig. 12.20) are taken while scanning laterally over the sample and both topographic and elasticity maps are recorded. However, in order to obtain reliable local elasticity measurement of the cell, sensitivity of the photodetector needs to be determined accurately. This can be determined from the slope of the force– distance curves taken on the bare surface of glass coverslips where there are no cells present. In Fig. 12.21a a height image of an RBC, reconstructed from the force measurement is shown, revealing the typical erythrocyte shape of a bi-concave disc. Simultaneously the 2D elastic properties of the cell, in terms of Young’s modulus, are obtained (Fig. 12.21b). At every point across the scanned area the corresponding approach curve can be acquired (Fig. 12.21c). For calculating the membrane elasticity we used the loading force required to indent the cell by ∼ 100 nm. Since the contact area between tip and cell is not known, and also the tension in the cell center dip is not well determined, only force curves taken on the rim of the “doughnut” were further considered for the calculation of the Young’s modulus. The results of the calculated Young’s moduli of CF and non-CF RBCs are presented in Fig. 12.22. As indicated by the histograms, the data show that the RBCs from patients with CF exhibited a two-fold increase in stiffness compared to RBC from healthy donors. Clearly, the deficiency of CFTR in the CF RBC membranes, directly or indirectly, leads to a reduced deformability. Considering the fact that CFTR is present in a very low amount even in healthy cells, only ∼ 640 copies per cell, it appears rather unlikely that its depletion would lead to a direct alteration of membrane elasticity (based on lipid/protein ratio). It seems more likely that the protein is involved in a secondary pathway, e.g. acting via the cytoskeleton a change in elasticity might occur. For instance, reduction of the elasticity of mouse F9 embryonic carcinoma cells deficient of vinculin, a membraneassociated protein that plays a role in linkage of the cytoskeleton, has been shown recently [58]. Possibly impaired volume regulation as observed in CF cells [59]

Fig. 12.22. Distribution histograms of the Young’s modulus of CF (light gray) and non-CF (dark gray) RBCs. Each distribution represents data from three different individuals. The Gaussian fits revealed a mean value of 5.8 ± 0.1 kPa (n = 341) for the RBCs from the healthy donors and 9.9 ± 0.2 kPa (n = 458) for the RBCs from CF patients

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changes intracellular pressure leading to an increased membrane tension and thus to stiffening of the membrane. Further studies are needed to clarify this phenomenon, however, the use of the force–mapping AFM to investigate the elasticity of cells in various pathological conditions certainly presents a new direction for single cell diagnostics and a better understanding of diseases.

12.6 Summary The combination of AFM with conventional techniques, as well as AFM itself, allows answering biomedical questions of high interest. We could show this clearly for CFTR with single molecule imaging and observation of structural dynamics in native cell membranes. AFM also allows identification and determination of CFTR at single molecule level. The observation that the lack of CFTR influences the mechanical and, therefore, rheological properties of RBC could lead to a novel therapeutic approach for CF treatment. Regarding the fact that the defect of a single protein causes lethal diseases, research at the single molecule level would become vital in the future. Acknowledgements. We thank Dr. Rainer Matzke, Ludwig Maximilians University Munich, Germany, for the force mapping analysis. We are also grateful to Dr. Johannes Haeberle, Dr. Angelika Duebbers and Dr. Sabine Falk, Department of Pediatrics, University Hospital Muenster, Germany, for the supply with patients’ blood. The work was supported by DFG (German Research Foundation) grant SFB 629 (A6) and EU grant Tips4cells.

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14. Radmacher M, Tillmann RW, Fritz M, Gaub HE (1992) Science 257:1900 15. Muller DJ, Engel A, Matthey U, Meier T, Dimroth P, Suda K (2003) J Mol Biol 327:925 16. Fotiadis D, Liang Y, Filipek S, Saperstein DA, Engel A, Palczewski K (2004) FEBS Lett 564:281 17. Shahin V, Albermann L, Schillers H, Kastrup L, Schafer C, Ludwig Y, Stock C, Oberleithner H (2005) J Cell Physiol 202:591 18. Pesen D and Hoh JH (2005) Biophys J 88:670 19. Schillers H, Danker T, Schnittler HJ, Lang F, Oberleithner H (2000) Cell Physiol Biochem 10:99 20. Swihart AH, Mikrut JM, Ketterson JB, Macdonald RC (2001) J Microsc 204:212 21. Larmer J, Schneider SW, Danker T, Schwab A, Oberleithner H (1997) Pflugers Arch 434:254 22. Prince LS, Workman RB, Jr, Marchase RB (1994) Proc Natl Acad Sci U S A 91:5192 23. Seino S (1999) Annu Rev Physiol 61:337 24. Kunzelmann K, Schreiber R, Nitschke R, Mall M (2000) Pflugers Arch 440:193 25. al-Awqati Q (1995) Science 269:805 26. Moyer BD, Loffing J, Schwiebert EM, Loffing-Cueni D, Halpin PA, Karlson KH, Ismailov II, Guggino WB, Langford GM, Stanton BA (1998) J Biol Chem 273:21759 27. Weber WM, Cuppens H, Cassiman JJ, Clauss W, Van DW (1999) Pflugers Arch 438:561 28. Schillers H, Danker T, Madeja M, Oberleithner H (2001) J Membr Biol 180:205 29. Zerhusen B, Zhao J, Xie J, Davis PB, Ma J (1999) J Biol Chem 274:7627 30. Wang S, Yue H, Derin RB, Guggino WB, Li M (2000) Cell 103:169 31. Riordan JR, Rommens JM, Kerem B, Alon N, Rozmahel R, Grzelczak Z, Zielenski J, Lok S, Plavsic N, Chou JL (1989) Science 245:1066 32. Schillers H, Shahin V, Albermann L, Schafer C, Oberleithner H (2004) Cell Physiol Biochem 14:1 33. Higgins CF and Linton KJ (2001) Science 293:1782 34. Schmitt L and Tampe R (2002) Curr Opin Struct Biol 12:754 35. Chang G and Roth CB (2001) Science 293:1793 36. Locher KP, Lee AT, Rees DC (2002) Science 296:1091 37. Chami M, Steinfels E, Orelle C, Jault JM, Di Pietro A, Rigaud JL, Marco S (2002) J Mol Biol 315:1075 38. van Veen HW, Margolles A, Muller M, Higgins CF, Konings WN (2000) EMBO J 19:2503 39. Rosenberg MF, Callaghan R, Ford RC, Higgins CF (1997) J Biol Chem 272:10685 40. Eskandari S, Wright EM, Kreman M, Starace DM, Zampighi GA (1998) Proc Natl Acad Sci USA 95:11235 41. Wang S, Yue H, Derin RB, Guggino WB, Li M (2000) Cell 103:169 42. Zerhusen B, Zhao J, Xie J, Davis PB, Ma J (1999) J Biol Chem 274:7627 43. Raghuram V, Mak DD, Foskett JK (2001) Proc Natl Acad Sci USA 98:1300 44. Wang S, Yue H, Derin RB, Guggino WB, Li M (2000) Cell 103:169 45. Hinterdorfer P, Baumgartner W, Gruber HJ, Schilcher K, Schindler H (1996) Proc Natl Acad Sci USA 93:3477 46. Allison DP, Hinterdorfer P, Han W (2002) Curr Opin Biotechnol 13:47 47. Stroh CM, Ebner A, Geretschlager M, Freudenthaler G, Kienberger F, Kamruzzahan AS, Smith-Gill SJ, Gruber HJ, Hinterdorfer P (2004) Biophys J 87:1981 48. Stroh C, Wang H, Bash R, Ashcroft B, Nelson J, Gruber H, Lohr D, Lindsay SM, Hinterdorfer P (2004) Proc Natl Acad Sci USA 101:12503

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13 Scanning Probe Microscopy: From Living Cells to the Subatomic Range Ille C. Gebeshuber · Manfred Drack · Friedrich Aumayr · Hannspeter Winter · Friedrich Franek

Abbreviations AFM ATP BDPA CDOS ESD HOPG ID MCI MEMS MR MRFM MRI NEMS PS PSD rms SEM SPM UHV VD

atomic force microscopy adenosine triphosphate a, g-bisdiphenylene b-phenylallyl charge density-of-states electron stimulated desorption highly oriented pyrolytic graphite interstitial defect multiply charged ion microelectromechanical system magnetic resonance magnetic resonance force microscopy magnetic resonance imaging nanoelectromechanical systems potential sputtering photon stimulated desorption root mean square scanning electron microscopy scanning probe microscopy ultra-high vacuum vacancy defect

13.1 Introduction In this chapter the reader will be introduced to scanning probe microscopy of samples varying by seven orders of magnitude in size (Fig. 13.1). The largest samples presented are living cells, measuring some hundreds of micrometers. Small units of life, biomolecules with only some tens of nanometers, are the next sample. They are investigated while interacting with each other in real-time. One more step down in size, small ion-induced defects on atomically flat crystals represent structures in the nanometer regime. New data storage devices might result from such investigations. Finally, single electron spin detection (dozens of atomic layers beneath the surface) and the imaging of atom orbitals extend scanning probe microscopy to the subatomic regime. Gathering of 3D atomic-level information of (bio)molecules embedded in

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Fig.13.1.The major types of microscopy cover at least eight orders of magnitude in size. Common examples for every scale are given. Note that scanning probe microscopy covers seven orders of magnitude

their natural environment or single defect imaging in bulk silicon might be possible with these new techniques in the near future. These versatile applications demand methods such as scanning tunneling microscopy at ultra-low temperatures (1.6 K) or atomic force microscopy in ultra-high vacuum (10−11 mbar). Furthermore, in many cases, specially engineered and/or functionalized scanning probe tips are needed.

13.2 Cells In Vivo as Exemplified by Diatoms 13.2.1 Introduction to Diatoms Diatoms [1] are unicellular microalgae with a cell wall consisting of a siliceous skeleton enveloped by an organic case essentially composed of polysaccharides and proteins [2]. Diatoms are small, mostly easy to cultivate, highly reproductive and, since many of them are transparent, they are accessible by different kinds of optical microscopy methods. The cell walls form a pillbox-like shell (siliceous exoskeleton). This shell consists of two valves and a series of girdle bands. Diatoms vary greatly in shape, ranging from box-shaped to cylindrical; they can be symmetrical as well as asymmetrical and exhibit an amazing diversity of nanostructured frameworks (Fig. 13.2).

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Fig. 13.2. Siliceous exoskeletons of three diatom species imaged with scanning electron microscopy. Top: Tricaeratium favus, whole cell (left), detail (right). Bottom: Roperia tessellata (left) and Achnathes brevipes (right). Reprinted with permission from Gebeshuber IC, Thompson JB, Del Amo Y, Stachelberger H, Kindt JH (2002) Mat Sci Technol 18:763 [4] © 2002 IoM Communications Ltd.

These naturally nanostructured surfaces gained the attention of nanoscientists, and diatom nanotechnology developed as a new interdisciplinary field of research [3]. Diatoms are found in freshwater, brackish and marine environments, as well as in moist soils, and on other regularly moist surfaces. They are either freely floating (planktonic forms) or attached to a substratum (benthic forms), and some species may form colonies in the form of chains of cells of varying length. Individual diatoms range from two micrometers up to several millimeters in size, although only few species are larger than 200 micrometers. Diatoms as a group are very diverse with 12,000 to 60,000 species reported [5, 6]. These unicellular organisms are interesting from the point of view of materials science and biomimetic studies, since they master challenges as diverse as building nanostructured glass-like shells with high load capacity (a problem interesting for lightweight structures architecture) and engineering strong and robust adhesives that are stable in wet environments (most man-made adhesives fail to bond in wet conditions, owing to chemical modification of the adhesive or its substrate). Furthermore, diatoms excel at preventing dissolution of their silica shells in water owing to a covering layer (up-to-date technology is currently facing the problem that man made glass fiber reinforced polymers show rapid deterioration when used in water). Currently, human chemical synthesis cannot produce siliceous structures with the hierarchical structural detail of the diatom frustules nor can ordered siliceous structures be produced synthetically under the benign conditions of diatom biomine-

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ralization. Biosilicification occurs at ambient temperatures and pressures, whereas artificial chemical synthesis of silica-based materials (e.g. resins, molecular sieves and catalysts) requires extreme conditions of temperature, pressure and pH. 13.2.2 SPM of Diatoms The first AFM study of diatoms was presented in 1992 [7]. In this study, the surface structure of six different diatom species collected from a mud sample was imaged after the cells had been briefly rinsed with ethanol to kill, clean and immobilize them. Topography and micromechanical properties like elasticity and hardness of dead diatom cells were reported by Almquist et al. in 2001 [8]. In contrast to these AFM images of dead cells, topography and micromechanical properties (such as viscoeleastic properties, adhesion forces and hardness) of the surface of the living diatom cell has been investigated [e.g. 5, 10–13]. Lee and co-workers combined scanning electrochemical microscopy and scanning optical microscopy to obtain simultaneous electrochemical and optical images of living diatoms in a constant-current mode [13]. This kind of microscopy might prove useful in mapping the biochemical activity of a living cell. The defense potential of the diatom shell was investigated by Hamm and coworkers by measuring its strength [14]. It was found that diatoms are remarkably strong by virtue of their architecture and the material properties of the diatom silica. In 2004 Arce and co-workers used the AFM to compare the adhesion of diatoms to several surfaces. Tipless AFM cantilevers were functionalized with living diatom cells, and the surfaces investigated were tested with the same diatom bioprobe [15]. 13.2.2.1 Diatom Topography as Investigated with AFM Owing to the poor adhesion to the substrate, it is impossible to obtain stable images of most benthic diatom species with the AFM. AFM-compatible diatom species can be selected from a large sample by following a simple and effective strategy: Freshwater aquarium plants covered with benthic diatoms are placed in a jar filled with water, as well as two left-handed European freshwater snail species, Physa fontinalis and Planorbarius corneus, and some glass slides. In the following weeks, the diatoms will colonize the jar and the glass slides. The snails will feed on the diatoms, predominantly leaving the species behind, which obviously strongly attach to the substrate. By this strategy, Gebeshuber and co-workers [10] selected three different diatom species: Eunotia sudetica, Navicula seminulum and a yet unidentified species, and subsequently imaged them in contact mode AFM (Fig. 13.3). The natural adhesives of these diatoms, which attach them to the substrate as well as to each other (all of them are colonial forms), prove to be sufficiently strong that stable AFM imaging conditions are achieved without further sample preparation.

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Fig. 13.3. AFM image of parts of two living diatom cells of the species Navicula seminulum growing on a glass slide. Note that the flat area does not correspond to the surface of the glass slide, but is determined by the maximum possible extension of the z-piezo of the microscope. Image acquired using AFM contact-mode imaging in water, imaging parameter topography, scan size 8 × 8 µm2 , scanning frequency 1 Hz. Reprinted with permission from Gebeshuber IC, Kindt JH, Thompson JB, Del Amo Y, Stachelberger H, Brzezinski M, Stucky, GD, Morse DE, Hansma PK (2003) J Microsc 212:292 [10] © 2003, The Royal Microscopical Society

The cells are imaged in their culture medium or in tap water while they are still growing on the glass slides. Tapping-mode as well as contact mode imaging is easy to achieve as long as engaging the cantilever takes place on the cell surface. Navicula seminulum grows in stacks of cells pointing out from the glass slide. These chains of cells can be about 10 cells high, as investigated by SEM (data not shown). Figure 13.3 reveals detailed surface patterning of the top valve faces of two adjacent cells of Navicula seminulum. The chains of Eunotia sudetica and of the yet unidentified species grow with the valve faces perpendicular to the surface of the glass slide, allowing for AFM investigation of the girdle bands. The cells are alive and continue to divide after imaging. 13.2.2.2 Diatom Adhesives Investigated by SPM Most man-made adhesives fail to bond in wet conditions, owing to chemical modification of the adhesive or its substrate. Engineering strong and robust underwater adhesives that are stable in wet environments is a challenge to current technology. Diatoms produce excellent adhesives that are stable and robust in wet environments. Phase images depict the phase delay between the drive and response of the cantilever. These images contain information about the energy dissipated during

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the interaction of the AFM tip with the sample, and can help us to understand the viscoelastic and adhesion properties of the surfaces investigated, specifically of the organic material responsible for diatom adhesion. Because phase imaging highlights edges and is not affected by large-scale height differences, it provides clearer observation of fine features that can be hidden by rough topography (Fig. 13.4). To investigate the natural adhesives utilized to attach cells to each other and to the substratum, it was tried to probe the cleft between two connected diatom cells with the AFM. In the yet unidentified species, the cleft at the cell–cell interface proved too deep. In this region, even the use of electronbeam-deposited AFM tips with high aspect ratio merely results in tip imaging. Phase imaging reveals slight differences (2◦ ) in viscoelastic and adhesion properties of the two adjacent valves. Eunotia sudetica, by contrast, is very convenient for in situ investigation of the diatom adhesive at the cell interface, because there is barely any cleft between adjacent cells and valve undulations are less pronounced than

Fig. 13.4. (a) The adhesives in the contact region of two cells of Eunotia sudetica are apparent as small topographic features on the slightly undulated cell interface. The corrugation of the bead-like structures is between 10 and 20 nm, and their lateral dimension and spacing is about 1 mm. (b) In the phase image these features are far more striking. The diatom adhesive causes a phase lag of about 10◦ compared with the rest of the frustule surfaces, where on a single frustule it is within 1◦ . Note the 2◦ interfrustule phase step, which reveals slightly different viscoelastic properties of the two neighboring valves. Tapping mode, topography and phase, scan size 10 × 10 mm2 , scan rate 5 Hz. Note that for better view (b) is rotated clockwise by 90◦ as compared with (a). Reprinted with permission from Gebeshuber IC, Kindt JH, Thompson JB, Del Amo Y, Stachelberger H, Brzezinski M, Stucky, GD, Morse DE, Hansma PK (2003) J Microsc 212:292 [10] © 2003, The Royal Microscopical Society

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Fig. 13.5. Force–distance curves. Left: no adhesion can be recognized on the diatom surface. Right: representative data for the diatom adhesive that attaches Eunotia sudetica to the substrate. Several debonding events occur. Reprinted with permission from Gebeshuber IC, Kindt JH, Thompson JB, Del Amo Y, Stachelberger H, Brzezinski M, Stucky, GD, Morse DE, Hansma PK (2003) J Microsc 212:292 [10] © 2003, The Royal Microscopical Society

in the other species investigated (Fig. 13.4). The diatom adhesive is apparent as small topographic features at the cell interface. The bead-like structures are 10– 20 nm high, have lateral dimensions of about 1 µm and are about 1 µm apart. The phase image clearly depicts the altered viscoelastic properties of these structures: the diatom adhesive causes a phase difference of up to 10◦ compared with the phase difference on the rest of each of the two frustules, where it is within 1◦ on each, apart from a 2◦ phase difference between the two adjacent valves, a feature which also appears in the other species, where the adhesives are not accessible because of deep clefts between the single organisms. Force–distance curves on the surface and on the adhesive of Eunotia sudetica reveal basic differences in adhesion properties (Fig. 13.5). On the diatom surface, no adhesion force can be detected (Fig. 13.5 left). The diatom adhesive, by contrast, is strong and robust in the wet environment. To gain reproducible access to this natural adhesive, a chain of Eunotia sudetica that was embedded in a densely packed field of Navicula seminulum was scraped away from the glass slide with an STM-tip mounted on a three-dimensional micromanipulator. Over a period of several hours, force–distance curves were taken on the adhesive molecules that were used to attach the diatom cells to the glass slide (Fig. 13.5, right). No change in the basic shape of the force–distance curves can be detected within hours of repetitive pulling in the area where the colony was located. Typically, several debonding events occur until the natural adhesive molecules finally debond at a tip–surface separation of about 600 nm. For a detailed description of this study, see [4, 10].

13.3 Interaction of Large Organic Molecules Conformational diseases such as Parkinson’s disease, Alzheimer’s disease, kuru, scrapie, BSE and vCJD (variant Creutzfeldt-Jakob Disease) result from misfolded proteins aggregating into detrimental structures like amyloid fibers [16–18].

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The amount of protein involved ranges from scarcely detectable to kilograms. Partial unfolding might expose significant regions of the polypeptide chain to the outside world, allowing the protein to aggregate and convert into amyloid fibrils. Once formed, the strong hydrogen bonding between molecules can make this process effectively irreversible. As with crystallization, the formation of amyloid fibrils is “seeded” by preformed aggregates, a phenomenon that might also be responsible for the rapid progression of sporadic diseases such as Alzheimer’s once the symptoms become evident. BSE, for example, has almost undoubtedly resulted from the highly unnatural practice of feeding young cows on the remains of old ones, with the disease then being transmitted to humans as vCJD. Both kuru and BSE have virtually disappeared as a result of effective action taken once their origins were understood. The proteins that have emerged under evolutionary pressure are normally robust enough to resist reversion to aggregated states. Evolutionary processes have selected sequences of amino acids with the remarkable ability to form monomeric structures in which the main chain is folded in a unique way within the mass of close-packed side chains, preventing it from interacting with other molecules. Furthermore, “chaperone” proteins help to protect against such changes. Chaperones are proteins whose function is to assist other proteins in achieving proper folding: They prevent protein aggregation by providing encapsulated hydrophobic environments that allow the protein to fold properly. Many chaperones are heat or cold shock proteins, that is, proteins expressed in heat or cold shock conditions. The reason for this behavior is that protein folding is severely affected by extreme temperatures. Chaperones act to counteract the potential damage. Although most proteins can fold in the absence of chaperones, a minority strictly requires them. A large number of chaperones need adenosine triphosphate (ATP) to function properly. Chaperones recognize unfolded proteins by the hydrophobic residues these expose to the solvent. Exposed hydrophobic residues are unusual for properly folded proteins. Since the environment of the cell is characterized by hydrophilic groups (mostly water), incompletely folded or misfolded proteins with exposed hydrophobic groups have a tendency to aggregate to larger structures, where again, the hydrophobic residues would be hidden from the surrounding. Chaperonins are a subset of chaperone proteins found in prokaryotes, mitochondria and plastids. The AFM has proven to be a useful tool for studying proteins at the single molecule level. For a review on single molecule techniques in biomedicine and pharmacology, see [19]. Many of the single molecule studies with the AFM have been restricted by noise and speed limitations. The first protein–protein interactions on the single molecule level imaged in real time were presented in 2000 [20]. This study demonstrated the enormous contributions AFM can make to molecular biology. Bulk results are interesting, but there are many valuable properties that can only be investigated on the single molecule level. This work was enabled by the development of small cantilevers [21–23]. Small cantilevers allow for faster imaging and faster force spectroscopy of single biopolymers, because they have higher resonant frequencies and lower coefficients of viscous damping.

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A new generation of AFMs using small cantilevers will enable the study of biological processes with greater time resolution, possibly at video refresh rates. Furthermore, small cantilever AFMs allow to narrow the gap in time between results from force spectroscopy experiments and molecular dynamics calculations. The small cantilevers are fabricated out of low stress silicon nitride. They are ten micrometers long, have widths of 3–5 mm, and their thickness is about 75 nm. These cantilevers can measure smaller forces than larger cantilevers with the same spring constant because they have lower coefficients of viscous damping. The prototype small AFM detects the motion of small cantilevers by using high numerical aperture optics to focus a laser beam onto the cantilever and then measuring angular changes in the reflected light beam. This microscopy was used to observe, in real time, the interactions between individual molecules of the Escherichia coli chaperonin protein GroES binding to and then dissociating from individual E. coli GroEL proteins, which were immobilized on a mica support. Both X-ray crystallography and cryoelectron microscopy studies have been used to resolve the structures of GroEL and the GroEL–GroES complex in different stages of the folding cycle (Fig. 13.6, e.g. [24–29]). A prototype small cantilever AFM [23] image of both GroEL deposited on mica and the GroEL–GroES complex repeatedly without the aid of fixing agents (Fig. 13.7). GroEL adsorbs to mica in end-up orientation. The average diameter of the molecules in this image agrees with the X-ray and cryoelectron microscopy data. Upon the addition of GroES and ATP into the buffer solution, GroES molecules were observed as features that extend 3.6 ± 1 nm higher than the GroEL film (Fig. 13.8). The height of these features is also consistent with X-ray crystallography and cryoelectron microscopy data. The same sample region can be scanned repeatedly without excessively disturbing the GroEL–GroES complexes (for details, see [20]).

Fig. 13.6. Cryoelectron microscopy images of GroEL (left) and the GroEL–GroES complex. The height of the GroEL molecule is about 15.1 nm, the height of the GroEL–ES complex is about 18.4 nm. Upon interaction with ADP or ATP, domain movements occur, as indicated. Reprinted with permission from Roseman AM, Chen S, White H, Braig K, Saibil HR (1996) Cell 87:241 [29] © 1996, Elsevier

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Fig. 13.7. GroEL film deposited on mica scanned in two dimensions (left) and in one dimension (right). In this image of GroEL, the movement along the slow scan axis was disabled half way through the scan. From then on the AFM tip repeatedly scanned the same line of proteins. Each horizontal line, therefore, shows changes in time of an individual molecule. Reprinted with permission from Viani MB, Pietrasanta LI, Thompson JB, Chand A, Gebeshuber IC, Kindt JH, Richter M, Hansma HG and Hansma PK (2000) Nature Struct Biol 7:644 [20] © 2000, Nature Publishing Group

Therefore, in order to obtain the temporal resolution required for observing the formation and dissociation of the GroEL–GroES complexes in the presence of Mg-ATP, the sample was scanned in one dimension rather than two (Fig. 13.8). The time/height diagram of the protein lines displays repetitive well-defined step-like variations in height (Fig. 13.8). The magnitude of these steps is 3.6 ± 1 nm. The observed height variations result from GroES molecules attaching to and then separating from the respective GroEL molecules. Without GroES and Mg-ATP no such steps can be observed.

Fig. 13.8. Tapping mode AFM in liquid. Top: after the addition of GroES and Mg-ATP into the buffer solution, variations in height along the lengths occur in the single protein lines, as exemplified by arrows I and II. Bottom: time/height diagram of the protein lines indicated with the arrows in the top image. The height changes between two values that differ by 3.6 ± 1 nm. This indicates the binding and unbinding of GroES. The cryoelectron microscopy images of GroEL and the GroEL–GroES complex are from Roseman et al., 1996 (reprinted with permission, © 1996, Elsevier). Adapted with permission from Viani MB, Pietrasanta LI, Thompson JB, Chand A, Gebeshuber IC, Kindt JH, Richter M, Hansma HG, Hansma PK [20] (2000) Nature Struct Biol 7:644 [20] © 2000, Nature Publishing Group

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Fig. 13.9. Histogram of measured GroEL–GroES complex lifetime in the presence of Mg-ATP. Individual GroES molecules attach to and then separate from the same GroEL molecule 18 times during an observation period of about 120 seconds. Note the absence of events with lifetimes < 2 seconds. This is interesting in itself, telling us about the GroEL-GroES complex lifetime on the single molecule level, and furthermore indicates gentle measuring, since strong disturbance of complex formation by the cantilever would also lead to subsecond complex lifetimes. Reprinted with permission from Viani MB, Pietrasanta LI, Thompson JB, Chand A, Gebeshuber IC, Kindt JH, Richter M, Hansma HG, Hansma PK [20] (2000) Nature Struct Biol 7:644 © 2000, Nature Publishing Group

A histogram of the complex lifetime for a single GroEL molecule that was investigated for about 120 seconds is shown in Fig. 13.9. During this time interval, 18 times a complex with GroES has formed. The distribution of complex lifetime peaks near five seconds and the average lifetime is ∼ (7 ± 1) s (n = 18). In future application of this kind of single molecule studies with the AFM, misfolded proteins could well be involved and, e.g. the effect of various pharmaceuticals on folding efficiency could be tested.

13.4 Nanodefects on Atomically Flat Surfaces Most of the small structures currently used in technology are in the micrometer range. One reason for this is silicon micromachining technology, which works fast and at low cost in this regime. However, needs for increased data-storage density and smaller devices call for nanometer-sized structures. Nanofabrication techniques comprise techniques such as electron beam and nano-imprint fabrication, epitaxy and strain engineering, scanning probe techniques, as well as self-assembly and template manufacturing [30]. Nanotransfer printing is a more recent high-resolution printing technique, which uses surface chemistries as interfacial “glues” and “release” layers to control the transfer of solid material layers from stamp relief features to a substrate [31].

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One important way to produce nanostructures on surfaces involves kinetic sputtering by “fast” ions. However, fast ions unavoidably cause unwanted radiation damage. As opposed to this, potential sputtering (PS), i.e. desorption induced by the potential energy of slow multiply charged ions (MCI), holds great promise for more gentle nanostructuring of insulating surfaces [32, 33]. It can cause high sputter yields even at such low ion impact energies where kinetic sputtering and defect creation in deeper layers is not possible. While the physical mechanisms of PS have been the subject of extensive investigation [34–38], technical applications of slow MCI have so far remained largely unexplored, despite the fact that they provide unique opportunities for etching, ultra-thin film growth and nanostructure fabrication. The AFM is the microscope of choice for investigating ion induced nanodefects on flat crystals, because of its unprecedented resolution and of the fact that it can also image insulating materials. 13.4.1 Ion Bombardment of Highly Oriented Pyrolytic Graphite (HOPG) HOPG is used as a diffracting element in monochromators for X-ray and neutron scattering and as a calibration standard for STM and AFM. The graphite surface is easily prepared as a clean atomically flat surface by cleavage with an adhesive tape. HOPG is, therefore, used in many laboratories as the surface of choice for “seeing atoms”. Surface defects in HOPG produced by the impact of individual (singly charged) ions have already been investigated via STM/AFM by a number of groups [40–49, and further references therein]. However, first results were reported only recently for impact of slow multiply charged ions and the effect of the projectile charge state (or potential energy) on the size of the produced nanodefects [49–52]. Moreover, in most previous studies, either STM in air was used or the irradiated samples were transported in air towards STM inspection after ion bombardment. If, e.g., chemical bonds at the surface are broken due to the ion impact, impurities could preferentially adsorb at these sites and thus change the topography of the surface (and the resulting STM image) during contact with air. Therefore, here MCI bombardment has been followed by STM/AFM investigations without breaking the ultra-high vacuum. In this way, possible influences from target surface exposure to air can be ruled out. Figure 13.10 shows STM and AFM scans of the HOPG surface before bombardment. The STM image of HOPG bombarded with 800 eV Ar+ ions reveals a large number of individual nanosized defects as a result of ion bombardment (Fig. 13.11). In AFM scans of the same surface, no significant topographic changes could be detected [53]. For very highly charged projectile ions, surface defects have recently also been observed in AFM studies [51, 52]. Meguro and co-workers found that HCI impact and subsequent treatment either by electron injection from an STM tip or by He-Cd laser irradiation induce a localized

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Fig. 13.10. Highly oriented pyrolytic graphite imaged in ultrahigh vacuum with atomic resolution. Left: scanning tunneling microscopy image, image size 4×4 nm2 . Right: atomic force microscopy image, image size 1 × 1 nm2

transition from sp2 to sp3 hybridization in graphite, resulting in the formation of nanoscale diamond-like structures (nanodiamonds) at the impact region [54]. In an investigation of HOPG bombarded with 400 eV Ar+ and Ar8+ ions involving Raman spectroscopy, Hida and co-workers found that the charge state of the ions as well as their mass have an influence on the disordering of HOPG and that the defects introduced by Ar8+ are not simple vacancies, but assumed to be vacancy clusters in contrast to their results for Ar+ irradiation [55]. Several hundred defects from different sample positions have been statistically analyzed for each projectile type (Ar+ , Ar8+ , Ar9+ ).

Fig. 13.11. Highly oriented pyrolytic graphite bombarded with 800 eV Ar+ ions imaged with STM in ultrahigh vacuum. Image size 100 × 100 nm2 . The ion induced nanodefects are clearly visible

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Figure 13.12 (right trace) shows the enlarged STM image of a typical defect on HOPG created by the impact of a single Ar+ ion of 800 eV kinetic energy The only surface defects found in the STM images are “protrusions” (hillocks) with a mean lateral size of 0.8–1.25 nm and an average equivalent height of 0.22 nm. They are randomly dispersed on the originally flat surface. Their area density is in good agreement with the applied ion √ dose, implying that nearly every single ion √ impact has caused one protrusion. A 3 × 3R30◦ surface, as characteristic for interstitial defects in HOPG [56–58], surrounded by undisturbed surface parts is observed in the vicinity of most defects (see Fig. 13.12). Scanning with the AFM down to atomic resolution on the irradiated surface did not show any significant topological changes due to ion bombardment. Therefore, we conclude that the nanodefects produced by slow ion impact are of electronic rather than of topographic nature. For impact of singly charged ions, our findings are in good agreement with previous observations [43, 57]. As a remarkable result, however, it was found that the measured mean diameter of the “hillocks”, and to a somewhat lesser extent their “height”, increase with the projectile charge state [53]. In a careful STM study, Hahn and Kang [57] showed that generally two kinds of defects in HOPG are created by low energy (100 eV) Ar+ bombardment, namely carbon vacancy defects (VDs) and interstitial defects (IDs) formed by trapping the projectile beneath the first carbon plane. Both types of defects are detected as protrusions in the STM topographic image. The dangling bonds at the VD site cause an enhancement of the local charge densityof-states (CDOS) near the Fermi energy, seen as a protrusion in the STM image [57]. The protrusion observed in the STM image at ID sites results from a small geometric deformation of the graphite basal plane due to the trapped projectile (not large enough to be visible in our AFM √ scans)√ and an apparently larger electronic 3 × √3R30◦ surface was reported [57] defect due to an increased CDOS. A √ only for IDs but not for VDs. From this 3 × 3R30◦ superlattice structure also

Fig. 13.12. Highly oriented pyrolytic graphite bombarded with 800 eV Ar+ ions imaged with 2 STM in ultrahigh vacuum with atomic resolution (right). Image √ size√10 × 10 nm . The fast Fourier transform (left) of the Ar+ ion-induced defect reveals a 3 × 3R30◦ surface: the ion induced features are larger than the features from the HOPG lattice and they are rotated with respect to them by 30 degrees

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observed in our experiments (see Fig. 13.12), we therefore conclude that the majority of the “hillocks” observed are due to IDs, or VDs created along with IDs. The strong increase of the lateral protrusion size with increasing charge state of the projectile ion is interpreted as a “pre-equilibrium” effect of the stopping of slow multiply charged ions in HOPG, as has so far only been observed for higher charge states [44]. Although MCI are converted already into neutral hollow atoms (i.e., an atom whose inner shells remain essentially unoccupied) during their approach towards the surface, their captured electrons remain in highly exited states until surface impact, where they are gradually peeled off and replaced by conduction band electrons forming a partial screening cloud around the MCI [59]. Before final deexcitation of the hollow atom can take place within the solid, reduced screening should result in a strongly increased energy loss of the projectiles. According to SRIM-2000 (© IBM) calculations [60], the mean range of 150 eV Ar projectiles in HOPG is about two monolayers. An increased stopping and straggling of the higher charged Ar projectiles would lead to IDs located closer to the surface, as well as to more VDs due to a higher momentum transfer to the carbon atoms of the first plane. Because of the extreme surface sensitivity of STM, this pre-equilibrium effect in the stopping power is not masked by (equilibrium) bulk effects and is apparently observable with unprecedented clearness. Extending pertinent work by other groups with singly charged ions only, our combined STM/AFM studies revealed nanodefects that comprise a disturbance of the electronic density-of-states of the surface rather than its topography. Whereas the size of these defects increases with the ion charge (here up to q = 9), as expected for any conducting target surface they showed no evidence for potential sputtering. For more detailed information on these studies, see [50, 53]. 13.4.1.1 Revealing the Hidden Atom in Graphite by Low-Temperature AFM Despite the proverbial ease of imaging graphite by STM with atomic resolution, every second atom in the hexagonal surface unit cell remains hidden, and STM images show only a single atom in the unit cell. The reason for this is that the tunneling current is not a function of the surface topography, but of the local electronic structure. On the graphite surface, there are two different types of carbon atoms in the basal plane, as distinguished by the presence (α) or absence (β) of a carbon atom in the plane immediately below the surface. The α atoms are located directly above another α atom, in the layer directly underneath, the β atoms are located above a hollow site. These local electronic structure variations imply that the STM can only detect every other atom on the graphite surface. Consequently, an alternative imaging method is required to detect the “hidden” α atoms on the graphite surface [61]. Also in contact-mode AFM images of graphite the quasi-atomic resolution images show only one protrusion per unit cell [62]. Recent progress in dynamic AFM allows researchers to routinely achieve true atomic resolution on conductors and insulators [63, 64], but once again only one

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maximum within a hexagonal unit cell of the graphite surface was obtained in the attractive noncontact mode [65]. In 2003, Hembacher and co-workers presented measurements with a lowtemperature atomic force microscope with pico-Newton force sensitivity that reveal the hidden surface atom [66]. The instrument used in this investigation is a combined ultrahigh vacuum (UHV) STM/AFM to simultaneously probe the charge density at the Fermi level and the total charge density of graphite by recording tunneling currents and forces, respectively. The instrument is immersed in a liquid He bath cryostat, yielding a sample temperature of 4.89 K and exceptionally low thermal drifts of about 0.02 nm/h (at room temperature, even with drift correction, currently 2–10 nm/h are achieved). To protect the microscopy from external vibrations, the setup is built on a foundation with a mass of 30,000 kg. In their dynamic AFM images of graphite, recorded at small oscillation amplitudes and with weak repulsive forces, both the α atoms and the β atoms are detected. The reason for this is that the repulsive forces utilized in AFM involve different electrons in the tungsten tip than in the STM mode. Revealing the hidden atoms in graphite by means of room-temperature AFM might become possible with miniaturized AFMs based on nano- or microelectromechanical systems (NEMS/MEMS) technology (since they show small drift). In such an instrument, the operating frequency could be commensurately increased and there would be no need for a 30,000 kg fundament [61]. 13.4.2 Bombardment of Single Crystal Insulators with Multicharged Ions Systematic STM/AFM investigations on nanoscopic defect production at atomically clean insulator surfaces of Al2 O3 after bombardment by slow (impact energy ≤ 1.2 keV) singly and multiply charged ions under strict UHV conditions is the topic of this section. It will be demonstrated that on monocrystalline insulator surfaces, well-defined topographic features of typically nm extensions are produced (“potential sputtering”). For Al2 O3 , there exists a clear dependence of the defect size on the projectile ion charge. These results are discussed in view of possible new nanoscopic surface structuring and modification methods for which the kinetic projectile energy plays only a minor role. Impact of slow ions on solid surfaces can give rise to inelastic processes that modify the geometric and electronic structure at and below the surface, cause emission of electrons and photons as well as neutral and ionized target particles (atoms, molecules, clusters), remove surface-adsorbed material and lead to projectile neutralization. The transfer of electrons between surface and projectile possibly acts as precursor for the above-mentioned processes and makes them proceed irrespective of the kinetic projectile energy. The importance of such “electronic” processes increases with multicharged projectile ions and their role is elucidated when slow ions of the same kinetic energy, but with different charge states are applied as projectiles.

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For certain insulator surfaces, the impact of slow multicharged ions (MCIs) Zq+ gives rise to considerably stronger ablation than the well-established kinetic sputtering by neutral or ionized projectiles. First experimental evidence for this PS was reported for alkali-halide surfaces and explained by “Coulomb explosion” [67], i.e. the creation of small positively charged surface spots from the rapid electron capture by impinging MCI, and the subsequent ablation because of strong mutual target ion repulsion. “Coulomb explosion” was also invoked in order to explain AFM observations of blister-like defects on mica samples produced by highly charged ions Zq+ (kinetic energy 1–3 keV/atomic mass unit) [36, 68]. However, studies for impact of slow (≤ 1 keV) MCI on thin polycrystalline films of alkali-halides (LiF, NaCl) and Al2 O3 deposited on quartz microbalance crystals [69] suggested a different explanation for PS, namely defect-stimulated desorption induced by very efficient electron capture [35]. It has been established that such desorption processes are induced by electrons (electron stimulated desorption, ESD) or photons (photon stimulated desorption, PSD) on such materials where self-trapping of specific crystal defects proceeds via electron–phonon coupling in the crystal lattice [70]. However, such defect trapping as the prerequisite for PS may also be caused or at least supported by the kinetic projectile energy (“kinetically assisted PS” [37]), which could also explain some PS-like effects reported for target species where no electron–phonon coupling can take place, i.e. for semiconductors like Si and GaAs [68]. In any case, for slow ion impact, the self-trapping mechanism is most relevant for PS. Consequently, for metal and semiconductor surfaces no slow MCIinduced PS can be observed, so far [71]. As the surface region from which a slow MCI does capture electrons should be rather small (nm extensions), it is probable that the surface defects caused by PS are of similar size. In order to study such defect structures, we applied AFM in UHV on monocrystalline target surfaces of insulator species for which PS by slow MCI impact has already been demonstrated on polycrystalline thin films [37, 69, 71]. The results for Al2 O3 presented below are of possible interest for nanostructuring these surfaces. Observations of slow ion-induced nanodefects on different atomically clean target surfaces were performed under strict UHV conditions with a combined AFM/STM instrument (UHV-AFM/STM, OMICRON Nanotechnology GmbH, Germany). Nanodefects were looked for on freshly prepared surfaces of sapphire c-plane Al2 O3 (0001) after irradiation with low doses of slow singly and multiply charged ions. In order to avoid disturbing noise from an ion irradiation chamber directly attached to the AFM/STM instrument, a transportable UHV vault for target transfer, which was alternatingly coupled via UHV locks to the target ion irradiation chamber and the AFM/STM was used. This procedure kept the target surfaces under permanent UHV conditions after initial cleaning, thermal annealing, and during subsequent slow ion irradiation until completion of the AFM/STM inspection. Ion irradiation of the insulator surfaces was accompanied by low-energy (≤ 4 eV) electron flooding to compensate for surface charge-up, which otherwise strongly inhibits AFM observation or makes it even impossible. The electron gun was arranged at 2 cm distance

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to the sample. All AFM observations were made in the contact mode, with the base pressure in the AFM/STM chamber kept at about 10−10 mbar during measurements. The singly and multiply charged ions for target irradiation have been extracted from a 5 GHz electron cyclotron resonance ion source [72], magnetically analyzed and guided via electrostatic lenses to the UHV irradiation chamber. The ions were decelerated in front of the target surface to their desired impact energy (≤ 1.2 keV). Uniform irradiation was assured by rapidly scanning the ion beam across the target surface by means of deflection plates. 13.4.2.1 Production of Slow Ion-Induced Surface Defects on Al2 O3 Insulator Targets Polished Al2 O3 (0001) c-plane single crystals (TBL Kelpin, Neuhausen, Germany) were CO2 snow cleaned (to remove micrometer and submicrometer particles and hydrocarbon-based contamination) and then annealed in UHV for 3 h at 400 ◦ C. This preparation technique yields very flat crystal surfaces. AFM contact mode studies on 14 samples prepared by the standard preparation technique revealed a root mean square (rms) roughness of 0.093 ± 0.06 nm rms. Bombardment with Ar ions of different charge states and kinetic energies (500 eV Ar+ and Ar7+ , 1.2 keV Ar+ , Ar4+ and Ar7+ ) results – as seen in AFM contact mode – in hillock-like nanodefects (see Fig. 13.13). The ion-induced defects on the sapphire single crystal surface can be removed by annealing at 450 ◦ C for 5 h. The density of nanodefects does not directly correspond with the applied ion dose: an ion dose of 5 × 1012 ions/cm2 , which is equivalent to five ions per 10 nm × 10 nm, leads to a rather small, however reproducible, density of defects on the sapphire surface: about 10 nanodefects per 1000 nm × 1000 nm can be observed after bombardment in the energy range reported here. This is equivalent

Fig. 13.13. UHV AFM contact mode image of sapphire (Al2 O3 , c-plane 0001) bombarded with 500 eV Ar+ (left image) and Ar7+ (right image) ions. The nanodefects induced by Ar7+ ions (which have the same kinetic but higher potential energy than the Ar+ ions) are considerably higher and wider than those caused by singly charged ions. The defects are real topographic features; the units on the three axes are nanometers. Reprinted with permission from Gebeshuber IC, Cernusca S, Aumayr F, Winter HP (2003) Int J Mass Spectrom 229:27 [53] © 2003, Elsevier Science B.V.

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to a dose to defect ratio of 5000. More detailed experiments with different ion doses are needed. Analysis of the statistics of random impacts will clarify how many individual ion impacts are needed to form a visible nanodefect on the insulator surface. A possibly similar migration and subsequent recombination of point defects at the surface has previously been reported for silicon bombarded by 5 keV He ions above 160 K [73]. In fact, the only case where the number of defects corresponded fairly well to the applied ion dose was for the conducting HOPG samples (see Sect. 13.4.1). The Al2 O3 c-plane proved to be the insulator surface showing most clearly a dependence of the ion bombardment induced defects with the kinetic energy and charge states of the projectiles. 500 eV Ar+ ions produce defects that are about 1 nm high (Fig. 13.13) and have lateral dimensions of some tens of nanometers (one should keep in mind that the height is more accurately measurable with the AFM than lateral dimensions), whereas the defects produced by 500 eV Ar7+ ions are several nanometers high (Fig. 13.13) and show lateral dimensions of about 100 (!) nanometers. At higher kinetic energy the differences in the slow ion-induced nanodefects on the sapphire c-plane became even more distinct. 1.2 keV Ar+ -induced defects are up to about 8 nm high and their width is some 10 nm. For a higher charge state such as Ar4+ , two different kinds of defects occurred on the sapphire surface. They have about the same height, but their lateral dimensions vary considerably: some are nearly 200 nm wide, whereas the smaller defects are only about 50 nm wide. The height of both kinds of defects is about 2 nm. For Ar7+ , only one kind of defect was visible in the AFM images, with about 50 nm diameter and about 2 nm height (for a more detailed description of these results and for similar investigation on SiO2 surfaces, see [53]). Al2 O3 is, therefore, a good candidate for PS-induced nanostructuring. This material is relevant for applications in microelectronics and nanotechnology.

13.5 Subatomic Features In this section, the detection of atomic orbitals and single electron spins by means of SPM is described. In many cases, sophisticated signal acquisition techniques have to be applied, and the instruments have to be operated at very low temperature, since extremely small drift is required. 13.5.1 Atom Orbitals Silicon and tungsten are the two chemical elements that already have been investigated with SPM regarding their atomic orbitals.

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13.5.1.1 Silicon (111)-(7 × 7) Surface Publications concerning the imaging of subatomic features with the AFM started in the year 2000, when Giessibl and co-workers published their paper on imaging of subatomic features on the reconstructed silicon (111)-(7 × 7) surface [74]. For a review on semiconductor surface reconstruction, see [75]. A scientific discussion, in which Hug and co-workers questioned this result by proposing that the subatomic features are caused by a feedback artifact, followed this publication [76]. In the course of this argument, Giessibl and co-workers presented refined calculations, showing striking similarities to the experimental images (see Fig. 13.14). In 2003, Huang and co-workers presented a theoretical work demonstrating the feasibility of seeing atomic orbitals on the Si(111)-(7 × 7) surface with AFM [77].

Fig. 13.14. Refined calculations of the normalized frequency shift of a single adatom on the reconstructed silicon (111)-(7 × 7) surface (right) performed by the Giessibl group, showing striking similarities with the experimental images (left). Reprinted with permission from Hug HJ, Lantz MA, Abdurixit A, van Schendel PJA, Hoffmann R, Kappenberger P, Baratoff A, Giessibl FJ, Hembacher S, Bielefeldt H, Mannhart J (2001) Science 291:2509 [76] © 2001, AAAS

13.5.1.2 Tungsten In 2004, Giessibl and co-workers finally ended this discussion by presenting images of an individual tungsten atom by AFM at a resolution of 77 pm [78]. The diameter of a tungsten atom is 274 pm. Four distinct peaks that are attributed to highly localized electron clouds can be identified (Fig. 13.15). The experiment was performed in UHV at a temperature of about five Kelvin. The microscope was isolated from vibrations by a 30 t foundation and from sound and electromagnetic stray fields by a metal chamber. In contrast to STM (which only probes the most loosely bound electrons with energies at the Fermi level) AFM can resolve the charge density variations within a single atom, because the forces between the AFM tip and the sample are of electrostatic nature.

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Fig. 13.15. UHV low temperature (5 K) AFM constant-height mode image reveals four-fold symmetry in the amplitudes of the higher harmonics signal (centered close to the maximum of the tunneling current, data not shown). Reprinted with permission from Hembacher S, Giessibl FJ and Mannhart J (2004) Science 305:380 [78] © 2004, AAAS

The electron structure originates from the quantum-mechanical nature of tungsten bonding: tungsten develops a body centered cubic crystal structure such that every tungsten atom is surrounded by eight nearest neighbor atoms, causing “arms” of increased charge density which point to the next neighbors. Four of these precisely localized electron clouds are visible on surface atoms. The role of tip and sample was switched in the experiment: the front atom in a sharp tungsten tip was imaged by a light carbon atom of a graphite surface. The reason a light atom was used for probing was to minimize image blurring, since the mapping of one atom with another atom always involves a convolution of the electronic states. The tunneling current is confined to the top atom because of the sharp increase of tunneling probability with decreasing distance. Instead of measuring static deflections or frequency changes, higher harmonics triggered by forces between the tip and the sample are recorded in this technique. These higher harmonics are much more sensitive to short-range interactions than static deflections or frequency changes. 13.5.2 Single Electron Spin Detection with AFM and STM Single-spin detection is a vital goal for read-out in quantum computing, and single nuclear spin detection could solve the problem of how to distinguish between materials at the atomic level. Several research groups have reported various single spin-detection methods [79–86]. In 1989, Manassen and co-workers presented the first direct observation of the precession of individual paramagnetic spins on partially oxidized silicon (111) surfaces [79]. They used an STM to detect the modulation in the tunneling current at the Larmor frequency. The Larmor frequency is the frequency at which magnetic resonance can be excited. It is given by the Larmor equation, which states that the resonant frequency is proportional to the overall (macroscopic and microscopic) magnetic field. Balatsky and Martin presented the theoretical explanation of this result [87] in 2001.

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Fig. 13.16. Spin detection through the union of high-resolution microscopy and resonance techniques. The sample is a HOPG surface coated with clusters of organic BDPA molecules. In the applied magnetic field, the electron-spin vectors associated with free radicals in the molecules precess at a certain frequency. The STM tunneling current is modulated at the precession frequency. Detecting the modulation effectively measures electronic spin in the molecule. Reprinted with permission from Manoharan HC (2002) Nature 416:24 [88] © 2002, Nature Publishing Group

In 2002, Durkan and Welland published an article that essentially reproduced this experimental result with a different sample: BDPA (a, g-bisdiphenylene bphenylallyl) on HOPG [80]. The idea of combining magnetic resonance (MR) with force microscopy in magnetic resonance force microscopy (MRFM) was published as a concept in 1991 [89]. Sidles settled on force microscopy because the performance of induction coils, the detectors in conventional MR, scales unfavorably with size. Shrinking the coil to detect a single spin reduces the signal irretrievably below noise. A force microscope, on the other hand, becomes more sensitive the smaller it gets. In 1992, Rugar and co-workers demonstrated that the force exerted by 1012 electron spins could be detected at room temperature with a conventional cantilever for AFM [90]. Since then they have improved their spin detection limit by 12 orders of magnitude: MRFM was proposed as a means to improve detection sensitivity to the singlespin level, and thus enable 3D imaging of (bio)molecules with atomic resolution [91, 92]. MRFM is essentially a combination of 3D magnetic resonance imaging (MRI) with the unprecedented resolution of AFM. For an overview on MRFM, see Hammel and co-workers, 2003 [93] and for the theory of spin relaxation in MRFM, see Mozyrsky et al. 2003 [94]. In the year 2004, the force exerted by a single electron spin was measured by MRFM ([86], Fig. 13.17).

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Fig. 13.17. A wiggling cantilever with a tiny CoSm magnet is the key element of a magnetic resonance force microscope. Elaborated signal acquisition makes it possible to detect a single electron spin dozens of atomic layers beneath the surface. In this way, scanning probe microscopy left the surface regime. Perhaps even atomic resolution images of molecules beneath the surface might be possible in the near future. Reprinted with permission from Rugar D, Budakian R, Mamin HJ, Chui BW (2004) Nature 430:329 [86] © 2004, Nature Publishing Group

The force detected in the Rugar 2004 experiment is a million times smaller than the forces usually encountered in AFM (van der Waals forces, electrostatic forces). The single electron spin was buried 250 nm below the surface of an irradiated vitreous silicon sample and exerted a force of 2 aN (2 × 10−18 N). The sample had been prepared by irradiation with a 2 Gy dose of 60 Co gamma rays, producing a low concentration of Si dangling bonds containing unpaired electron spins known as E  centers. Unpaired electrons and many atomic nuclei behave like tiny bar magnets. Estimated spin concentration was between 1013 and 1014 cm−3 . The experiment was performed at 1.6 K in a small vacuum chamber that fits within the bore of a superconducting magnet. The low operating temperature minimizes thermal noise and reduces the relaxation rate of the spins. The force exerted by a single electron spin is the smallest ever detected. Currently, the smallest volume elements in an image must contain at least 1012 nuclear spins for MRI-based microscopy [95], or 107 electron spins for electron spin resonance microscopy [96]. The cantilever used in the experiment is only 100 nm thick and had to be aligned vertically to the surface. In the conventional AFM configuration with the cantilever parallel to the surface, van der Waals forces and electrostatic forces would make it stick on the surface. Directly on the cantilever a strong 150 nm wide CoSm magnet

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is attached. It generates a field gradient of 200,000 T/m. The cantilever is slowly scanned over the surface. A laser interferometer records the cantilever deflections and sophisticated measurement signal acquisition techniques are needed for successful single spin detection. The strong magnetic field gradient allows for distinguishing magnetic resonance signals arising from different spatial locations, enabling accurate spin localization. By scanning the tip over the sample, a local magnetic resonance force is detected, which corresponds with a spatial resolution of about 25 nm. This spatial isolation of the signal is also the main argument that a single spin is being detected. Currently this method is very slow. As Stokstad mentions in his “Science News of the Week” article on the Rugar experiment, scanning a 170 nm stretch of the irradiated silicon sample took several weeks [97]. MRFM could serve as an invaluable tool for the implementation of a spinbased solid state quantum computer. It provides an attractive means for addressing the characterization and control of the fabrication process of the device during its construction and the readout of the computational result [98, 99]. If developed further, the MRFM technique could prove useful for investigating the atomic structure inside materials used in the electronics industry and to image biomolecules – such as proteins – at atomic resolution. However, to reach this goal, nuclear spins have to be detected. Nuclear spins are harder to detect than electron spins, because a proton’s magnetic moment is 658 times smaller than that of an electron.

13.6 Conclusions and Outlook In this review, we have presented scanning probe microscopy across dimensions from large samples like single cells, via single biomolecules and nanometer small ion induced defects on crystal surfaces to subatomic features like electronic orbitals and single electron spins. Scanning probe microscopy is on its way to a standard laboratory method: subatomic features can be imaged, and with magnetic resonance force microscopy it has even left the two-dimensional surface regime. Perhaps in the not too distant future 3D-imaging of (complex) molecules, at surfaces or in the bulk state, with atomic resolution might become possible with these powerful techniques. The 3-D MRFM would also deliver chemical specific information because each magnetic nucleus has a unique gyromagnetic ratio. Acknowledgements. Part of this work was supported by the Austrian Science Fund (FWF) and was carried out at Vienna University of Technology. Part of this work was funded by the “Austrian Kplus-Program” and was done at the “Austrian Center of Competence for Tribology”, AC2 T research GmbH.

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31. Rogers JA (2004) Stamping techniques for micro and nanofabrication: methods and applications. In: Bhushan B (ed) Springer handbook of nanotechnology. Springer, Berlin Heidelberg New York, p 185 32. Arnau A, Aumayr F, Echenique PM, Grether M, Heiland W, Limburg J, Morgenstern R, Roncin P, Schippers S, Schuch R, Stolterfoht N, Varga P, Zouros TJM, Winter HP (1997) Surf Sci Rep 27:113 33. Winter HP, Aumayr F (2002) Europhys News 6:215 34. Sporn M, Libiseller G, Neidhart T, Schmid M, Aumayr F, Winter HP, Varga P, Grether M, Niemann D, Stolterfoht N (1997) Phys Rev Lett 79:945 35. Aumayr F, Burgdörfer J, Varga P, Winter HP (1999) Comm Atom Molecul Phys 34:201 36. Schenkel T, Hamza AV, Barnes AV, DH Schneider (1999) Progr Surf Sci 61:23 37. Hayderer G, Cernusca S, Schmid M, Varga P, Winter HP, Aumayr F, Niemann D, Hoffmann V, Stolterfoht N, Lemell C, Wirtz L, Burgdörfer J (2001) Phys Rev Lett 86:3530 38. Hayderer G, Schmid M, Varga P, Winter HP, Aumayr F, Wirtz L, Lemell C, Burgdörfer J, Hägg L, Reinhold CO (1999) Phys Rev Lett 83:3948 39. Porte L, de Villeneuve CH, Phaner M (1991) J Vac Sci Technol B 9, 1064 40. Coregater R, Claverie A, Chahboun A, Landry V, Ajustron F, Beauvillain J (1992) Surf Sci 262:208 41. You HX, Brown NMD, Al-Assadi KF (1992) Surf Sci 279:189 42. Mazukawa T, Suzuki S, Fukai T, Tanaka T and Ohdomari I (1996) Appl Surf Sci 107:227 43. Mochiji K, Yamamoto S, Shimizu H, Ohtani S, Seguchi T, Kobayashi N (1997) J Appl Phys 82:6037 44. Reimann KP, Bolse W, Geyer U, Lieb KP (1995) Europhys Lett 30:463 45. Habenicht S, Bolse W, Feldermann H, Geyer U, Hofsäss H, Lieb KP, Roccaforte F (2000) Europhys Lett 50:209 46. Neumann R (1999) Nucl Instrum Meth B 151:42 47. Hahn R, Kang K, Song S, J Jeon (1996) Phys Rev B 53:1725 48. Hahn R, Kang K (1999) Phys Rev B 60:600 49. Minniti R, Ratliff LP, Gillaspy JD (2001) Phys Scr T92:22 50. Hayderer G, Cernusca S, Schmid M, Varga P, Winter HP, Aumayr F (2001) Phys Scr T92:156 51. Terada M, Nakamura N, Nakai Y, Kanai Y, Ohtani S, Komaki K, Yamazaki Y (2004) Observation of an HCI-induced nano-dot on an HOPG surface with STM and AFM In: Rudzikas Z (ed) Abstracts HCI-2004 12th international conference on the physics of highly charged ions, European Physical Society, p 208 52. Terada M, Nakamura N, Nakai Y, Kanai Y, Ohtani S, Komaki K, Yamazaki Y (2005) Nucl Instrum Meth Phys Res B 235:452 53. Gebeshuber IC, Cernusca S, Aumayr F and Winter HP (2003) Int J Mass Spectrom 229:27 54. Meguro T, Hida A, Koguchi Y, Miyamoto S, Yamamoto Y, Takai H, Maeda K, Aoyagi Y (2003) Nuc Instrum Meth B 209:170 55. Hida A, Meguro T, Maeda K, Aoyagi Y (2003) Nuc Instrum Meth B 205:736 56. Hahn R, Kang K, Song S, Jeon J (1996) Phys Rev B 53:1725 57. Hahn R, Kang K (1999) Phys Rev B 60:6007 58. Krasheninnikov AV, Elsin F (2000) Surf Sci 519:454 59. Winter HP, Aumayr F (1999) J Phys B: At Mol Opt Phys 32: R39 60. Ziegler JF, Biersack JP, Littmark U (1985) The stopping and range of ions in matter 1. Pergamon, New York 61. Hersam MC and Chung Y-W (2003) Proc Natl Acad Sci 100:12531 62. Albrecht TR and Quate CF (1988) J Vac Sci Technol A 6:271 63. Morita S, Wiesendanger R, Meyer E (2002) (eds) Noncontact atomic force microscopy. Springer, New York

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14 Surface Characterization and Adhesion and Friction Properties of Hydrophobic Leaf Surfaces and Nanopatterned Polymers for Superhydrophobic Surfaces Zachary Burton · Bharat Bhushan

14.1 Introduction Superhydrophobic surfaces, as well as low adhesion and friction, are desirable for various industrial applications. Hydrophobic (water-repellent) surfaces can be constructed either by using low surface energy materials or by chemically treating surfaces with materials such as polytretafluoroethylene, silicon, or wax. Another technique that can be used to increase the hydrophobic properties of a hydrophobic surface is to increase the surface area by increasing surface roughness. If a surface is initially hydrophilic, then introducing roughness to that surface will make it even more hydrophilic. Wetting (hydrophilic property) is characterized by the contact angle of a surface and occurs when the surface has a contact angle of θ < 90◦ , whereas if the surface is hydrophobic, the value of the contact angle is greater than 90◦ . The contact angle depends on several factors, such as roughness, the manner of surface preparation, and surface cleanliness (Adamson, 1990; Israelachvili, 1992; Bhushan, 1999, 2002, 2005). Models have been presented in the past to determine how roughness affects hydrophobicity. Wenzel (1936) developed the first model, which is based on the consideration of net energy decrease during spreading of a droplet on a rough surface. A rough surface has a larger solid-liquid interface area, leading to larger net energy, and it is responsible for the increase of contact angle for a hydrophobic surface and the decrease of the contact angle for a hydrophilic surface. Wenzel developed an equation that relates the roughness with the contact angles of a flat surface of a certain material and that of the rough surface of the same material and is given by: cos θ = Rf cos θo ,

(14.1)

where θ = contact angle of a rough surface, θo = contact angle of a flat surface, and Rf = roughness factor of the rough surface. The roughness factor is defined as the ratio of the total surface area of the rough surface and the projected area of the rough surface or the footprint of the total surface area. This model predicts that introducing roughness will only increase the surface hydrophobicity if θo is greater than 90◦ . If θo is less than 90◦ , then the contact angle for the rough surface will decrease with increasing Rf . Cassie and Baxter (1944) extended Wenzel’s equation, which was originally developed for the homogeneous solid–liquid interface, for the composite interface.

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For this case, there are two sets of interfaces: a liquid–air interface with the ambient environment surrounding the droplet and a flat composite interface under the droplet involving solid–liquid, liquid–air, and solid–air interfaces. This model shows that when roughness increases, the contact angle approaches 180◦ . However, it does not provide any particular form of dependence of the areas of the solid–liquid and liquid–air interfaces and does not explain under which conditions the composite interface forms. Johnson and Dettre (1964) showed that the homogeneous and composite interfaces correspond to the two metastable states of a droplet. Based on understanding the effect of roughness on the contact angle and the roughness distribution found in leaves, Nosonovsky and Bhushan (2005) presented optimal designs for superhydrophobic surfaces. Using the models presented above, researchers have been able to produce highly hydrophobic surfaces that have been fabricated directly by incorporating high roughness to the surface (Miwa et al., 2000; Kijlstra et al., 2003). In the last ten years, researchers have paid attention to the study of hydrophobic materials that can be found in nature, primarily hydrophobic leaves. The leaf surfaces of hundreds of different plant species have been studied to see the effect of roughness and hydrophobicity (Neinhuis and Barthlott, 1997; Wagner et al., 2003). One plant species in particular has given researchers the motivation to study leaf structures and see how they affect hydrophobicity: nelumbo nucifera (lotus). Lotus leaves have a very high contact angle with water and show strong self-cleaning properties called the “lotus effect” (Barthlott and Neinhius, 1997). By measuring the contact angle and studying images from a scanning electron microscope (SEM), a correlation between the leaf roughness and its hydrophobicity has been studied, but a quantitative surface characterization of the leaf surface has not been completed. Hydrophobic lotus leaves repel water using multiple mechanisms. First, the surface of the leaf is usually covered with wax crystals, which are a mixture of large hydrocarbon molecules, measuring about 1 nm in diameter, and which are very hydrophobic alone. Secondly, the surface of the leaves is very rough due to papillose epidermal cells that create papillae or bumps on the surface of the leaf. The combination of the thin wax film and the larger bumps on the surface of the leaf provides the ability for the leaf to be hydrophobic. Burton and Bhushan (2005a) studied lotus leaves along with another leaf of interest, colocasia esculenta, in previous works to determine surface characteristics along with their adhesion and friction properties. After characterizing the surface of hydrophobic leaves, the qualities that give them their hydrophobic nature must be implemented on new and different surfaces. These new surfaces can then be tailored in specific ways to optimize both hydrophobicity and reduced adhesion and friction. Material selection and roughness distribution are two of the key components in producing these hydrophobic surfaces that are desirable for various industrial applications (Gould, 2003). The inherent contact angle, when the surface is flat, of the material selected along with the roughness distribution chosen, based on previous studies and models, will determine how the surface behaves. Two of the critical tribological properties for materials in micro/nanoscale applications are hydrophobicity and the real area of contact. Wetting results in formation of menisci at the interface between solid bodies during sliding contact, which in-

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creases adhesion and friction. As a result, the friction force is greater than the dry friction force (Bhushan, 1999, 2002, 2004). When the real area of contact increases, there are more asperity interactions between the two surfaces and adhesion and friction increases. With increased roughness, the number of asperities in contact is reduced and therefore, the real area of contact is reduced, leading to decreased adhesion (Bhushan, 2002). Introducing uniform patterns on a surface is one way to decrease the real area of contact when another surface comes into contact with the patterned surface. The two mechanisms, meniscus force contributions and the real area of contact, that determine the adhesive force, both play a role as roughness is introduced to a surface. The interaction between a flat surface and a rough surface with uniform patterns present on the surface changes whether or not the material is hydrophobic or hydrophilic. Figure 14.1 shows a diagram of a flat surface in contact or out of contact with a rough surface with a uniform pattern. The first surface shows the formation of menisci over individual asperities of the rough surface, which come into contact with the flat surface. Meniscus force is dependent upon the number of asperities and the contact angle at individual asperities (Bhushan, 2005). The second surface shows a meniscus interaction with multiple asperities on a hydrophilic material. For a hydrophilic material, wetting occurs and the valleys on the surface will be penetrated by the water creating large menisci over multiple asperities and valleys, leading to increased adhesion and friction. Based on Wenzel’s model (14.1), θ1 will decrease with roughness and the surface will become more hydrophilic. The third surface shows a meniscus interaction with multiple asperities on a hydrophobic material. The water does not wet the surface, thus the water sits on top of the asperities with

Fig. 14.1. Diagram showing the interaction between a flat surface and a rough surface with water present. The effect of individual versus multiple asperities is shown, along with the different behavior of a hydrophilic surface and a hydrophobic surface (Burton and Bhushan, 2005b)

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an increased θ2 based on Wenzel’s model, leading to reduced adhesion and friction from a hydrophilic material. In this chapter, we examine the surface roughness of these hydrophobic leaves using various methods of measurements made by Burton and Bhushan (2005a). Along with measuring and characterizing surface roughness, the contact angle and adhesion and friction properties of these leaves are also considered. The knowledge gained by examining these properties of the leaves and by quantitatively analyzing the surface structure, will be helpful in designing superhydrophobic surfaces. Also in this chapter, both samples with no pattern (hydrophobic and hydrophilic) and samples with a pattern (hydrophobic and hydrophilic) are examined based on the work by Burton and Bhushan (2005b). By investigating these combinations of surface properties, the effect of contact angle and real area of contact can be determined by measuring the adhesion and friction. To further examine the effect of meniscus force and real area of contact, scale dependence is considered with the use of AFM tips of various radii. The effect of relative humidity is also investigated to see environmental effects to adhesion and friction.

14.2 Experimental Details 14.2.1 Instrumentation The contact angle, a measure of surface hydrophobicity, was measured using a Rame– Hart model 100 contact angle goniometer. The measurements were made using demineralized deionized water droplets. Surface hydrophobicity is an important property, as it determines the strength of the adhesive interaction between sliding surfaces resulting from meniscus bridge formation (Bhushan, 1999, 2002, 2003, 2005). All measurements were made at 22 ± 2 ◦ C and 50 ± 5% RH and were reproducible to within ±2◦ . The tall bumps on freshly cut lotus and colocasia leaves present a problem when measuring surface roughness with an AFM. In order to obtain the surface dimensions that most accurately represent the surface structure found on the leaves growing in nature, an optical profiler (NT-3300, Wyko Corp., Tuscon, AZ.) was used (Burton and Bhushan, 2005a). The tall bumps on the leaves are well within the Z-range limitation of the optical profiler and, therefore, the entire vertical range of the leaf can be measured. A greater Z-range is a distinct advantage over other types of surface roughness measurements, but it only has a maximum lateral resolution of approximately 0.6 µm. A scan size of 120 µm × 90 µm, which is the highest magnification for the optical profiler, was used to scan the leaves. For additional surface roughness, adhesion and friction measurements on the leaf surfaces, a commercial AFM (D3100, Nanoscope IIIa controller, Digital Instruments, Santa Barbara, CA) was used (Burton and Bhushan, 2005a). AFM has a Z-range of about 7 µm and can only make measurements on dried lotus and colocasia, since the P–V distance of fresh lotus and colocasia is greater than 17 µm. Two different AFM tips were used in the study. A square pyramidal Si(100) tip with a native oxide layer, which has a nominal radius of 20 nm on a rectangular Si(100) cantilever with a spring

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constantof3 N m−1 wasusedtomakesurfaceroughnessmeasurementsatanormalload of 50 nN and a frequency of 0.5 Hz. Adhesion and friction measurements were made using a 15 µm radius silica ball that was mounted on a gold coated triangular Si3 N4 cantilever with a nominal spring constant of 0.6 N m−1 . The large radius tip was used to see the maximum effect of the large bumps found on the surface of the leaf when the tip is in contact with the leaf surface. Adhesive force was made using the single point measurement of a force calibration plot (Bhushan, 1999, 2002, 2004, 2005). All friction measurements were made during a 50 µm × 50 µm scan at 22 ± 1 ◦ C and 50 ± 5% RH. Surface height maps were measured using both a 50 µm × 50 µm scan and a 100 µm × 100 µm scan to show a different number of bumps on the leaf surface. Adhesion and friction measurements on the nanopatterned polymers were made using the same commercial AFM (Burton and Bhushan, 2005b). Experiments were performed using four different radii tips to study the effect of scale dependence. Large radii AFM tips were primarily used in the study. Fifteen µm radius and 3.8 µm radius silica balls were mounted on a gold coated triangular Si3 N4 cantilever with a nominal spring constant of 0.6 N m−1 . A square pyramidal Si3 N4 tip with nominal radius 30–50 nm on a triangular Si3 N4 cantilever along with a square pyramidal Si(100) tip with a native oxide layer which has a nominal radius of 20 nm on a rectangular Si(100) cantilever were used for smaller radii tips. The spring constants for the Si3 N4 cantilever and the Si(100) cantilever were 0.12 N m−1 and 3 N m−1 , respectively. The adhesive force was determined by making many measurements using a single point measurement of a force calibration plot as well (Bhushan, 1999, 2002, 2005). The contact angle was again measured using a Rame–Hart model 100 contact angle goniometer. The same demineralized distilled water droplets were used for making contact angle measurements. All measurements were made at 22 ± 1 ◦ C and 50 ± 5% RH, unless otherwise stated, and were reproducible to within ±2%. 14.2.2 Samples Figure 14.2a shows an SEM micrograph of lotus and colocasia, which shows the surface roughness that is present on the surface of the leaf. Figure 14.2b shows two more SEM micrographs with higher magnification of a lotus leaf to show the roughness of the wax crystals covering the bumps (Burton and Bhushan, 2005a). The two leaves were obtained from two different sources. Lotus leaves are perennials and only grow during specific times of the year because of the weather. Lotus needs at least a constant temperature of 18 ◦ C to grow and typically grows from the end of May to the beginning of October. The leaves were purchased from Aquarius Water Gardens in Ramsey, Indiana. Colocasia, on the other hand, can be found to grow at all times throughout the year and is readily available. The leaves used in the study were taken from the Franklin Park Conservatory in Columbus, Ohio. To set up the leaves for measurements they were prepared in a specific manner. Each leaf was cleaned by placing it under running water to remove any contaminants by way of the “Lotus effect” (Barthlott and Neinhuis, 1997). Then a 20 mm × 20 mm square was cut from the leaf, between the veins, and placed on the measuring platform with double sided tape as adhesive. For optical profiler measurements the leaves were scanned as soon as possible after being cut, so as to reduce the effect of the dynamic shrinking found to occur after cutting. The leaves for AFM measurements were dried

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Fig. 14.2. (a) SEM images of nelumbo nucifera (lotus) and colocasia esculenta. (b) Two high magnification SEM images of lotus leaf to show a more detailed structure (Burton and Bhushan, 2005a)

for 24 hours before being measured because after this time period the leaves had shrank their maximum amount and the leaf surface was stable. Measurements were also made on leaves that did not have the wax present on the surface. To remove the wax from the surface but keep the surface structure of the leaf intact, acetone was lightly rubbed on the surface of the leaf, which removed the wax from the leaf. Comparisons between the measurements made with the wax present and with the wax removed were made to determine what effect the acetone had on the leaf surface. Two types of polymers were used in the study to make the nanopatterned surfaces, PMMA and MINS. PMMA was chosen because it is a polymer often found in MEMS/NEMS devices and MINS was chosen as a comparison tool (Burton and Bhushan, 2005b). For each of these polymers, there are three types of surface structures: film, low aspect ratio asperities (LAR, 1 : 1 height to diameter ratio) and high aspect ratio asperities (HAR, 3 : 1 height to diameter ratio). The roughness (σ) and peak-to-valley distance (P–V) for PMMA film was measured using an AFM with values σ = 0.98 nm and P–V = 7.3 nm. The diameter of the asperities near the top is approximately 100 nm and the pitch of the asperities (distance between each asperity) is approximately 500 nm. Figure 14.3 shows SEM images of the two types of patterned structures, LAR and HAR, on a PMMA surface. The patterns are created using a mold produced from a master using soft lithography (Choi et al.,

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Fig. 14.3. SEM images of the patterned polymer surface. Both LAR and HAR are shown from two magnifications in order to see both the asperity shape and the asperity pattern on the surface (Burton and Bhushan, 2005b)

2004). A UV-curable polymer with high modulus was used to fabricate the mold in order to produce densely-packed sub-100 nm structures with high aspect ratio. According to the model presented in the Introduction, when introducing roughness to a flat surface, the hydrophobicity will either increase or decrease depending on the initial contact angle on a flat surface (Wenzel, 1936; Nosonovsky and Bhushan, 2005). The materials chosen were initially hydrophilic, so to obtain a sample that is hydrophobic, a self-assembled monolayer (SAM) was deposited on the sample surfaces. The samples chosen for the SAM deposition were the flat film and the HAR for each polymer. The SAM perfluorodecyltriethoxysilane (PFDTES) was deposited on the polymer surface using vapor phase deposition technique. PFDTES was chosen because of the hydrophobic nature of the surface. The deposition conditions for PFDTES were 100 ◦ C temperature, 400 Torr pressure, 20 minutes deposition time and 20 minutes annealing time. The polymer surface was exposed to an oxygen plasma treatment (40 W, O2 187 Torr, 10 seconds) prior to coating (Lee et al., 2005). The oxygen plasma treatment is necessary to oxidize any organic contaminants on the polymer surface and to also alter the surface chemistry to allow for enhanced bonding between the SAM and the polymer surface. 14.2.3 Roughness Factor The roughness factor, Rf , needs to be calculated for the leaf surface to incorporate the effect of roughness on the contact angle. If a surface is a flat plane, then Rf is

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Fig. 14.4. Diagram describing the method used to calculate the true surface area of the leaf surface from an AFM scan (Burton and Bhushan, 2005a)

equal to one, whereas if roughness is added to the surface, then Rf will increase. To obtain an approximation of the Rf for the two different leaves, a model has been developed that will calculate the true surface area and the area footprint and produce their ratio (Burton and Bhushan, 2005a). This model uses the AFM scans of the leaves and uses the height of each data point, along with its location in the matrix of data points to determine the total surface area. Figure 14.4 is a diagram showing how the true area is calculated for each scan area. For an n × n matrix of data points, there are (n − 1) × (n − 1) patches of area that are created. For each patch, a hypotenuse is made to make two right triangles. Using the Z-height for each data point along with its position in the matrix, the area of the two triangles created can be calculated and added together to get the entire area of the patch. Using this technique for each patch and adding all the patches together will give an approximation for the true surface area for the scan and we can divide that by the total scan area or footprint to get the ratio, Rf . Using this approximation for Rf , calculations can be made on contact angles of the flat surface if the contact angle of the rough surface is measured. This method of calculating the roughness factor for a surface is limited to a square scan size and is only used with AFM scans. 14.2.4 Test Matrix for Nanopatterned Polymers To study the effect of scale dependence, the adhesive force between the four AFM tips mentioned above with flat and patterned polymer films of two materials was examined. There are 16 tip/surface structure combinations when using a bare polymer, but with the PFDTES coatings on PMMA and MINS film and HAR, there

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are an additional 16 combinations (Burton and Bhushan, 2005b). This will allow for complete characterization of the adhesive force of the patterned surfaces with varying tip radii. Figure 14.5 is a diagram showing the effect of the different radii on the patterned surface. For small radii, such as the 20 nm and 50 nm tips used in this experiment, the tip can easily fit between the asperities and therefore, there is less effect from the asperities. The 3.8 µm radius tip will sit on the asperities but may also come in contact with the flat polymer between the asperities if the aspect ratio is low enough. The 15 µm radius tip will only sit on the asperities and will not come into contact with the substrate. Experiments in varying relative humidities show the dependence of hydrophobicity for a given surface roughness on adhesion and friction. Dry and wet friction and adhesion can vary dramatically, because the dominant mechanism has a transition from real area of contact to meniscus forces. Therefore, the effect of relative humidity was also studied by performing measurements in 5, 50, and 80% RH. For these experiments, a tip of radius 15 µm was used to measure both adhesion and coefficient of friction for both the film and patterned polymer surfaces along the surfaces with the PFDTES coating. Both LAR and HAR were studied to determine the effect that taller asperity will have on adhesion and friction.

Fig. 14.5. Diagram showing the effect of different radii on the nanopatterend surface. Small radii can fit between the asperities, while large radii rest on top of the asperities (Burton and Bhushan, 2005b)

14.3 Results and Discussion Lotus and colocasia are two leaves that exhibit extreme hydrophobic behavior, which has inspired researchers to understand why and how the surface behaves this way. Measurements have been made using the instrumentation discussed above to understand the mechanisms behind their hydrophobic behavior (Burton and Bhushan, 2005a). As a first step to realizing this phenomenon, nanopatterns on a polymer surface have been produced and to understand the behavior of these surfaces, various tests of adhesion and friction have been conducted. Below is a discussion of the results for these two studies (Burton and Bhushan, 2005b).

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14.3.1 Hydrophobic Leaf Surfaces In order to completely understand the nature of hydrophobic leaves, a comprehensive study of the surface and its properties must be performed. Using the various methods discussed above, the surfaces of the leaves have been studied and measured so that an understanding of the mechanisms that are responsible for its hydrophobic nature has been accomplished. Below is a discussion of the findings of the study. 14.3.1.1 Contact Angle Measurements The contact angles for lotus and colocasia both with wax and without were measured and are presented in the first bar chart of Fig. 14.6. The calculated contact angles using the approximated Rf from (14.1) are also presented. For both leaves the contact angle is dramatically reduced when the wax is removed from the surface. This shows that the leaf material itself is a hydrophilic material and the combination of the wax and the roughness of the leaf is what creates such a hydrophobic surface.

Fig. 14.6. Contact angle measurements and calculations for the leaf surfaces, both with and without wax and both fresh and dried leaves (Burton and Bhushan, 2005a)

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The approximation of the roughness factor for the leaves was made using an AFM scan. The AFM scans were made on the surfaces that had been dried and, therefore, the true surface area was smaller than that of a fresh leaf. Modifications need to be made to calculate Rf on a fresh leaf measured using an optical profiler that gives data in a rectangular matrix. The approximated values of Rf for lotus and colocasia are 1.55 and 1.52, respectively. Using these values, along with the contact angles from both the wax and no wax surfaces, the contact angles for flat wax and flat plant material can be calculated for both leaves. It was found that the contact angle on flat wax is approximately 126◦ for both leaves. These values are also compared to the contact angle of a water droplet against paraffin wax surface that was reported as 104◦ by Craig et al. (1960) and Kamusewitz et al. (1999). The contact angle for flat plant material was estimated to be 76◦ for lotus and 72◦ for colocasia using the calculated Rf values. The second bar chart in Fig. 14.6 shows the contact angles for the two leaves, both fresh and dried. There is a decrease in the contact angle for each leaf when it has been dried. This decrease is present because a fresh leaf has taller bumps than a dried leaf, which will give a larger contact angle, according to (14.1). When the surface area is at a maximum compared to the footprint area, as with a fresh leaf, the roughness factor will be at a maximum and will only reduce when shrinking has occurred after drying. 14.3.1.2 Surface Characterization Using an Optical Profiler As stated previously, using an optical profiler allowed measurements to be made on fresh leaves, which have a large P–V distance. Three different surface height maps can be seen for lotus in Fig. 14.7a and for colocasia in Fig. 14.7b. In each figure a tilted 3D and flat 3D maps along with a 2D profile in a given location of the flat 3D map. These figures also show the maps for leaves with the wax present and the wax removed in order to demonstrate that the surface structure is consistent after the wax has been removed. Table 14.1. Bump statistics for lotus and colocasia. Fresh leaves measured using optical profiler and dried leaves using AFM Leaf

Lateral spacing

Bump (µm)

Ridge (µm)

Bump Bump Ridge Peak Mid- Peak Peak Mid- Peak to bump to ridge to ridge to valley width radius to valley width radius (µm) (µm) (µm) height height Lotus AFM-dried Optical-fresh

18 17

– –

– –

9 18

10 11

6.5 7

– –

– –

– –

Colocasia AFM-dried Optical-fresh

34 37

17 18

36 38

5 11

11 11

6.5 4.5

5 12

8 7

4.5 3.5

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Figure 14.7a shows that the bumps on the leaf are randomly distributed on the entire surface and that the structure found with the optical profiler correlates will with the SEM images shown in Fig. 14.2a and b. A scan size of 120 µm × 90 µm was used to obtain a sufficient amount of bumps to characterize the surface but also to maintain enough resolution to get an accurate measurement. Using these scans, different bump statistics can be found and for lotus there are four specific quantities that characterize the surface: bump to bump distance and bump height, width and radius. These quantities can be found in Table 14.1, which also shows the statistics for all measurements made with both the optical profiler and the AFM. Figure 14.7b shows the optical image for colocasia. This leaf shows a much different structure to lotus and correlates well with the SEM image in Fig. 14.2a. The surface structure for colocasia has bumps similar to lotus, but there is a ridge surrounding each bump, which completely isolates it. With these ridges, the bumps have a hexagonal packing geometry, which allows for the maximum number of bumps in a given area. Both the bumps and ridges contribute to the hydrophobic nature of colocasia, since they both create pockets of air between the droplet of water and the surface. Table 14.1 shows the bump statistics found for colocasia leaves and there are a few different statistics added because of the ridges structure. For colocasia, bump to ridge and ridge to ridge along with ridge height, width and radius have been added to Table 14.1. In comparison between lotus

Fig. 14.7a. Surface height maps and 2D profile of a lotus leaf using an optical profiler. For the lotus leaf, a bump is defined as a single, independent microstructure protruding from the surface

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Fig.14.7b.Surface height maps and 2D profile of colocasia using an optical profiler. For colocasia, a bump is defined as the single, independent protrusion from the leaf surface, whereas a ridge is defined as the structure that surrounds each bump and is completely interconnected on the leaf (Burton and Bhushan, 2005a)

and colocasia, it can be seen that the distance of bump to bump for lotus is very comparable to the distance of bump to ridge for colocasia. This shows that both leaves have similar spacing for their large structures present on the surface. It can also be shown that the bump width and radius is similar for both leaves, but the bump height is larger for lotus leaf. The ridges on colocasia are both taller and skinnier than the bumps, but still have a similar shape in the a crosssection. Figure 14.8a and b shows the 2D profiles in Fig. 14.7a and b, and an increased magnification of two bumps on lotus and a bump and ridge on colocasia. A curve fit has been fitted to each profile to see exactly how the bump shape behaves. For each leaf a second-order curve fit has been given to the profiles to see how closely the profile is followed. The radius of curvature for any function is known to be: 3/2
1 + y (x)2 , (14.2) R(x) = y (x) where R(x) = radius of curvature, y (x) = first derivative of the function, and y (x) = second derivative of the function. By using the second-order curve fit of the profiles, the radius of curvature can be found. The values found using this calculation are shown in Table 14.1.

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Fig. 14.8. (a) Curve fit for two bumps on a lotus leaf using an optical profiler. The radius of curvature is calculated from the parabolic curve fit of the bumps. (b) Curve fit for one bump and one ridge on a colocasia leaf using an optical profiler. The radius of curvature is also calculated from the parabolic curve fit (Burton and Bhushan, 2005a)

14.3.1.3 Leaf Characterization Using an AFM 14.3.1.3.1 Surface Characterization For measurements using an AFM on the leaf surfaces, the leaves were completely dried out prior to experimentation due to the large P–V distance and the dynamic shrinking present after cutting the leaf. Figure 14.9a shows the 50 µm and 100 µm scans that were made on the lotus leaf to fully characterize the surface of the leaf.

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Fig. 14.9a. Surface height maps and 2D profile showing the top scan and bottom scan of a lotus leaf because the P–V distance of a dried lotus leaf is greater than the Z-range of an AFM

The AFM has a limitation on the Z-range distance that can be traveled by the piezo of 7 µm. The dried lotus leaf has a P–V distance of approximately 10 µm and the AFM cannot fully scan the image due to the lack of traveling distance capability of the piezo. Therefore, a new method had to be developed to fully determine the bump statistics. In order to compensate for the P–V distance, two scans were made for each scan size: one measurement that scans the tops of the bumps and another measurement that scans that bottom or valleys of the bumps. By first scanning the upper half of the bumps and then scanning the lower half of the bumps, the total height of the bumps is imbedded within the two scans. It can be seen in the surface

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Fig. 14.9b. Surface height maps and 2D profile of colocasia using an AFM (Burton and Bhushan, 2005a)

height maps in Fig. 14.9a that the scans of the lotus leaf can be taken separately and spliced together in the 2D profile to create the full profile of the leaf. The 2D profiles in the right-hand side column of Fig. 14.9a take the profiles from the top scan and the bottom scan for each scan size and splice them together to get the total profile of the leaf. The four bump statistics for the total profile of the AFM scan of the lotus leaf can be found in Table 14.1, and it can be seen that the values correlate well with the optical profiler scans, except for the bump height, which decreases by more than half because of the shrinking of the leaf. Figure 14.9b shows the 50 µm and 100 µm surface height maps for colocasia. When colocasia is dried, there is no problem with the P–V distance and the travel distance of the AFM piezo. Therefore, the entire surface profile can be measured in a single scan. The AFM scan shows very consistent results in the surface structure as compared to both the optical profiler scans in Fig. 14.7b and the SEM images in Fig. 14.2a. The nine bump and ridge statistics for the AFM scans of colocasia can be found in Table 14.1, and correlate well with the optical scans, except that the bump and ridge height is much lower than the optical scans due to the shrinking. Figure 14.10a and b shows the curve fit of two bumps from the top scan from the lotus leaf and a bump and ridge profile from the colocasia leaf. The lotus leaf profiles are not complete due to the piezo traveling problem, but the peak of the bump is the most important section because that is the location where the water droplets come into contact with the surface. Therefore, looking at the peak of the bump and curve fitting that profile will give a good approximation of the surface radius of curvature. All four profiles have been given a second-order curve fit to see how these bumps behave. Using (14.2) the radius of curvature was found and is presented in Table 14.1.

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Fig. 14.10. (a) Curve fit for two bumps on a lotus leaf using an AFM. The radius of the curvature is calculated from the parabolic curve fit of the bumps. (b) Curve fit for one bump and one ridge on a colocasia leaf using an AFM. The radius of the curvature is also calculated from the parabolic curve fit (Burton and Bhushan, 2005a)

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14.3.1.3.2 Adhesive Force and Friction of Hydrophobic Leaves Adhesive force and friction measurements made on lotus and colocasia leaves are presented in Fig. 14.11. For each type of leaf, adhesive force measurements were made on leaves that were both fresh and dried with either the wax present or the wax removed. The dried leaves, regardless of whether wax was present or not, had a lower adhesive force than the fresh leaves. When the leaves are fresh there is moisture within the plant material that causes the leaf to be soft and when the tip comes into contact with the leaf sample, the sample will deform elastically and a larger real area of contact between the tip and sample will occur and the adhesive force will increase. After the leaf has dried, the moisture that was in the plant material is gone and when the tip comes into contact with the leaf sample, there is not as much deformation of the leaf and the adhesive force is decreased, because the real area of contact has decreased. The adhesive force increases when the wax is removed from the leaf surface regardless of whether the leaf is fresh or has been dried. This increase in adhesive force is due to the decrease in contact angle when the wax is removed from the leaf surface. The increase in adhesive force from wax present to wax removed is not as large as the decrease in adhesive force from fresh to dried, so therefore, the

Fig. 14.11. Adhesive force and coefficient of friction for lotus and colocasia, both with and without wax, and for both fresh and dried leaves. All measurements were made using a 15 µm tip (Burton and Bhushan, 2005a)

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dominant mechanism in adhesive force is the real area of contact between the tip and leaf sample, rather than an increase meniscus force that arises when a surface is hydrophilic. The coefficient of friction was only measured on a dried plant surface rather than including the fresh surface because the P–V was too large to scan back and forth with the AFM to obtain friction force. As expected, the coefficient of friction increases when the wax is removed from the leaf surface, similar to the adhesive force results. This increase is due to the reduction of contact angle from a wax covered leaf to a leaf with the wax removed. 14.3.1.3.3 Dynamic Shrinking Effects of the Leaf Both leaves showed dynamic shrinking effects after a small section of the leaf was initially cut away from the larger leaf. This is due to the evaporation of the water that is present in the leaf structure. As the water evaporates, the surface reduces in vertical height but the lateral shape and structure stay intact and constant. Figure 14.12a

Fig. 14.12. (a) AFM surface height map and 2D profile showing the dynamic shrinking of a colocasia leaf. (b) Plot showing the P–V distance of both lotus and colocasia as a function of time from being cut (Burton and Bhushan, 2005a)

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shows an AFM scan on colocasia during the shrinking process. At the beginning of the scan, the peak of the bump is out of range of a fully retracted AFM tip. As the scanning progresses, the profile of the leaf decreases until the piezo is fully extended at the end of the scan and the bottom of the leaf is out of range of the tip. To determine whether this was dynamic shrinking of the leaf or whether the leaf was tilted enough to extend further than the piezo, the sample was allowed to fully evaporate while the AFM was in the same position as the first scan. When the scan was conducted after the leaf had fully evaporated, the surface profile was completely flat and it was possible to scan all the peaks and valleys. Figure 14.12b also shows the effect of dynamic shrinking of the leaves. This plot shows the P–V height of the two leaves at different times from when they were cut. It can be shown that on a logarithmic scale of time, the leaves shrink to some constant value of the P–V distance after a certain amount of time. 14.3.2 Nanopatterned Polymers Implementing the lessons that are learned through nature is not complete until a thorough study is performed to discover the properties of a new surface that is created. By making nanopatterns on a polymer surface, the process of producing “biomimetic” surfaces has begun, but more experimentation and characterization is necessary. Using methods described previously, the tribological properties of the nanopatterned polymers have been studied and the results are discussed below. 14.3.2.1 Contact Angle Measurements The initial experiment performed on the various materials was to determine the static contact angle. Figure 14.13 shows the results obtained using a method described

Fig. 14.13. Bar chart showing the contact angles for different materials and for different roughness (Burton and Bhushan, 2005b)

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earlier (Burton and Bhushan, 2005b). These values correlate well with the model describing roughness with hydrophobicity (Nosonovsky and Bhushan, 2005). For both the PMMA and the MINS materials, the contact angle decreased with increased roughness. Since both PMMA and MINS are hydrophilic materials, this is expected. When the polymers were coated with PFDTES, the film surface became hydrophobic. For a hydrophobic surface, the model predicts an increase of contact angle with roughness, which is what happens when PMMA HAR and MINS HAR are coated with PFDTES. 14.3.2.2 Adhesion Studies and Scale Dependence Adhesive forces can arise when the presence of water in the environment causes meniscus bridges to form around the contacting and near contacting asperities as a result of surface energy effects. A negative Laplace pressure inside the curved menisci results in an attractive force called the meniscus force. The value of the meniscus force is given by the product of the pressure difference and the immersed surface area of the asperity. This intrinsic attractive force may result in high friction and wear (Bhushan, 2003). The total meniscus force, Fm , is obtained by summing the meniscus forces from all individual contacting and near contacting asperities where meniscus bridges are formed (Bhushan, 2002), and is given by the expression Fm = 2πRt γ (cos(θ1 ) + cos(θ2 )) N(t) ,

(14.3)

where Rt = radius of the contacting AFM tip radius; γ = surface tension of the liquid film; θ1 and θ2 = contact angles for the lower and upper sample, respectively; N(t) = number of contacting and near contacting asperities where menisci build up in time ‘t’. The surface hydrophobicity determines the meniscus bridge formation at the contact interface. Scale dependent effects of adhesion and friction are present because the tip/surface interface changes with size. The meniscus force will change by varying either the tip radius, the hydrophobicity of the sample or the number of contact and near-contacting points. Figure 14.14 shows the dependence of tip radius and hydrophobicity on the adhesive force for PMMA and PFDTES coated on PMMA. By changing the radius of the tip, the contact angle of the sample, and adding asperities to the sample surface, the adhesive force will change due to the change in the meniscus force and the real area of contact. The two plots in Fig. 14.14 show the adhesive force on a linear scale for the different surfaces with varying tip radius. The first bar chart in Fig. 14.14 is for PMMA film and PFDTES coated on PMMA film and shows the effect of tip radius and hydrophobicity on adhesive force. For increasing radius, the adhesive force increases for each material, but decreases from PMMA film to PFDTES on PMMA film. With a larger radius, the real area of contact increases and the adhesion is increased. The hydrophobicity of PFDTES on PMMA film reduces meniscus forces, which in turn reduces adhesion from PMMA film. The dominant mechanism for the hydrophobic film is tge real area of contact and not the meniscus force, whereas with PMMA film, there is a combination of real area of contact and meniscus forces.

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Fig. 14.14. Scale dependent adhesive force for PMMA film vs. PFDTES on PMMA film and PMMA HAR vs. PFDTES on PMMA HAR (Burton and Bhushan, 2005b)

The second bar chart in Fig. 14.14 shows the results for PMMA HAR and PFDTES coated on PMMA HAR. These samples show the same trends as the film samples, but the increase in adhesion is not as dramatic. This is because of the decrease in real area of contact for each radius from a flat film. Again, meniscus forces do not play a large role in adhesion for PFDTES on PMMA HAR, and the increase in adhesion is due to the real area of contact. With PMMA HAR, a combination of both meniscus forces and real area of contact contribute to the adhesion. Figure 14.15 shows the same data as Fig. 14.14, but MINS is the polymer used and the PFDTES is coated on MINS instead of PMMA. The same trends are present in the adhesive force values, but the only difference is that MINS film has a very large adhesion for both the microscale tips, which is due to the AFM tip conforming to the soft MINS sample (Moore, 1972). This is the opposite trend to that seen for the PMMA samples. All other trends are similar. Figure 14.16 explicitly shows the adhesive force data for three PMMA surfaces and a PFDTES coating on two PMMA surfaces when just the 15 µm radius tip is used in ambient conditions. The data show the effect of both real area of contact and contact angle on the adhesive force. While the contact angle decreases from PMMA film to LAR and HAR, the change is not dramatic enough to cause the large reduction in adhesion. Therefore, the effect of real area of contact is the dominant mechanism

Fig. 14.15. Scale dependent adhesive force for MINS film vs. PFDTES on MINS film and MINS HAR vs. PFDTES on MINS HAR (Burton and Bhushan, 2005b)

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Fig. 14.16. Adhesive force values for PMMA film, LAR and HAR along with PFDTES on PMMA film and HAR to show the effect of real area of contact and contact angle (Burton and Bhushan, 2005b)

for the reduced adhesion. The same is true for the samples with a PFDTES coating present. The contact angle increases as expected when roughness is introduced, but the dramatic decrease in adhesion between PFDTES on PMMA and PFDTES on PMMA HAR is more heavily dependent on the reduced real area of contact. To examine the effect of increased contact angle on adhesive force, it is necessary to look at the drop between PMMA film and PFDTES on PMMA film along with the difference between PMMA HAR and PFDTES on PMMA HAR. Since the real area of contact is the same for each comparison, only the increased contact angle due to the PFDTES coating is responsible for the drop in adhesive force. 14.3.2.3 Effect of Relative Humidity on Adhesive Force and Coefficient of Friction The influence of relative humidity was studied in an environmentally controlled chamber. The results from varying surface roughness, hydrophobicity and relative humidity are summarized in Figs. 14.17a and 14.18a, for PMMA and MINS, respectively. Experiments were also run on PMMA and MINS film and HAR with a PFDTES coating and are shown in Figs. 14.17b and 14.18b. In Figs. 14.17a and 14.18a, film, HAR and LAR were used to see the change in adhesion and friction for each type of surface structure. Only film and HAR were used for Figs. 14.17b and 14.18b to show the difference in the two extremes of the surfaces. For these experiments, only the 15 µm radius tip was used to study the effect from the asperities on the patterned surfaces. The results for PMMA film, LAR and HAR is shown in Fig. 14.17a. For the adhesive force values there is a decrease from PMMA film to LAR to HAR for the three humidities. The decrease between LAR and HAR is very small, which means that the contact area is about the same for a single point measurement. There is, however, a large decrease in the adhesive force from film to LAR and HAR. When examining the effect of relative humidity, the data show a larger difference between PMMA film at different humidities than for either of the patterned surfaces. For a flat

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Fig. 14.17. (a) Effect of relative humidity on adhesive force and coefficient of friction for PMMA film, LAR and HAR. (b) Effect of relative humidity on adhesive force and coefficient of friction for PFDTES on PMMA film and HAR (Burton and Bhushan, 2005b)

film, meniscus bridges are the dominant factor in the adhesion, but for a patterned sample the dominant factor is still the contact area and not the formation of menisci. At 5% RH the only factor in the adhesion is the area of contact and not the formation of menisci. The data shows that there is a smaller difference at 5% in adhesion than compared to the difference at 80% RH. Coefficient of friction data also follow a similar trend to the adhesion data. There are larger differences between the values at 80% than at 5%, because the shearing of menisci when two surfaces slide together requires a larger force than when no liquid is present. Results for PFDTES coating on PMMA film and HAR are shown in Fig. 14.17b. The adhesion values are much lower than those for PMMA film and PMMA HAR and that is primarily due to the lack of meniscus bridge formation because of the hydrophobic contact angle of PFDTES. There is a decrease in adhesion between PFDTES film and PFDTES HAR, which is directly related to the area of contact difference between a film and HAR. Looking at the data across the three humidities, there is not much change in the values. Since the surfaces are hydrophobic, meniscus bridges are not the determining factor in the material adhesion. The coefficient of friction is also lower for PFDTES than for PMMA. There is a slight increase in the change between PFDTES film and PFDTES HAR for increasing humidity. This shows that force required to shear menisci by sliding a tip across the surface has more effect than the meniscus force contributing to adhesion. Figure 14.18a shows the results of varying relative humidity for MINS film and HAR. The trends for MINS film and HAR follow the same trends that occur with PMMA. There is a much larger difference between the adhesion values for MINS

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Fig. 14.18. (a) Effect of relative humidity and coefficient of friction for MINS film, LAR and HAR. (b) Effect of relative humidity on adhesive force and coefficient of friction for PFDTES on MINS film and HAR (Burton and Bhushan, 2005b)

film and MINS LAR and HAR because of the increased real area of contact for MINS film. When a coating of PFDTES is deposited on the MINS surface, film and HAR, the adhesion and coefficient of friction values show the same trends with varying relative humidities as with PMMA coated with PFDTES.

14.4 Summary Hydrophobicity, as well as low adhesion and friction, is desirable for many industrial applications. A technique to obtain surfaces that exhibit these types of properties is to study what is found in nature and learn from its characteristics. This chapter aims to do precisely that, learn from nature and apply that understanding to different surfaces. Hydrophobic leaves, such as lotus and colocasia, provide perfect samples from which to learn and in turn apply those same principles to materials such as polymers and SAMs. Introducing patterned roughness, similar to that found on leaves, is the first step in realizing “biomimetic” surfaces that can be applied to other industrial applications. This chapter has shown that a combination of surface roughness and a thin wax film gives leaves, such as lotus and colocasia, their hydrophobic nature. By removing either the roughness or the thin wax, the surface properties change dramatically, so therefore, it can be seen that both are inherently important to maintain a hydrophobic surface. It has been shown that when the wax was removed from the rough leaf

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surface, the contact angle drops dramatically and the surface becomes hydrophilic. Wenzel’s model relates the contact angle and roughness together by the use of a roughness factor. The roughness factor for lotus and colocasia has been calculated through the use of surface height maps from AFM scans and this roughness factor can then be used to calculate the contact angles for a flat surface of the same material. In addition to calculating the roughness factor and contact angles for the hydrophobic leaves, the geometric characteristics of the two leaves have been analyzed. The bump spacing distance for lotus and colocasia is similar, but the only difference is that for lotus the distance is from bump to bump, while for colocasia the distance is from bump to ridge. While the bump spacing is of similar distance, bump height is different between the two samples. For both fresh and dried leaves, the bumps on the lotus leaf are taller than those on the colocasia leaf, which leads to a higher roughness factor and an increased contact angle. In addition to surface roughness, adhesion and friction are also of importance when characterizing the surface of the leaf. The adhesive force increases from dried leaves to fresh leaves, regardless of whether wax is present or not, due to the moisture that is present in the plant material when the leaf is fresh. This moisture causes the leaf to be very soft and the real area of contact will increase as an upper sample is pressed into the surface. The coefficient of friction also increased when the wax was removed from the leaf surface because of increased meniscus forces in the lateral direction. One property from the leaves that was learned during the implementation of the study was a dynamic shrinking effect when a section of the leaf is cut away. It became apparent during testing that as the moisture from the leaf evaporates, the peak-to-valley distance will reduce to some minimum amount after a certain amount of time. Results found for the nanopatterned polymer samples were similar to those found for hydrophobic leaves. It was found that increasing roughness on a hydrophilic surface decreases the contact angle, whereas increasing roughness on a hydrophobic surface increases contact angle. The increase in contact angle for the polymers with the SAM as a thin film was not as large as that for hydrophobic leaves because the roughness factor on leaves is much larger than that for the patterned polymers. For a flat film, with increasing tip radius, the adhesive force increases due to increased real area of contact between the tip and the flat sample and meniscus force contributions. Introducing a pattern on a flat polymer surface will reduce adhesion and coefficient of friction because of the reduction of the real area of contact between the tip and the sample surface, if the tip is larger than the size of the asperities. In addition, introducing a pattern on a hydrophobic surface increases contact angle and decreases the number of menisci, which then decreases the adhesive force. It was also seen that introducing a hydrophobic film to any hydrophilic surface, flat or patterned, will reduce adhesion and friction due to fewer meniscus bridge formations. Adhesion and the coefficient of friction increase with increasing RH for every sample and decrease from film to LAR to HAR for every sample. When PFDTES is coated on the PMMA and MINS samples, the adhesion and coefficient of friction decrease, but follow the same trends as the bare polymer. These trends are due to the formation of more menisci at higher relative humidities. In addition, with an increase in relative humidity, the increase in adhesive force for PMMA film is more dramatic than for the patterned samples due to larger menisci formations for a film sample.

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References 1. Adamson AV (1990) Physical chemistry of surfaces. Wiley, New York 2. Barthlott W, Neinhuis C (1997) Purity of the sacred lotus, or escape from contamination in biological surfaces Planta 202:8 3. Bhushan B (1999) Handbook of micro/nanotribology, 2nd edn. CRC Press, Boca Raton, FL 4. Bhushan B (2002) Introduction to tribology. Wiley, New York 5. Bhushan B (2003) J Vac Sci Technol B 21:2262 6. Bhushan B (2004) Springer handbook of nanotechnology. Springer, Berlin Heidelberg New York 7. Bhushan B (2005) Nanotribology and nanomechanics – an introduction. Springer, Berlin Heidelberg New York 8. Burton Z, Bhushan B (2005) Ultramicroscopy. in press 9. Burton Z, Bhushan B (2005) Nanoletters 5:1607 10. Cassie A, Baxter S (1944) Trans Faraday Soc 40:546 11. Choi SE, Yoo PJ, Baek SJ, Kim TW, Lee HH (2004) J Am Chem Soc 126:7744 12. Craig RG, Berry GC, Peyton FA (1960) J Phys Chem 64:541 13. Gould P (2003) Mater Today 6:44 14. Israelachvili JN (1992) Intermolecular and surface forces, 2nd edn. Academic Press, London 15. Johnson RE, Dettre RH (1964) In: Fowkes FM Contact Angle, Wettability, and Adhesion, Adv Chem Ser, Vol 43, American Chemical Society, Washington DC, p 112 16. Kamusewitz H, Possart W, Paul D (1999) Colloids Surf A: Physicochem Eng Aspects 156:271 17. Kijlstra J, Reihs K, Klami A (2002) Colloids Surf A: Physicochem Eng Aspects 2006:521 18. Bhushan B, Hansford D, Lee KK (2005) J Vac Sci Technol A (in press) 19. Miwa M, Nakajima A, Fujishima A, Hashimoto K, Watanabe T (2000) Langmuir 16:5754 20. Moore DF (1972) The friction and lubrication of elastomers, 2nd ed. Pergamon, New York 21. Neinhuis C, Barthlott W (1997) Ann Bot 79:667 22. Nosonovsky M, Bhushan B (2005) Microsys Technol 11:535 23. Wagner P, Furstner R, Barthlott W, Neinhuis C (2003) J Exper Botany 54: 1295 24. Wenzel RN (1936) Indust Eng Chem 28:988

15 Probing Macromolecular Dynamics and the Influence of Finite Size Effects Scott Sills · René M. Overney

Abbreviations a aT c cn C Cp Di DR G G∗ E E∗ EA F FADH FAPP FN FF h H I kB kT kN L M n P pm R RG S T Tc

contact radius, radius of hydrostatic core thermal (horizontal) shift factor radius of plastic deformation constant contact stiffness calibration factor heat capacity indentation diameter rim diameter Gibb’s free energy, shear modulus reduced shear modulus Young’s modulus reduced elastic modulus activation energy force adhesion force applied force normal force friction force penetration depth, enthalpy, tip height instrument signal Boltzmann constant torsional spring constant normal spring constant cantilever length mass reciprocal of work hardening index pressure mean contact pressure gas constant, contact radius of curvature radius of gyration entropy, sensitivity temperature critical temperature

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Tg TL TM TR Uo V Vf Vm v vd vo W X Y α β δ φ γ Γ µ σ τ τα τe τm Ω xd ζ

glass transition temperature cantilever thickness melting temperature reference temperature activation barrier volume free volume molar volume velocity dewet velocity characteristic velocity cantilever width rheological factor yield stress thermal conductivity internal damping factor, excluded cone angle film thickness strain stress activation volume surface tension lateral force calibration factor coefficient of friction stress shear strength alpha relaxation time extrinsic (experimental) time intrinsic (material) time contact junction volume dissipation length rim height

15.1 Introduction Miniaturization trends in electronic, mechanical, optical, and biomedical devices have brought the nanoscale to the forefront of the engineering design arena. In systems reduced to nanoscopic dimensions, bulk statistical averaging and continuum models are jeopardized. Interfacial constraints lead to bulk-deviating molecular dynamics; material and transport properties are altered. Engineering efforts must work within these constraints, or yet, utilize the constraints as design opportunities. Today’s challenge lies in obtaining convenient access to the molecular mobility, using novel approaches, such as real-space scanning probe techniques. With this, we can begin to optimize molecular designs based on the critical lengths that are set by nanotechnological device applications. Polymers and functionalized macromolecules belong to a class of materials that are particularly well-suited for bottom-up, molecular design approaches. In solid

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state form, one of the foremost important phenomena is thus the glass transition, as it dictates the material’s properties, particularly its transport properties. The glass transition is rooted in the underlying molecular mobility, which itself, is strongly influenced by nanoscopic constraints [1]. In this chapter, we focus on recent scanning probe microscopy (SPM) developments that address issues related to the glass transition in confined polymer systems. Particular emphasize is given to the local probing of molecular dynamics near the glass transition, the influence of finite size constraints on these dynamics, and the impact of the molecular mobility on current nanotechnological developments in polymer thin films. We discuss the frictional dissipation in SPM with respect to the availability of particular molecular relaxations. In polymer melts near the glass transition, nanoscopic friction reveals a highly cooperative dissipation phenomenon. This phenomena is known in the open literature as the heterogeneous dynamics of glass formers. It introduces a critical length scale, over which collective molecular motion occurs, i.e. the size of a cooperatively rearranging region (CRR). In the bulk, this dimension ranges from a collection of monomeric segments on the subnanometer scale to several nanometers, involving molecular ensembles [2]. The nanoscopic size of the CRRs will lead our discussion towards the impact of dimensional constraints in thin film systems. With shear modulated force microscopy (SM-FM) and friction force microscopy (FFM) techniques, we address the molecular restructuring and material anisotropy due to interfacial constraints; which can lead to plasticization near interfaces in polydisperse and heterogeneous systems, and modified dewetting kinetics and instabilities in thin film systems. Having addressed the impact of nanoscopic constraints on local molecular mobility, we return to current technological challenges in nano-electromechanical systems (NEMS). We explore how the contact mechanics in the thin films used for terabit data storage [3] are compounded by: (i) high strain rate, nano-impact conditions, (ii) the proximity of the underlying substrate, and (iii) material anisotropy near the interface. We highlight one issue related to this NEMS application, namely, strain shielding and confined plasticity at the polymer-substrate interface, which leads to undesired rim formation during thermomechanical recording. However, first we begin with a brief review of the glass transition and molecular mobility, followed by an introduction to macromolecular probing techniques involving SPM.

15.2 The Glass Transition and Molecular Mobility Describing material behavior in terms of transport properties requires, in addition to the structural properties, knowledge of dynamic properties such as molecular mobility. Particularly for condensed, amorphous systems like polymers, accessing molecular mobility is essential. Paramount to any discussion of molecular mobility is the glass transition. By definition, the glass transition is the reversible change in an amorphous material (e.g. polystyrene) or in amorphous regions of a partially crystalline material (e.g. polyethylene), between a viscous or rubbery condition and a hard, relatively brittle one [4]. The temperature at which the transition occurs is defined as the glass transition temperature, Tg .

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The term glass transition is used in the materials community pervasively, implying that it describes a well-understood material phenomenon. Tg is frequently treated as a material property. However, similar to other phenomenological properties, such as friction, a large ambiguity exists. The problem in describing the glass transition, or reporting the transition temperature unambiguously arises from: diverging instrumental observables; critical parameters, such as measurement rates or areas; and sample preparation techniques that generate material anisotropy. The differences arising from these issues has led to various interpretations and diverging theoretical models. For example, in the discussion that follows, we will differentiate various aspects of thermodynamic versus kinetic approaches to the glass transition. The definition of the glass transition offered above depends on one’s perception of the terms solid and liquid. Materials may be classified as solids and liquids by either considering their rheological response, or by analyzing the thermodynamic phase of the system. A rheological material description is concerned about stressstrain and stress-strain-rate relationships. A solid-like behavior exhibits a rheological behavior characterized by a purely stress-strain relationship. Conversely, a liquidlike behavior is a purely stress versus strain-rate dependent process, which cannot be described with a stress-strain relationship. Any real material will exhibit various degrees of both behaviors, depending on the intrinsic mobility and on the extrinsic stress and stress rate. From the thermodynamic perspective of free energy changes between equilibrium states, one may identify the solid-liquid phase transition by a discontinuity in the first partial derivatives of the Gibbs free energy, G, with respect to the relevant state variable (e.g. temperature, T , and pressure, P), as illustrated for the volume-temperature plot in Fig. 15.1. Discontinuities, as expressed in the first partial derivatives of the Gibbs free energy are found in the temperature relationships of the volume, V ; entropy, S; and enthalpy, H, as described in       ∂G ∂(G/T ) ∂G = V; = −S; = H. (15.1) ∂P T ∂T P ∂(1/T ) P

Fig. 15.1. Volume discontinuity. First-order thermodynamic transition between liquid and solid (TM = melting temperature)

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Mesophases between solid and liquid phases that are found in polymeric systems include the states of a glass and a melt. The glass state is known to exist also for many non-polymeric materials. From a structural viewpoint, a solid can be either crystalline, amorphous (unstructured) or partially amorphous-crystalline. A glass is an amorphous solid and can exhibit both solid- or liquid-like behaviors. The melt behaves rheologically liquid-like; yet, exhibits a short-range order that is similar to the amorphous solid, but absent in perfect liquids. The melt state compared to the corresponding glass-state shows the same structure, but exhibits large amplitude molecular motions, such as translational, rotational, and conformational motions. Large amplitude motions generally operate on the picosecond (10−12 s) time-scale. Around the glass transition temperature, the time-scale of this large amplitude motion is slowed to milliseconds or even seconds [5]. Empirically it has been found that for many glasses with mobile units the size of one to six atoms, called beads, the heat capacity increases “abruptly” by about 11 J (mol K)−1 at the glass transition temperature [5]. Discontinuity in the heat capacity is known to exist and can be caused by second-order transitions. Second-order transitions are considered as order–disorder transitions, and express a continuous behavior of the free energy and its partial derivatives, and a discontinuous behavior for the second partial derivative with respect to the relevant state variable. Hence there are no discontinuities in S, V or H at the glass transition temperature, but the discontinuities lie in the heat capacity, Cp , the isothermal compressibility, κ, and the coefficient of thermal expansion, α:  2         Cp ∂ ∂ G ∂S ∂H ∂(G/T ) = = = CP , = Cp : − ∂T 2 P ∂T T ∂T ∂(1/T ) P P ∂T P (15.2a)  2    ∂ G ∂V κ: = = −κV , (15.2b) 2 ∂P T ∂P T  α:

∂ ∂T



∂G ∂P



  = T

P

∂V ∂T

 = αV .

(15.2c)

P

First-order and second-order transitions are illustrated in Fig. 15.2. If compared to property changes in glasses around the glass transition temperature, one finds some similarity between the glass transition and the second-order transition. There are, however, significant differences. Cp , κ and α values are always smaller and nearly constant below Tg compared to the values above Tg . This is in contrast to the second-order transition. A more disturbing finding is that Tg measurements are highly heating/cooling rate dependent, which does not occur for a “true” secondorder transition [6]. Based on the similarity of the glass transition with a second-order thermodynamic transition, the Ehrenfest approach may be applied [6]. Equilibrium criteria requires G glass = G melt , and the analogous form of the Clausius–Clapeyron equation is: ∆H dP . = dTg T ∆V

(15.3)

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It follows for a second-order phase transition dTg ∆κ T ∆α = = dP ∆α ∆Cp

or

 ∆κ∆Cp  Tg = . ∆α2 T =Tg

(15.4)

However, for most polymers, the change of Tg with pressure has been found to be [7]: dTg ∆κ < dP ∆α

and

dTg T ∆α , ≈ dP ∆Cp

(15.5)

suggesting that the glass transition is not a true second-order thermodynamic transition. Recognizing the thermal and loading rate dependencies of the glass transition process, the glassy state can be described as a non-equilibrium state. This approach requires, in addition to the state variables, an internal order parameter. In other words, from the concept of an order–disorder transition, where the glass is the ordered state, the internal order parameter describes the departure from equilibrium conditions. Fox and Flory suggest that the appropriate order parameter is the free volume [6]. The free volume, Vf , is defined as the void space within the polymer phase that is not occupied by the molecules themselves, and may be quantified by the difference between the total volume, V , and the molecular volume, Vm . The molar volume is the sum of the hypothetical volume in a void free melt at absolute zero and the volume expanded due to thermal vibrations. The relation for the free volume is then: 
 (15.6) Vf = V + Vm ∆α T − Tg − 1 . Just below Tg , the molecular mobility is so drastically reduced that a non-equilibrium state would become effectively frozen, suggesting a constant free volume below Tg . From Fig. 15.2, it is seen that ∆α = 0, and with V and Vm exhibiting the same temperature dependence, Vf becomes constant, see Fig. 15.3. In the melt state between the glass and liquid states, i.e. for temperatures between Tg and the melting temperature, Tm , the material can be treated as a supercooled

Fig. 15.2. The nature of material property changes at Tg compared to those of first- and secondorder thermodynamic transitions

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Fig. 15.3. Free volume diagram as a function of temperature

fluid. Building from Eyring’s model for supercooled liquids [8], the viscosity may be expressed in the form of:   ∆G a kB T ; ηo = , (15.7) η = ηo exp kb T CE νa with ∆G a as the height of free energy barrier to be crossed by Eyring’s jump, the Boltzmann constant kB , the the viscosity constant ηo , deformation va , and a constant CE . With decreasing temperature, i.e. T → Tg , the Arrhenius behavior breaks down, and the viscosity is represented by a power law, or by the empirical Williams– Lendel–Ferry (WLF) relationship [9]:   −c1 (T − Tg ) η(T ) log , (15.8a) = η(Tg ) c2 + T − Tg where T → Tg from above; and the constants c1 and c2 are defined as: c1 = B/(2.303 f g ) , c2 = f g /αf ,

(15.8b) (15.8c)

where B is a constant taken as unity according to Doolittle [6], f g is the fractional free volume, Vf /V , in the glass transition region, and αf is the coefficient of thermal expansion of the free volume. The apparent activation energy, E A , associated with this kinetic model becomes [10]: E A = −2.303Rc1 c2

T2 , (c2 + T − TR )2

(15.9)

where T ≥ Tg , TR is a reference temperature, and R is the gas constant. At T = Tg , the activation energy takes the form [10]: E A = −2.303R(c1 /c2 )Tg2 .

(15.10)

Comparing the above theories, one finds that the free volume model presumes that the entire motion of atoms results only from the distribution of free volume without crossing the energy barrier. Conversely in the kinetic model, one

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assumes that the atomic motions are the consequence of a co-operative rearrangement of an assembly of structural units under the effect of thermal fluctuations, which allow the jump over the energy barrier separating the initial and final configurations. It has been very difficult to experimentally establish a preference for either of the two theories. We will show in Sect. 15.4 that SPM measurements in polymer systems favor the kinetic interpretation of the glass transition. However, we will first introduce in the following section, two scanning probe techniques that are especially well-suited for the necessary thermorheological studies.

15.3 Macromolecular Probing Techniques A diverse array of instrumental techniques are employed for glass transition studies. The most classical methods for obtaining Tg are calorimetric measurements (differential scanning calorimetry, DSC) that record the specific heat capacity as a function of the temperature, Cp (T ) [11]. Other methods involve dilatometric measurements for the determination of the specific volume, mechanical property measurements (thermomechanical analysis, TMA, and dynamic mechanical analysis, DMA), and dielectric measurements [4]. Near-edge X-ray absorption fine structure (NEXAFS) spectroscopy [12], X-ray diffraction [13], slow-positron-annihilation spectroscopy (SPAP) [14,15], Brillouin light scattering (BLS) [16,17], photon correlation spectroscopy and quartz crystal microbalance techniques [18], spectroscopic ellipsometry (SE) [19], attenuated total reflection (ATR) [20], and SPM [21–27] have all been employed to determine Tg for thin polymer films. Compared to most spectroscopic and scattering techniques, SPM techniques benefit from the real space molecular sensitivity of a nanoscopic probe. The SPM cantilever tip can be operated in any number of creative approaches for probing nanospace. Two SPM methods that have proved useful in polymer relaxation dynamics and glass transition studies are SM-FM and FFM [27, 35]. Both of these techniques are concerned with the application and measurement of lateral forces, and may be classified more generally under lateral force microscopy (LFM). Before we proceed with the experimental details of these techniques, we will first lay a theoretical foundation for the underlying contact mechanics and discuss appropriate LFM calibration methods. 15.3.1 Static Contacts Contact between two smooth elastic surfaces was first investigated by Hertz, who proposed a simple model, where both the size and shape of contact followed from the elastic properties of the bodies. This model was later extended by two models, Derjaguin–Muller–Toporov (DMT) [28] and Johnson-Kendall–Roberts (JKR) [29], to account also for adhesion. While in the DMT model the adhesion was considered outside the contact, the JKR model restricted the adhesion to the contact

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zone. Thus, the force acting between the two spheres, composed of both the adhesive and loading forces, is different depending on the model chosen. The “pulloff force”, Fadh , i.e. the critical negative load, at which two surfaces of combined radii R suddenly break apart, is proportionally related to the work of adhesion ∆γ . The proportionality factor is −1.5πR and −2πR in the JKR or DMT limit, respectively. The apparent discrepancy between the two models was resolved by David Tabor (1977) [30], who suggested a correction parameter, referred to as the Tabor coefficient µT , which compares the adhesive interaction strength with the intrinsic deformation properties (i.e. modulus) of the materials. Greenwood and Johnson suggested a Tabor coefficient of the form [31]:  µT = σo

R ∗2 E ∆γ

1 3

.

(15.11)

where σo is the maximum adhesive stress and the reduced modulus, E ∗ , defined as: E∗ =



1 − ν12 1 − ν22 + E1 E2

−1 ,

(15.12)

where E i and νi are the corresponding Young’s modulus and the Poisson ratio, respectively. A similar relationship was introduced by Maugis [32] with: 

16 λ=2 9π

1/3

σo∗



R ∗2 E ∆γ

1 3

,

(15.13)

assuming a constant adhesive stress σo∗ represented by a square well (“Dugdale”) interaction potential. Barthel, and Greenwood and Johnson showed that Maugis’ “Dugdal approximation” is also applicable to more general potentials [33], and to predict load-separation curves and pull-off forces that are adequate. It could be shown that if µT or λ exceed 5, the JKR model applies, i.e. tensile and compressive surface forces have to be considered, and for µT or λ smaller than 0.1 the DMT model is applicable. Based on Maugis’ analytical solution to adhesive contact problems, Carpick et al. developed a “generalized equation” for the normalized contact area between the contact limits of the JKR and DMT models, using a single fitting parameter α, which is related to Maugis’ elasticity parameter as follows [34]: λ = −0.924 × ln(1 − 1.02α) .

(15.14)

The fitting parameter α is given by the variation of the contact radius a with the ratio of the applied load, Fapp , and the adhesive force, Fadh , by [34]: a = a0 (α)



α+

2  1 + Fapp /Fadh(α) 3 . 1+α

(15.15)

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Here, the contact area at zero load, a0 , and the Fadh are dependent on α. For α = 0 and α = 1, (15.15) provides the normalized contact radius in the DMT and JKR limit, respectively, with a contact radius at zero load of: a03 =

3 R 9 πγR2 (6πγR) = (JKR) , ∗ 4E 2 E∗

(15.16)

a03 =

3 R 3 πγR2 (2πγR) = (DMT) .1 4 E∗ 2 E∗

(15.17)

and

15.3.2 Modulated Contacts Now, let us turn our attention to SPM type contacts that involve sinusoidal modulations in either the normal (z) or lateral (x) direction. The contact stiffness experienced during normal modulation experiments is typically defined as the gradient of the equilibrium force between tip and sample, and is given as [35]: kc,z = 2aE ∗

(15.18)

The normal contact stiffness kc,z is experimentally obtainable from normal displacement measurements, which are distributed between two springs in series; i.e.: ∆z = ∆z c + ∆z N

(15.19)

where ∆z c and ∆z N correspond to the elastic deformation of the sample (or more generally the contact) and the elastic normal cantilever displacement, respectively. The elastic constant, ktot,z , corresponding to the total normal deformation ∆z is thus related to the sample contact stiffness kc,z and the normal cantilever stiffness kN , as: 1 ktot,z

=

1 1 + . kc,z kN

(15.20)

For small in-plane lateral displacements in x, similar equations can be derived under the assumption of no-slip. For a sphere-plane geometry, the lateral stiffness of the contact kc,x is provided by Mindlin’s theory [36, 37] as: kc,x = 8aG ∗

(15.21)

with G∗ = 1



2 − ν12 2 − ν22 + G1 G2

−1

Note that for a Hertzian contact the radius is given by a3 =

(15.22) 3 R 4 E∗

FL .

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where G 1 and G 2 are the shear moduli of the sample and the probing tip, respectively, and ν1 and ν2 are the corresponding Poisson’s ratios [38]. In analogy to the normal deformation, we introduce the total lateral elastic constant as: 1 1 1 = + , ktot,x kc,x kT

(15.23)

where kc,x and kT stand for the lateral contact stiffness and the torsional cantilever stiffness, respectively. As for normal deformations, it is generally assumed that the shear deformation of the cantilever is restricted to the bending of the bar, and thus, any tip deformations are neglected. This assumption is appropriate for soft organic materials; however, it may breakdown when contacting hard samples like silicon wafers. For force modulation measurements, the modulation load, Fmod , is varied around the equilibrium load, Fo , with an oscillating perturbation, often in the form of a sine wave. The modulation signal is generally provided by a function generator, and may be applied to either the cantilever or the sample. A first-order approximation for the overall force in the modulation direction, i, provides: Fi = Fo +

∂Fmod ∆xi , ∂xi

(15.24)

where ∂Fmod = ktot,i , ∂xi

(15.25)

and i = z or x for normal or lateral modulation, respectively, and ∆xi represents the corresponding input modulation amplitude. The equilibrium load Fo represents the combination of the applied and adhesive loads for normal force modulation, Fapp and Fadh , respectively. In shear modulation, Fo is either zero under no-slip conditions, or corresponds to the friction force, FF , in a sliding contact. 15.3.3 Calibration of Lateral Forces in Scanning Probe Microscopy Lateral forces are still relatively difficult to quantify accurately. Due to the geometric uncertainties in SPM probes, mathematical calibration methods are often inaccurate. Hence, at least two experimental calibration techniques have been offered: a lateral contact stiffness calibration [37], and a blind friction calibration [39]. Both methods assume that the normal force, FN , and hence the normal cantilever stiffness, kN , are known. The normal force is the sum of the applied and adhesive loads, i.e. FN = Fapp + Fadh , where the applied load is determined by: Fapp = kN

∆IN − INo , S

(15.26)

where kN is the normal lever stiffness, S is the sensitivity of the detection scheme (generally a photodiode), ∆IN is the normal deflection signal (i.e. the setpoint value

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in feedback control), and INo is the initial, out-of contact, normal deflection signal. The sensitivity and adhesion force are determined from force-displacement (FD) curves. Note that for studies on compliant materials, the adhesion force determined from FD curves is generally convoluted with the contact area. To avoid load dependent changes in the contact area, the adhesion force should be determined from friction versus load measurements, e.g. see Fig. 15.7. With commercially available cantilevers, a range for kN is specified by the manufacturer. Due to limitations in the production process, the specified range for kN may span one order of magnitude. The prudent microscopist often seeks a more accurate calibration. For bar shaped cantilevers, the normal and torsional stiffness may be calculated based on the lever geometry, i.e: EWTL3 , (15.27a) 4L 3 GWTL3 kT = , (15.27b) 3L H 2 where E and G are the Young’s and shear moduli, respectively. The geometric parameters W, TL , and L are the width, thickness, and length of the cantilever, respectively; and H it the height of the probing tip at the end of the lever. Any uncertainty in TL is propagated in (15.27) with a power of three; hence, an accurate value for TL is necessary. Again, manufacturer specifications are usually broad. The first resonance frequency in the normal direction, measured via spectrum analysis, can be used to determine TL more accurately [35]: √

2 12π ρ ν1 L 2 . TL = (15.28) (1.875104)2 E kN =

For silicon cantilevers, the density ρ is 2.33 × 103 kg m−3 and the modulus E is 1.69×1011 N m−2 [35], and (15.28) becomes TL (m) = 7.23×10−4 (s m−1 )·v1 (s−1 )· L(m)2 . Alternatively, the normal spring constant for a lever of any geometry may calibrated by measurement of the thermally activated power consumption [40], or by the addition of known masses (styrene spheres) [41]. Once the cantilever is calibrated for normal forces, the next step is the lateral force calibration. The lateral contact stiffness approach is based on SM-FM operation (Fig. 15.4), which uses lock-in detection to relate the lateral displacement (modulation input, ∆xi ) with the lateral force signal (amplitude response, ∆x R ). On any sample, a plot of ∆x R versus ∆xi exhibits two regimes, a static region where ∆x R increases linearly with ∆xi , and a sliding region where ∆x R saturates at the friction force. The slope of the static region is a direct measure of the overall lateral contact stiffness, related with the calibration factor C, i.e.:  d(∆x R )  ∗ = Cktot,x . (15.29) ktot,x = C d(∆xi ) static Substituting (15.21) and (15.29) into (15.23) gives: 1 ∗ ktot,x

=

C C . + ∗ 8G a kT

(15.30)

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Fig. 15.4. Working principle of shear modulated force microscopy

For a bar shaped cantilever, (15.27a) and (15.27b) may be used with G = E[2(1 + v)]−1 to determine the torsional cantilever stiffness, i.e.: 2 kT = kN 3(1 + ν)



L H

2 (15.31)

Alternatively, the torsional stiffness may be obtained by using the Sader [42] and Neumeister [43] formulas. The difficulty with (15.30) lies in selecting the appropriate model for the contact radius, a. Assuming Hertzian contact, Piétrement et al. [37] have shown that this procedure works well for silicon and mica. The Hertzian (or DMT) contact radius is:  a=

3R 4E ∗

1/3 1/3

FN ,

(15.32)

where R is the radius of curvature of the SPM tip, and (15.30) becomes: 1 ∗ ktot,x

=

C 1/3 βFN

+

C , kc

where β = 8G ∗



3R 4E ∗

1/3 .

(15.33) −1/3

∗ A linear fit to the experimentally measured 1/ktot,x versus FN gives an intercept, b, which from (15.33), C = bkc . Finally, the force associated with a lateral displacement of ∆xi is FL = C∆x R . This calibration method becomes cumbersome when more sophisticated models are used for the contact radius in (15.30). For example, Carpick’s [34] general contact area equation (15.15) requires knowledge of the lateral (friction) force, as well as the

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tip radius of curvature, to determine the fit parameter α. Numerical methods would be required to iteratively fit the contact radius and the calibration curves. The blind friction calibration is model independent and avoids these complications by directly measuring a calibration factor on a well-characterized, commercially available silicon standard that has a prescribed friction coefficient, µSi–Si . The trade-off, however, is the possibility of surface contamination on the silicon standard, which would alter the actual friction coefficient. To avoid this, careful silicon treatment is necessary [39]. From Amonton’s law, it is known that FL = µSi–Si · FN .

(15.34)

Using a well-defined cantilever that was characterized by scanning electron microscopy (SEM), Buenviaje et al. determined a value of µSi–Si = 0.18 ± 0.03 [39]. The lateral forces experienced by the cantilever tip are directly proportional to the lateral deflection signal of the SPM detection system, i.e. FL = Γ · ∆IL ,

(15.35)

where the proportionality constant Γ is the calibration factor being sought, and ∆IL is the lateral deflection signal. ∆IL is measured on a well-treated silicon oxide surface for a range of normal forces, FN . For positive applied loads (Fapp > 0), a linear fit to the measured ∆IL (FN ) gives the calibration curve ∆IL = m cal · FN .

(15.36)

Dividing (15.34) and (15.36) yields: FL =

µSi–Si · ∆IL . m cal

(15.37)

Thus the calibration factor Γ in (15.35) becomes: Γ =

0.18 ± 0.03 µSi–Si = . m cal m cal

(15.38)

With a value for Γ , (15.35) may be used to quantify the lateral forces measured by the SPM detection scheme. The silicon treatment is necessary to generate a clean and stable silicon oxide surface. This is not to be confused with stripping or hydrogen passivation techniques, e.g. HF treatment, which remove the surface oxide layer and render an unstable surface. The procedure of Buenviaje et al. [39] requires sequential sonication of the silicon calibration sample; first in acetone for 15 minutes, then in methanol for 30 minutes (HPLC grade from commercial sources). The sonication steps are followed by rinsing with ultra-pure water. Finally, the silicon calibration standard is heated above 100 ◦ C in a low humidity environment, preferably a vacuum oven, to remove excess water. This procedure provides a reproducible calibration sample for up to two hours, depending on the post-treatment environmental conditions, i.e. relative humidity. With a calibrated SPM system, one is prepared for experimental endeavors based on the following lateral force probing techniques.

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15.3.4 Shear Modulation Force Microscopy (SM-FM) Characterization efforts using SPM modulation techniques seek to infer material specific information from the elastic (or dissipative) nature of the probing contact. Shear modulation force microscopy (SM-FM) is one approach that is especially well-suited for surface rheological studies. SM-FM has proven to be particularly successful in determining crosslinking densities and structural phase transitions in polymeric systems [26, 27]. The working principle of SM-FM is sketched in Fig. 15.4. It involves a nanometer sharp cantilever tip that is maintained in contact with a sample surface, under a constant load of roughly (5–100) nN. The tip is laterally modulated with a nanometer amplitude, ∆xi , that avoids any tip–sample slipping. Using lock-in techniques, the modulation response, ∆x R , is analyzed relative to ∆xi . The response amplitude is a measure of the total elastic constant, ktot,x , and the intrinsic sample behavior is captured through the relations in (15.21) and (15.23). Characteristic of most SPM techniques, two experimental difficulties arise: the accurate determination of the true contact area (radius a in (15.21)), and accurate evaluation of the cantilever stiffness, k T in (15.23). This raises the important point of calibration methods (discussed above). However, in simple thermo-rheological studies like glass transition temperature measurements, the complications associated with a poorly defined contact area and lever stiffness are inconsequential. For thermal analyses, the sample temperature is increased stepwise by (0.5– 2.0) ◦ C increments. At each temperature, thermal equilibrium is obtained before any viscoelastic responses are recorded. The response amplitude, ∆x R , is plotted versus temperature. For glass transition measurements, the Tg is determined from the “kink” in the response curve, as reported in Fig. 15.5a. Below Tg , the probing depth of SM-FM is on the order of 1 nm, which allows substrate-independent measurements down to film thicknesses of a few nanometers. Any surface effects less than 1 nm in depth [44] cannot be addressed under these conditions. The slow creeping process above Tg is documented elsewhere [45]. While the accuracy of SM-FM Tg measurements compares well with other techniques [46], Fig. 15.5b, SM-FM also offers the versatility for probing rheological properties in confined sample geometries. It is important to note that the SM-FM technique described here is a non-scanning method. The reason is briefly described: To obtain high accuracy in Tg measurements it is essential not to induce, by other means than temperature, changes in the contact area. This is to avoid system-driven artifacts in the contact stiffness, kc,x . To be precise, kc,x (AL , G ∗ ) in (15.21), i.e. the resistance of the contact to deform, is dependent on (a) the laterally projected contact area, AL , (e.g. the side wall of an indentation tip), and (b) the relative shear properties of the two materials, G ∗ . Thus, any local plastic deformation, for instance, the generation of a deformation wave (Schallamach wave) [47] that travels ahead of a scanning SFM tip, can change kc,x . Plastic deformation is intrinsically rate- and load-dependent. Therefore, it is not astonishing that scanning methods, such as the friction force microscopy, have revealed scan rate dependent apparent Tg values [25]. By placing the SFM tip stationary at constant load onto the polymer surface, contact area changes occur only due to temperature induced changes in the sample modulus, i.e. there are no load

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Fig. 15.5. SM-FM glass transition temperature, Tg , measurements. (a) The modulation amplitude response indicating the Tg of polystyrene. (b) Comparison of SM-FM Tg values as a function of molecular weight against other methods and theory. (Source for (b): [46])

induced changes in the contact radius, a, and the cantilever stiffness, kL , is essentially constant. Consequently, the experimental observable in the SMFM method, ktot,x , is changing only due to changes in the polymer material properties. With this, the “kink”, observed in Fig. 15.5a is a true measure of the transition property. 15.3.5 Friction Force Microscopy (FFM) The advantages of the non-scanning SM-FM technique were highlighted above. Now, let us discuss the complimentary advantages of the scanning approach of FFM. In fact, both methods may be superimposed and conducted simultaneously, if the time-scales for the SPM feedback system, modulation, and scanning do not overlap. Nevertheless, we will restrict ourselves here to the principles of FFM and discuss the inherent tribological attributes of this method. Friction force microscopy simulates a single asperity provided by an ultra-sharp tip on a soft cantilever, pictured in Fig. 15.6. The small contact area, on the order of the molecular dimensions, is insufficient to confine macromolecules and generally allows discussing friction results in terms of thermodynamic equilibrium. Hence, FFM

Fig. 15.6. Working principle of friction force microscopy (FFM)

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Fig. 15.7. Adhesion correction of friction measurements on poly(methyl methacrylate)

is not appropriate to reflect on tribological issues involving large area confinement effects. FFM offers sufficient sensitivity for friction measurements on the molecular scale, and has been used to detect molecular stick-slip behavior [48]. Although FFM images are valuable for assessing surface heterogeneity and the decomposition of blends, investigations of macromolecular dynamics require a quantitative friction analysis. The ability to conduct thermal, rate- and load-dependent friction studies makes FFM especially well suited for investigating the time-temperature nature of viscoelastic materials. The friction force, FF , is measured through the torsional bending of the cantilever during scanning, pictured in Fig. 15.6. The hysterisis in the lateral displacement signal, between forward and reverse scans, is proportional to the energy dissipated through friction. Absolute values for the friction force are determined by first calibrating the cantilever and detection scheme with one of the methods described in Sect. 15.3.3. Its important to note that any changes to the laser alignment will invalidate the calibration. Further, it is important that friction analyses on compliant materials are adhesion corrected, see Fig. 15.7. This is necessary to account for loaddependent changes in the contact area, i.e. FF must be described in terms of the total normal force, which is the sum of the applied load, Fapp , and the adhesion force, Fadh . 15.3.6 Tribological Models for FFM The frictional resistance to sliding of the FFM tip is generally discussed in terms of a thermal activation model, the Eyring model [8], which employs a regular series of potential barriers that are continuously overcome during the sliding process. Briscoe et al. [49] applied this idea to interpret the frictional behavior observed on

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molecularly smooth, soap-like lubricants, and derived the following shear strength versus velocity v relationship [49]:   v kB T 1 ln (15.39) τ= + (Q + PΩ) . φ vo φ The barrier height, E, is composed of the process activation energy Q; the compression energy PΩ, where P is the pressure acting on the volume of the junction Ω; and the shear energy τφ, where τ is the shear strength acting on the stress activation volume φ. T represents the absolute temperature, and vo is a characteristic velocity related to the frequency of the process and to a jump distance. The stress activation volume φ can be conceived as a process coherence volume, and interpreted as the size of the moving segment in the unit shear process, whether it is a part of a molecule or a dislocation line. Thus, Eyring’s model predicts a linear relationship of friction (the product of the shear strength and the active process area) in pressure and temperature, and a logarithmic relationship in velocity. The Eyring model has been verified in experiments on solid lubricants of an inherent, highly-ordered structure [49], and also for a liquid system where a series of potentials is built up and overcome in the course of the shear process [50]. Furthermore, Gnecco et al. [51] showed in an ultrahigh vacuum FFM study on sodium chloride, that the concept of the Eyring model also applies for dry friction on an ordered surface. Thus, a molecular theory of friction could be derived from a very simplistic model of an apparent sinusoidal-corrugated surface potential over which a cantilever tip is pulled. However, such a simple model assumes there is no noise present, such as thermal noise, and thus, the driven tip leaves the potential well when the barrier vanishes at the instability point. This leads to recent theoretical treatments that consider barrier-hopping fluctuations associated with thermal noise, i.e. creep models [52–54]. With creep, the FFM tip slips to the next potential well at lower energy values than those prescribed by the barrier height. Early considerations of thermal fluctuations by Heslot et al. [54] led to a friction force that is logarithmically dependent on the velocity, v, similar to the Eyring model: FF = const. + ln(v) .

(15.40)

In Heslot’s linear creep model, the barrier height is proportional to the frictional force. Sang et al. [53] argued that with an absorbing boundary condition, i.e. an elastic deformation of the overall potential due to the driven motion of the cantilever, the barrier height becomes proportional to a 3/2 power law in the friction force. Sang’s modifications resemble a ramped creep model, and lead analytically to the following friction-versus-velocity relationship:  2/3 (15.41) FF = Fc − ∆FF ln v∗  , where v∗ represents a dimensionless velocity, ∆FF ∝ T 2/3 , and Fc is an experimentally determined constant [53]. The same relationship of friction with velocity was also derived for the maximum spring force by Dudko et al. [52]. Although there is currently no experimental data available that would provide friction force measurements over a sufficiently large temperature and velocity range

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to verify the ramped creep model, the stronger supporting argument for ramped creep is its comparison to the numerical solution of the Langevin equation. The Langevin equation combines the equation of motion (including the corrugated surface potential and perfect cantilever oscillator in the total potential energy, E) with a random force, ξ(t), to account for the thermal noise, i.e.: M x¨ + Mβ x˙ +

∂E(x, t) = ξ(t) , ∂x

(15.42a)

where

  2πx k 2 . E(x, t) = (R(t) − x) − Uo cos 2 λ

(15.42b)

x is the position of the cantilever stage, β is the microscopic friction coefficient or dissipation (damping) factor, λ is the lattice constant, Uo is the surface potential barrier height, M and k represent the mass and the spring constant of the cantilever, respectively. Equation (15.42a) was solved numerically by both groups, Sang et al. [53] and Dudko et al. [52], assuming  a Gaussian fluctuation-dissipation relation for the random force, i.e. ξ(t)ξ(t  ) = 2MβkB Tδ(t − t  ), where δ(t − t  ) is a Dirac function. Sang confirmed the ramped creep model and Dudko showed that a force reconstruction approach from the density of states, accumulated from the corresponding Fokker–Planck equation, is equivalent with the Langevin equation. At this point, let us consider the possibility that hindered, or frozen, relaxation states of an amorphous polymer could be activated in the course of a frictional sliding process, and thus, give rise to barrier-hopping fluctuations not unlike the ones discussed above for highly-ordered surfaces. Isothermal friction-velocity curves for glassy polystyrene are presented in Fig. 15.8. Quasi-logarithmic friction-velocity relationships are found, which agree with the above theoretical models [49, 52–54], and resemble FFM experiments on ionic crystals in ultrahigh vacuum [51] and in lubricated sliding [50].

Fig. 15.8. Friction force-scan velocity isotherms for FFM measurements on glassy polystyrene (MW = 96.5 k, MW /MN = 1.04, Tg = 373 K, FN = 15 ± 2 nN)

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The friction measurements in Fig. 15.8 are scaled by the creep models (equation 15.40 and 15.41) in Figs. 15.9a and 15.9b. The ramped creep model in Fig. 15.9a, provides a marginally better fit than the linear creep model, Fig. 15.9b. The fit quality of the ramped versus linear creep model could be expected to increase for a system that is less overdamped, i.e. a stiffer spring with respect to β [55], and with measurements over larger velocity and temperature ranges. The potential barrier, which is continuously overcome during sliding across glassy polystyrene is associated with the hindered rotation of the phenyl side-chains, 7 kcal mol−1 [56]. Evaluation of the barrier height is discussed in Sect. 15.4. Considering that the creep models (a) fit the friction data reasonably well, and (b) are in accordance with a fluctuation model based on a Gaussian fluctuation distribution, it appears that there is little or no correlation between the individual phenyl rotations that are relaxed during the shear process. It is because of this weak correlation that similar frictional dissipative behaviors are observed on both highly structured (crystalline) surfaces and the unstructured (amorphous) glassy PS. The FFM results and associated discussion of molecular friction on a glassy polymer illustrate the effectiveness of rudimentary non-equilibrium models that incorporate simple potentials with thermal fluctuations. Deviations from the models are expected, particularly for correlated fluctuations, i.e. memory effects in relaxation processes. Addressing the issue of the so-called non-Markovian behavior of sliding systems demands a more rigorous theoretical treatment, such as the generalized Fokker–Planck equation with a system specific, statistical kernel [57–60]. The discussion above is founded strictly on tribological principles; however, the experimentally determined potential barrier for the PS example is attributed to a rheological relaxation process. One would expect then that friction could also originate from other relaxations. For example, Hammerschmidt et al. have identified the β relaxation as the primary dissipation mechanism in FFM measurements on poly(methyl methacrylate) [23]. The question of to what extent the intrinsic rheological properties are coupled with external tribological attributes in FFM measurements

Fig. 15.9. Collapse of the friction data from Fig. 15.8 to creeping friction models. (a) Ramped creep [53] (regression R2 = 0.9124). Inset: Fc is determined from the intercept of FF versus T 2/3 for a fixed ratio T/v = 1 K/(nm/s) [53]: Fc = 44.5 nN. (b) Linear creep [54] (regression R2 = 0.909). Inset: Fc is determined from the intercept of FF versus T for a fixed ratio T/v = 1 K/(nm/s) [53]: Fc = 32.6 nN

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has not been answered unambiguously. This results, in part, from varied experimental conditions, as well as inappropriate assumptions during the data analysis. Operating the FFM tip at conditions that induce wear or other plastic deformation processes will produce external tribological attributes. This is sometimes difficult to avoid. The relative humidity is another key parameter which effects FFM measurements. For a relative humidity greater than roughly 30%, a capillary neck is formed at the FFM tip due to physisorbed water [61]. In this scenario, the FFM measurements reflect the behavior of a two-phase system. In the following section, we attempt to move past some of these issues, and address the utility of FFM for inferring intrinsic rheological characteristics of polymers.

15.4 Internal Friction and Dynamics near the Glass Transition A nanoscopic description of polymer dynamics involves, in general, only two parameters: an internal, or monomeric, friction coefficient and an appropriate macromolecular length scale [62]. Monomeric friction dictates the degree of local segmental motion, and thus, is responsible for the bulk viscoelastic properties of polymers. The macromolecular length scale provides a measure for the range of energy transfer, for instance, the size of cooperatively rearranging regions (CRRs) in the heterogeneous dynamics of glass formers. The measurement of nanoscopic critical lengths warrants a local probing technique, such as SPM. This point is illustrated below with molecular insight into the energy dissipation processes in amorphous polystyrene (PS), a material technologically relevant to photonics [63], electronics [64], and nanoelectromechanical systems (NEMS) [3]. We show how both the energetics involved in frictional dissipation and the length scale over which the energy is dissipated can be directly linked to the molecular relaxation and clustering processes that evolve during the glass transition. 15.4.1 Molecular Relaxations The origin for frictional dissipation in elastomeric materials has been in question for nearly half of a century. Since Grosch [65] (1963) and Ludema and Tabor [66] (1966), a molecular length scale has been accessible in friction experiments involving elastomers in sliding contact with hard surfaces. However, because of the macroscopic nature of these early investigations, segmental chain slippage could only be suspected as the basic mechanism for sliding dissipation [65, 66]. Early interpretations by Schallamach [67] and Ludema and Tabor [66] addressed the friction related segmental motions of the polymer chain from two different viewpoints: Schallamach considered the friction force in terms of a fully adhesive, rate-dependent molecular debonding model, introduced by Frenkel [68] and Eyring [8] and later improved by Chernyak and Leonov [69]. Ludema and Tabor, on the other hand, suggested an adhesive viscoelastic model in which the energy dissipated during sliding is lost in deformation of the soft material. In recent work involving smooth macroscopic sliding contacts, the importance of both processes during steady sliding was recognized [70,71].

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Recent FFM studies have benefited from the molecular sensitivity of the SPM probe. A first glance of frictional behavior on polystyrene near its glass transition is illustrated with the friction coefficient, µ, in Fig. 15.10. The frictional dissipation mechanism shifts from side chain relaxation in the glass phase to backbone relaxation in the melt phase. The transition is not abrupt, but ranges over 15 K, starting at the glass transition temperature (Tg = 373 ± 1 K). The dissipation mechanisms in Fig. 15.10 were determined from independent FFM friction-velocity analyses, below and above Tg . An energetic analysis of FFM results begins with the superposition of friction-velocity isotherms, FF (v)|T , using the method of reduced variables [10], Fig. 15.11. This linear approach serves to decouple the thermal and rate contributions to the friction force. While the thermal behavior is captured in the horizontal aT shift function, the rate behavior is portrayed in the resulting superposed friction master curve. The mathematical mechanics of the superposition are pictured in Fig. 15.12. Below Tg , the Arrhenius behavior aT in the inset of Fig. 15.11a provides an activation energy of 7 kcal mol−1 . This corresponds to the hindered rotation of the phenyl ring side chains about their bond with the backbone [72], also referred to as the γ -relaxation [73]. Above Tg , the Arrhenius representation of aT in the inset of Fig. 15.11(b) provides an apparent activation energy of 88 kcal mol−1 , which coincides with the 90 kcal mol−1 energy barrier for the α-relaxation of the PS backbone [74]. The WLF behavior expected above Tg predicts a temperature dependent activation energy for the α-relaxation, (15.9). In the WLF formalism, the constants c1 and c2 depend on the chosen reference temperature, TR , used for the superposition [9]. For TR = 388 K, the experimentally determined values are c1 = 16 and c2 = 114. The corresponding activation energy at Tg , by (15.10), is 89 kcal mol−1 , which is close to the 88 kcal mol−1 value deduced from the Arrhenius

Fig. 15.10. Friction coefficient, µ, and corresponding molecular dissipation mechanisms for atactic polystyrene (Mw = 96.5k Tg = 373 K)

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Fig. 15.11. Friction master curves for atactic polystyrene. (a) Superposition below Tg with (inset) corresponding aT shift factor. (b) Superposition above Tg , with (inset) corresponding aT shift factor

representation in the inset of Fig. 15.11b. The activation energies represent the potential barrier that is continuously overcome during steady sliding of the FFM tip. Thus, the molecular origin for polymeric friction lies in the rheological relaxation processes that are available in a given temperature range. The qualitative difference in FF (v)|T curves below and above Tg is insignificant; a bell-shaped friction-velocity behavior can be expected in both regimes. Under ideal conditions, it is only a question of the accessible velocity range. Ludema and Tabor [66] explained the FF (v) peak with respect to the variation of the contact area and the shear strength with scan velocity. Thus, friction expressed as FF (aT v) = σ (aT v) A[E(v)] will exhibit a bell-shape curve similar to Fig. 15.11b, where σ represents the shear stress, A the real contact area, and E(v) the viscoelastic modulus. On the molecular scale, the qualitative rate behavior of both the shear strength and modulus, and thus the shape of the FF (v) curve, originates from the interplay of two dominating time scales: (i) the extrinsic drive time, τe , dictated by the sliding velocity, v, and (ii) the intrinsic material response time, τm , which in this case is the α-relaxation time. In the vicinity of the FF (v) peak, the two competing processes occur on comparable time scales. The friction force increases or decreases with increased sliding velocity depending on whether the extrinsic time leads or trails the material response time, respectively. Generally the interplay between intrinsic and extrinsic times is discussed with their ratio, the Deborah number. Since the material response above Tg has been identified as the α-relaxation, the particular FF (v) peak pictured in Fig. 15.11b is distinguished as the α-peak. No bell-shaped frictionvelocity isotherms are observed below Tg , because reaching the time-scale for phenyl rotations would demand high sliding speeds of mm s−1 to cm s−1 , unachievable with conventional SPM. 15.4.2 Structural Heterogeneity and Relaxation near the Glass Transition While the energetics associated with the dissipation process are deduced from the horizontal aT shift, dynamical and structural information are inferred from the fric-

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tion peak intensity, similar to spectroscopic techniques. The friction analysis below Tg only involved classical horizontal shifting, which defines aT in Fig. 15.12a. Additional vertical shifts, ∆FF , are necessary in the transition region between Tg and Tg + 15 K, Fig. 15.12b. The application of vertical data shifts must be considered thoughtfully. Inspection of the α-peak intensity, FF,max (T ), in Fig. 15.13 reveals the maturation of the α-relaxation from Tg to Tg + 15 K. The strong 4.8 nN K−1 temperature dependence of FF,max in the transition regime is caused by the heterogeneity of two structural phases. Conceptually, small domains of the melt phase begin to appear at Tg , yielding a relatively weak α-peak intensity. As the temperature increases, remnant glassy domains, or threads, are consumed by the melt; thus the α-peak intensity increases. Once the melt phase is fully developed at T > Tg + 15 K, a temperature independent α-peak intensity is observed. Hence, the vertical shift used in Fig. 15.11b, ∆FF (T ), represents the departure from equilibrium of a sturcturally heterogeneous melt. The above behavior concurs with the present understanding of vitrification between the crossover temperature Tc and Tg , where Tc > Tg [2]. Above Tc , glass forming polymers exhibit a single relaxation process. As the temperature is reduced below Tc , bifurcation of the relaxation process leads to both slow (α-backbone) and fast (side chain) relaxation processes [75,76]. As Tg is approached, the slow process becomes locked; while the fast process continues below Tg [75]. The onset of the bifurcation is evident in FF,max (T) at 388 K in Fig. 15.13. Here, the α-peak intensity, FF,max (T), reveals an impedance of the α-relaxation on cooling below 388 K. Only the α-peak is observed with conventional SPM (Fig. 15.11b); as noted above, the time-scale for relaxation of the phenyl side chains is not accessible. However, the transition from side chain to backbone relaxation is apparent in the friction coefficient in Fig. 15.10. The friction coefficient reveals three regimes: (i) a single glassy phase below Tg , where dissipation occurs only through phenyl rotations; (ii) a structurally heterogeneous system within 15 K above Tg , where dissipation occurs through a combination of spatially distributed fast (phenyl) and slow (backbone) relaxations; and (iii) a homogeneous melt above 388 K, with dissipation solely through the higher energy α-relaxation.

Fig. 15.12. Representative shifts for superposition of friction data. (a) The horizontal shift applied all FF (v) isotherms defines the temperature dependent aT function. (b) The vertical shift, ∆FF (T), is only necessary for FF (v) isotherms between Tg = 373 K and Tc = 388 K

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Fig. 15.13. Friction peak intensity, FF,max (T), for the α-relaxation in atactic polystyrene. ∆FF (T) = FF,max (T > Tg + 15) − FF,max (T)

15.4.3 Cooperative Molecular Motion During the Glass Transition The existence of structural and dynamic heterogeneity around Tg is consistent with conclusions drawn from isothermal multidimensional nuclear magnetic resonance (NMR), dielectric spectroscopy, photobleaching, dynamic light scattering, and quasielastic neutron scattering studies [2]. Since Adam and Gibbs [77], structural relaxation near the glass transition is visualized in terms of a correlated motion of polymer segments or domains, giving rise to dynamic heterogeneities [2, 75, 78–80]. While the time scale of dynamic heterogeneities can be directly inferred from scattering experiments, the size of the cooperatively rearranging regions (CRRs) (typically 1– 3 nm [2,78,81,82]) generally has not been directly obtainable and involves model assumptions. In particular, a temperature-resolved description of the cooperation length is expected to provide vital microscopic information towards the ongoing mysteries of the glass transition [78]. An unambiguous evaluation of this small length scale warrants a direct, spatially nanoscopic investigation of the glass forming dynamics, avoiding the averaging effects associated with conventional ensemble measurements [83]. The extent to which neighboring chain segments and adjacent molecules participate collectively in the dissipation, or relaxation, process is deduced from the intrinsic characteristics of the friction peak in Fig. 15.11b. In early evaluations of the dissipation length in elastomers, Grosch [65] and Ludema and Tabor [66] combined the velocity at the friction peak with the frequency for the maximum viscoelastic loss, and deduced a length scale on the order of 5–10 nm. Similarly, the frictionvelocity results in Fig. 15.11b are related to dielectric spectroscopy data [84] for PS of comparable molecular weight (Mw = 90.0 k, Mw /Mn = 1.06). It is founded that interpretations of dielectric relaxations are related directly to the timescale for mechanical relaxation [85]. With the specific knowledge of the α-relaxation times τα (T) from the dielectric data and the critical velocities vo (T) corresponding to the friction peaks, the length scale over which energy is dissipated during an α-relaxation event may be expressed as: xd (T) = vo (T) · τα (T) .

(15.43)

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The dissipation lengths xd (T) for polystyrene are presented in Fig. 15.14 as a function of the reduced temperature, TR , which captures the position within the observed range of the glass transition, i.e. TR = (T −Tg )/(T −Tc ). The values of Tc and Tg are 388 K and 373 K, respectively. In the fully developed melt (T > 400 K), a lower limit of ∼ 0.3 nm for xd (T), corresponds to the relaxation of individual monomer segments. On cooling from 403 K to 384 K, the dissipation length increases steadily from 0.3 to 2.1 nm, following a power law relation of the form xd ∼ TR )−φ , where the power law exponent φ is 1.89 ± 0.08. The xd (T) behavior is consistent with predictions for CRR growth dynamics, and suggests that frictional energy is dissipated throughout the CRR domain in polymer melts [88]. While the dissipation lengths represent the degree of molecular coordination during relaxation, the power-law exponent φ captures how segmental coordination grows as the glass transition is approached. This interpretation is consistent with the kinetic model of the glass transition in Sect. 15.2. On closer approach to Tg (T < 384 K), we find a strong deviation from the above power law behavior. Dissipation occurs in domains up to 31 nm, which cannot be explained solely based on heterogeneous growth of CRRs. The divergence of xd (T) near Tg has been attributed to long-range relaxation modes that may couple with the α-relaxation mode of the FMM signal, e.g. the normal-mode (overall chain dynamics) or Fischer-modes (ultra-slow modes) [88]. The large size of the dissipation lengths deserves particular attention. The size of the dissipation lengths in PS near the glass transition grows from single molecular segments to domains of tens of nanometers in diameter. Compared to structures in

Fig. 15.14. Dissipation lengths xd for the α-relaxation in polystyrene. In the power law region −φ (solid line: xd ∼ TR , φ = 1.86 ± 0.09), frictional energy is dissipated throughout cooperatively rearranging regions (CRRs) in a structurally and dynamically heterogeneous melt [88]. Close to Tg , the power-law relation breaks down, and energy is dissipated beyond individual CRRs, possibly coupling to longer range relaxation modes. Inset: Corresponding polystyrene α-relaxation times, τα , determined from the FFM friction peaks and equation (15.43) (closed circles) compared to dielectric spectroscopy measurements of [84] (open circles)

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modern device technologies, e.g. ultrathin films and nanocomposites involving sub100 nm dimensions, one can expect a competition between material and device length scales. Consequently, material properties in dimensionally constrained systems are likely to be modified from their original bulk values [89], which is the topic discussed in the following section. The impact of dimensional constraints on the propagation (or attenuation) of molecular cooperation, φ, will dictate the thermal range over which the glass transition occurs. Constraints leading to enhanced coordination (high φ – more restricted mobility) would increase the local Tg ; while finite size effects that prevent coordination (low φ – less restricted mobility) would reduce the local Tg . Given the technological importance of Tg , the continued evolution of thin film applications stands to benefit from accurate characterization of xd (T) and φ in confined geometries. Not only frictional dissipation, but all transport processes are hinged upon the same intra- and inter-molecular degrees of freedom available to particular motions, e.g. charge carrier transport in organic thin film transistors, light emitting diodes, and molecular electronic devices.

15.5 Constraints and Structural Modifications near Interfaces The discussion thus far has focused on SPM techniques and bulk-material behaviors. In polymer thin films, when film thicknesses approach the nanometer scale, structural, material, and transport properties become increasingly dominated by interfacial and dimensional constraints. Rheologically modified boundary layers are often formed at interfaces, within which anisotropic constraints lead to bulk-deviating behaviors. This section is devoted to exploring rheological boundary layers at polymer interfaces. A variety of material responses are illustrated with several FFM and SM-FM studies, and a visualization of the molecular configuration at interfacial boundaries is gradually developed with each successive example. 15.5.1 Interfacial Plasticization The conceptually intuitive process of heterogeneous diffusion serves as a worthy starting point for a discussion about rheological modifications at interfaces. This is illustrated for a multiphase, binary thin film system, in which low molecular weight components (LMCs) leach from an underlying film into the surface film, forming an interdiffusion zone at the interface. FFM studies were conducted on poly(methyl methacrylate) (PMMA) films supported on either crosslinked epoxy or silicon substrates. For PMMA films on epoxy substrates, the friction coefficient, µ, in Fig. 15.15 decreases with increasing film thickness. For thicker films, µ approaches the friction value of PMMA on silicon. The friction coefficient may be considered constant, if one assumes that (a) the shear modulus is constant, and (b) the adhesion force is only a function of the contact area, i.e. a constant physical and chemical bonding strength between the FFM tip and sample. Holding to these assumptions and considering that

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Fig. 15.15. FFM friction coefficient measurements on PMMA reveal interfacial plasticization for films supported on epoxy substrates, as low molecular weight components leach from the epoxy into the PMMA

the FFM probe (silicon) is much stiffer than PMMA, it follows that changes in µ reflect changes in the PMMA modulus. The friction coefficient for the 35 nm films is significantly higher with epoxy substrates than with silicon substrates. However, the friction coefficient on thicker epoxy supported films reaches the low value found on the thin, 35 nm silicon supported film, appearing substrate independent. The friction gradient suggests leaching of LMCs from the epoxy into the PMMA, illustrated in Fig. 15.15, essentially softens, or plasticizes, the film and reduces the PMMA modulus. The extent of the softening, and modulus depression, is proportional to the concentration of LMCs (CLMC ) at the surface, which in turn, is a function of film thickness, δ. At a thickness of 100 nm, the friction coefficient matches that of the 35 nm Silicon supported PMMA, indicating no detectable plasticization, or LMCs, at the surface. This interdiffusion across interfaces highlights the importance of substrate chemistry for thin film applications. In this case, a 100 nm thick boundary layer is rheologically modified due to the plasticization effects of interdiffused low molecular weight components. 15.5.2 Dewetting Kinetics In the prior discussion, chemical transport processes are responsible for rheological modifications. The impact associated with physical and dimensional constraints is perhaps, less intuitive. Nevertheless, various groups have reported bulkdeviating structural and dynamic properties for polymers at interfaces [13, 90–93]. For example, reduced molecular mobility in ultrathin PS films was reported based on forward recoil spectroscopy measurements [13]. The contribution of the substrate to rheological modifications becomes apparent in dewetting studies with binary films of PS on polyethylene-co-propylene (PEP), which are supported on silicon substrates (high interaction surface) [90]. The dewetting kinetics in Fig. 15.16 were determined from a time-series of SPM topography

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images, and reveal a critical PEP film thickness, δCRIT , below which the dewetting velocity (Vd ) decreases with decreasing film thickness, and above which Vd remains constant. Independent FFM measurements on silicon supported PEP films also indicate a critical film thickness, δCRIT , below which the friction decreases with decreasing film thickness, and above which it remains constant. In both studies, the critical PEP film thickness in Fig. 15.16 corresponds to approximately 100 nm. The dewetting kinetics and friction forces both suggest the presence of a rheologically modified PEP boundary adjacent to the silicon interface. For δPEP < δCRIT , the decreasing friction represents an increase in the PEP modulus. This translates to an increasing glass-like behavior, or loss of mobility, as the silicon interface is approached through the PEP phase. It is this loss of PEP mobility that is responsible for decreasing the dewetting velocity. To identify the source of this rheological gradient, the PEP-Silicon interactions were effectively masked by first spin casting a low interaction foundation layer of poly(vinyl pyridine) (PVP) on the silicon. The dewetting velocity of the PS/PEP/PVP film is reported as the solid circle in Fig. 15.16 and remained constant, even at PEP film thicknesses below δCRIT . This anomalous finding unveils the high interfacial interactions between PEP and silicon as responsible for the apparent PEP vitrification inside the interfacial boundary.

Fig. 15.16. Dewetting velocity (vd ) and friction (FF ) measurements on PS/PEP systems reveal a 100 nm interfacial boundary layer. Data from [90]

15.5.3 Disentanglement Barriers The current picture of the rheological boundary attributes its formation to interfacial constraints on the molecular mobility. In the past, interfacial effects were considered

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to be confined to the pinning regime, typically on the order of a few nanometers. However, FFM disentanglement studies on PEP films [94] and NMR tracer diffusion measurements in PS [92] have revealed that the interfacial boundary may extend up to 10 radii of gyration (RG ) beyond the interface. Simple surface pinning alone has been ruled out since, at this distance, the probability of a polymer molecule making direct surface contact is nearly zero. FFM friction measurements on silicon supported PEP films (RG = 24 nm) offer insight into the source of these far-field molecular constraints. A transition in the friction coefficient at a critical load (P) is seen in Fig. 15.17. The higher friction coefficient below the critical load P portrays a dissipative behavior consistent with viscous plowing through an entangled PEP melt. At loads exceeding P, the reduced friction coefficient represents a chain slipping phenomenon similar to a shear banding behavior. Thus, the critical load may be conceptualized as an effective activation barrier for disentanglement [94]. The boundary layer thickness and information about the conformational structure within the boundary are elucidated from the film thickness dependence of P based on a three-step scenario: The absence of the disentanglement transition (P) in the 20 nm films and the ubiquitous low friction, chain slipping suggest that the PEP molecules are highly disentangled within a sublayer immediately adjacent to the substrate. (ii) In the 75–230 nm films, the disentanglement transition (P) increases linearly with film thickness until the bulk P is reached. The sub-bulk P values indicate an intermediate regime of partial disentanglement, the extent of which diminishes with increasing film thickness until the bulk entanglement density is recovered. This far-field disentanglement (∼ 10RG from the substrate) is attributed to the strain imposed during spin casting. The preservation of the di(i)

Fig. 15.17. FFM measurements on PEP films reveal a critical load (P) marking a transition from viscous shearing to chain sliding. Data are from reference [94]

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sentangled structure in the melt reflects an anisotropic diffusion process, where partially disentangled chain ends diffuse into the more porous structure [92] of a sublayer [94]. (iii) Finally, for films thicker than 230 nm, the polymer behaves like the bulk elastomer and loses any memory of the underlying silicon. The picture of rheological boundary layers now reflects a two-phase system comprised of a sublayer and an intermediate regime. The mobility constraints are ascribed to the strain imposed during spin casting, paired with interfacial interactions in the sublayer and anisotropic diffusion in the intermediate regime. 15.5.4 Interfacial Glass Transition Profiles It has been recognized that several factors are intricately responsible for the departure of Tg in ultrathin films, from the bulk value [27, 44, 45, 95–99]; e.g. the proximity of a free surface, substrate interactions, and process-induced anisotropy. Here, we address the effects of spin casting on the interfacial Tg profile of amorphous polymer films, along with the use of chemical crosslinking as a mobility control. SM-FM Tg measurements on PS films (Mw = 12 k) are presented in Fig. 15.18. For film thicknesses, δ > 200 nm, the Tg values correspond to the bulk Tg of

Fig. 15.18. (Top) film thickness, δ, dependence of Tg for PS films (Mw = 12 k) compared to the bulk Tg from Fox–Flory theory. (Bottom) rheological boundary model for the observed Tg (δ) relation (SL = sublayer). Data from [89]

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95 ◦ C [24]. A two-phase boundary layer is encountered within ∼ 200 nm of the substrate: (a) Tg values are depressed relative to the bulk in a sublayer with a thickness on the order of RG , i.e. one order of magnitude beyond the persistence length [100]; and (b) Tg values exceed the those of the bulk in the intermediate regime. This non-monotonic Tg (δ) relationship is interpreted considering two competing processes that affect the relaxation dynamics: (a) shear induced structuring and (b) interdiffusion [92, 94, 101]. Shear structuring creates an interfacial region where the spin casting shear stresses induce polymer stretching and or disentanglement (structural deformation). The second process involves the interdiffusion between the entropically cooled interfacial region and the unperturbed bulk phase. With a strong precedence for shear structuring in PS solutions [102, 103] and considering the shear stress profiles during spin casting [104], it is reasonable to propose that the effects of spin casting extend from the substrate to the boundary with the bulk phase. In this scenario, the extent of structural deformation is related to the shear stress profile during casting. Alternatively, the shear structuring may extend only through the sublayer, and interdiffusion alone may be responsible for the conformational restructuring in the intermediate regime. For this case, the molecular mobility is limited by the propagation of holes, or packets of free volume, which facilitate conformational rearrangements [105]. Spin casting films of increased molecular weight (Mw ) had the effect of shifting the Tg (δ) profiles further from the substrate, by ∼ 10 nm kDa−1 [89]. The bulk Tg is recovered at ∼ 250 nm for all films in the Mw range of (12–21 k). The influence of Mw on the internal structure of the boundary layer appears more pronounced on the sublayer thickness than on the far-field boundary of the intermediate regime. This suggests that the overall boundary thickness depends more strongly on the spin casting shear stresses than on molecular dimensions. When the molecular weight is increased by crosslinking pre-cast PS-BCB films, the Tg (δ) profiles exhibit a similar qualitative behavior before and after crosslinking [89], indicating a preservation of the rheological anisotropy after crosslinking at 250 ◦ C, ∼ 150 ◦ C above Tg . The crosslinking yields an overall Tg increase of 7 ± 3 ◦ C; however, in contrast to the Mw dependence discussed above, no spatial shift is found in the Tg (δ) profiles. Since crosslinking occurs after spin casting, the shear stresses that create the shifted Tg (δ) profiles are not present. Hence, the Tg (δ) profiles are impacted differently for each condition of increased Mw , because of the sequence of treatments. The two-phase model for rheological boundary layers has evolved to include interfacial interactions that lead to the formation of a less dense sublayer adjacent to the interface. The thickness of the sublayer is characterized, in part, by the molecular dimensions and the interaction potential at the interface. The coupled effects of shear-induced structuring during spin casting and anisotropic relaxation and transport constraints during annealing are responsible for the creation of an intermediate regime between the sublayer and bulk phase. The overall rheological boundary may extend up to two orders of magnitude beyond the polymer’s persistence length, and the molecular restructuring within the boundary is thermally stable well above Tg . Finally, the impact of mobility constraints (e.g. crosslinking) on the structure within boundary layers depends on the sequence of the film preparation process, i.e. constraints incorporated before and after casting exhibit different rheological outcomes.

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Given the technological relevance of spin casting, the effect of structural modifications in nanoscopic systems is seen with wide interest, across many disciplines. In what follows, we explore how rheological constraints are encountered in some of the mechanical operations involved with nano-electromechanical systems (NEMS).

15.6 Mechanical Operations in Nanoscopic Polymer Systems The length scales for cooperative molecular motion in Sect. 15.4 and for interfacial boundaries in Sect. 15.5 ranged from tens to roughly one hundred nanometers. Compared to structures in modern device technologies, e.g. ultrathin films and nanocomposites involving sub-100 nm dimensions, one can expect a competition between material and device length scales. We have demonstrated above, how material properties in confined geometries may be modified from their original bulk values. At this point, one must anticipate the extent to which such rheological modifications contribute to current technological challenges. Mechanical operations have traditionally been one of the most important pathways for technological evolution. Normally, the goal lays in maintaining control of some particular motion. Currently, one concern deals with the implication of finite size effects in the contact mechanics associated with nanoelectromechanical (NEMS) applications. Particularly relevant is the process of scanning probe, thermomechanical data storage [3, 106]. Thermomechanical data storage (TDS) relies on writing, reading, and erasing nanometer sized data bits in thin polymer films, offering densities up to Tb in−2 [3,106]. In essence, the TDS writing operation is a high speed (MHz), elastic-viscoplastic polymer indentation process, Fig. 15.19. The polymer storage media must be designed to achieve the narrow range of physiochemical properties necessary for: high data density, fast data rates, high durability, long shelf life, and low power consumption. The ideal polymer should be easily deformable for bit writing; however, the written bits must be stable against dewetting, thermal degradation, and wear. Each indented bit represents a metastable state of the deformed volume, and will either initiate spontaneous dewetting (film instability) or strive for recovery of the initial unstressed state (bit instability) [107]. The delicate balance between these instability nodes constitutes one optimization scenario in the design of polymeric

Fig. 15.19. Scanning probe, thermomechanical data storage: Creating uniform bit indentations in sub-100 nm thick polymer films requires an understanding of the interfacial rheology

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storage media. Furthermore, media (and data!) wear must be minimized during scanning operations. In particular, topographical protrusions, in the form of piled-up rims around the indented bits, are regions susceptible to wear. The presence of rims also adversely affects the writing density. Rims interact non-linearly with adjacent bits, lowering the signal-to-noise ratio of bit detection and requiring a relaxation of the indentation pitch (data density). From the perspectives of media wear and data density, a suitable polymer storage media exhibits a weak propensity for rim formation during indentation. In this section, we explore how the material modifications associated with dimensional constraints make themselves apparent during nano-contacting operations. We investigate strain shielding at the substrate interface, and its implications on rim formation, during high strain-rate indentations in thin polystyrene films. Further, the role of material anisotropy in the distribution of indentation loads will be elucidated with the interfacial Tg profiles from Sect. 15.5. First, let us commence with a theoretical background for the contact mechanics associated with the isotropic bulk-material case. 15.6.1 Indentation Contact Mechanics During normal indentation of an elastic-plastic material, when the yield point of the more ductile material is first exceeded, the onset of plastic (anelastic) deformation commences. Initially, the plastic region is small and completely contained by the surrounding elastic material. Hence, the plastic strains are of the same order of magnitude as the surrounding elastic strains. The plastically displaced material is fully accommodated by elastic expansion of the surrounding solid. This is referred to as confined deformation because the flowing or plastically deforming volume is fully constrained by the surrounding elastic medium. As the applied strain is increased with an enlarged load or sharper indenter, a greater pressure beneath the tip is required to produce the necessary expansion. Eventually, sufficient pressure is achieved where the plastic region reaches the free surface, allowing the displaced material to escape via unconfined plastic flow along the sides of the indenter. The onset of plastic yield, or confined deformation, is assessed by applying an appropriate yield criterion. The two most commonly applied criteria are the Tresca’s maximum shear stress criterion, where yielding occurs when the maximum shear stress, or half the difference between the maximum and minimum principle stresses, reaches the yield stress in pure shear or half the yield stress in simple compression (or tension) [38]:   1 1 Y 1 |σ1 − σ2 | , |σ2 − σ3 | , |σ3 − σ1 | = k = , (15.44) max 2 2 2 2 and the von Mises’ shear strain-energy criterion, where yielding occurs once the deformation energy equals the deformation energy at yield in simple compression or pure shear [108]. Therefore, by the von Mises criterion, yielding occurs when the square root of the second invariant, √ J2 , of the stress deviator tensor, Sij , reaches the yield stress in simple shear or 1/ 3 of the yield stress in simple compression:

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 J2 =

1 Sij 2



1/2 =

117

 1/2 1 (σ1 − σ2 )2 + (σ2 − σ3 )2 + (σ3 − σ1 )2 6

Y =k= √ , 3

(15.45)

where σ1 , σ2 , and σ3 are the principle stresses in the state of complex stress, and k and Y represent the yield stresses in pure shear and simple compression (or tension), respectively. For detailed analysis of the state of complex stress and formulation of the yield criteria, the reader is referred to [109]. Experiments on isotropic metals support the von Mises criterion over Tresca’s; however, the discrepancy between the two is relatively small considering the variability in k or Y and the inherent anisotropies in most materials [38]. Therefore, it is generally acceptable to apply Tresca’s criterion for its mathematical simplicity. Relating the stresses from the yield criteria to the mean contact pressure under the indenter, pm = cY ,

(15.46)

where, for the onset of constrained plastic yield, c has a value of about 0.5 for conical indenters, and may vary depending on the indenter geometry and the friction at the interface [38]. The onset of unconfined plastic flow, i.e. the point when the plastic yield zone reaches the free surface, is expected to occur when the contact pressure reaches the yield stress given by rigid-plastic theory. Based on a number of numerical analyses and indentation measurements with rigid spheres and cones in elastic–plastic halfspaces, Johnson [38] determined a value of c ∼ 2.8 in (15.46). In the transitional regime, when the contact pressure lies between 0.5 ∼ 3Y , plastic flow is contained by the surrounding elastic material. The resulting deformation is generally in the form of radial expansion with roughly hemispherical contours of equal strain [38]. Based on these observations, Johnson [110] developed a simple cavity model of elastic-plastic indentation, Fig. 15.20. The cavity model assumes that directly beneath the indenter contact surface, a hemispherical core with a radius equal to that of the projected contact area, a, has a hydrostatic stress component equal to the mean contact pressure, pm . Immediately beyond the core lies the plastic zone, and at the core-plastic boundary, the radial stress component in the plastic zone equals the hydrostatic stress of the core. Within the plastic zone, stresses and displacements have radial symmetry, and the plastic strains gradually diminish with increasing radial distance, until they match the elastic strains at the elastic–plastic boundary, c (c > a). Based on Hill [109], the stresses in the plastic zone, a ≤ r ≤ c, are characterized by: c 2 c 1 σθ σr = −2 ln − , = −2 ln + , (15.47) Y r 3 Y r 3 and in the elastic zone, where r ≥ c 2  c 3 1  c 3 σθ σr =− = , . Y 3 r Y 3 r

(15.48)

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Fig. 15.20. Cavity model of elastic-plastic indentation by a rigid cone. The mean contact pressure, pm , directly beneath the contact is supported by a hydrostatic core with radius a. Beyond the core, unconstrained plastic deformation extends through the hemisphere where the pressure exceeds the yield stress by roughly three-fold [38]. The plastic front with radius c is preceded by elastic strain that accommodates pressures insufficient of producing yield

At the core-plastic boundary, the core pressure is given by:  σ  c 2 pm r  = − + . = 2 ln  Y a r=a a 3

(15.49)

Equation (15.51) implies that the elastic-plastic boundary coincides with the coreplastic boundary, c = a, at pm = 2/3Y , and at reduced pressures, no plastic flow occurs. Therefore, the cavity model predicts that the onset of plastic yield occurs at pm = 2/3Y , which is close to the value of c ∼ 0.5 reported by Johnson [110]. The difference is attributed to β and friction at the interface. Radial displacement of matter at the core-plastic boundary, r = a, during an increment of penetration, dh, must accommodate the volume of material displaced by the indenter. Neglecting core compressibility, conservation of core volume requires: 2πa2 du(a) = πa2 dh = πa2 tan(β)da . The radial displacements within the plastic zone are given by [109]:   c 2  r  du (r) Y = 3 (1 − ν) . − 2 (1 − 2ν) dc E r c

(15.50)

(15.51)

Equations (15.50) and (15.51) are used to locate the elastic-plastic boundary, c, recognizing that for a conical indenter, geometrical similarity of the strain field with continued penetration requires dc/da = c/a = constant:    c 3 E tan β 1 + 4(1 − 2ν) . (15.52) = a 6(1 − ν) Y

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The core pressure is determined via substituting c/a into (15.48), and for an incompressible material, i.e. ν = 0.5:    pm 2 1 E tan β = 1 + ln . (15.53) Y 3 3 Y The hydrostatic core pressure appears to be solely dependent on the parameter (E/Y ) tan β, which represents the ratio of the strain imposed by the indenter (tan β) to the strain capacity of the indented material (Y/E). Generally, the indentation pressure under elastic, elastic-plastic, and fully plastic conditions is correlated as dimensionless contact pressure, Pm /Y , versus dimensionless strain, (E/Y ) tan β. The above analysis was limited to elastic-perfectly plastic materials with a constant yield stress. Tabor has shown that the perfectly plastic analysis may be applied, with good approximation, to materials that strain harden according to the power law relation:  YR = σo

εR εo

 n1

,

(15.54)

if Y in (15.53) is replaced by a representative flow stress YR measured at a representative strain εR , [111]. In (15.54), n is the reciprocal of the work hardening index, and σo is the work hardening coefficient. For a conical indenter, the representative strain is approximated by [38]: εR ≈ 0.2 tan β .

(15.55)

The scenario is somewhat more complicated for the case of viscoelastic plastic indentation. Many materials, notably polymers, exhibit viscoelastic behavior, which is characterized by a time and temperature dependent stress-strain relationship. The issue becomes one of determining the time-dependence of the contact area and pressure distribution, which result from a prescribed loading. In cases where the corresponding solution for a purely elastic material is known, the simplest approach to this problem, based on Radok, consists of replacing the elastic constant with the corresponding integral operator from the viscoelastic stress-strain relations, i.e. the creep compliance or relaxation functions [38]. In the general isotropic case, (E/Y ) tan β captures the essence of the mechanics, hence is referred to as the rheological factor X. With interfacial systems, where finite size effects may lead to material anisotropy, one has to be additionally concerned with the direction of the rheological gradients. We will show in Sect. 17.3.2 that the material response to indentation is distributed between two mechanical scenarios depending on the direction of the interfacial modulus and Tg gradients. However, let us revisit the TDS recording process, and describe the outcome of the indentation process, i.e. a material’s propensity to form piled-up rims (or to sink in), in terms of the rheological factor X.

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15.6.2 Rim Formation During Indentation During indentation of a rigid plastic solid, the displaced material appears in the piledup rim around the periphery of the indentation site. With elastic-plastic materials, some, if not all, of the displaced material is accommodated by radial expansion of the elastic surroundings. Briscoe et al. found that for indentation and scratch hardnesses studies of PMMA, the measured yield stress is strongly dependent on both the indenter geometry (related to strain) and applied strain rate. During normal indentation with conical indentors of large excluded angles (β = 75◦ ), PMMA deforms by extrusion to the free surface with the creation of a piled-up rim. With blunter cones, i.e. lower β, deformation occurred elasto-plastically resulting in little or no pile-up [112]. In nano-scratch studies on PMMA, Adams et al. demonstrated that the height of the pile-up will increase with tan β [113]. In a similar study on polycarbonate, Jardret et al. observed distinctly different pile-up formations on nanoscratch samples of identical hardness. The difference in pile-up height is attributed to the strain, with increased rim heights for larger strains, i.e. larger tan β [114]. With a 2D finite element approach, Ramond-Angélélis modeled piled-up rim formation in viscoelastic-perfectly plastic materials as a function of the rheological factor X. These results are reproduced in Fig. 15.21 and suggest that for values of X
10, the deformation during indentation is mainly elastic with little pile-up, and that for X  100, the deformation is primarily plastic resulting in substantial pile-up [115]. Pile-up formation in viscoelastic materials is also dependent on the strain rate. At high strain rates, PMMA displays a noticeable strain softening behavior that becomes more pronounced with increasingly higher strain rates and is absent at reduced strain rates (
10−5 s−1 ) [112]. Consequently, the yield stress decreases with increased strain rate, and is accompanied by the appearance of shear bands, which have been attributed to the onset of pile-up [116, 117]. The effect of a high strain rate at large strains, i.e. high tan β, may also induce adiabatic heating within the shear bands, which would promote large inhomogeneous strains, as well as

Fig. 15.21. Crosssectional view of elastoplastic indentation under load and after unloading for a rheological factor, X, ranging from 1– 1000. Results obtained by Ramond-Angélélis with a 2D finite element model [115]

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enhanced strain softening [112]. On the other hand, strain hardening tendencies also affect pile-up. A large capacity for strain hardening advances the plastic zone further into the material, thus decreasing pile-up adjacent to the indenter [118]. For an elastic-plastic material that strain hardens according the power law in (15.56), Matthews proposed the indenter penetration depth, h, as follows [118]:   1 2n + 1 2(n−1) ζ − 1, (15.56) = h 2 2n where ζ represents the vertical dimension with respect to the neutral surface of a piled-up rim, or sunken depression, at the periphery of the indentation, Fig. 15.22. For a conical indenter: h+ζ ∼ = a tan β . Combined with (15.56), the indentation depth becomes: 2(n−1)  2n a tan β h=2 2n + 1

(15.57)

(15.58)

For h/(a tan β p) > x (i.e. n < 3.8), a sunken depression is formed, and when n exceeds 3.8, h/(a tan β p) < x and a piled-up rim is formed. In viscoelastic materials, such as polymers, strain hardening should not be ignored. The pile-up formed during the nano-scratch studies on PMMA revealed a maximum hardness value at the rim apex, which decayed asymptotically to the hardness of the unperturbed film with increasing distance from the indentation site [113]. Both the rim height and the extent of strain hardening increased with the applied strain, i.e. tan β [113]. In addition, Adams et al. observed that the hardened pile-up of an existing scratch reduces the depth of a subsequent parallel scratch within the strain hardened area. This is important in the context of thermomechanical data storage where ultra high storage densities are sought by minimizing the pitch of indented data-bits. A tight indentation pitch with overlapping strain hardened zones would likely result in non-uniform indentation depths, sacrificing the signal to noise ratio during bit detection.

Fig. 15.22. Peripheral deformation for opposing extremes of stress sensitivity. Sunken depressions versus piled-up rims for materials that exhibit strong versus weak strain hardening susceptibilities, respectively

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15.6.3 Strain Shielding and Confined Plasticity in Nanoscopic Polymer Systems Our discussion thus far has been limited to indentations in bulk materials. The formation of piled-up rims has been attributed to the strain, strain capacity, strain rate, and strain hardening susceptibility of the material. In confined systems, a rigid boundary interacting with the stress field during indentation (bit writing) may alter the stress and strain distributions, leading to bulk-deviating mechanical responses [119–122]. For indentations in compliant films, increased rim heights are observed when elastic strain and plastic flow are constrained, or shielded, by a rigid substrate [119–122]. In the case of rigid films on compliant substrates, the plastic yield of the underlying substrate accommodates an enhanced sink-in of the surface around indentation sites [120]. For interfacial systems like TDS, one would expect the material response to scale with any internal rheological gradients (Sect. 15.5.4), in addition to the contribution from the underlying substrate. The combined influence of rigid dimensional constraints and material anisotropy during indentation has been addressed with high-rate, SPM indentation studies typical of the TDS process [123], and is discussed in the following two sections. A representetive indentation is pictured in Fig. 15.23.

Fig. 15.23. SPM image and geometric evaluation of a residual indentation in polystyrene (Rim height, ζ indentation depth, h; rim diameter, DR ; and indentation diameter, Di )

15.6.3.1 Substrate Constraints in Thin Film Operations For indentation mechanics in confined systems, the rim height ζ is influenced by both process conditions (e.g. normal force, FN ) and geometric conditions (e.g. film thickness). Hence, it is natural that the rim height scales with the indentation depth, i.e. h(FN ), and that substrate constraints are best assessed with respect to the ratio of the rim height to the indent depth, ζ/h. In Fig. 15.24, the load normalized height to depth ratios, ζ/h = (∂ζ/∂FN )(∂h/∂FN )−1 , are reported for indentations in thin polystyrene films (Mw = 12 k). For film thicknesses, δ, exceeding ∼ 100 nm, the

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Fig. 15.24. Strain shielding at the substrate interface is evident in the load normalized ratio of rim height to indentation depth (ζ/h). For PS on a rigid silicon substrate, rim heights are enhanced for films thinner than 100 nm; a compliant PS-BCB buffer masks the substrate constraints

ζ/h ratio displays a constant value of approximately 0.2, which reflects the bulk material response. For film thicknesses below 100 nm, the rim height increases with decreasing film thickness. This behavior depends on the substrate material. The rim enhancements were effectively masked by adding a compliant 230 nm thick crosslinked buffer film (PS-BCB) between the rigid substrate and the indented PS film. Substrate effects during quasi-static indentations, such as enhanced rim heights because of strain shielding, are well-known for indentation depths exceeding 10 to 30% of the film thickness [119–122]. However, the substrate effects in Fig. 15.24 were observed for residual indent depths significantly less than 10% of the film thickness. Elastic recovery on unloading may be ruled out [123] based on a quasistatic rheological factor of X = 38, which exceeds the critical value (∼ 30) for fully plastic deformation [38]. Moreover, for X = 38, the elastic-plastic simulations of Ramond-Angélélis in Fig. 15.21 indicate a uniform elastic recovery of roughly 10% in both the indent depth and diameter [115]. The seemingly far field effects are attributed to the high strain rates (2 × 103 to 1 × 104 s−1 ) [123]. These rates exceed those of classical quasi-static indentation, and fall within the range of impact dynamics [124]. The main difficulty with nano-impact studies is that the inertial and strain-rate effects are usually coupled [125]. The characteristics of wave propagation inevitably depend on the strain-rate dependence of the material properties. At strain rates of 103 –104 s−1 , polystyrene succumbs to viscoplastic flow at a nearly constant flow stress of ∼ 20 MPa [126]. This suggests that the propagation speed of a plastic stress wave, cp (σ) = (1/ρo ∂σ/∂ε)1/2 [124], approaches zero above the flow stress. ρo is the density of the unloaded material, and ∂σ/∂ε is the slope of the stress-strain curve at a given strain and strain rate. Thus, any plastic stress waves generated in the polymer films are likely to attenuate rapidly [124]

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(exponentially [127]) as they propagate from the impact site. Consequently, the energy carried by the pressure pulse is dissipated through the plastic deformation processes [127]. Now, let us consider the nature of these plastic deformations, along with any associated interference from the rigid substrate. Based on the indentation cavity model in Fig. 15.20, it is reasonable to assume that the plastically deformed volume is hemispherical with a radius, c, equal to one half of the rim diameter, DR , in Fig. 15.23 [38, 122]. Thus, the rim diameter (radius) approximates the penetration depth of plastic deformation. In this case, the appropriate scaling parameter is the ratio of the depth of plastic deformation to the film thickness, c/δ. Under this formalism, the rim heights (ζ/h) are revisited in Fig. 15.25 as a function of c/δ. A sudden increase in the rim height is found when the plastic radius exceeds ∼ 65% of the film thickness. The rim enhancement results from elastic strain shielding at the rigid substrate, i.e. the material can no longer accommodate strain by elastic expansion in the −z-direction. The ζ/h ratio levels off once the plastic deformation zone comes into direct contact with the rigid substrate. The origin of the plateau at c/δ > 1 is not entirely clear, but may arise from geometric changes of the plastic domain boundary (spherical to cylindrical) or from an increasing hydrostatic interaction with the substrate. Again, strain shielding was effectively masked in systems with a PS-BCB buffer film on the silicon substrate, even for plastic zone radii in excess of the film thickness. This suggests that, relative to silicon, the modulus and yield stress of the crosslinked PS-BCB are sufficiently similar to the PS homopolymer to promote a more effective stress distribution across the interface. This can be referred to as a modulus-matched interface. In the absence of modulusmatching, shear stresses will concentrate at the interface [128], potentially activating dewetting instabilities and compromising film stability.

Fig. 15.25. Substrate contribution to strain shielding in thin polystyrene films (ζ is the rim height, h is the indentation depth, c is the plastic (rim) radius, and δ is the film thickness; dotted lines are guides)

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15.6.3.2 Structural Anisotropy near Interfaces To this point, the competition between material driven length scales and system dimensions emerges with strain shielding at the rigid substrate. Now, let us consider the influence of structural anisotropy in the vicinity of the interface. This discussion is motivated by the findings in Sect. 15.5.4, which suggest strain and diffusion induced restructuring over a length scale on the order of 100 nm. The nature of the interfacial Tg profiles in Fig. 15.18 reveals a non-monotonic gradient in the thermomechanical properties. That is, along with the Tg , the modulus should be expected to follow a similar trend, with a bulk exceeding maximum at approximately 60 nm from the interface. Beyond this point, the modulus should decrease asymptotically to the bulk value, at roughly 150–200 nm from the substrate. An effective modulus may be deduced from the residual indentation geometry by considering the ratio of pm / tan β, where the mean contact pressure pm represents the applied stress, and tan β is the residual strain. The pressure pm is defined as FN /πa2 , where a is the contact radius (taken as 1/2 the distance between the rim apices in Fig. 15.23). The resulting modulus gradient with respect to the film thickness is pictured in Fig. 15.26 together with the interfacial Tg profile for the same material (Fig. 15.18). Significant similarities exist between the modulus and Tg profiles in Fig. 15.26. Viewing the glass transition as a mobility barrier, an increase in Tg offers resistance to molecular mobility, and the associated rigidity is accompanied by an increase in the modulus. Hence, the individual thermal and mechanical responses should be expected to coincide. The formation of these rheological gradients was discussed

Fig. 15.26. The interfacial thermal and mechanical response profiles for thin polystyrene films are consistent with the rheological boundary layer model in Sect. 15.5. The modulus data were determined from indentations with applied loads ranging between 170–190 nN, and the Tg data are from Fig. 15.18. The dotted line is drawn as a guide

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in Sect. 15.5, and is attributed to shear induced structuring during the spin casting process and to anisotropic diffusion during annealing. The shape of the thermomechanical profile in Fig. 15.26 implies: for films thicker than 150 nm, the material responds like the bulk; for film thicknesses between 60–120 nm the surface is more compliant than the immediate sub-surface; and for film thicknesses below ∼ 60 nm, the surface is more rigid than the immediate sub-surface. Under these conditions, the indentation pressures are distributed between two asymptotic limits: (i) a compliant surface with a rigid sub-surface and (ii) a rigid surface with a compliant sub-surface. For the latter case of a more compliant sub-surface, one would expect a negative rim height, or enhanced sink-in effect. [120] However, it appears that inertial confinement at the rigid substrate counterbalances any sink-in tendencies associated with material anisotropy. Beyond the immediate implications in thermomechanical storage, our discussion sheds a new light on the development of polymer thin film applications. With an understanding of how the interfacial boundary layers are formed (Sect. 15.5), and knowledge of how they influence transport operations, the ability to cater interfacial profiles for desired material behaviors offers a new spectrum of design opportunity.

15.7 Closing Remarks Recent SPM developments provide fundamental insight into mesoscopic dynamical properties that are relevant in nanotechnological applications involving thin films. Two methods have been discussed; shear modulation force microscopy (SM-FM) and friction force microscopy (FFM). The two complementary methods offer the means of tracking thermo-rheological transitions in confined geometries. SM-FM is a convenient and reliable method for determining thermally activated transition points and spatial transition profiles in anisotropic systems. A molecular analysis of the transition process is obtained with FFM. FFM investigations of the dynamics and kinetics in polymer films reveal activation energies related to molecular relaxations, and provide insight to the finite size limitations on structural relaxation near transition points. For instance, direct access to the temperature resolved length scale for cooperative motion during the glass transition is obtained. Nanotechnological thin film applications, such as the NEMS process for terabit thermomechanical storage, rely on very specific relaxation and transition properties in sub-100 nm systems. Ultimately, achieving the desired performance goals requires materials with a molecular structure that is engineered to function within the system constraints. In polymer films, when film thicknesses are reduced to the sub-100 nm scale, the structural, material, and transport properties become increasingly dominated by interfacial and dimensional constraints. Rheological boundary layers are formed at interfaces, due to shear induced structuring and anisotropic diffusion during film preparation. Rheological gradients near interfaces lead to bulkdeviating behaviors. These gradients are quantified with interfacial glass transition (Tg ) profiles, which provide a molecular structural model of the boundary and allow characterization of the constraints.

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Continued thin film optimization and development efforts focus on utilizing interfacial constraints as engineering design opportunities. On the nanoscale, precise material engineering is only possible with an understanding of the polymer dynamics near interfaces. Tailored relaxation properties and enhanced conformational stability may be achieved through control of the interfacial conditions, molecular weight, crosslinking density, and film thickness. Hence, the characterization and control of interfacial boundary layers becomes increasingly important to nanotechnological applications. In NEMS applications that involve thin polymer films, the rheological gradient in the boundary region dictates contact pressures; while the substrate itself can lead to stress and strain shielding at the interface, which compromises film stability. Modulus-matching techniques, i.e. generating a quasi-continuous modulus gradient between opposing faces, offer enhanced interfacial stress transmission and improved stability and durability of the interface. To this end, a resurgence of design methodologies is not impossible, moving from traditional scaling approaches, to a mesoscopic approach where internal rheological gradients are catered to achieve the desired performance characteristics. Acknowledgements. We would like to acknowledge Tomoko Gray from the University of Washington, Chemical Engineering Dept. for contributions to Sect. 15.4.1.

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16 Investigation of Organic Supramolecules by Scanning Probe Microscopy in Ultra-High Vacuum Laurent Nony · Enrico Gnecco · Ernst Meyer

16.1 Introduction The adsorption of medium-sized aromatic molecules on surfaces has become a subject of intensive study motivated by the prospect of hybrid molecular electronic devices [1]. The operation of such devices should be governed by the electronic properties of a single or, at most, a few of the constituent molecules. With this goal in mind, numerous groups have used scanning tunneling microscopy (STM) to study a variety of molecules adsorbed primarily on metal surfaces. Besides atomic-scale spatial resolution, STM provides the means for an “accurate placement of molecules in appropriate position and orientation to form a device” [1]. However, as discussed [1], many hurdles remain on the way towards the development and the integration of useful molecular electronic devices. In particular, it is desirable to isolate the device electrically. The extension of atomic-scale characterization and manipulation studies to surfaces of insulators is, therefore, of high interest. It is also quite challenging because STM can no longer be applied and has to be replaced by atomic force microscopy (AFM), unless one deals with ultrathin insulating films on metals as substrates. A more fundamental motivation for such studies is to understand the delicate balance between intermolecular and molecule-substrate interactions that determines the mobility and aggregation of molecules as well as their eventual ordering on ionic substrates. This chapter is a review of STM and AFM investigations of molecules down to single molecules on metals, semiconductors and insulators, including ultrathin insulating films on metals. The review was restricted to aromatic molecules with intermediate size, e.g. consisting of up to about 100 atoms. Molecules used to form self-assembled monolayers such as silanes or thiols are not reviewed. The theoretical analysis of the mechanisms leading to molecular assembling, as well as practical applications, like nanomotors, are not discussed neither. Investigating molecules down to a single specimen requires a very clean environment, particularly for objects with typical dimensions of about 1 nm. Therefore, the review is focused on investigations performed under ultra-high vacuum (UHV) conditions, either at room temperature or at low temperature. Molecules with biological relevance (DNA, proteins, . . .), the analysis of which usually requires the use of liquid environment, are excluded.

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The first STM investigations of fullerenes on metals and semiconductors were early review by Sakurai et al. [2]. More complex organic molecules on metals were more recently reviewed by Barlow et al. [3] and Rosei et al. [4]. Compared to STM, there are much fewer single molecule studies by AFM available. A potential reason is that the technique is more demanding and usually requires the use of non-contact-AFM (nc-AFM) in UHV. Alternatively, tapping mode can be used. However, for technical reasons, which are discussed in the following section, this mode is restricted to operate under atmospheric conditions. This prevents single molecule investigations from being carried out. The chapter is organized as follows. Section 16.2 introduces the concepts of organic molecular beam epitaxy (OMBE), STM and dynamic AFM methods. Section 16.3 gives a survey of the most commonly used molecules for STM and nc-AFM investigations in UHV. From Sects. 16.4 to 16.6, we have reviewed STM and nc-AFM investigations of molecules on metals, semi-conductors and insulators, respectively. Finally, Sect. 16.7 reviews important works dealing with molecular manipulation, which up to now have been restricted to STM and usually at low temperature.

16.2 Methods 16.2.1 Organic Molecular Beam Epitaxy (OMBE) This section introduces the concept of OMBE. Detailed information can be found, for instance, in the review by Hooks et al. [5]. MBE is a widely-used method, initially targeted at semiconductors industry, for growing layered materials on surfaces with great precision and purity. Each layer of the multi-layered compounds consists of ultra-pure elements, delivered to the surface as a beam of gas. Atoms or molecules of the gas deposit on the substrate to form the growing layer. The technique offers tremendous control of the layer thickness. The growth rate can be sufficiently slow that layers only a few atoms thick can be produced reliably. Thicker layers are obtained with longer deposition times. The cleanness of the substrates for atomic-scale control of the deposited layer requires MBE to be performed at low pressures, usually within UHV chambers, e.g. at pressures of about or lower than 10−10 mbar. The bulk materials to be deposited (metals, molecules. . .) are placed within effusion cells, so-called Knudsen-cells (K-cells). A simple effusion cell consists of an open crucible, surrounded by a heater filament, usually tungsten, or tantalum. The crucible can consist of metal, usually tantalum, or of ceramic, usually pyrolytic Boron Nitride. The assembly is housed in a metal cell with several layers of tantalum foil heat shielding to improve the cell’s heating efficiency and reduce the heat load on the surrounding chamber. A water-cooling circuit along the shielding lowers the heat load as well. The cell is mounted on a vacuum flange with feedthroughs for power and thermocouple connections. Prior to deposit, the bulk material is slowly degassed

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of its contaminants (water, solvents, . . .). The material can then be sublimed as soon as the temperature of the crucible overcomes the sublimation temperature at the chamber pressure. The beam intensity or flux is controlled by the temperature. The thermocouple in contact with the crucible provides an accurate temperature reading. This signal provides feedback to the proportional-integral temperature controller for a precise temperature regulation, a key point for precise and reproducible MBE growth. A shutter located at the output of the K-cell provides an “on-off” control of the flux. The substrate to which the materials are deposited is spatially located in front of the beam and can be heated upon requirement. When the materials are deposited, the substrate is transferred under UHV conditions for analysis. The deposition rates vary from one application to another. For organic mole˚ per minute are typically used. Therefore, a mono-layer cules, rates of a few A is typically deposited within a couple of minutes. However, for single molecule analysis, it is required to deposit only a few molecules. This is achieved by depositing fractions of molecular monolayers. This is why this mode is often referred to as the sub-monolayer regime. The MBE growth can be monitored in real-time using a reflective high energy electron diffraction (RHEED) system. The system includes an electron gun, which directs an electron beam towards the substrate at a shallow angle (1–2◦ ). A phosphor screen detects the diffracted beam. As the substrate surface changes, so does the pattern detected at the screen. RHEED monitors surface structure and smoothness, and measures growth rates. Alternatively, quartz-balance thickness monitors (QBTM) and/or mass spectrometers can be used. QBTM include a piezoelectric quartz, which is excited and vibrates in its eigenfrequency (5 MHz or 7 MHz upon model). The adsorption of gas atoms changes its mass, resulting in a drop of the frequency that is monitored as a function of time. The drawback of the technique, despite being accurate down to rates of a few ˚ per minute, is the calibration of the frequency changes. When depofractions of A siting materials, the crystalline properties of which are well-known, the calibration is straightforward. However, when depositing molecules, for which no crystal structure is available, the calibration is trickier. The control of the amount of material deposited is then more empirical and has to be cross-checked with STM or AFM images. An overall drawback of the MBE technique applied to organic molecules is that molecules can decompose due to the excess of heat. In such a case, the molecules do not deposit intact on the surface. This problem is particularly critical for medium-sized molecules which are known to be difficult to sublime. Consequently, alternative techniques are being developed like electro-spray deposition. However, on the contrary to K-cells, electro-sprays are not yet a standard. The technique requires a complex and specific setup for UHV-compliance. The emergence of scanning probes techniques in the early 80’s opened the way to investigations of surface phenomena of MBE-prepared samples. In parallel, the emergence of molecular films as candidates for functional electronic materials triggered numerous investigations, initially by STM. These works naturally led in the early 90’s to more detailed STM investigations, down to single molecules, among which organic molecules (cf. the following sections for references). For the latter, MBE turned into OMBE.

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16.2.2 Scanning Tunneling Microscopy (STM) The scanning tunneling microscope was invented by Binnig and Rohrer in 1982 [6] who were awarded the Nobel Prize for it (1986). One year later, the atomic resolution of the 7 × 7 reconstruction of the Si(111) surface [7] sealed the advent of the technique which began to spread out in laboratories all over the world. The work by Binnig and Rohrer opened the field of real-space microscopy, thus opening the door to nanoscience and nanotechnology. This section briefly introduces the STM technique. For details, cf., for instance, [8–17]. 16.2.2.1 Overall Functioning In STM, piezoelectric transducers bring a sharp metallic tip down to a distance of ˚ with a metallic sample (Fig. 16.1). The wave functions of the electrons a few A of both electrodes (the tip and the surface) overlap. A bias voltage (Ubias ) applied between the sample and the tip causes electrons to tunnel from (to) the tip to (from) the surface upon the sign of the bias. The resulting tunneling current It can range from a fraction of pA to a few nA upon the materials, distance and bias. The tunneling current is amplified with a preamplifier, usually located close to the tip, which increases the signal to noise ratio. The preamplifier is a current-tovoltage converter (I–V converter) with high impedance (∼ 100 MΩ). Its design, as well as the choice of components, is crucial for a good sensitivity of the apparatus. The converter output is digitalized with an analog to digital converter (AD converter) and sent to a feedback loop. The loop is designed to keep constant a preset value of It , referred to as setpoint current Itset , during (x, y) scanning. The feedback loop consists

Fig. 16.1. Sketch of an STM. A sharp metallic tip is in close proximity to a metallic sample. The bias voltage applied between the two electrodes causes a tunneling current to flow between them. The dependence of the current as a function of the distance between electrodes provides high spatial resolution

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in a proportional-integral controller. The output is the z channel controlling the displacements of the piezoelectric transducer in the z direction, e.g. perpendicularly to the (x, y) scanning plane. Since piezoelectric materials require high voltages (∼ 250 V), the x, y and z signals, after proper analog conversion (DA converter), are amplified with a high voltage stage (HV converter). The proportional and integral gains of the feedback loop, K P and K I , respectively, have to be judiciously chosen to make the z-piezo as reactive as possible while preserving and overall stable behavior while scanning. Thus, while scanning, the tip is moved forwards or backwards such that It remains constant and equal to Itset . This operation mode is referred to as the “constant current mode”. Obviously, the larger It , the closer to the surface the tip. 16.2.2.2 A Short Theory of Tunneling Current According to quantum mechanics, a particle with an energy E = eUbias (−|e| being the elementary electron charge) can√penetrate the classically forbidden potential barrier Φ > E over a length ∼
/ 2m(Φ − E). When Ubias is small compared to the barrier height, the tunneling barrier is roughly rectangular (Fig. 16.2) and electrons can tunnel through it. It then strongly depends on the vacuum gap between the tip and the sample. It has been calculated by taking into account the local density of states (LDOS) of the sample close to the Fermi level, ρS (E F ):

√ √ 2mΦz (16.1) ≈ Ubias ρS (E F ) e−1.025 Φz . It ≈ Ubias ρS (E F ) exp −2


Fig. 16.2. Energy diagram of an idealized tunneling gap in STM. If the tip is positively biased (compared to the sample potential at 0 V) as sketched here, the electrons tunnel from the sample surface at the Fermi level to the tip. This is also referred to as “imaging the filled states” of the sample, by opposition to its “empty states” wherein Pauli’s principle allows the tip electrons to tunnel when the tip is negatively biased

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In this formula, Φ is the work function of the sample, e.g. the barrier “height”, m the electron mass and
Planck’s constant. For metals, Φ ≈ 4 eV, therefore, ˚ the current drops by an order of magnitude. This when z is increased by 1 A, strong distance dependence is the foundation for the atomic resolution capability of STM. For more references regarding the theoretical description of the tunneling process, cf. for instance the works by Bardeen [18], Tersoff and Hamann [19, 20], Baratoff [21], and Chen [22]. 16.2.2.3 Instrumental Aspects Achieving atomic resolution with an STM requires the mechanical vibrations between tip and sample to be smaller than the atomic corrugation. This condition is met by a microscope design, e.g. tip holder, sample holder and actuators, insuring the utmost stability and proper vibration isolation, for instance, by means of springs, table with air-damped feet, . . . These points have been described in detail in [11] and [12]. Note also that an interesting discussion about noise and its consequences in STM is given by Giessibl in the second chapter of [23]. Regarding the tips, for STM experiments in air, they are often made of platinum– iridium PtIr, because the material does not oxidize easily and the Ir makes the alloy harder compared to pure Pt. PtIr tips are usually shaped by cutting a PtIr wire with a wire cutter. For UHV applications however, tungsten (W) is preferred because it is harder. The tip preparation is then more demanding. A popular method consists in carefully electrochemically etching the W wire into a KOH or NaOH solution. Many factors, among which the moment when the chemical etching must be stopped, have to be controlled accurately to get atomically sharp tips. However, the authors usually agree on the point that no method leads to reliable sharp tips. Nevertheless, each experimenter has his own “preparation recipes” that are usually jealously kept secret. 16.2.2.4 Beyond the “Constant Current” Mode For certain applications, in particular manipulation (cf. Sect. 16.7) it is useful to turn off the feedback loop. Then the tip scans the surface at constant height, provided that the z-drift is weak enough to be negligible. This is readily achieved at low temperatures, for which the results are the most numerous. This mode is referred to as the “constant height mode”. Finally, beyond its ability to produce images of surfaces with a metallic character on the atomic scale, STM can as well be applied to determine physical parameters of the surfaces, such as barrier heights or LDOS. These experiments are referred to as “spectroscopic modes”. One externally adjustable parameter such as the bias voltage or the z-distance, is varied while an experimentally available property is measured, for instance the current I(V) or I(z), or its derivatives, d ln(It )/dV ∝ LDOS, or d ln(It )/dz ∝ Φ.

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16.2.3 Atomic Force Microscopy (AFM) A couple of years after the advent of STM, Binnig and coworkers [24] invented the atomic force microscope. At this time, the technique was found as a complementary tool to STM by extending its unique imaging capabilities to insulating surfaces. Out of this, AFM has continuously been developed, improved and used in a tremendous number of research fields, from fundamental research to industry and from fundamental physics to chemistry, biology, . . .. Searching the key word “AFM” in the INSPEC database gives, for instance, about 16,000 entries vs. 12,200 (only!) for STM. An historical review of AFM can be found in the first chapter of the book by Morita et al. [23]. A lot of prerequisites for understanding this section can be found in the books by Meyer [16], Morita [23] and Bhushan [17], wherein we particularly recommend part B, § 11 to 15. Let us finally recall that we here only focus on the AFM dynamic modes which are the most relevant for single molecules investigations. Therefore, the contact mode where the tip is constantly in contact with the surface is not introduced. 16.2.3.1 General Considerations The concept of atomic force microscopy is based on the measurement of forces between the tip and the surface, among which are the van der Waals forces. Their universal character, based on the averaged interaction between fluctuating dipoles, makes AFM usable on any type of surface. The technique, therefore, can be applied to insulating surfaces. The design of an AFM, including damping stage, transducers, HV converters, AD and DA converters, feedback loop, and the digital interface, looks pretty much like an STM. The major difference comes from the detection method of the force instead of the tunneling current. Most standard AFMs use integrated tips grown at the end of microfabricated cantilevers (silicon or silicon nitride). The microfabrication process uses methods well-established in the semiconductors industry. For dynamic mode applications (tapping or non-contact, cf. next section), cantilevers have the typical dimensions reported in Table 16.1. To detect the force occurring between the tip and the surface, most instruments use the beam deflection method [26–28]. A laser beam is reflected at the rear side of the cantilever. A photosensitive detector monitors the deflection either of the normal bending mode or of the lateral bending mode of the cantilever. A variant of the beam-deflection method is the optical laser interferometer [29]. The cantilever deflection can also be detected between the cantilever and a counter electrode [30,31]. The last class of cantilevers is referred to as “self-sensing cantilevers” consisting of piezoresistive [32,33] and piezoelectric cantilevers [34–37]. Piezoelectric cantilevers have the advantage of being sensor and actuator for dynamic measurements at the same time, which has successfully been exploited in UHV [35, 37]. Commercially available tuning forks are cheap piezoelectric sensors with high frequency and spring

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Table 16.1. Datasheet of non-contact cantilevers for beam deflection method in non-contact atomic force microscopy (from NanosensorsTM , [25]) Technical data Thickness (µm) Mean width (µm) Length (µm) Force constant (N/m) Resonance frequency (kHz)

Nominal value

Specified range

7 38 225 48 190

6.0–8.0 30–45 215–235 21–98 146–236

constants. High-resolution images in dynamic mode have been achieved by attaching metallic tips (tungsten) to such quartz tuning forks [37]. In atomic force microscopy, the interaction range of the different types of forces is of great importance, since, upon tip geometry and material, they contribute differently to the measured force. For UHV applications, four types of forces are usually considered: – – – –

Short-range forces van der Waals forces Electrostatic forces Magnetic forces

Short-range forces, so-called chemical forces, arise from the overlap of electron wave functions, like during STM operations and from the repulsion between ion cores. The range of these forces is consequently comparable to the extension of the electrons wave functions, namely a few angstroms. The attractive short-range forces are of the order of 0.5–1 nN per interacting atom at tip–sample distances comparable to the STM operation. The decay length ranges from 0.05 nm for metals, up to 0.2 nm for covalent bonding. The main contribution to van der Waals forces for materials consisting of chemical species that do not carry permanent dipoles is the dispersion force. This force originates from the averaged interaction between instantaneous dipoles induced by the electric field of the surrounding atoms. The van der Waals force between macroscopic bodies is usually calculated by pairwise summation over the interacting bodies. This gives rise to a geometric factor, a distance dependance and a constant that depends on the properties of the interface, the Hamaker constant, H. For a spherical tip with a radius R and a plane at a distance D, the van der Waals interaction force is FVDW = −

HR . 6D2

The minus denotes an attractive interaction. H typically scales as 10−20 J and for tips’ radii of about 30 nm, the van der Waals force is about a few nN. Electrostatic forces are due to localized charges on insulating tips and samples or to the contact potential difference between conductive tips and samples. They obey Coulomb’s law and usually occur at large distances from the sample. They can be compensated with an adequate potential between the tip and the sample.

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The forces that act on magnetic dipoles (tip and sample) located in a magnetic field are called magnetic forces. On the contrary to other forces, these forces only occur in the presence of a magnetic field. It is difficult to easily obain an estimate of the strength and the range of these forces, because the magnetization of the sample may be influenced by the magnetic interaction with the magnetization of the tip and vice versa. For details, cf. [16]. 16.2.3.2 Dynamic Modes In dynamic modes, changes in vibration properties of the cantilever due to tipsample interactions are measured. These properties include eigenfrequency, oscillation amplitude and the phase between excitation and cantilever oscillation. Two main dynamic modes are distinguished: tapping mode, so-called amplitude modulation AFM (am-AFM), and non-contact mode (nc-AFM), so-called frequency modulation AFM (fm-AFM). Dynamic modes were initially developed to reduce the shear force occurring between the tip and the surface when scanning in contact. Both modes are differentiated by the feedback parameters used for distance control. A complete review of dynamic methods has been given by Garcia and Perez in 2002 [38] and a more nc-AFM oriented review has been given by Giessibl in 2003 [39]. 1. Tapping mode In tapping mode, the cantilever is kept vibrating at constant drive frequency and drive amplitude. The frequency is chosen slightly above, equal, or below the cantilever eigenfrequency, but it remains constant throughout the experiment. A lock-in amplifier detects the amplitude and the phase of the oscillations with respect to the excitation (Fig. 16.3). Oscillation amplitudes range from 10 up to 100 nm. When scanning the surface, the amplitude is reduced due to an intermittent contact during each cycle. The amplitude reduction is used as control parameter for the tip-sample distance. The feedback loop then strives to keep constant a preset value of amplitude reduction, compared to the oscillation amplitude of the free cantilever. When operating in air, large oscillation amplitudes are required to overcome attractive capillary forces by the restoring force of the cantilever spring. Because the distance dependence of the tip-sample force is non-linear, the origin of the image contrast is closely related to the non-linear dynamics of the cantilever interacting with the surface. A deep understanding of the coupling is, therefore, required for quantitative analysis. The non-linearity is readily observed by performing approach curves, which are equivalent to I(V ) curves in STM. The changes of the amplitude and phase are recorded as functions of the tip-surface distance for a given (x, y) location. Many theoretical and experimental works have been dedicated to the study of the non-linearities and have shown how to extract relevant information out of them, such as adhesion, dissipation, Young’s modulus, and charges distribution [40–44]. Nowadays, tapping mode investigations are rather performed in air, or in liquids, and are mainly targeted at polymers science and at biological molecules, for which the use of the liquid environment is desirable.

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Fig. 16.3. Scheme of the instrumentation in tapping mode

It is indeed not a trivial task to use the technique under UHV conditions, because the cantilever quality factor, Q, is then large. Q is inversely proportional to the dissipated energy of the cantilever in the surrounding medium and, therefore, to the time spent to reach the steady state. With the above-mentioned non-contact cantilevers, at 10−10 mbar and at room temperature, Q typically yields 30,000. In air, this value drops down to about 300. The time after which the cantilever is in the steady state is given by ∆ts ≈

6Q . f0

Considering Q = 300 and f 0 = 190 kHz, then ∆ts ≈ 10 ms. This requires significantly lowering the scanning speed in order to ensure that the cantilever remains in the steady state while acquiring an image, say at least a few seconds per line. The situation is much worse in UHV (Q ∼ 30,000), where ∆ts ≈ 1 s. Acquiring an image consisting of 256 × 256 samples would then require at least 256 × 256 × ∆ts ≈ 18 h! 2. Non-contact AFM The former difficulty has been overcome by the development of non-contact AFM in 1995 [33]. Furthermore, it is currently the only operation mode providing true atomic resolution on metals, as well as on insulating surfaces and images with a quality comparable to STM on homogeneous surfaces. Beyond the references already given, progress in experimental and theoretical works is documented in the proceedings of a series of workshops [45]. Unlike the tapping mode, the cantilever is not driven at a constant frequency. It is excited at a frequency equal to its fundamental bending resonance frequency  f 0 , slightly shifted by the tip-sample interaction. Sufficiently large oscillation amplitude prevents snap into contact. A quality factor exceeding 104 , readily achieved in UHV, together with frequency detection by demodulation, provides high force

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sensitivity [46, 47]. This is why the technique is essentially used in vacuum, e.g. down to 10−6 mbar, or in UHV. A phase-locked loop (PLL) is typically used as an accurate frequency demodulator (Fig. 16.4). Since  f 0 varies with the tip-surface distance, it deviates from f 0 , the fundamental bending eigenfrequency of the free cantilever. Upon approaching the surface, the tip is first attracted, in particular by van der Waals forces, which decrease  f 0 . The negative frequency shift, ∆ f =  f0 − f0 , varies rapidly with the minimum tip-distance d, usually as d −n with n ∼ 1.5, and then as exp(−d/λ), a few Angstroms above the surface, owing to short-range chemical and/or steric forces. When ∆ f is used for distance control, contrasts down to the atomic scale can be achieved. Another specific feature of the nc-AFM technique is that the tip oscillation amplitude, A, is kept constant while approaching the surface or while scanning the surface at constant ∆ f . Controlling the phase of the excitation so as to maintain the cantilever on resonance and to make the frequency matching a preset  f 0 -value, as well as the amplitude of the excitation so as to keep the tip oscillation amplitude constant, requires a dedicated electronics. Amplitude control is usually achieved using a proportional integral controller (PIC), whereas phase and frequency control can be performed in two ways. In both cases, the AC deflection signal at the cantilever end is filtered, then phaseshifted, and finally multiplied by the amplitude PIC output and by a suitable gain. The most common method consists in using a band-pass filtered deflection signal, usually referred to as the self-excitation mode. The second method consists in using the PLL to generate the time-dependent phase of the excitation signal. The PLL output is driven by the AC deflection signal and phase-locked to it, provided that the PLL settings are properly adjusted. The PLL continuously tracks the frequency of the oscillator  f 0 with high precision. Moreover, the phase shift introduced by the PLL itself can be compensated.

Fig. 16.4. Scheme of the instrumentation in nc-AFM

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The nc-AFM technique, therefore, requires operating three controllers in parallel: the PLL, the amplitude controller and the distance controller, which keeps constant a preset ∆ f value while scanning. The amplitude controller output gives a map of the dissipated energy between the tip and the surface. It is often referred to as the damping signal.

16.3 Molecules This section briefly introduces the organic molecules most frequently used in the SPM investigations which are reviewed in this chapter. Their chemical structure is reported in Table 16.2. The discussion of the chemical synthesis of these molecules is beyond the goal of this chapter and is not presented. 16.3.1 Fullerenes Fullerenes are structurally similar to graphite, which is composed of a sheet of linked hexagonal rings, except that they contain pentagonal (sometimes heptagonal) rings preventing the sheet from being planar. The smallest and most common fullerene is C60 (buckminsterfullerene). The C60 molecule has a cage structure and is formed by 12 pentagons and 20 hexagons, which resemble a soccerball (cf. Table 16.2a). 16.3.2 Porphyrins A porphyrin consists of four pyrrole rings joined by methene bridges (Table 16.2b). Porphyrins combine easily with metal atoms, which can be accommodated in the central cavity of the molecules. Iron, zinc, copper, nickel, and cobalt containing porphyrins are known, but other metals can be inserted. New porphyrin-based molecules have been recently synthesized, in particular by Bonifazi et al. [48]. They consist of a double porphyrin core with original substituents and are referred to as double-fused porphyrins. The chemical structure of the Cu-tetra[3,5-di-tert-butylphenyl]porphyrin (CuTBPP) molecule, which frequently appears in SPM studies, is shown in Table 16.2c. In this molecule four di-tbutylphenyl (TBP) substituents form legs able to decouple the porphyrin ring from the substrate onto which the molecule is deposited. 16.3.3 Phthalocyanines A phthalocyanine (Pc) is a macrocyclic compound with an alternated N-C ring structure (cf. Table 16.2d). The molecule has a fourfold symmetry and can “host” hydrogen and metal cations in its center by coordinate bonds with the four isoindole nitrogen atoms. The central atoms can carry additional ligands. Most of the elements can coordinate to the phthalocyanine molecule. Therefore, a variety of phthalocyanine complexes exist.

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Table 16.2. Chemical structures of the molecules reviewed in this chapter. The convention of colors is: grey = Carbon; white = Hydrogen. The other atomic species have been depicted with their chemical symbol. The hydrogen atoms have not always been depicted. The molecules sizes have been arbitrary scaled such that their dimensions are not comparable. (a) Buckminsterfullerene (C60 ). (b) Porphyrin. (c) Cu-tetra[3,5-di-tert-butylphenyl]porphyrin (Cu-TBPP). The substituents have arbitrarily been drawn in the plane of the porphyrin ring. (d) Copper-phtalocyanine. (e) Chloro-[subphthalocyaninato]boron-(III) (SubPc). (f) Perylene3,4,9,10-tetracarboxylicdianhydride (PTCDA). (g) Perylene-3,4,9,10-tetracarboxylic-3,4,9,10diimide (PTCDI). (h) Landermolecule. The four TBP substituents have been arbitrarily drawn perpendicularly to the aromatic board of the molecules. (i) 4-[trans-2-(pyrid-4-yl-vinyl)]benzoic acid (λ-PVBA). (j) δ-PVBA. (k) Decacyclene (DC). (l) Hexa(tertio-butyl)decacyclene (HtBDC)

Subphthalocyanines (SubPc, cf. Table 16.2e) are large polar molecules, which differ in several ways from the usual fourfold symmetric phthalocyanines. The central metal atom is replaced by boron, which is sp3 coordinated to a chlorine atom

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placed in apex position and to three, instead of four, isoindoline rings. In contrast to the mostly planar phthalocyanines, the SubPc is cone-shaped. The properties and potential applications of SubPc and related molecules were reviewed in 2002 [49]. 16.3.4 Perylene Derivatives The perylene molecule and its derivatives are suitable materials for the use in molecular electronic devices. Perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride (PTCDA) and -diimide (PTCDI) (cf. Table 16.2f and g, respectively) are planar molecules, which have been widely used for SPM investigations. They are also model systems for OMBE. 16.3.5 Lander Molecules Lander molecules (so named because of their resemblance to the Mars Lander) consist of an aromatic board and four TBP legs which elevate the board from the substrate on which the molecules are deposited (cf. Table 16.2h), similarly to the Cu-TBPP. A single Lander molecule (C90 H98 ) is about 1.7 nm long and 1.5 nm wide. Further “Lander-based” molecules were then synthesized, such as the Violet Lander (VL) and the Double Lander (DL). The Violet Lander (C108 H104 ) has a longer central board (not reported in Table 16.2). The Double Lander has a 3.7 nm long board and eight lateral legs (not reported in Table 16.2). Lander molecules were synthesized as prototypes of molecular nanowires. Even when adsorbed on a metallic support, the board may ideally act as a wire segment. The height of the molecular wire is about 0.4 nm and is, therefore, well-suited to interact electronically with a metallic pad, which is one or two molecular layers high. 16.3.6 PVBA Molecules The structure of 4-[trans-2-(pyrid-4-yl-vinyl)]benzoic acid (PVBA) is shown in Table 16.2i and j. A mirror operation is required to transform the 2D chiral λ-PVBA (Table 16.2i) and δ-PVBA (Table 16.2j). A hydrogen atom is free to transfer from one oxygen atom to the other. PVBA is a planar rigid molecule, which includes a pyridyl group as the head and a carboxylic acid group as the tail, thus being ideal for self-assembly. 16.3.7 Decacyclene and Derivatives Hexa(tert-butyl)decacyclene (HtBDC) consists of an aromatic ring system (decacyclene, DC), built out of a central benzene ring, connected to three naphthalene subunits (cf. Table 16.2l and k, respectively).

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16.4 Molecules on Metals 16.4.1 STM Investigations 16.4.1.1 Fullerenes In the beginning of the 90’s, gold surfaces were the first metallic substrates used for STM investigations of C60 [50–53]. Already in the first studies, fullerene molecules were found to form close-packed hexagonal overlayers on gold. The adsorption of C60 induces substrate reconstructions on the Au(111) and Au(110) surfaces, whereas the Au(100) surface structure does not seem to be affected by the C60 adsorption. Close-packed hexagonal overlayers, accompanied by substrate reconstruction, were also observed on Al(111) [54, 55] and Ag(110) [56]. On Ag(100), Giudice et al. noticed the formation of different domains with two different molecular orientations [57]. In each domain, bright C60 molecules were resolved which were attributed to inhomogeneous charge distributions and different chemical bonding with the substrate. A recent investigation by Hsu et al. showed that C60 rather forms an incommensurate close-packed phase on Ag(100) [58]. The bright-dim contrast of the molecules is attributed to local substrate restructuring underneath the dim molecules (Fig. 16.5). Murray et al. revealed differences in C60 growth on Cu(110) and Ni(110) [59]. On Cu(110), a distorted hexagonal overlayer is found, due to strong adsorbate–adsorbate forces. On Ni(110), the C60 –Ni interaction prevails, which leads to a substrate reconstruction and the formation of (100) microfacets. The same group also investigated how an oxygen layer modifies the adsorption of fullerene on Cu(110) [60]. The deposition of fullerene on Au/Ni(110) leads to the formation of self-assembled one-

Fig. 16.5. (a) C60 /Ag(100) STM image with bright (B), dim (D) and medium (M) contrast of C60 . (b) Profile of C60 molecules along [113]. Courtesy of [58]

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dimensional rows of C60 molecules [61]. The template for these molecular wires is given by the chain structures formed by the gold atoms. The group of Kern combined STM with different surface characterization techniques to investigate the adsorption of C60 on Pd(110) and Cu(100) [62,63]. At high temperatures, the formation of well-ordered structures was observed in both cases. Again, the rearrangement of the substrate played a crucial role. More recently, Pai et al. showed that the growth of C60 on Cu(111) results in substrate reconstructions that strongly affect the adlayer relaxation [64]. Fullerene molecules on Cu(221) were also investigated very recently [65]. Bonifazi and coworkers have reported one- and two-dimensional fullerene patterns onto pre-organized porphyrin monolayers on silver surfaces following a bottom-up approach [6] (Fig. 16.6). For that purpose, they have used specifically synthesized single- and double-fused porphyrins. The arrangement of the fullerene

Fig. 16.6. STM images of C60 assembly. (a) Left: STM image showing the preferential direction of the chain-like assembly of C60 on a previously deposited monolayer of diporphyrin molecules (DP) (image size: 77 × 65 nm2 ). Right: proposed model for the chain-like assembly (a = 7.5◦ ). (b) Detailed view of the before (left) and after (right) manipulation sequence of the C60 molecule on a layer of DP (image size: 21×21 nm2 ). The arrow traces the lateral displacements of the STM tip during the manipulation and the ellipse indicates the intact layer of DP after repositioning of the C60 molecule; the circle denotes a C60 molecule that vanished during the repositioning experiment. Courtesy, from [66]

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molecules on the patterned layer is controlled by the porphyrin structure. They as well report single C60 manipulation on top of the porphyrin monolayer. Some authors reported STM images of C60 revealing some internal molecular features [67–70]. The interpretation of these images is not straightforward and will not be discussed in our review. 16.4.1.2 Porphyrins The first STM studies of porphyrin molecules on metal surfaces were carried out by Jung et al. in 1996 [71, 72]. STM images of Cu-TBPP consist of four bright lobes, which correspond to the phenyl-based ligands (Fig. 16.7). The porphyrin core is electronically decoupled from the substrate and does not contribute significantly to the images. When adsorbed on Cu(100), the molecule retains a conformation close to the minimum energy in vacuum, which results in a square pattern. In contrast, two

Fig. 16.7. Cu-TBPP molecules (a) on Cu(100), (b,c) on Au(110), and (d) on Ag(110) (images size: 10 nm). Courtesy of [71]

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distinct configurations were detected for Cu-TBPP molecules adsorbed on Au(110), corresponding to antisymmetric tilts of two opposite side groups. The most pronounced conformational change, however, was observed when the molecules were adsorbed on Ag(110). In such a case, the single adsorption state is characterized by a dihedral angle of 30◦ . These findings clearly indicate that the Cu-TBPP conformation is driven by the nature of the molecule-surface interaction. The conclusions by Jung et al. were supported by Moresco et al., who reported low-temperature studies of Cu-TBPP molecules on different copper surfaces [73]. On Cu(100) the porphyrin molecules revealed only one orientation, due to the high symmetry of the substrate. On Cu(111) eight lobes were observed, and the apparent height of Cu-TBPP was lower than on Cu(100). In such a case, the legs lay flat on the substrate and the two end butyl groups of each leg gave origin to two lobes per leg in the STM image (Fig. 16.8). On Cu(211) two different orientations were detected. The molecules were either oriented parallel to the step edges or rotated 45◦ . In both cases eight lobes were revealed. The adsorption of a platinum porphyrin derivative on Cu(100) was studied by Yanagi et al. [74]. The molecules form two-dimensional rectangular islands in equilibrium with a diffusional gas phase. Dependence of the equilibrium conditions on the sample-tip bias voltages is presented. On Au(111) at low temperature, Yokoyama et al. observed monomers, trimers, tetramers or extended wire-like structures formed by substituted porphyrin molecules [75] (Fig. 16.9). Each structure corresponds in a predictable fashion to the geometric and chemical nature of the porphyrin substituents, which mediate the interaction between individual adsorbed molecules.

Fig. 16.8. (a) Experimental STM images of a TBPP molecule deposited on Cu(111). Following the close-packed directions of the substrate, the molecules show three different orientations, rotated by 60◦ with respect to each other. (b) Calculated STM images of TBPP on Cu(111). Courtesy of [73]

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Fig. 16.9. Supramolecular aggregations of substituted porphyrin molecules on Au(111) (STM images at 63 K and molecular models): (a,e,i) H2 -TBPP, (b,f,j) CTBPP, (c,g,k) cis-BCTBPP, (d,h,l) trans-BCTBPP (image sizes: first column: 20 nm, second column: 5.3 nm). Courtesy of [75]

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16.4.1.3 Phthalocyanines Metal phthalocyanines were the first organic molecules investigated by STM (cf. also Sect. 16.5.1). Single CuPc molecules on polycrystalline silver surfaces were distinguished by Gimzewski et al. [76]. The molecules on flat areas were found to diffuse during scanning, whereas atomically rough regions guaranteed stable adsorption. The adsorption of CuPc on Cu(100) was investigated by Lippel et al. in 1989 [77]. Their images were the first ones revealing the internal structure of a molecule. Two different orientations were recognized. More recently, Walzer et al. studied the initial adsorption of SnPc on graphite and gold surfaces [78]. On graphite in the sub-monolayer regime, SnPc form substrateinduced molecular chains (Fig. 16.10). On the contrary, dense packed structures consistent with molecules symmetry are revealed within SnPc monolayers. Molecular chains in the submonolayer regime were also reported with CuPc molecules adsorbed on graphite [79]. However, no chains were observed on the Au(111) surface. On Ag(111), Lackinger et al. distinguished a disordered and an ordered phase of SnPc [80]. For the ordered phase, a rectangular unit cell with a two-molecular base was found. Images with sub-molecular resolution allowed distinguishing between two different adsorption states in which the central Sn-atom is pointing either towards or out of the surface. Lu et al. [81] investigated and compared more systematically the adsorption properties of several MPc molecules (M = Fe, Ni, Co, Cu) on Au(111). In spite of the strong influence of the central metal atom on the tunneling images due to different d orbital characters, they found that the geometry adsorption of the molecules looks

Fig. 16.10. SnPc on graphite, thickness 0.5 ML. Image size: 34 nm, T = 35 K. Courtesy of [78]

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similar. Therefore their conclusions point out the weak influence of the metal atom on the self-assembly process, mainly governed by van der Waals interactions. In contrast, the chemical substitution of the surrounding hydrogen atoms of the molecule influences the molecule-molecule as well as molecule-substrate interactions, as shown by Irie et al. [82] and recently by Abel et al. [83]. Irie et al. investigated the molecular structure of the fully-chlorinated copper phthalocyanine (CuPcCl16 ). Compared to the non substituted molecule, a different self-assembly process was observed due to a strong effect of polarity originating from the electronegative chlorine atoms. Abel et al. investigated the self-assembly process of ZnPcCl8 (Fig. 16.11a) on Ag(111) and found a surprising structural evolution due to the sequential formation of intermolecular hydrogen bonds. The first structure (Fig. 16.11b) is similar to the CuPcCl16 one reported by Irie et al. while the second (not depicted) and third (Fig. 16.11c) ones result in the formation of four and eight hydrogen bonds, respectively. They conclude that the final striped structure, readily observed in Fig. 16.11c, originates from an anisotropic stress due to the chemical substitution which increases the molecule-substrate interaction. The growth of SubPc on Au(111) was studied by Mannsfeld et al. [84]. While very mobile at submonolayer coverage, the molecules form a highly oriented molecular layer in the monolayer or multilayer regimes. Entire gold terraces are occupied without any visible sign for the existence of domain boundaries. The molecules stand upright on the substrate with three isoindolyl groups attached to the gold surface. In the second monolayer, the molecular film exhibits a commensurate growth with the molecules growing upside-down on top of the first monolayer. In another study, Berner et al. investigated adsorption of SubPc on Ag(111) [85]. At low coverage, a 2D gas lattice is present, whereas at medium coverage 2D condensed molecular islands are observed in coexistence with the 2D lattice gas. In these condensed islands, the molecules assemble into a well-ordered honeycomb pattern (Fig. 16.12). At higher coverage (above 0.5 ML), the molecules organize into a 2D hcp pattern, in equilibrium with a dense 2D gas phase.

Fig. 16.11. (a) Chemical structure of the ZnPcCl8 molecule. Half of the sixteen peripheral hydrogen atoms have been substituted with Chlorine atoms. (b) STM image of a monolayer of ZnPcCl8 molecules in an early formation step on Ag(111). The molecules are arranged similarly to CuPcCl16 [82]. Image size: 20 × 20 nm2 . (c) After a while, the molecules form highly regular striped structures due to the formation of intermolecular hydrogen bonds (inset). Image size: 20 × 20 nm2 . Courtesy of [83]

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Fig. 16.12. SubPc molecules on Ag(111) with a molecular coverage of 0.3 ML. A condensed island with honeycomb pattern (c) coexists with a 2D lattice gas (g). Step edges are decorated by SubPc molecules that form an irregular pattern (s). Image size: 51 × 41 nm2 . Courtesy of [85]

16.4.1.4 Perylene Derivatives The crystal structure of PTCDA molecules grown on gold surfaces was first studied by Schmitz-Hübsch et al. [86]. On the reconstructed Au(111) surface, three different structures were observed. Their orientation differs from the Au substrate, suggesting that the corrugation potential seen by the molecules is small compared to the lattice potential. On Au(100), the molecules form two different structures [87]. On unreconstructed areas of the surface, a herringbone structure is found, while on the reconstructed Au(100)hex surface, closely spaced rods of closely packed molecules are observed. The aggregation of PTCDA molecules on Ag(111) and Ag(110) was investigated by Glöckler et al. [88]. The molecules lie flat on these surfaces and form large ordered islands. On Ag(111) herringbone structures are observed, which resemble those of net planes of the corresponding molecular crystals. On the (110) surface, brick-walllike structures are found (Fig. 16.13). Submonolayer coverages of PTCDA on Ag(110) were investigated at room and low temperatures by Böhringer et al. [89]. The group of Flipse reported on the growth of PTCDA on Ni(111), after having passivated the substrate by an oxygen treatment [90]. The passivation allowed the molecules to diffuse on the substrate and form ordered structures, depending on growth rate and coverage. For submonolayer coverage, a herringbone-like strucFig. 16.13. Nucleation of islands for a submonolayer coverage of on the flat terraces of the Ag(110) surface: (a) PTCDA. (b) DM-PBDCI (images size: 70.4 nm). The arrow marks the position of a boundary between two reflectional domains. Courtesy of [88]

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Fig. 16.14. C60 heptamers trapped wihin a PTCDImelamine network grown on Si(111) (scale bar: 5 nm). Courtesy, from [91]

ture was observed. As the growth rate increased, a polycrystalline film was formed. Domains within the polycrystalline structure exhibited two strip-like phases of molecular ordering. A herringbone-like structure was observed upon annealing, which was accompanied by decomposition of the PTCDA molecules. Theobald et al. investigated an open honeycomb network formed when PTCDI is co-adsorbed with melamine on a silver-terminated silicon surface [91]. Melamine, which has a three-fold symmetry, forms the vertices of the network, while the straight edges correspond to PTCDI. The large pores of the network were used as traps for other molecules. Upon sublimation of C60 molecules, heptameric clusters were formed within the pores (Fig. 16.14). Clusters formed in different pores were aligned and all oriented parallel to the principal axes of the Si(111) surface. Stöhr et al. studied the growth of PTCDA on Cu(110) when varying the surface coverage from the submonolayer to the multilayer regime [92]. For submonolayer and monolayer coverage, the PTCDA molecules induce a restructuring of the underlying Cu(110) surface by addition or removal of Cu-rows. For higher coverages,

Fig. 16.15. STM-image of a crystallite of PTCDA, three facets can be seen. Image size: 74 × 72 nm2 . Inset: molecularly resolved image of the top layer of the crystallite (image size: 10 × 8 nm2 , the unit cell is indicated). Courtesy of [92]

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PTCDA grow in the Stranski–Krastanov (SK) mode, thus forming well-ordered 3D crystallites (Fig. 16.15). Both top layer and flanks were resolved down to the single molecule scale. The growth of PTCDA on Ag(111) was studied by Chkoda et al. [93]. By increasing the substrate temperature between 180 and 420 K, a transition from a homogeneous layer-by-layer film growth to SK growth was observed. The formation of 3D crystalline islands was also reported by Guillermet et al., who recently investigated the growth of PTCDI films on Pt(100) [94]. 16.4.1.5 Lander Molecules The first STM images of Lander molecules were reported by Langlais et al. [95]. On flat terraces of a Cu(100) surface, each molecule showed four lobes corresponding to the four TBP spacers, pretty much as for the features observed for the Cu-TBPP molecules. The molecules adsorbed on double atomic steps oriented with their long axis perpendicular to the step and formed a molecular wire. An exponential decay in the conductance of the wire with distance from the contacted end was observed, in agreement with theoretical calculations. Rosei et al. imaged Lander molecules on different copper surfaces at low temperature (100 K) [96]. On Cu(110), the four lobes of each molecule were arranged in three possible conformations: one rectangular achiral shape, with the four legs parallel to each other and two rhomboidal chiral shapes, with antiparallel legs. The molecules were deposited at room temperature and, due to the rapid diffusion, most of them were found at step edges. After manipulating single molecules, it was found that the adsorption is accompanied by the formation of copper nanostructures protruding from the step edge, to which the molecules are anchored (Fig. 16.16). The

Fig. 16.16. (a)–(d) Manipulation of Lander molecules from a step edge on Cu(110) (images size: 13 nm). (e) Tooth-like structure observed after removal of a single molecule (image size: 5.5 × 2.5 nm2 ). Courtesy, from [96]

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distances between the four lobes and the apparent height of the molecule decrease when it is moved to a flat terrace. Theoretical calculations confirmed that the gain in energy by adsorbing the molecule on the “tooth” relative to the flat terrace is higher than the energy required for creating the tooth. Upon adsorption of the molecules at low temperature (150 K), no reconstruction of the Cu step edges was observed. The adsorption of Lander molecules on Cu(100) was studied by Kuntze et al., who also detected chiral arrangements of the molecules [97, 98]. Zambelli et al. investigated the adsorption of Violet and Double Landers on copper surfaces [99, 100]. On Cu(100), each VL molecule appears as four bright lobes arranged in a nearly rectangular configuration. No contrast can be associated with the central board. The DL molecules were imaged as two rows of four lobes in a nearly rectangular configuration on Cu(100) (Fig. 16.17). On a Cu(111) surface structured with double steps of cobalt, Zambelli et al. observed that not only the legs were free to rotate, but also the central boards were distorted when the molecules lay at the edges of the steps. Similarly to Single Landers, VLs also induce surface reconstruction on Cu(110), as recently reported by Otero et al. [101]. The structure induced by the VL is longer and often wider than the one induced by the SL.

Fig. 16.17. (a) STM image of D-Lander molecules adsorbed at Cu(100) steps (scale bar: 5 nm). (b) STM profiles of the two leg rows for the D-Lander molecule in the inset. Courtesy of [100]

16.4.1.6 PVBA Molecules The group of Kern et al. studied the adsorption of PVBA molecules on different metal surfaces [102, 103]. On Pd(110), isolated and immobile molecules, lying flat in two distinct orientations, are found. On Cu(111), flat molecules in dendritic islands coexist with isolated molecules at low temperatures, whereas on Ag(111) the molecules revealed a complex aggregation, which reflects the surface mobility and attractive interactions between molecular endgroups. Annealing at 300 K leads to the formation of molecular stripes, which consist of two PVBA chains. In another study, they found that homochiral PVBA molecules self-assemble in supramolecular chiral hydrogen-bonded twin chains, which order into nanogratings [104] (Fig. 16.18). The supramolecular chirality is strictly correlated over µm domains without intimate molecular contact. On Pd(111), Perry and coworkers revealed molecular dimers and trimers [105]. Different chiralities showed specific orientations upon adsorption.

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Fig. 16.18. (a) Chirality of PVBA upon confinement to two dimensions. The respective species are designated l-PVBA and d-PVBA; the mirror symmetry is reflected by a dashed line. (b) STM topographs of the two possible supramolecular chiral twin chains from self-assembly of PVBA on Ag(111) (image size: 4 × 13.5 nm2 ; adsorption temperature: 300 K, measured at 77 K). The corresponding models for the energetically favored configurations reveal the underlying chiral resolution (hydrogen bonds indicated by dashes). Courtesy, from [104]

16.4.1.7 DC and HtBDC Molecules Gimzweski et al. observed that HtBDC molecules on Cu(100) act as single-molecule rotors operating within supramolecular bearings [106]. Single molecules can assume two different configurations. One corresponds to a rotating state and the other to an immobilized state. Calculations of the energy barrier for rotation of these two states showed that it is below the thermal energy at room temperature for the rotating state and above it for the immobilized state. The group of Besenbacher studied the adsorption of DC and HtBDC molecules on Cu(110) [107–109]. HtBDC molecules are anchored to the surface through the formation of a characteristic trench base in which 14 Cu atoms are dug out of the surface layer in two neighboring close-packed rows (Fig. 16.19). On the contrary, the DC molecules do not induce any restructuring of the surface and no ordered structures are observed at low coverages. 16.4.1.8 Other Molecules Other STM investigations of organic molecules on metal surfaces have been attempted. They focused on the adsorption of oligothiophenes on silver [110], para- and meta-xylene on rhodium [111], adenine, trimesic acid, pentacene, iodobenzene, . . ., on copper [112–115], cysteine and terephthalic acid on gold [116, 117] . . .

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Fig. 16.19. (a) HtBDC double row structure. (b) The trenches in the substrate are revealed after manipulating the molecules aside. (c) Model of the double row structure (images size: 10.5 × 6.9 nm2 ). Courtesy of [107]

16.4.2 Non-Contact AFM Investigations 16.4.2.1 Fullerenes In recent work, Mativetsky et al. investigated C60 thin films (2–3 monolayers) on Au(111) [118]. The close-packed C60 surface is imaged by nc-AFM with molecular resolution (Fig. 16.20). Enhanced corrugation and stretching of the C60 lattice are observed at step edges. Based on a calculation of the force required to displace an

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Fig. 16.20. Non-contact AFM images of C60 films on Au(111). Images size: (a) 6 nm; (b) 5 nm; (c) 12 nm. Courtesy, from [118]

edge molecule, they propose that the edge effects are the result of tip-induced displacements of edge molecules. While imaging small clusters of C60 , some molecules are removed, leading to structural rearrangements of the clusters. 16.4.2.2 Porphyrins As shown in the former section, numerous works were dedicated to the study of porphyrins on metals by STM. Regarding the nc-AFM technique, surprisingly, only a few investigations were attempted. One of the most striking result was found by Loppacher et al. with Cu-TBPP on Cu(100). Despite the fact that they used tunneling current to image the molecules, they measured the energy required to switch one of the “legs” of the molecule (Fig. 16.21) [119, 120]. The comparison between experimental and calculated force curves shows that the rotation of the leg requires less than 10−19 J, which is four orders of magnitude lower than state-of-the-art transistors. The only images of Cu-TBPP on Cu(100) reported in the literature using frequency shift as feedback signal have been obtained by Nony et al. [122]. Rectangular islands of molecules can be identified (Fig. 16.22b). Rows of single mole-

Fig. 16.21. (a) Frequency-distance curves recorded on the pure Cu(100) substrate (solid curves) and above the legs of a Cu-TBPP molecule (dashed curves). (b) Subtracting the two kinds of curves, the short-range interaction between the tip-apex end and the molecule leg is revealed. (c) An algorithm developed by Giessibl [121] was used to directly extract the short-range tipmolecule force out of the data in (b). The grey area gives the experimental work produced by the tip apex (47 zJ). Courtesy of [120]

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Fig. 16.22. Topographic images of the Cu(100) surface partially covered by ordered monolayer islands of Cu-TBPP molecules. (a) Overview image obtained using the frequency shift for distance control (image size: 127 nm). (b) Zoom showing rows of molecules and some internal structure (image size: 8 nm). (c) High-resolution image recorded using the tunneling current for distance control (image size: 8 nm). Four lobes can be recognized on each molecule, similarly to Fig. 16.7. Courtesy of [122]

cules, with some blurry internal structure are revealed. For comparison, Fig. 16.22c shows an image obtained with the same oscillating tip using instead the time averaged tunneling current for distance control. The significant difference in contrast quality between STM and nc-AFM images of molecular films is found to be a general finding either on conducting substrates or on insulating substrates (cf. Sect. 16.6.2). The authors note some reasons for that difference, which all stem from the different interactions responsible for the contrast in the two methods. First, the short decay length of the tunneling current selects very few atoms, which probe the electronic overlap between tip apex and surface. In force microscopy, tip asperities as far as two or three nanometres from the surface can contribute to local force variations, thereby producing a more blurred contrast in high-resolution images. Tip sharpness is, therefore, a prerequisite to expect achievement of a high vertical, but also lateral, contrast on heterogeneous surfaces. Second, unstable atomic configurations at the tip apex perturb nc-AFM experiments more

Fig. 16.23. Non-contact AFM images of MSTBPP molecules (in the inset) on Au(111). Smaller and larger circles show the positions of the methylthiophenyl legs and di-t-butylphenyl legs, respectively. Images size: (a) 29 nm; (b) 8.5 nm. Courtesy of [123]

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than STM experiments. Such instabilities produce large fluctuations in the tunneling current, but can eventually lead to more stable rearrangements; it is often a question of patient scanning until a stable tunneling tip is formed, in a kind of self-stabilizing process. In contrast, atomic scale instabilities near the tip apex of an nc-AFM can produce variations of the total force, thus disturbing the imaging process. In order to enhance the interaction with a metal substrate and thus to reduce the molecules’ mobility, Tanaka et al. introduced a methylthiophenyl group into TBPP [123]. The MSTBPP molecules so obtained were adsorbed onto an Au(111) surface and investigated by nc-AFM (Fig. 16.23). With a coverage of 0.2 ML, the molecules fully occupy the step edges. Submolecular resolution has been achieved, which testifies that the molecules’ mobility is indeed reduced. 16.4.2.3 Phthalocyanines Yoda et al. investigated CuPc on the Au(111) surface in the multilayer regime [124]. Structures with periodic spacing and sub-molecular features are successfully imaged. The various types of contrasts observed are interpreted in terms of chemical interactions between the tip and the spatial electron density of the chemically active molecular orbitals. Besides, energy dissipation on the molecular scale is revealed within monolayer films. The high-resolution contrast in the dissipation images is discussed in connection with the random fluctuation of molecules within the film. 16.4.2.4 Perylene Derivatives In 1998, Gotsmann et al. were the first authors to report molecular resolution on PTCDA thin films deposited on Ag(110) by means of nc-AFM [125] (Fig. 16.24).

Fig. 16.24. Non-contact-AFM image of a monolayer of PTCDA on Ag(110) (image size: 30 nm). Courtesy of [125]

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Later on, Krause et al. investigated the same molecule deposited on an Ag(111) substrate in the multilayer regime (5 to 20 nm) by nc-AFM and X-ray diffraction [126]. The crystal structure and morphology of the thin films is examined in detail as a function of the growth parameters. Coexistence of alpha- and beta-like structures is found for a variety of growth conditions. A growth temperature-dependent morphology transition from smooth films to well-separated islands is observed which is related to changes of the crystal structure. 16.4.2.5 Other Molecules Uchihashi et al. [127] investigated a monolayer of adenine adsorbed on graphite. The adenine molecules were found to pack into a rectangular lattice (Fig. 16.25) and detailed features within the molecule were resolved. They also investigated molecular packing structures, defects and domain boundaries on adenine and thymine films on Au(111) [128]. Detailed features of individual molecules are revealed, thus allowing distinguishing adenine and thymine.

Fig. 16.25. (a) Non-contact AFM image of an adenine lattice and cross-sectional profile of the ˚ image. (image size: 7 nm). The unit cell of adenine lattice with dimension a = 21.0 ± 1.5 A, ˚ was sketched by a white rectangle. (b) A molecular packing structure model b = 8.8 ± 0.7 A of adenine film on graphite proposed previously. The hydrogen bonds were described by dotted lines. Courtesy of [127]

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16.5 Molecules on Semiconductor Surfaces 16.5.1 STM Investigations 16.5.1.1 Fullerenes Several groups investigated the adsorption of C60 molecules on semiconductors. Li et al. observed that C60 forms monolayer islands on GaAs(110), which are wellordered and commensurate with the substrate [129]. Thus, the molecules are highly mobile due to their weak interaction with the surface. Similar results were obtained for C84 , C82 , C78 , C86 , and C70 grown on a similar substrate [130]. The adsorption and nucleation of C60 on GaAs(100)-2 × 6 was investigated by Xue et al. [131]. The first molecules lay in missing-dimer rows, whereas at increasing coverage they nucleated into clusters and then formed double chains when the first monolayer is completed. Ordered SK islands (cf. Sect. 16.4.1) were observed above the third layer with a large number of screw dislocations (Fig. 16.26). The adsorption of C60 and C84 on Si(100)-(2 × 1) was investigated by Wang et al., who found that both of the molecules occupy the trough surrounded by four neighboring dimers and form strong bonds with the Si substrate [132]. Multiple-layer adsorption of C60 and C84 resulted in formation of ordered crystalline islands with the fcc(111) configuration. Internal structures of the molecules were also resolved, suggesting that the rotation of individual fullerenes was suppressed. On Si(111)-

Fig. 16.26. C60 multiple-layer film grown on the GaAs(100)-2 × 6 surface. Images size: (a) 22 × 20 nm2 ; (b) 10.5 × 9 nm2 . A large number of screw dislocations (indicated by the white arrows) can be observed in (a). (c) Details of the bonding configuration between the neighboring layers. Courtesy of [131]

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(7 × 7) no ordered structures were found by Li et al. [133]. However, a subsequent investigation by Chen et al. revealed that by increasing the adsorbate coverage, structured phases of fullerenes are formed, due to stronger interactions among the C60 molecules [134]. This result is in contrast with another study by Xu et al., who state that several monolayers of adsorbates are required for the formation of ordered structural phases [135]. The rearrangement of C60 after annealing was also investigated [136]. On Si(110)-(16 × 2) [137] and Ge(111)-c(2 × 8) [138], only random distributions of C60 molecules were reported. The adsorption of C60 on TiO2 (100)-(1 × 3) was studied by Murray et al., who observed a fcc C60 (110) double layer [139]. This structure differs significantly from those observed on other substrates, which are either dominated by intermolecular interactions or interactions with the substrate, suggesting that, in the present case, both effects play an important role. 16.5.1.2 Phthalocyanines Single CuPc molecules on Si(100)-(2×1) were first observed by Rochet et al. [140]. Kanai et al. revealed that the molecules are deposited with the molecular plane parallel to the substrate surface and have three kinds of adsorption configurations [141]. The images of the CuPc are modified by the electronic state of the Si(100) surface. This behavior suggests strong interaction between the molecule and the substrate. The molecular images on the Si(111) surface have a unique bias-voltage dependence. At a sample bias of 1.6 V, the molecule looks transparent by STM, and becomes dark like a vacancy at 1.2 V. From the bias dependence, the electronic interaction between the CuPc molecule and the Si surface is discussed. Capobianchi et al. investigated the adsorption of titanium bis-phthalocyanine on GaAs(100) and HOPG [142] (Fig. 16.27). On GaAs the molecules align along dimer rows, typical of the (2 × 4) reconstruction. On HOPG, irregular channels are

Fig. 16.27. (a) GaAs area after TiPc2 deposition (image size: 11.2 nm). The arrow shows an example of a two-molecule cluster. A simplified picture of the surface is given in (b) wherein the molecules are represented by filled grey circles. Courtesy of [142]

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formed, suggesting an auto-assembling of the molecules between themselves rather than a strong interaction with the substrate. 16.5.1.3 Perylenes An STM investigation of PTCDA molecules adsorbed on hydrogen passivated Si(100) surfaces was reported by Chen et al. [143] (Fig. 16.28). The molecules were evaporated at high temperatures and detected at room temperature. At 200 ◦ C, small clusters with an average size of 3.5 nm were observed. These clusters have high mobility and most of them are trapped at surface defects. By increasing the evaporation temperature up to 230 ◦ C, larger clusters with lower mobility appear. When increasing further the evaporation temperature (250 ◦ C), crystals with dendritic shape and average size of 150 nm are formed. Molecular resolution on the terraces allowed to identification of the molecular mechanism involved in the growth of the dendritic crystals.

Fig. 16.28. (A) STM image (image size: 118 nm) of a PTCDA single crystal, (B) an enlarged area (image size: 39 nm) of the upper left corner, (C) an enlarged area (image size: 40 nm) of the lower part of the crystal, (D) further enlarged flat terrace (image size: 12 nm) with molecular resolution. Courtesy of [143]

16.5.1.4 Other Molecules The adsorption of smectic liquid crystals on molybdenum disulphide [144], alkenes, styrene, vinylferrocene and tetramethylpiperidinyloxy on silicon [145–150] and a naphthalene derivative (NTCDA) on Ag/Si(111) [151] have also been studied. No STM investigations of Lander, PVBA or decacyclene-based molecules on semi-conducting surfaces have been reported to our knowledge.

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16.5.2 Non-Contact AFM Investigations 16.5.2.1 Fullerenes Kobayashi et al. imaged crystalline islands of C60 molecules on Si(111)-(7 × 7) by nc-AFM with molecular resolution [152] (Fig. 16.29). Some imaging artifacts, such as contrast inversion, are related to energy dissipation phenomena and to tip effects. A contact potential difference observed in the multilayer regime is related to charge transfer from Si dangling bonds to C60 .

Fig. 16.29. (a) Noncontact AFM image of C60 crystalline islands on Si(111)-(7 × 7) (image size: 300 nm). (b) Non-contact AFM image taken on a single C60 crystalline island (image size: 20 nm). Courtesy, from [152]

16.5.2.2 Phthalocyanines The group of Matsushige investigated CuPc molecules on MoS2 in the monolayer and in the multilayer regimes [153]. Submolecular resolution was successfully obtained in both topographic and dissipation images of CuPc monolayers. Regarding topographic contrasts, the influence of short-range chemical interactions is particularly considered while the dissipation contrasts are discussed in relation to the tip-induced molecular fluctuations. A molecularly-resolved nc-AFM image was also obtained on a CuPc multilayer, which revealed the structural difference between the monolayer and multilayer surfaces. The energy dissipation measured on these surfaces showed distinctive differences reflecting the different structural stabilities within the films. Furthermore, local surface modification of a CuPc monolayer is demonstrated. This is a direct evidence for the existence of energy transfer from the vibrating cantilever to the molecules through dissipative tip-sample interactions. 16.5.2.3 Perylenes To our knowledge, no nc-AFM investigations with these molecules on semiconducting surfaces have been reported.

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16.5.2.4 Acetate, Formate and Propiolate Molecules In 1999, the group of Onishi published atomic-scale images of a TiO2 (110)-(1 × 1) surface and individual formate and acetate ions adsorbed on the surface by nc-AFM in UHV [154]. In contrast to previous STM studies imaging five-fold coordinated Ti atoms, outermost atoms of bridge-bound oxygen ridges of the surface were resolved as protruding rows by nc-AFM. High-resolution images of the surface revealed that the bridging oxygen atoms on terraces ordered in a (1 × 1) periodicity. Randomly distributed point and multiple defects of oxygen atoms were also imaged as dark spots. The (2 × 1) overlayer of formate and acetate ions was resolved as ordered bright spots. Dispersed formate ions at a low coverage were also observed as bright spots between the bridging oxygen ridges along the [001] direction. In a second paper, they reported kinetic aspects of molecules on terraces and steps of a TiO2 (110)-(1 × 1) surface, which may be relevant to oxide catalysis [155]. Two years later, formate (HCOO− ) and acetate (CH3 COO− ) molecules were identified molecule-by-molecule on TiO2 [156] (Fig. 16.30). The character of the tipmolecule force responsible for the observed image contrast is discussed. They have also addressed the origin of the contrast forming the images with acetate (CH3 COO− ) and trifluoroacetate (CF3 COO− ) molecules adsorbed on a TiO2 (110) [157, 158] (Fig. 16.31). The trifluoroacetate is represented as a short protrusion in the constant frequency-shift topography when compared to the acetate. A permanent dipole moment on the CF3 group is proposed to compensate for the moment of the COO− group of the opposite direction and reduce the electrostatic force between the tip and the molecule. In [159], they presented an nc-AFM image of a mixed monolayer composed of propiolate (HCdropCCOO− ) and formate molecules prepared on a TiO2 (110)(1 × 1) surface. The height difference between the propiolate and formate in the

Fig.16.30.Formate and acetate molecules adsorbed on the TiO2 (110) substrate. (a) Top- and sideviewed space-filling model. One acetate and five formates are shown. Dark and gray particles represent Ti and O atoms of the substrate. (b) Atom geometry of a formate and acetate adsorbed in the bridge configuration. Atom-atom distances are presented in nm. The C − C and C − H bond lengths follow those in free HCOOH and CH3COOH molecules. Courtesy of [156]

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Fig. 16.31. Constant frequency-shift topography images of (a) acetate and (b) trifluoroacetate monolayers on TiO2 (110) (images size: 9 nm). Courtesy from [157]

nc-AFM image is smaller than the physical height difference. A simple simulation involving van der Waals force variations between the tip and the monolayer-covered surface reproduces the experimental findings. In 2000, Fukui and Iwasawa published [160]. Fluctuating molecules of acetate ions in the (2 × 1)-acetate overlayer on TiO2 (110)-(1 × 1) are observed by ncAFM. Each acetate ion adsorbed on its stable site is observed as a bright round protrusion. The ions order with a (2 × 1) periodicity. Besides, they found that acetate ions located at a domain boundary with different phases along the [001] direction can move along the [001] direction during scanning, thus giving stripes in the images. They conclude that unstable regions for acetate ions are formed at domain boundaries. The phenomenon is explained in terms of repulsive and attractive interactions between acetate ions and hydroxyl hydrogen atoms, which are formed by dissociative adsorption of the acetic acid. 16.5.2.5 Other Molecules Sasahara et al. investigated monolayers of di- and tri-fluoroacetate and trifluoroacetate on titanium oxide [161]. The chemical identity of individual adsorbed molecules is determined in the mixed monolayers. The permanent dipole moment of the fluorine-substituted terminal groups perturbs the microscope topography images via the electrostatic coupling with the tip.

16.6 Molecules on Insulating Surfaces Despite promises, as outlined in the Introduction, investigations of organic molecules on ultrathin insulating films on metals and on bulk insulators by scanning probe microscopy are still scarce in the literature. Note that recently, a review of the electronic properties of the ultrathin insulating films on metals has been published by Schintke and Schneider [162].

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16.6.1 STM Investigations Rauscher et al. used stepped Si(111) surfaces with self-organized CaF1 /CaF2 stripe patterns as a mask for selective adsorption of 3,10-di(propyl)perylene [163]. These molecules adsorbed preferentially on CaF1 nanostripes, rather than on CaF2 . Large assemblies of parallel, equidistant stripes 1–15 nm wide were fabricated. The group of Ho has investigated the vibronic states of single porphyrins [164] and of single C60 and C70 molecules [165] by scanning tunneling microscopy on a thin layer of Al2 O3 grown on a NiAl(110) substrate at low temperature. With the porphyrins, vibrational properties are observed in the light-emission spectra that depend sensitively on the different molecular conformations and correspond to electronic states observed by scanning tunneling spectroscopy. The high spatial resolution of the STM enables the demonstration of variations in light-emission spectra from different parts of the molecule. With the fullerenes, equally spaced features are observed in the differential conductance (dI/dV ) which are clearly resolved in d2 I/dV 2 spectra. These features are as well attributed to the vibronic states of the molecule. The vibronic progressions are sensitive to the molecular orientations and can have different spacings in different electronic bands of the same molecule. Vibronic states are not resolved in molecules adsorbed on the metal surface. Very recently, Repp et al. employed ultrathin insulating NaCl films (1 to 3 ML) to decouple individual pentacene molecules from Cu(111) [166]. The experiments have been carried out at low temperature. Direct images of the unperturbed molecular orbitals of individual molecules were obtained, substantiated by elastic scattering quantum chemistry calculations (Fig. 16.32).

Fig. 16.32. Pentacene molecules on one and two layers of NaCl on Cu(111). Numbers indicate the layer thickness. The long axis of a pentacene molecule is aligned parallel to one of the polar 011 directions of the NaCl(100) films, as deduced from the orientation of the nonpolar NaCl step edge. The center of a pentacene molecule is located on top of a Cl ion of the NaCl film, which was determined indirectly with the help of coadsorbed Au adatoms (inset). Courtesy of [166]

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16.6.2 Non-contact AFM Investigations 16.6.2.1 Thin Molecular Films Sommerhalter et al. investigated and compared the growth of C60 and heterofullerenes C59 N on graphite, WSe2 and mica at different substrate temperatures by nc-AFM [167]. Whereas C60 nucleates in well-shaped trigonal and hexagonal islands, C59 N forms extended dendritic agglomerates. Compact and oriented islands were found only above 250 ◦ C. The formation of dendroids indicates that C59 N stack strongly to the edges of the islands. The mobility of C59 N on graphite and WSe2 is rather high and comparable to that of C60 on the same materials. On mica, only small islands are observed for both C60 and C59 N, indicating a low mobility of both molecules. Schlettwein et al. studied the growth of PTCDA and C4 -PTCDI on the (100) faces of freshly cleaved single crystal, NaCl, KCl, and KBr [168]. Their crystalline motifs varied widely depending on the substrate and growth conditions, and a form of layered growth was revealed in the first few monolayers of deposition for both adsorbates. Yamada et al. investigated the local structures and electrical properties of ferroelectric molecular films on KCl(100) [169]. The “ferroelectric” molecules, vinylidene fluoride oligomers have large dipole moment due to the difference in the electron affinity between the fluorine and the hydrogen atoms. The initial stage of epitaxial growth on KCl was revealed. Durr et al. reported extraordinary structural order along the surface normal in thin films of the organic semiconductor diindenoperylene (DIP) deposited on silicon-dioxide surfaces [170]. Individual monolayers of essentially upright-standing DIP molecules could be observed in TEM images indicative of high structural order, whereas nc-AFM images showed large terraces with monomolecular steps ˚ high. approximately 16.5 A

Fig. 16.33. AFM images of ca. 1–2 equivalent monolayer coverages of PTCDA on (a) KBr(100), and (b) KCl(100) (images size: 6 mm). Courtesy of [168]

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16.6.2.2 Single Molecules Only a few investigations of single molecules on bulk insulating surfaces by AFM in UHV are available. To our knowledge, no studies have been reported at low temperature.

Fig. 16.34. Non-contact AFM image of a KBr(001) surface (image size: 400 nm) displaying terraces separated by regularly spaced monatomic steps, which form part of a growth spiral after deposition of a submonolayer of Cu-TBPP molecules; the molecules decorate the step edges. Courtesy, from [122]

Fig. 16.35. (a) Non-contact AFM image of the KBr(100) surface after electron irradiation (image size: 150 nm). Monatomic steps and pits, one layer deep, are visible. The bar indicates the location of the section shown in the inset. (b)–(d) Non-contact AFM images of SubPc molecules on the electron-irradiated KBr(001) surface. (b) The molecules decorate steps and fill pits of width smaller than 15 nm (image size: 100 nm). (c) No molecules are observed on the KBr terraces. Molecular self-assembled structures are revealed within two pits. The arrow indicates a 2-nm-wide pit trapping a small number of molecules (four or five). The square denotes the scanning area shown in the plot (image size: 27 nm) (d) Molecular resolution reveals that the structures are tilted 45◦ with respect to the pit edges (image size: 18 nm). Courtesy of [122]

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In [122], Nony et al. investigated the adsorption of two kinds of porphyrin (Cu-TBPP) and perylene (PTCDA) derived organic molecules on KBr(001) and Al2 O3 (0001) by nc-AFM in UHV. The goal of these experiments was to assemble ordered molecular arrangements on insulating surfaces at room temperature. Despite well-ordered islands of Cu-TBPP molecules were successfully imaged on Cu(100), the same molecules aggregated in small clusters at step edges, rather than forming ordered monolayers, on KBr and Al2 O3 (Fig. 16.34). In order to overcome the molecules’ mobility at room temperature, artificial monolayer-deep rectangular pits were created in the KBr(001) by electron irradiation of the surface. Even if molecular resolution was not achieved, it was found that the pits acted as traps to confine small molecular assemblies. In a second paper [171], the same group evaporated SubPc molecules on a similarly prepared KBr sample. Molecular resolution of the molecules confined within the pits was reported for the first time (Fig. 16.35). The analysis by Nony et al. shows that the molecules self-assembled in a specific fashion only inside pits below 15 nm in size. No ordered aggregates of molecules are observed on flat terraces. This tends to indicate that the molecules still diffuse therein. The nucleation mechanism is attributed to the high electrostatic potential in the corner sites of the pits, which strongly traps the molecular dipole.

16.7 Manipulation of Single Molecules In the early 90’s, Eigler and co-workers used for the first time the tip of a low temperature STM to manipulate individual atoms on a metallic surface [172]. These experiments have since been successfully reproduced, notably by the group of Rieder [173]. Controlled repositioning of individual molecules on metal and semiconductor surfaces was later on also achieved. Adsorbate-adsorbent interactions, as well as adsorbate-adsorbate and tip-adsorbate interactions, are decisive for STM manipulation. 16.7.1 STM Investigations 16.7.1.1 Fullerenes Displacement of C60 molecules previously adsorbed on a Si(111)-(7 × 7) surface were first reported by Maruno et al. [174]. Threshold conditions at which a molecule starts moving were investigated in relation to tunnel current and tip bias voltage. Direct contact or close proximity between tip and C60 are required for movement of the molecules to occur. Fullerene molecules were also manipulated by Beton et al., who formed simple patterns on Si(111) and Ag/Si(111) [175, 176]. On Si(100)-(2 × 1) intramolecular features were observed, suggesting that C60 undergoes rotation during displacement [177]. Transfer of a molecule from sample to tip (or vice versa) changed both the imaging and manipulation properties of the STM tip.

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Controlled displacements of C60 along a monoatomic step of a Cu(111) surface were performed by Cuberes et al. They built a “nanoabacus” in which single molecules acted as “counters” [178]. They also moved fullerene molecules on a molecular monolayer (dimethyl bianthrone) previously grown on a similar surface [179]. Lateral patterns were assembled without disrupting the substrate. Butcher et al. investigated the absorption of the heterofullerene C59 N on Si(100)(2 × 1) [180]. The molecules are adsorbed into monomers in the troughs between silicon dimer rows. The authors used the STM tip also to manipulate the molecules parallel and perpendicular to the dimer rows in a controlled fashion. It was found that the Si(100)-(2 × 1) surface inhibits conversion to (C59 N)2 dimers. 16.7.1.2 Porphyrins Room temperature manipulation of large molecules was first achieved by Jung et al., who disrupted an island of Cu-TBPP on Cu(100) by dragging the STM tip over it and then displaced individual molecules to form a hexagonal ring [71].

Fig. 16.36. Demonstration of C59 N manipulation: (a)–(c) Parallel to the Si(100)-(2 × 1) dimer rows. (d)–(f) Perpendicular to the dimer rows. (images size: 8 nm); (g) Six molecules before manipulation; (h) The same six molecules after manipulation to precise positions. Courtesy of [180]

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Fig.16.37.STM images showing the rotation of a leg induced by (a)–(c) lateral and (d)–(e) vertical manipulation. The lateral manipulation was performed in the direction indicated by the arrows in (a) and (b) at a tunneling resistance of 6 × 104 Ω; (b) shows the result of the manipulation in (a), and (c) shows the result of the manipulation in (b). (e) Result of the vertical manipulation performed by positioning the tip on the point indicated with a circle on image (d). (f) Calculated STM scans of the Cu-TBPP molecule across an ON leg (dotted line), an OFF leg (dashed line), and across two opposite OFF legs (continuous line). Courtesy, from [181]

Later, at low temperature and on Cu(211), Moresco et al. found that, although the force applied by the tip is not strong enough to translate the molecule, it can induce the rotation of individual legs in and out of the plane of the porphyrin ring, thus realizing a molecular switch [181] (Fig. 16.37). The idea is to control the tunneling current by intramolecular conformational changes of the molecule, ensuring either a high or a low resistance R through the junction formed with the STM tip. The current passing through a single leg is strongly dependent on its orientation, which can be switched mechanically by the STM tip apex. When the legs lie nearly flat on the surface, eight lobes per molecule are imaged. The same group has also reported lateral manipulations on Cu(111) [182,183]. Most parts of these investigations were performed in the constant height mode. Thomas et al. used the STM tip to break strips of zinc porphyrins on graphite sliding the molecules laterally across the surface [184]. They found that the direction of molecular translation is constrained by the intermolecular forces within the supramolecular array, which defines preferential directions for molecular slip and not simply by the scanning direction. 16.7.1.3 Phtalocyanines Yanagi et al. observed a reversible, orientational switching of SubPc molecules with STM [185]. The asymmetric, polar molecules adsorbed in an epitaxial array on a Cu(100) surface, initially with its axial chlorine atom either upward or downward. After scanning at a negative bias the upward molecules turned upside down, while all molecules switched to the upward orientation at a positive bias. This flip-flop switching of the molecular array would lead to an information density of 60 Tbit/cm.

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16.7.1.4 Lander Molecules The group of Rieder investigated the contact between the molecular wire group of a Lander molecule and the edge of a Cu(111) monoatomic step [186]. Reproducible contact and decontact of the wire was obtained by manipulating the Lander at low temperature. The electronic standing wave patterns on the copper surface served to monitor the local electronic perturbation caused by the interaction of the wire end with the step edge, giving information on the quality of the contact. They also induced controlled conformational changes with the STM tip to single Lander molecules adsorbed on Cu(110) [187] (Fig. 16.38). By means of a gentle lateral manipulation process, just one pair of molecular legs could be rotated reversibly, keeping the central board fixed and in electronic interaction with an atomic Cu wire underneath.

Fig. 16.38. Manipulation series of a Lander molecule adsorbed on a wire. (a)–(c) STM images (images size: 4.5 nm) of different conformations. The corresponding line scans across the legs in the [1–10] direction are plotted in (d)–(f) (line scans A across the “lower” pairs of legs ˚ for clarity, across the “upper” ones in the STM images). (g)– and B, shifted vertically by 1.5 A (i) Shematic models of the molecular conformations obtained after a conformation refinement. Courtesy, from [187]

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16.7.1.5 Other Molecules Lu et al. observed that chlorobenzene (C6 H5 Cl) on Si(111)-(7×7) can be dissociated by the application of voltage pulses to the probing tip, thereby generating chemisorbed chlorine atoms [188]. Sloan et al. studied the desorption yield of cholorobenzene from the same surface as a function of the tunneling current and the sample bias voltage [189]. Their results suggest that desorption is driven by the population of negative (or positive) ion resonances of the chemisorbed molecule by the tunneling electrons (or holes). Hla et al. induced chemical reactions on individual iodobenzene molecules by STM [190]. The reaction steps involved the separation of iodine by using tunneling electrons, bringing mechanically together two resultant phenyls by lateral manipulation and, finally, their chemical association to form a biphenyl molecule mediated by excitation with tunneling electrons. Although carbon monoxide (CO) molecules do not fit with the general context of “medium-sized aromatic molecules”, we want to mention the striking results by Heinrich et al. [191] anyway. They arranged CO molecules in atomically precise configurations, called “molecule cascades”, where the motion of one molecule causes the subsequent motion of another, and so on in a cascade of motion similar to a row of toppling dominoes. Isotopically pure cascades were assembled on a Cu(111) surface with a low-temperature scanning tunneling microscope. They present a cascadebased computation scheme that has all the devices and interconnections required for the one-time computation of an arbitrary logic function. 16.7.2 Non-contact AFM Investigations To our knowledge, no investigation dealing with controlled manipulations of individual molecules by nc-AFM has been reported. Some authors report involuntary displacement of molecules such as C60 or Cu-TBPP [118, 122]. Despite the fact that some attempts have been reported on manipulation of single atoms on a Si(111)-(7 × 7) surface [192], the controlled manipulation of nano-objects, among them molecules, at surfaces by non-contact AFM still remains highly challenging. Some hope could come from the emerging field called lateral dynamic force microscopy, wherein the tip oscillates parallel to the surface by exciting the lateral bending mode of the cantilever [193]. The vertical position of the tip is then controlled by tunneling current, which would a priori restrict the technique to conducting samples. However, the major advantage of that technique is that it gives access to forces required to manipulate the objects, which are not accessible with STM manipulations.

16.8 Conclusions In conclusion, we have shown how scanning probe microscopy has been applied to investigate, isolate and manipulate different organic molecules on metal, semicon-

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ductor and insulating surfaces. The same chemical compounds give rise to different structures, depending on several factors, such as the adsorbate coverage, the substrate orientation or the temperature. Self-assembled patterns formed on the step edges of insulating surfaces – or raised from metal substrates by specifically designed molecular “legs” – can be used as molecular wires. The different conformations assumed by single molecules can be viewed as different logical states of a digital circuit. Scanning probe microscopy might become one of the essential ingredients to design future molecular electronics devices. Well-defined experiments to investigate self-assembly characteristics and to measure the mechanical and electrical properties of the individual molecules will be performed. Internal degrees of freedoms of the molecules and mechanical instabilities are rather complex phenomena, which will need both experimental and computational efforts to achieve the required degree of control of these novel molecular electronics devices. Acknowledgements. The authors are grateful to Alexis Baratoff and Luca Ramoino (NCCR, Univ. of Basel, Switzerland), Renato Buzio (CNR-INFM, Univ. of Genova, Italy), Karine Mougin (ICSI, CNRS, Mulhouse, France), Mathieu Koudia and Mathieu Abel (L2MP, Univ. of AixMarseille III, France) for discussions and critical reading. This work was supported by the Swiss National Center of Competence in Research (NCCR) on “Nanoscale Science” of the University of Basel.

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Kruse P, Johnson ER, Di Labio GA, Wolkow RA (2002) Nano Lett 2:807 Pitters JL, Piva PG, Tong X, Wolwok RA (2003) Nano Lett 3:1431 Basu R, Guisinger NP, Greene ME, Hersama MC (2004) Appl Phys Lett 85:2619 Greene ME, Guisinger NP, Basu R, Baluch AS, Hersam MC (2004) Surf Sci 559:16 Keeling DL, Oxtoby NS, Wilson C, Humphry MJ, Champness NR, Beton PH (2003) Nano Lett 3:9 Kobayashi K, Yamada H, Horiuchi T, Matsushige K (2000) Appl Surf Sci 157:228 Fukuma T, Kobayashi K, Yamada H, Matsushige K (2004) J Appl Phys 95:4742 Fukui K, Onishi H, Iwasawa Y (1999) Appl Surf Sci 140:259 Iwasawa Y, Onishi H, Fukui K, Suzuki S, Sasaki T (1999) Faraday Discuss 114:259 Sasahara A, Uetsuka H, Onishi H (2001) J Phys Chem B 105:1 Sasahara A, Uetsuka H, Onishi H (2001) Phys Rev B 64:121406 Sasahara A, Uetsuka H, Onishi H (2001) Surf Sci 481:L437 Sasahara A, Uetsuka H, Ishibashi TA, Onishi H (2002) Appl Surf Sci 188:265 Fukui K, Iwasawa Y (2000) Surf Sci 464:L719 Sasahara A, Uetsuka H, Onishi H (2003) Langmuir 19:7474 Schintke S, Schneider WD (2004) J Phys: Condens Matter 16:R49 Rauscher H, Jung TA, Lin JL, Kirakosian A, Himpsel FJ, Rohr U, Mullen K (1999) Chem Phys Lett 303:363 Qiu XH, Nazin GV, Ho W (2003) Science 299:542 Liu N, Pradhan NA, Ho W (2004) J Chem Phys 120:11371 Repp J, Meyer G, Stojkovic SM, Gourdon A, Joachim C (2005) Phys Rev Lett 94:026803 Sommerhalter C, Pietzak B, Lux-Steiner MC, Nuber B, Reuther U, Hirsch A (1999) Surf Sci 435:486 Schlettwein D, Back A, Schilling B, Fritz T, Armstrong NR (1998) Chem Mat 10:601 Yamada H, Fukuma T, Umeda K, Kobayashi K, Matsushige K (2002) Appl Surf Sci 188:391 Durr AC, Schreiber F, Munch M, Karl N, Krause B, Kruppa V, Dosch H (2002) Appl Phys Lett 81:2276 Nony L, Gnecco E, Baratoff A, Alkauskas A, Bennewitz R, Pfeiffer O, Maier S, Wetzel A, Meyer E, Gerber C (2004) Nano Lett 4:2185 Eigler DM, Schweizer EK (1990) Nature 244:524; Stroscio JA, Eigler DM (1991) Science 254:319; Heller EJ, Crommie MF, Lutz CP, Eigler DM (1994) Nature 369:464 Bartels L, Meyer G, Rieder KH (1997) Phys Rev Lett 79:697 Maruno S, Inanaga K, Isu T (1993) Appl Phys Lett 63:1339 Beton PH, Dunn AW, Moriarty P (1995) Appl Phys Lett 67:1075 Beton PH, Dunn AW, Moriarty P (1996) Surf Sci 362:878 Moriarty P, Ma YR, Upward MD, Beton PH (1998) Surf Sci 407:27 Cuberes MT, Schlittler RR, Gimzewski JK (1996) Appl Phys Lett 69:3016 Cuberes MT, Schlittler RR, Gimzewski JK (1997) Surf Sci 371:L231 Butcher MJ, Jones FH, Moriarty P, Beton PH, Prassides K, Kordatos K, Tagmatarchis N (1999) Appl Phys Lett 75:1074 Moresco F, Meyer G, Rieder KH, Tang H, Gourdon A, Joachim C (2001) Phys Rev Lett 86:672 Moresco F, Meyer G, Rieder KH, Tang H, Gourdon A, Joachim C (2001) Phys Rev Lett 87:088302 Moresco F, Meyer G, Rieder KH, Tang H, Gourdon A, Joachim C (2001) Appl Phys Lett 78:306 Thomas PJ, Berovic N, Laitenberger P, Palmer RE, Bampos N, Sanders JKM (1998) Chem Phys Lett 294:229 Yanagi H, Ikuta K, Mukai H, Shibutani T (2002) Nano Lett 2:951

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17 One- and Two-Dimensional Systems: Scanning Tunneling Microscopy and Spectroscopy of Organic and Inorganic Structures Luca Gavioli · Massimo Sancrotti

Abbreviations 1D 2D 3D DFT DOS HREELS HOMO LDA LEED LUMO ML MOCN RT STM STS UPS

One dimension Two dimensions Three dimensions Density functional theory Density of states High-resolution electron energy loss spectroscopy Highest occupied molecular orbital Local density approximation Low energy electron diffraction Lowest unoccupied molecular orbital Monolayer Metal-organic coordination networks Room temperature Scanning tunneling microscopy Scanning tunneling spectroscopy Ultra-violet photoemission spectroscopy

17.1 Introduction The physical and chemical properties of low-dimensional structures depend on their size and shape, and can be very different from those of bulk matter. For inorganic crystals, the break in translational symmetry at a surface creates electronic properties that differ from those in the bulk crystal and localize at the surface layer [1, 2]. If structures have at least one dimension small enough that quantum-mechanical effects prevail, their behavior can be particularly interesting. Besides the effort of growing low-dimensional structures to obtain actual 1D conductors [3–15], to highlight quantized effects for 2D structures [16–21], to explore magnetic properties in low dimension [22–24], a lot of research has been stimulated to understand the mechanisms driving the long-range ordering and the interaction between substrate and adsorbate layers. Arbitrary atomic-scale structures can be assembled with the tip of a scanning tunneling microscope (STM), either through direct displacement of adsor-

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bed atoms [6, 7, 25, 26], either through tip-assisted decomposition of chemical species [27, 28]. Such methods suffer a lack of serial character. Approaches where a large number of structures can be created in parallel are the self-organized growth [3–5, 9, 10, 13, 14, 29–33], the controlled deposition of size-selected clusters from the gas phase [34], and the use of templated substrates [3, 4, 9, 10, 12, 29]. The growth is controlled by the balance between kinetics (impingement rate and surface diffusion) and thermodynamics (surface and interface energies) [35–37]. Fast surface diffusion and low impingement rates favor the formation of large islands and layer-by-layer growth, while poor adhesion (low interface energy) promotes aggregation and 3D growth modes. Moreover, the substrate-adsorbate and the adsorbate-adsorbate interactions can provide new ingredients that might modify the formation of the growing layer, giving rise to long-range ordered structures [12, 13, 15, 31, 33, 38–42]. Investigation of organic adlayers is at present an active area of research, as the semiconducting electrical properties of these materials make them promising candidates for plastic electronic device applications [43–45]. Because charge mobility and injection in organic crystals depend strongly on molecular orientation and packing, controlling the structure and the morphology of organic thin films is a key issue to obtain useful applications. Moreover, the electronic properties of molecular 2D film are strongly influenced by the energy level alignment at the contacts [46–53]. For instance, the determination of the HOMO–LUMO gap is of fundamental interest to understand charge transport and injection barriers at the metal-film interface [47–51, 54, 55]. For nonreactive organic molecules, like pentacene, adhesion is relatively small on most surfaces, although it can be adjusted by optimizing the choice and the preparation of the substrate. For example, chemical treatment of the Si(001) surface allows the growth of large size (up to 0.1 mm) single-crystal pentacene grains [56] with “standing-up” molecules, i.e. molecules with the long axis aligned with the surface normal. It has been proved that a smooth surface of a weakly chemically active substrate, such as Ag(111), allows for the epitaxial growth of commensurate, lying-down, highly ordered films of large, π-conjugated organic molecules, like PTCDA (3,4,9,10-perylenetetracarboxylic dianhydride) and oligothiophenes [57, 58]. Attempts to grow 1D laterally ordered thin films of molecules with no reactive groups like pentacene on any weakly interacting (111) metal surfaces indicates that either substrate-mediated interactions [13] or control over the kinetic energy of impinging molecules [42, 59] are required to obtain long-range ordering of the molecules. As in the case of inorganic adsorbates, the presence of a templated structure on the substrate greatly improves the formation of 1D long-range order [12, 32], although a careful choice of growth parameters is required to facilitate the selfassembling mechanism. In this chapter, we want to briefly review some examples of long-range ordered structures obtained by either inorganic or organic adlayers on substrates that have been investigated using the STM. The structural information that can be obtained by STM is also complemented by the scanning tunnelling spectroscopy (STS) investigation of the electronic properties at the atomic scale, which is crucial in the comprehension of low-dimensional systems.

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17.2 Basic Principles of STM and STS In this section, we briefly review the principles of STM and STS, referring the reader to a complete theoretical treatment for details [60]. The most widely used STM operation mode is the constant current imaging, in which a feedback loop keeps the tunneling current constant at a given bias voltage by adjusting the distance between the tip and the sample. The height (z) adjustment at each rastering point of the tip provides the ‘topography’ z(x, y). The problem arises in the interpretation of such a z(x, y) map, since not only topographic features contribute, but the electron density distribution affects the tunneling current [60–64]. In order to understand z(x, y), one has to evaluate a theoretical expression for the tunneling current. The simplest case is represented by an electron tunneling through a one-dimensional rectangular potential barrier with height V0 and width s, shown in Fig. 17.1 (for a complete description of other tunneling cases we refer the reader to [60]). The solutions for the time-independent Schrödinger equation Hψ = Eψ in the three regions are: ψ1 = eikz + Ae−ikz , −xz

ψ2 = Be

ψ3 = De

ikz

+ Ce , xz

k2 = 2m E/
2 ,

(17.1a)

x = 2m(V0 − E)/
, 2

,

2

(17.1b) (17.1c)

where
is Planck’s constant divided by 2π. The important quantity is the barrier transmission coefficient T , which is the ratio of the transmitted density to the incident current density T = jt / ji = |D|2 . By imposing the continuity conditions for the wave functions and their derivatives at z = 0 and z = s, one obtains, in the limit of a strongly attenuating barrier (xs 1) [60], k2 x 2  e−2xs , T∝
2 k + x2

(17.2)

with the decay rate given by  x = 2m(V0 − E)/
. From (17.2) we observe that the dominant contribution to T is due to the exponential factor and is typical of tunneling, independent of the actual barrier shape.

Fig. 17.1. One-dimensional rectangular barrier with height V0 and width s

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The three-dimensional case is conveniently treated by using Bardeen’s formalism, which treats the tunneling through the barrier perturbatively [65]. If one considers the tunneling process between the sample surface and the metal tip, the tunneling current is given by I=


  2πe  
  f E µ 1 − f (E ν + eU) − f (E ν + eU) 1 − f E µ
µν  
 ·  Mµν  δ E ν − E µ , (17.3)

where f(E) is the Fermi function, U is the bias voltage applied to the sample, Mµν is the tunneling matrix element between the unperturbed electronic states ψν of the sample surface and ψµ of the tip, and E ν (E µ ) is the energy of the state ψν (ψµ ) in the absence of tunneling. The presence of the delta function describes the energy conservation in the case of elastic tunneling. The key of the expression is the calculation of the tunneling matrix element, which Bardeen has shown to be written as [65] 
 −
2 dS · ψν∗ ∇ψµ − ψν ∇ψµ∗ , Mµν = (17.4) 2m where the integral has to be evaluated over any surface lying entirely within the vacuum barrier region separating the sample and the tip. We can see that, to obtain the matrix elements, explicit expressions of the sample and tip wave functions are needed. Since the atomic structure of the tip is usually not known, one needs to model the tip wave function to perform the calculation. The first application of the transfer Hamiltonian to STM assumed a tip with radius R and an s-type only (quantum numbers l  = 0 neglected) wave function [61, 62], and small applied bias voltage. Hence, (17.3) becomes  
2 ψν r 2  δ (E ν − E F ) , (17.5) I ∝ U · n t (E F ) · e2x R 0 µν

where E F is the Fermi energy, r0 is the center of curvature of the tip, n t (E F ) is the density of states at the Fermi level for the tip, and the decay rate x = (2mφ)1/2 /h depends on the effective potential barrier height φ. The quantity  
2 ψν r 2  δ (E ν − E F ) (17.6) n s (E F , r0 ) = 0 µν

is the charge density from electronic states at the Fermi level [61,62], i.e. the surface local density of states (LDOS) at E F , evaluated at the center of curvature of the tip. Due to the sample wave function exponential decay in the z-direction normal to the surface towards the vacuum, one finds 
2 2 ψν r  ∝ e−2x(s+R) . (17.7) 0

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Therefore the tunneling current of (17.5) is exponentially dependent on the tip to sample distance s: I ∝ e−2xs .

(17.8)

The interpretation of the tunneling current as contour map of the surface LDOS is limited to small applied bias (less than 0.5 V) and ignores the angular dependence of tip wave functions. Since most of the tips used for STM imaging are made of metals with a density of states at the Fermi level dominated by d states (tungsten or platinum-iridium), it becomes very important to consider the role of such states in the interpretation of STM images [64]. Moreover, the s-like wave function approximation would not explain the atomic resolution experimentally obtained on many metal surfaces. Simulation of tip apex states by first principle calculations has shown the presence of dz2 states near the Fermi level at the tip apex [66]. Therefore, one has to calculate the tunneling matrix elements considering the higher quantum number states. It is also a limit in the interpretation of STM constant current images as topographic representation of the surface features, since such l = 0 states act as filters for the tunneling current [64], and one should take much care in the assignment of the atomically resolved structures, without a comparison to ab-initio calculations of the electronic structure or comparison to other experimental techniques. So far, we have taken the low applied bias approximation to interpret the tunneling current. It has been shown [63] that for higher bias (volts) the bias-dependence of the tunneling current generally does not show Ohmic behavior and the constant current images can critically depend on the applied voltage. A finite bias enters through the summation of states that contribute to the tunneling current, and can lead to a distortion of tip and sample wave functions, as well as a modification of the energy eigenvalues [67]. Due to the difficult problem of derivation of distorted tip and sample wave functions, one usually takes as first approximation the undistorted zero-voltage wave functions and eigenvalues. Therefore, introducing the effect of finite bias U as a shift in energy of the undistorted wave functions or density of states by an amount eU, one can generalize (17.6) and (17.7), obtaining for the tunneling current eU I∝

n t (±eU ∓ E)n s (E) · T (E, eU) dE ,

(17.9)

where n t (E) is the density of states of the tip, n s (E) is the density of states of the sample, and T(E, eU) is the bias-dependent transmission coefficient. The consequences of such applied bias are summarized in Fig. 17.2 for the simplified case of a one-dimensional energy diagram of the tip and the sample. When a bias voltage U is applied to the sample, the energy levels shift upward (U negative, Fig. 17.2c) or downward (U positive, Fig. 17.2d) by |eU|, depending on the polarity of the bias. Therefore, one can probe either the occupied or the empty states of the sample surface, selecting the contributing electronic states by varying the amount of applied bias. Considering (17.9), one observes that, at a first approximation, the first derivative dI/dU reflects the local electronic density of states. The contribution of the transmission coefficient (that is bias-dependent as well) results in a smoothly

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Fig. 17.2. Energy level diagrams for tip and sample. (a) Independent sample and tip. (b) Sample and tip at equilibrium, separated by a vacuum gap. (c) Negative sample bias: electrons tunnel from sample into tip. (d) Positive sample bias: electrons tunnel from tip into the sample

varying background, which can be suitably subtracted by normalizing the acquired spectroscopic derivative by the I/V signal [68]. Since electrons in states with the highest energy ‘feel’ the smallest effective barrier height, most of the tunneling current arises from electrons near the Fermi level. This means that tunneling from sample to the tip is more sensitive to the empty states shape of the tip. Moreover, in the case of molecular overlayers, the interpretation of the STS spectra is complicated by localization and polarization effects, already observed in molecular solids [51], and by the variation of the electrostatic potential in the molecular conductor [69].

17.3 Inorganic Overlayers This section is concentrated on structures obtained by depositing inorganic materials, like metals or semiconductors, on substrates that can be low Miller index surfaces or vicinal surfaces. 17.3.1 1D Structures The adsorption of metals on semiconductor or metal surfaces involves the formation of strong bonds between the adatoms and the substrate. In particular, the highly lo-

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calized and directional bonds present on semiconductor surfaces are important in the determination of the local atomic structure. The formation of strong chemical bonds might also be the key issue in determining the electronic structure of the adsorbed layer. The adatom-substrate interaction is also responsible for charge redistribution between adsorbates and substrate, which can originate surface dipoles driving the organization of ordered low-dimensional structures. We have recently shown that it is possible to obtain 1D atomic chains on the III–V(110) surfaces with alkali metals other than Cs [9, 70]. The atomic and electronic structure of the Cs chains is still debated [3, 4, 71–77]. The Cs/InAs(110) atomic geometry, with two unequivalent adsorption sites for Cs adatoms [73], is in agreement with core-level investigations [4, 74, 75], while previous STM data on Cs/GaAs(110) [3,72] have been interpreted in terms of the formation of a symmetric zigzag chain along the [11¯ 0] direction, with a single adsorption site. Such geometry has been the basis for justifying the insulating nature of the Cs chains, observed by STS [3, 72], HREELS [76] and photoemission [77], in terms of electron correlation effects [78, 79]. A recent theoretical calculation [80] proposed an alternative explanation by considering unbalanced charge transfer between the alkali metals and the unoccupied dangling bonds of the substrate. The different charge transfer, inducing the splitting of the partially occupied surface band, gives rise to a semiconducting system without including correlation effects [80]. The STM images of the K/InAs(110) interface show formation of 1D potassium chains oriented along the [11¯ 0] direction, separated by a distance D that is a multiple of the substrate lattice constant a0 (see Fig. 17.3). The data analysis shows that the chains are self-organizing on the surface in order to maximize the reciprocal distance, due to the formation of dipoles perpendicular to the surface, confirming the generality of the model proposed for Cs/InAs(110) [4]. The charge transfer from the alkali

Fig. 17.3. (a) STM image (20 × 20 nm2 , V = −1.6 V, I = 0.8 nA) of potassium chains (θ = 0.17θSAT ) deposited on the InAs(110) surface kept at 420 K temperature. (b) Constant current profile taken from the gray line marked in the image. The length is given in integer multiples of the clean substrate surface lattice constant a0

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adatoms to the In empty dangling bonds results in a strong distortion of the clean surface atomic geometry. The observed distortion is however not consistent with the predicted STM charge density distribution, that is not including electron correlation effects to justify the semiconducting nature of the chains [80]. Therefore, the experimental data suggest that to understand such 1D systems, one should take into account both unbalanced charge transfer and electron correlations [70]. The basic importance of the substrate mediated interaction between adsorbates on flat surfaces can be observed also in the formation of very long silicon chains on the β-SiC(100) surface [5]. Figure 17.4 is an STM image showing the β-SiC(100) surface after a thermal treatment at 1320 K, presenting surprisingly long and straight dimer rows separated mostly by the same distance (about 1.9 nm). Such almost regularly spaced nanostructures, forming a periodic superlattice, indicate a long-range lateral order having 7 × 2 surface arrays. These atomic lines, located at about 0.2 nm above the surface, derive from the original β-SiC(100) reconstruction. Moreover, these lines are almost defect-free with few missing dimers only, and have their lengths limited by step edges only. Thermal atom desorption and surface atom diffusion have been proposed as possible mechanisms contributing to the formation of the lines, although this would not explain the formation of very isolated chains at higher temperature. The authors underline the fact that, due to the large lattice parameter mismatch between SiC and Si [81], the full Si layer on which atomic lines lie is a stressed layer. Such strain can have a strong long-range influence on atom surface diffusion and/or nucleation [82–84]. Interestingly, this Si atomic line configuration optimizes a maximum surface area free from adsorbate, allowing the Si layer to form up and down dimers in a c(4 × 2) array and subsequently reducing the surface stress. In the examples presented so far, the self assembling mechanism and the substrate-adsorbate interactions play the major role in the formation of the structures. The alternative approach to build low-dimensional systems is the single atom manipulation. Investigation of atomic chains fabricated by single-atom manipulation provides a powerful tool for studying fundamental electronic processes in nanosco-

Fig.17.4.STM topographs (80×80 nm2 , V = −3.0 V, I = 0.2 nA) of: (a) Si atomic lines forming a superlattice obtained after annealing at 1320 K. (b) Si atomic lines obtained after annealing at 1470 K. (c) Isolated single Si-atomic lines lying on the β-SiC(100)-c(4 × 2) surface obtained after annealing at 1420 K. The two top atomic lines are separated by 40 nm [5]. Reprinted figure with permission from Soukiassian P, Semond F, Mayne A, Dujardin G (1997) Phys Rev Lett 79:2498. © 1997 by the American Physical Society

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pic systems, because it allows both to direct and to probe quantum confinement. This is of particular relevance to metallic nanostructures, since here the Fermi wavelength is of the order of a few tenths of nanometers, which demands confinement to atomic-scale dimensions in order to achieve quantization phenomena. Recently, it has been shown that the formation of quantized chain-localized states in the pseudogap of the substrate bulk band structure is a general phenomenon observable even for homogeneous metallic systems [6]. Monatomic Cu chains built on the Cu(111) surface are investigated at low temperature. Figure 17.5 shows the square of the wave functions of the chainlocalized states, as determined from the spatial variation of the dI/dV signal at tunneling voltages where peaks in the LDOS are observed. In detail, the resulting dI/dV maps obtained for Cui chains with i equal to three, five, seven, and nine (cf. rows from top to bottom, left panel of Fig. 17.5) reveal clear symmetry properties of the corresponding eigenstates, which are indicative of quantum confinement in a 1D potential well. Each column includes states of defined order n, with n = 1 being the ground state with one single lobe and (n − 1) specifying the number of nodes for states of higher order. Figure 17.5 (right) shows contours of the dI/dV signal measured along a Cu15 chain, demonstrating that states with n lobes are accessible for orders as large as n = 8. Obviously, the chain ends induce an enhanced dI/dV signal at the outermost lobe positions. A similar observation has been reported for Au chains on Al(110) [7,8] and was attributed to two possible effects, namely, (i) the change in tip-sample separation while scanning over the chain edge with the feedback loop turned off [8], and (ii) the existence of zero dimensional defect states localized at the chain ends [7]. The dI/dV data show that the 1D chains are characterized by remarkably distinct quantum levels. The 1D band dispersion obtained from the spectra [6] is fully described within a tight-binding approach accounting for the

Fig. 17.5. Left panel: dI/dV maps measured at constant tip height showing the square of the wave function of the chain-localized states (tunneling parameters prior to opening the feedback loop: V = 1.0 V, I = 1.0 nA). Rows from top to bottom correspond to chains of three, five, seven, and nine atoms, while columns include eigenstates of fixed order n (n = number of lobes). Right panel: dI/dV contours measured along a Cu15 chain for orders n = 3 to n = 8 taken at the same initial tunneling parameters as the dI/dV maps (left) [6]. Reprinted figure with permission from Fölsch S, Hyldgaard P, Koch R, Ploog KH (2004) Phys Rev Lett 92:056803. © 2004 by the American Physical Society

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coupling between the atomic resonances associated with the chain atoms, in contrast to a free-electron-like behavior proposed for Au/(NiAl(110) chains [7]. As mentioned in the Introduction, the growth of 1D structures is largely favored by the presence of a suitable substrate template, which is often provided by a stepped or vicinal surface. A vicinal surface is obtained by miscutting a crystal a few degrees off with respect to the high-symmetry crystallographic directions. The minimization of the surface strain energy leads to the formation of regular arrays of steps, with a terrace width that can be chosen by selecting the miscutting angle. The substrate templates direct the one-dimensional growth providing preferred nucleation sites at the step edges. The formation of regular 1D gold chains on a Si(553) stepped surface has been used to study electron correlation effects in a one-dimensional metal [10]. The fractional band-filling proposed for the selfassembled structures would justify the preservation of metallicity in the system, despite the strong electron–electron correlation present in the structure. The same system has been used to explore the presence of end states, the zero-dimensional analogs of the two-dimensional states that occur at a crystal surface [29]. The break in translational symmetry at a crystal surface creates surface electronic properties that differ from those in the bulk crystal and localize at the surface layer [1]. In analogy to a 2D surface state formed at the surface of a bulk sample, an edge or step in a 2D structure breaks the 2D symmetry and can form a 1D edge state [11]. Likewise, a finite 1D chain of atoms should exhibit zero-dimensional end states at its termini.

Fig. 17.6. The effects of end states are visible by comparing STM constant-current mode (I = 0.1 nA) images of the same area (8 × 19 nm2 ) of Si(553)-Au at positive and negative sample biases. The chains appear shorter at sample bias V = +0.5 V (a) than V = −1 V (b) [29]. Reprinted from SCIENCE. Crain JN, Pierce DT (2005) Science 307:703

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The different chain length observed in the STM images of the same sample region taken at +0.5 V (Fig. 17.6a) and at −1.0 V (Fig. 17.6b) is a signature of the formation of end states. This apparent change in length is caused by a contrast reversal over the end atoms. At positive bias the end atoms are hardly visible and the atoms second from the end are enhanced, whereas at negative bias the end atoms are enhanced. Such a polarity contrast in STM indicates an underlying difference in the DOS for the empty and filled states near the ends of the chains. On the end atoms, the DOS is transferred from the empty to the filled states. The differential conductivity, measured by STS, provides direct evidence of the electronic variation near the ends of a chain. Figure 17.7 shows an example for a seven-atom chain with spectra taken beyond the end of the chain, over an end atom, and on an interior atom. Beyond the end of the chain, there is a clear gap with little intensity near the Fermi energy (Fig. 17.7, light gray). Over the end atom, the differential conductance exhibits a new peak at −0.75 V (Fig. 17.7, gray). In contrast, the interior atom (Fig. 17.7, black) has an additional peak at +0.5 V inside the band gap. The comparison with a simple tight-binding model shows that end effects can lower the energy (0.4 eV for the filled states in the five-atom chain) of the filled states within the chains, by inducing charge transfer from the interior of the chain to the end atoms. This mechanism is not applicable to previously studied chain systems of Au on NiAl(110) [7] and Cu on Cu(111) [6], which have only empty states. The formation of end states does not lower the energy unless they are filled, possibly explaining why a particle-in-a-box model was sufficient in these previous

Fig. 17.7. (a) STM topography image of a seven-atom chain. (b) Selected spectra taken in the region beyond the chain (light gray), over an end atom (gray), and over an atom second from the end (black). The set point voltages are V = −1.2 V. Spectroscopy curves are offset for ease of display and offset baselines for each are also included [29]. Reprinted from SCIENCE. Crain JN, Pierce DT (2005) Science 307:703

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studies. The formation of end states provides a mechanism, in addition to the Peierls distortion, to lower the total energy for 1D chains of finite length. Tailoring the 1D chain separations by appropriate selection of step width is the basis to allow the study of the properties of low-dimensional systems on templated substrates. The ideal system for the investigation of 1D electronic and magnetic properties is a set of parallel, equidistant, straight monatomic chains consisting of a magnetic element on a nonmagnetic substrate. The distance between the chains has to be large enough to allow mostly intrachain and only weak interchain interaction. In these respects, the vicinal Pt(997) surface represents an excellent substrate. It supports the 1D growth of various elements, in particular the growth of monatomic Co and Cu wires [22], which are arranged in an array of high regularity with a distance of 8 ± 1 atomic rows [23]. On the clean Pt(997) surface, repulsive interactions between adjacent steps suppress step meandering, resulting in steps that run parallel to each other (see Fig. 17.8). The growth of Co and Cu monatomic chains along the Pt step edges results in smooth monatomic row growth taking place above 250 K and 150 K for Co and Cu, respectively. The deposition of 0.12 ML in the allowed range of temperatures results in the decoration of each step by a single monatomic row. The inset in Fig. 17.8 shows Co monatomic chains decorating Pt steps after deposition at 250 K. Chains wider than one atomic row can be obtained by increasing the coverage up to 1 ML. Investigation of the electronic structure of such chains reveals that the exchange splitting of the monatomic Co chains is large (2.1 eV). This value can be compared with typical values for thin Co films (1.4–1.9 eV) [85] and for bulk Co (1.4 eV) [85]. This large number for the Co chains suggests that the corresponding local magnetic moments also have a considerable magnitude compared to Co films and to bulk Co. An enhancement of the exchange splitting can be explained in terms of the lowered dimensionality of the Co system. For a magnetic system, it is well-known that a reduction of its dimensionality from 3D to 2D causes an enhancement of its magnetic moments. This effect is essentially a consequence of the band narrowing

Fig. 17.8. STM topograph (90 × 90 nm2 , dz/ dx mode) of the clean Pt(997) surface. The terrace width distribution follows a Gaussian law with an average spacing of 2.01 nm. The step edges appear as white lines. The step down direction is from the upper right to the lower left. The inset shows the decoration of the Pt steps by single monatomic Co chains, indicated by the arrow [23]. Reprinted figure with permission from Dallmeyer A, Carbone C, Eberhardt W, Pampuch C, Rader O, Gudat W, Gambardella P, Kern K (2000) Phys Rev B 61:R5133. © 2000 by the American Physical Society

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due to the reduced atomic coordination in the 2D system. In the electronic structure, this results in a larger exchange splitting compared to the bulk. With the same argument, even larger magnetic moments and a larger exchange splitting can be expected for a 1D system. The last example of 1D structure showing the potential of such systems is the creation of a stepped structure on a high Miller index surface, to act as template for nanolithography. The emulation of a photoresist layer in ordinary microlithography has been recently investigated on the stepped Si(111)-(7 × 7) surface [86, 87], by controlled deposition of CaF2 , to obtain highly perfect step arrays. General growth models [88–90] predict a transition from island nucleation to step flow growth with increasing temperature, decreasing rate, and decreasing step spacing. Growth in general is a nonequilibrium process for which a particular outcome is determined by the combined influence of these parameters, together with the total coverage. Among the other types reported in the work, the growth modes of interest for CaF2 appears at moderate temperature (880–900 K), combined with a coverage between one and two monolayers: highly perfect CaF2 stripes are formed on top of a CaF1 monolayer (see Fig. 17.9). The stripes grown on CaF1 are formed exclusively on the top edges of Si steps [86]. In fact, they avoid the bottom edge to such an extent that, even for coverage very close to two monolayers, there is always an uninterrupted CaF1 gap between a stripe and a bottom edge of a Si step. A simple explanation for this behavior comes from the fact that the Ca-terminated interface, i.e. CaF1 layer underneath CaF2 rotates the lattice by 180° around the normal [91, 92]. The CaF2 stripes are then laterally mismatched with the adjacent Si step and avoid it. Position on top of the step, on the other hand, allows CaF2 to maintain its preferred orientation. Such homogeneous and continuous stripes can serve as templates for selective deposition of insulated metallic nanowires with widths in the single digit nanometer range. That would provide the essential ingredients for controlled nanolithography of wires and dots.

Fig. 17.9. CaF2 stripes grown on a stepped Si(111) surface coated by CaF1 . The STM image (100 × 100 nm2 ), showing the x derivative of the tip height, simulates illumination from the left. Note that the CaF2 stripes are attached to the top of the step edges. Downhill is to the right [86]. Reprinted with permission from Petrovykh DY, Viernow J, Lin JL, Leibsle FM, Men FK, Kirakosian A, Himpsel FJ (1999) Journal of Vacuum Science & Technology A 17:145. © 1999, AVS The Science & Technology Society

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17.3.2 2D Structures As for the 1D case, the growth of ordered nanostructures in two dimensions has been investigated extensively in the last years. The major route to obtain ordered nanometer size structures on a large scale is again the self-assembling process of adatoms. This process might be driven by substrate–adsorbate interactions or by adsorbate–adsorbate interactions. An important example of the former case is the fabrication of highly ordered, two-dimensional nanostructure arrays, through nucleation of deposited metal atoms on substrates with periodic patterns, defined by dislocations that form to relieve strain [16]. The strain-relief patterns are created spontaneously when a monolayer or two of one material is deposited on a substrate with a different lattice constant. Dislocations often repel adsorbed atoms diffusing over the surface, and so they can serve as templates for the confined nucleation of nanostructures from adatoms. By this technique, ordered arrays of silver and iron nanostructures on metal substrates are obtained. The array of Fe quantum dots in Fig. 17.10 shows the unique potential of the approach, which gives rise to a narrow distribution of island width. The repulsive nature of the dislocations is the key property transferring the periodicity of the dislocation network to a highly ordered two-dimensional island superlattice. The effect of stress on the growth mode for other nonreactive metals/semiconductor interfaces might result in the formation of 3D islands with widely varying heights, either on the clean substrate (Volmer–Weber growth) or after the completion of a few wetting layers [Stranski–Krastanov (SK) growth] [89]. To obtain tailored structures, an “electronic growth” mechanism developed theoretically for such systems has been proposed, in which the energy contribution of the quantized electrons confined in the metal overlayer can actually determine the morphology of the growing film, prevailing over the strain energy [93, 94]. The influence of the electronic states on the film growth and morphology has been verified on the Ag/Si(111) interface [17], on Pb/Si(111) [18,19], on Ag/As(110) [20], and on Ag/Fe(001) [21]. The

Fig. 17.10. STM image (80 × 80 nm2 ) of a periodic array of Fe islands nucleated on the dislocation network of a Cu bilayer on Pt(111) at 250 K [16]. Reprinted from NATURE. Brune H, Giovannini M, Bromann K, Kern K (1998) Nature 394:451

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two-step process devised to explore the quantum nature of the growth morphology and the corresponding transport properties consists in low temperature adsorption followed by annealing to room temperature [17]. 2D plateau-like Ag islands with a strongly preferred height are hence observed by STM (see Fig. 17.11a). By increasing the Ag coverage, the islands increase their number density and lateral extension with coverage with no change in height, eventually forming a percolated network of the same preferred height. Figure 17.11b shows the structure of the surface second layer before the completion of the percolated network. Such behavior strongly determines the transport properties of the film, which increase its conductivity once the percolation is reached. The formation of the islands with the same preferred height is explained considering the energetic balance between the quantization of the electronic states within the metal layer and the stress effects due to the adsorption on the substrate. The self-assembly mechanism due to long-range surface-state-mediated adatom interactions belongs to the class of systems driven by substrate-adsorbate interactions, and has been proposed as a route to realize ordered 2D layers, observed on metal surfaces [95]. In this scenario, the surface-state electrons attempt to screen the impurity represented by an adatom, giving rise to surface-state Friedel oscillations. Because of the Fermi cutoff in momentum space, not all the wave vectors contribute to the screening process [1]. As a result, at the Fermi energy E F , the LDOS oscillates around the impurity with a wavelength of λF /2 = π/kF , where λF is the Fermi wavelength and kF the Fermi wave vector. This variation of the LDOS at E F due to standing-wave formation modifies the adsorption energy of the adsorbates. For adatoms it appears to be energetically favorable to rest in regions of high LDOS at E F . Therefore, the interaction between the adsorbates, and consequently their mutual distance, is determined by the LDOS at E F . Such concepts are applied on the Ce/Ag(111) interface to realize a hexagonal 2D superlattice of metallic Ce

Fig. 17.11. (a) STM image (100 × 100 nm2 , V = 2.4 V, I = 0.8 nA) of 1 ML Ag film deposited on the Si(111)-(7 × 7) surface at 150 K and annealed at 300 K. (b) STM image (100 × 100 nm2 , V = 2.4 V, I = 0.8 nA) of 1.5 ML Ag film obtained with the same procedure [17]

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adatoms [96], demonstrating that a subtle balance of temperature, surface diffusion barrier, and concentration-dependent adatom interaction potential is decisive for the formation of the superlattice. Figure 17.12 shows a large-scale STM topograph after deposition of about 0.01 monolayer of Ce onto Ag(111). The Ce adatoms appear to form a hexagonal superlattice, which is found everywhere on the sample, covering the entire Ag(111) surface at a macroscopic scale. The inset of Fig. 17.12 shows the Fourier transform of the image confirming hexagonal order, which is stable up to 10 K. The systematic investigation of the electronic density of states of the system shows that the distance between two Ce adatoms in this superlattice depends on the Ce coverage [97]. Figure 17.13a shows an STM image of a hexagonal unit cell of the Ce adatom superlattice at T = 3.9 K. The dI/dV spectrum shown in Fig. 17.13d was measured in the center of the triangle formed by three Ce adatoms with an adatom distance of d = 3.2 nm. The first of two relatively broad peaks, observed at approximately 85 and 210 meV, is chosen to obtain the spectroscopic imaging of the differential conductance of Fig. 17.13b. The image shows a maximum of the LDOS in the center of the triangles, a faint one right on top of the Ce adatoms, and a minimum around the adatoms. Furthermore, the energy of the peaks depends strongly on the superlattice spacing d. The comparison with tight binding calculations, which well reproduce the experimental dI/dV spectra of Fig. 17.13d, reveals that the gap opening in the free Ag(111) structure (induced by the Ce adatoms) results in an energy gain for the interface that corresponds to a Ce–Ce distance of 3.2 nm. Therefore, the authors suggest that the stabilization of the superlattice is a consequence of gap openings in the surface-state band. Adsorbate–adsorbate interactions, which determine the structure of the overlayer, can be investigated by the adsorption of C60 on metal substrates. The C60 cage can assume different orientations on host substrates [98–103], highlighting the delicate balance between C60 –C60 and C60 -substrate interactions that drive the physics of fullerene adsorption on surfaces. To enhance the binding, the C60 molecules could choose some optimal orientations, could undergo structural distortions of the cage, and in some cases they could also induce structural instability and reconstruction of the host substrate [98–103]. A very important point is, therefore, to understand the nature of the interaction between C60 and the substrate and how the molecules orient themselves onto the crystal surface. High-resolution STM data allows us to

Fig. 17.12. Ce superlattice on Ag(111) at large scale at 4.8 K (240 × 192 nm2 , V = 200 mV, I = 30 pA). Inset: the Fourier transforms of the image confirm the 2D hexagonal superlattice structure [96]. Reprinted figure with permission from Silly F, Pivetta M, Ternes M, Patthey F, Pelz JP, Schneider WD (2004) Phys Rev Lett 92:16101. © 2004 by the American Physical Society

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Fig. 17.13. (a) STM image of a hexagonal unit cell of a superlattice of Ce on Ag(111) (7.5 × 7.5 nm2 , V = 100 mV, I = 10 pA). (b) dI/dV map of the same area at the energy of the first peak (85 meV) of the spectrum shown in panel (d). (c) TB calculation of the LDOS. In white (black) the maximum (minimum) of the LDOS. (d) TB calculation and dI/dV measurement in the center of the triangle formed by Ce adatoms (set point before opening the feedback-loop V = 109 mV, I = 5 pA). The calculation, in contrast to the measurement, does not include the contribution of bulk states to the LDOS [97]. Reprinted figure with permission from Ternes M, Weber C, Pivetta M, Patthey F, Pelz JP, Giamarchi T, Mila F, Schneider WD (2004) Phys Rev Lett 93:146805. © 2004 by the American Physical Society

resolve the molecular orientation and the local charge density distribution of each single molecule in the different phases of the C60 /Ge(111)-c(2 × 8) interface. In Fig. 17.14a, we show an image of the unoccupied electronic states of C60 √ STM√ molecules arranged in the ( 13 × 13)R14◦ phase [104–106]. By comparing the STM image with the ab initio calculations (Fig. 17.14c) [107], we can attribute each set of three white maxima to the pentagon-related charge density of states of the C60 ball LUMO. The image indicates that each molecule presents the same orientation with respect to the substrate, in agreement with the geometry determination obtained by other techniques [104–106]. √ √ Figure 17.15 is a high-resolution STM image of the (3 3 × 3 3)R30◦ phase obtained after annealing at 720 K. A close inspection of the image allows one to distinguish different lobes due to various orientations of the C60 . By drawing a parallelogram on the image, one observes that the molecules placed at each vertex have the same orientation, differing from the molecules located at opposite sides. This is schematized on the left-hand side of the figure, where equivalent molecules have the same gray scale. The observation of this arrangement provides direct evidence

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Fig. 17.14. (a) Empty states STM image (7.4 × 7.4 nm2 , I = 1.8 nA, V = 2.0 V) of C60 molecules deposited on the Ge(111)-c(2 √ × 8)√surface and annealed at 920 K, forming the ( 13 × 13)R14◦ reconstruction. (b) The C60 molecular cage. (c) Calculation of the LUMO orbital (from [107]). Reprinted with permission from Pascual JI, Gomez-Herrero J, Sanchez-Portal D, Rust HP (2002) J Chem Phys 117:9531. © 2002, American Institute of Physics

Fig.17.15.(a) Empty states STM image (5.3×5.8 nm2 , I = 1.6 nA, V = 2.0 V) of √ √ C60 molecules deposited on the Ge(111)-c(2×8) surface and annealed at 720 K forming the (3 3×3 3)R30◦ reconstruction. (b) The (2 × 2) model due to different cage orientations with respect to the substrate

that the (2×2) surface unit cell is due to unequivalent orientation of the C60 molecules and not to modifications of the underlying substrate. It is not completely clear whether the major contribution to the molecular orientation be dictated by the intermolecular interactions rather that the molecule-substrate interaction. From the STM data it seems that the adsorbate-adsorbate interactions are the dominant force in determining the formation of the (2 × 2) structure, although we cannot exclude the role of the substrate, since the overlayer symmetry is commensurated to the substrate. As we have seen in previous examples, the ordering of an adlayer on a substrate is dictated by two competing forces, the adsorbate-adsorbate interaction and the adsorbate-substrate interaction. If the adsorbate-adsorbate interaction is dominant, the adsorbate layer may be incommensurate. If the adsorbate-substrate interaction is dominant, the adlayer is usually commensurate. If the two forces are competitive, the

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resulting structure can be discommensurate: weakly incommensurate domains form in which the adsorbate layer is highly strained [108,109]. These domains are separated by a regular network of dislocations, where the strain is released. In the presence of competitive forces, multiple, nearly degenerate ground state configurations might be present for the system. When the competing interaction cannot find a configuration in which they are all satisfied, the system is said to be frustrated [110, 111]. The observation of spontaneous changing from one virtual ground state to another has been done by STM measurements on the pseudo (5 × 5) Cu/Si(111) structure [110]. The STM image of the system shows a strong dependence on the applied bias, revealing the appearance of bright features at high bias. Such features exhibit remarkable changes over time, as shown in Fig. 17.16. If one assumes that the observed domains on the surface are shifting between clockwiseand counterclockwise-rotated equivalent positions, the motion of the bright features is explained by considering odd binding configurations of the adlayer at the domain boundaries. It has been recently argued that the pseudo (5 × 5) structure could be induced by the presence of a charge density wave at the 2D electron gas [109]. The study revealed the presence of wave vector nesting, which does not reconcile with the formation of the adlayer structure. Therefore, the electron gas does not participate in the determination of the surface structure.

Fig. 17.16. STM snapshots (10 × 10 nm2 , I = 1.2 nA, V = 1.8 V) of the same surface location, with the bright features circled [110]. Reprinted figure with permission from Mortensen K (1991) Phys Rev Lett 66:461. © 1991 by the American Physical Society

17.4 Molecular Overlayers The aim of growing low-dimensional organic nanostructures to investigate their physical properties, which in general differs from the bulk case, is often limited by the type of interaction between the molecules and the substrate. If the interaction is strong, i.e. a chemical bond is formed, once the molecule is adsorbed on the surface it is bonded at the adsorption site and might diffuse very slowly on the surface, limiting the formation of regular structures on flat surfaces [112, 113]. If the interaction is weak, like on most flat metallic surfaces, the adsorbed molecules might have a large diffusion coefficient and, therefore, it becomes impossible to stabilize them in ordered 1D structures. A way of overcoming this limitation is the use of chemical substitutents [114] or of directional intermolecular interaction such as hydrogen bonds [31, 40, 115], to stabilize the self-assembled layer. This section is

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devoted to the description of some examples of ordered organic adlayers deposited on metal or semiconductor substrates. 17.4.1 1D Structures The control of aggregation of porphyrin molecules on gold (111) is obtained by using a cyanophenyl substituent, due to the simple structure and asymmetric charge distribution, to induce dipole-dipole interactions [114]. The authors show how the choice and assembling of the substituents into modified porphyrin molecules allow the realization of geometrical 1D molecular rows across the elbows of the herringbone patterns of the Au surface. In a similar way, supramolecular clusters of 1-nitronaphtalene (NN) are selforganizing in chains on the Au(111) surface due to the change of the charge distribution polarity along the molecule perimeter, favoring the formation of a bond between the oxygen atom of the molecule with the CH group of the neighboring molecule (Fig. 17.17a). The weak interaction with the gold substrate does not influence the self-assembling process [31], while the molecules at low coverage nucleates starting at the fcc elbows of the Au(111) surface reconstruction (Fig. 17.17a). This approach is not suitable for all molecules. In particular, π-conjugated molecules like pentacene cannot form hydrogen bonds, and the addition of carboxy units would alter the electronic properties of the original molecule. Therefore, the use of templates like regular arrays of steps has been suggested as a different approach [13, 32], in particular for molecules with planar aromatic rings. Due to the planar structure constituted by benzene rings, such a class of molecules should constitute a model system to study the substrate-molecule interactions, which might drive the formation of ordered nanostructures. In particular, self-assembling mechanisms

Fig. 17.17. (a) STM image of 0.7 ML NN taken at 50 K. Inset: structural formula of NN. The dashed line encloses the exclusion area resulting from steric repulsion. (b) Reconstructed Au(111) surface with 0.1 ML NN taken at 65 K [31]. Reprinted figure with permission from Böhringer M, Morgenstern K, Schneider WD, Berndt R, Mauri F, De Vita A, Car R (1999) Phys Rev Lett 83:324. © 1999 by the American Physical Society

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driven by substrate-mediated interactions can be an important way of obtaining tailored 1D structures. An interesting example of ordered molecular geometries driven by a flat substrate is given by the adsorption of pentacene on the Cu(110) surface [13]. RT deposition on a single pentacene layer results in a disordered phase, with the molecules arranged side by side (see Fig. 17.18a). A thermal treatment to 400 K induces the formation of well-ordered molecular rows extending along the [001] surface direction (Fig. 17.18b and 17.18c). The authors justify this behavior by the presence of a charge density wave in the 2D electron gas of the Cu surface, which by electron interaction with the molecule orbitals is creating a preferential diffusion channel for the molecules. Such a mechanism induces a long-range ordering of the molecular rows on the entire surface (Fig. 17.18c), which is observed in the LEED pattern. It is not clear although, whether such ordered rows possess an effective electronic 1D nature, since no measurements of the electronic structure of this system are present in the literature. Another recent example of long-range ordering of the molecular adlayer is obtained by pentacene deposition on Au(110) [33]. The initial molecular adsorption takes place in the gold channels and induces a new missing row reconstruction, modifying the pristine Au(110)-(2 × 1) symmetry to a (1 × 3) reconstruction. The new channels favor the formation of molecular rows, again with the long side facing each other (see Fig. 17.19a). The molecular ordering also extends up to coverage of 7 ML (see Fig. 17.19b), driven by the underlying molecular rows. It is worth noting that the interaction of a planar molecule with this metal surface produces a rather strong modification of the substrate atomic configuration upon annealing. As in the previous case, no information on the electronic structure of such a system is available. The importance of the substrate crystal structure in determining the molecular arrangement is evident from Fig. 17.20a, where the pentacene molecules assemble in√rows√with an orientation following the underlying domains of the Ag/Si(111)( 3 × 3)R30◦ honeycomb geometry [14].

Fig. 17.18. STM images (25 × 25 nm, V = 2.0 V, I = 0.5 nA) on the left-hand side compare the pentacene film structure (a) after deposition at RT and (b) after annealing at 400 K which leads to long-range ordering (c) (250 × 250 nm2 ) [13]. Reprinted figure with permission from Lukas S, Witte G, Wöll C (2002) Phys Rev Lett 88:28301. © 2002 by the American Physical Society

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Fig. 17.19. (a) STM image [70 × 70 nm2 and 10 × 10 nm2 (insert), V = 0.19 V, I = 0.1 nA] showing the molecular structure of the multilayer pentacene film. Schematic white shapes represent the side-by-side orientation in the molecular arrangement. (b) STM image (28 × 28 nm2 ) of the initial pentacene film formation. The pentacene molecules first adsorb in a headto-head orientation within the gold channels inducing a new 1 × 3 missing row reconstruction. Once the gold channels have been filled up, adsorption occurs on top of the gold rows with the molecules adopting a side-by-side orientation [33]. Reprinted figure with permission from Guaino P, Carty D, Huges G, McDonald O, Cafolla AA (2004) Appl Phys Lett 85:2777. © 2004 by the American Institute of Physics

Fig. 17.20. (a) STM image (40 × 40 nm2 , U = −1.5 V, I = 0.1 nA) of the lower density adsorption phase. Molecules are lying flat on the surface. A small ordered region is indicated by the parallelogram. Parallel and perpendicular shifts of the molecular rows are indicated by the white lines and circled region, respectively [14, 116]. Part (a) reprinted with permission from Surface Science 540, p. 107. © 2003 by Elsevier. Part (b) reprinted with permission from Journal of Physics Condensed Matter 15, p. S2693. © 2003 by Institute of Physics

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Fig. 17.21. STM image showing coexisting molecular structures of D cysteine on an Au(110)-(1 × 2) surface (42.5 × 42.5 nm2 , I = 0.1 nA, V = −1.2 V). The molecular double-row structure (1) is terminated at ascending (A) or descending (D) step edges or at defects on the terraces. Inset: a close-up of a double-row formed from D cysteine molecules (4 × 4 nm2 ). The unit cell of this structure is depicted in black [15]. Reprinted figure with permission from Kühnle A, Molina LM, Linderoth TR, Hammer B, Besenbacher F (2004) Phys Rev Lett 93:86101. © 2004 by the American Physical Society

The authors indicate that in this first adsorption phase, the rows are most likely formed due to the mutual interaction among the molecular quadrupoles, mediated by the charge transfer between molecule and substrate. STS data obtained on the molecular rows show that the molecular layer is semiconducting with an HOMO– LUMO gap of about 2.35 eV [116]. Another case of substrate-mediated intermolecular interaction is the adsorption of cysteine [HS-CH2 -CH(NH2 )-COOH] on the missing-row reconstructed Au(110)(1 × 2) surface [15]. The molecules preferentially adsorb in unidirectional trenches created by the removal of atoms from the close-packed gold rows of the missingrow reconstructed surface. DFT calculations indicate that the formation of extended molecular rows minimizes the energy cost associated with the gold surface rearrangement, providing an effective intermolecular attraction, which acts as the driving force for the molecular self-assembly. We have recently investigated a different approach to the task of obtaining 1D molecular wires, by using substrate templates made by arrays of steps. The steps are typical surface arrangements to minimize the total energy of a high-Miller index surface, or vicinal surface. By miscutting a crystal at an appropriate angle, one can in principle control the width of the steps on the surface. In our case, the clean Cu(119) vicinal surface, is obtained by miscutting the (001) surface at an angle of 8.9 degrees, and the (001) terraces have step edges running along the [11¯ 0]-direction. Figure 17.22 shows an STM image (b) of the clean surface with the ball model (a) of the ideal Cu(119), with a monoatomic step height of 0.18 nm, shifted by half surface lattice constant (a0 = 0.255 nm) from one step to the adjacent one, reflecting the bcc Cu crystalline structure. The measured width of the steps (L = 1.17 ± 0.05 nm) is in good agreement with the ideal value (1.16 nm) [12]. Note that the step edges are not perfectly defined and the step width is variable along a single terrace, in agreement with the expected kink motion along the step direction at room temperature [117]. Deposition of a single layer of pentacene molecule on the substrate kept at 373 K results in long-range ordered chain structures, as observed in the STM images (Fig. 17.23). The molecules are aligned in rows oriented along the steps and separated by the step width (1.7 nm). The measured size of the molecules is 1.62 and 0.73 ±

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Fig. 17.22. (a) Schematic drawing of the stepped Cu(119) surface, in which the main symmetry directions are indicated by arrows; (b) typical STM (20 × 20 nm2 , I = 1.0 nA, V = −1.0 V) image of the clean surface. Note that some steps present a larger than the average value

Fig. 17.23. STM images of the ordered pentacene rows at the completion of the first layer, deposited with Cu(119) substrate kept at 370 K. (a) 80 × 80 nm2 ; (b) 15 × 15 nm2 , V = −1.4 V, I = 0.8 nA

0.09 nm for the longer and shorter side, respectively, in good agreement with previous dimensions obtained on other copper surfaces by STM [13, 118]. This suggests that also in this system the benzene rings are parallel to the substrate surface. Moreover, the distance between the center of each molecule along a single row is 2.20±0.09 nm, very close to an integer multiple of the underlying Cu substrate lattice parameter a0 . Surprisingly, the pentacene single layer shows a 2D ordering extending over individual steps edges. The images show adjacent rows presenting an alignment also in the direction perpendicular to the steps, extending for several terraces. By measuring the position of two molecules lying in parallel rows, we obtain a relative shift of d = 0.12 ± 0.02 nm, i.e. half of the Cu surface lattice vector. The shift

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is most likely generated by the crystal structure of the underlying vicinal surface, in which a monoatomic step is shifted by 0.125 nm with respect to the underlying atomic plane. The chain–chain ordering can extend up to ten consecutive molecular chains, but every domain constituted by regular chains in phase can be shifted with respect to the neighbor domain by an integer multiple of the distance d. Substrate temperature is critical in determining the row alignment, since a long-range ordering of parallel rows has never been observed after RT deposition. This is consistent with the change in growth morphology of solid pentacene predicted between 300 K and 375 K, when the interaction is purely directed by van der Waals forces [119]. The increased thermal energy available on the surface allows the molecules to form ordered structures, suggesting the presence of a molecule–molecule interaction that drives a self-organization process of the pentacene arrays. However, the relative position of two adjacent rows is related to the substrate lattice constant, indicating that also the molecule-substrate interaction plays an important role in the determination of the actual geometric position of the rows. Figure 17.24a shows single molecules appearing as a rod with an increased charge density located at the ends, a lower intensity extending between two molecules along the step direction, and a weak intensity extending perpendicular to the steps. The charge density distribution suggests the structural model sketched in Fig. 17.24b. Based on the present experimental data, it is not possible to quantify structural intramolecular relaxations, hence the dimensions of the free molecule were drawn considering the geometrical positions of the carbon atoms taken from [119].

Fig.17.24.(a) High resolution STM image (3.8×3.8 nm2 , V = −1.6 V, I = 0.4 nA) of pentacene molecules deposited on the Cu(119) surface at 370 K. (b) Schematic model for the molecular adsorption on the step edges for the pentacene ordered layer. (c) Constant current profile taken from (a), with the pentacene molecule

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The gray shadow represents the electronic cloud measured by STM, which is larger than the geometrical structure of the molecule. In this model, we placed the central ring of the benzene molecule on the hollow site of the Cu(001) surface, which is the lowest-energy adsorption site for the benzene molecule on the same surface [120]. This position seems reasonable since it can accommodate mostly all benzene rings in the pentacene molecule in or close to the hollow adsorption site. With this hypothesis, we obtain a very good agreement between the expected center-to-center molecular distance (2.23 nm) with the observed value (2.20 nm). Furthermore, only the hollow adsorption site can justify the observed charge density extending between the molecules in the direction parallel and perpendicular to the steps, as demonstrated in the calculation for the hollow adsorption site of benzene adsorbed on Cu(100) reported in [120]. Such adsorption geometry for the pentacene molecule can also explain the line profile plotted in Fig. 17.24c, similarly extracted from a large set of STM images. The apparent height of the constant current profile between two molecules (0.04 ± 0.01 nm) implies that the pentacene molecules are lying flat. The two maxima observed along the long axis of the molecule, indicate that the molecule is slightly bent with respect to the surface plane. This signature might be due to the fact that the outer benzene rings (assuming there are negligible distortion and variations of the C–C bonds inside the molecule upon adsorption [120, 121]) do not perfectly correspond to a hollow site, but they are displaced by 0.03 nm. The different position in the plane could induce a tilting of the outer rings, which could induce the observed maxima at the ends of each molecule in the STM images. STM images at lower pentacene coverage show that all molecules adsorb with the long side parallel to the step edges, without clustering. At this stage, the molecular mobility at the surface is large enough to overcome any intermolecular interaction, since no ordered structures are observed. Preliminary STS data obtained on the molecular rows indicate that the system is semiconducting, in agreement with photoemission experiments on the same system, although the comparison between photoemission and STS is still under analysis. 17.4.2 2D Overlayers The large development of investigations on molecular overlayers is boosted by the need to understand the metal/organic interfaces. For instance, injection barriers and, therefore, operational voltages of electronic and optoelectronic devices like organic light-emitting devices are influenced by the energy level alignment at the contacts [46]. In particular, highly-ordered thin molecular films can provide a deeper insight into the physical processes at those interfaces. A lot of efforts have been devoted to understand the positions of energy levels with respect to the work function of substrate in a molecular layer adsorbed on surfaces, since this will determine the charge transfer behavior across the interface [47–51]. Problems arise in measuring the HOMO–LUMO gap by standard photoemission techniques, if the assumption of a common vacuum level for the substrate and the adlayer may not be applicable [51–53]. In fact, the formation on interface dipoles,

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favored by the large polarizability of organic molecules, can affect the energy level diagram of the interface. Such an example is provided by the hexa-pery-hexabenzocoronene (C42 H18 , HBC) films adsorbed on an Au(111) surface [122]. STM images and LEED show that HBC form an ordered 2D overlayer stable up to 870 K, with a hexagonally close packed structure of apparently flat-lying molecules. STS data taken on such layer reveal the HOMO peak at the same energy as found in UPS spectra, while the LUMO could not be measured directly due to limitations in the voltage ramp in order to avoid sample damage (Fig. 17.25a). The authors underline the importance of probing the electronic states via STS at large sample-tip distances, since the tip can modify the electronic properties under investigation. In Fig. 17.25b, the comparison between STS and UPS gives a misalignment of the vacuum level of about 0.8 eV, attributed to the interface dipole. The same group has also performed a direct comparison between STS and tight binding calculations on the same system [41]. Through the calculation of the transmission probability across the molecular layer, the HOMO − 1 and LUMO + 1 molecular states have been identified. Moreover, the comparison with experimental STS spectra indicated an underestimation of the electronic energy gap of about 1.2 eV [41]. Fig. 17.25. (a) Differential conductivity dI/dV and normalized dI/dV curves of a 2–3-ML-thick HBC film on Au(111), obtained numerically from the averaged I(V ) curves (12 repetitions). The curves were measured at a large tunneling gap for different positions, and no lateral dependence was found. A pronounced feature around V = −1.4 V appears in the normalized dI/dV curve. (b) Proposed interfacial energy-level diagram of the HBC/Au(111) interface for multilayer coverage [122]. Reprinted figure with permission from Proehl H, Toerker M, Sellam F, Fritz T, Leo K, Simpson C, Müllen K (2001) Phys Rev B 63:205409. © 2001 by the American Physical Society

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An alternative direct method to measure the energy at which electrons or holes can be injected into conductive states within the conjugated polymer has been recently reported [54,55]. The spectroscopic data are taken with the STM feedback active, and dipping the tip into the polymeric layers, constituted by Poly(9,9 -dioctylfluorene) (PFO) and Poly[(2-methoxy-5-dodecyloxy)-1,4-phenylenevinylene-co-1,4-phenylenevinylene] [poly(1,12)AOPV-co-PPV]. At a tip bias such that the Fermi level of the tip E 0F lies within the HOMO–LUMO gap, it is not possible to tunnel into states of the polymer, and the tip penetrates the organic film until charge can tunnel into the substrate [Fig. 17.26a]. By increasing the magnitude of the tip bias such that E 0F lies above the LUMO state, electrons can be injected into the polymer [Fig. 17.26b], and the surface of the organic material can be imaged instead [123]. Similar arguments hold for the HOMO and the injection of holes. Hence when E 0F crosses the threshold for electron or hole injection into the polymer, the tip rises above the surface of the substrate by a distance corresponding approximately to the thickness of the organic layer. Therefore, the step threshold, which is determined by linear extrapolation, marks the onset of charge carrier conductance. 2D molecular adsorbates on surfaces are of great importance in the construction of metal-organic coordination networks (MOCN). Such networks have attracted wide interest because they provide a novel route towards porous materials that may find applications in molecular recognition, catalysis, gas storage and sepa-

Fig. 17.26. (a) At small negative tip bias, electrons from the Fermi level E 0F of the STM tip can only access vacant states above E F of the gold substrate. Under these conditions, the STM tip penetrates the polymer layer and images the underlying gold. (b) As the tip bias is made more negative, electrons can eventually tunnel into vacant states in the polymer, and the tip images the polymer surface instead. Similar arguments apply for reverse polarity. (c,d) Typical relative tip height vs. tip voltage for (c) PFO (I = 0.1 nA for the positive branch and I = 0.05 nA for the negative branch), and (d) poly(1,12)AOPV-co-PPV (I = 0.05 nA) thin films deposited on Au(111) [54]. Reprinted figure with permission from Alvarado SF, Seidler PF, Lidzey DG, Bradley DDC (1998) Phys Rev Lett 81:1082. © 1998 by the American Physical Society

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ration [124, 125]. Recently, fabrication of surface-supported MOCNs comprising tailored pore sizes and chemical functionality by the modular assembly of polytopic organic carboxylate linker molecules and iron atoms on a Cu(100) surface have been demonstrated [126]. These arrays provide versatile templates for the organization of functional species at the nanoscale, as is demonstrated by their use to accommodate C60 guest molecules. The linker molecules are 1,4-dicarboxylic benzoic acid (terephthalic acid, TPA), 1,2,4-tricarboxylic benzoic acid (trimellitic acid, TMLA) and 4,1 ,4 ,1 -terphenyl1,4 -dicarboxylicacid (TDA). The endgroups, forming Fe-carboxylate with the coadsorbed iron, allow for the construction of MOCNs comprising surface-supported nanometer-size cavities with specific topology (see Fig. 17.27). The STM image in Fig. 17.27 shows the mesoscopic ordering of Fe-TPA MOCNs in domains extending up to 50 nm. In the high-resolution data in Fig. 17.27b and 17.27c, the formation of ladder-type and fully 2D interconnected networks is shown, the formation of which is controlled by the amount and ratio of the materials deposited. On complete 2D Fe-carboxylate reticulation, a trellis with a square unit cell and a cross-shaped cavity evolves, as shown in Fig. 17.27c. The work also shows that single C60 molecules are accommodated on the large cavities of

Fig. 17.27. (a) STM image of large extended regular domains formed by TPA-Fe coordination networks. (b) High-resolution image of ladder-type structures with two distinct types of nanocavities (marked by A and B), where not all available carboxylate groups are involved in coordination bonding. (c) Fully interconnected network with complete 2D reticulation, giving rise to square cavities (marked by C) [126]. Reprinted from NATURE MATERIALS. Stepanow S, Lingerfelder M, Dmitriev A, Spillmann H, Delvigne E, Lin N, Deng X, Cai C, Barth JV, Kern K (2004) Nat Mat 3:229

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the MOCN, which are favored by the stronger C60 interaction with the uncovered substrate [126].

17.5 Conclusions The review on low-dimensional systems reported provides just a little taste of the expanding field of nanoscale materials and structures. Many works are showing that qualitatively new behavior in the physical phenomena is often produced by the size constraints. Although such changes in behavior can be the dominant effects in nanoscale structures, we still have remarkably little experience or intuition for the expected phenomena and their practical implication. As surface scientists, we realize that we are just uncovering a wide world of physical phenomena involving complex systems spanning from physics to chemistry and biology. In particular, the study of simplicity will give way to the study of complexity as the unifying theme. In this world, simple structures interact to create new phenomena and assemble themselves into devices, or complicated structures can be designed atom by atom for desired characteristics. We hope that the few examples reported here will stimulate researchers to engage in the exploration of this exciting world. We would like to thank Mattia Fanetti, Maria Grazia Betti, Carlo Mariani and Cinzia Cepek as collaborators for the results we presented here. The nanospectroscopy facility in Brescia was funded by INFM under the Strumentazione Avanzata program. The research work presented here was funded by FIRB-MIUR project “Carbon-based micro and nanostructures”, by PRIN-MIUR project “Nanotribology”, and by the CARIPLO Foundation.

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18 Scanning Probe Microscopy Applied to Ferroelectric Materials Oleg Tikhomirov · Massimiliano Labardi · Maria Allegrini

18.1 Introduction Investigation of ferroelectrics with scanning probe microscopy (SPM) has some specific features inherent to the nature of such materials. Traditional SPM setups that provide surface characterization or visualization of grain structure in polycrystalline samples can be performed using customary SPM setups. However, these common techniques are insufficient to resolve the principal problem for ferroelectrics, namely, mapping of their polarization. Electrostatic and electromechanical interactions of the probe with a material under study affect the physical principles of imaging, and special efforts are necessary to optimize the microscope performance. In this chapter we will review the main SPM experimental approaches to observe and modify the structure of ferroelectric domains, as well as the principal results obtained in both science and technology of ferroelectrics. The chapter is divided into a few sections. It starts with a brief description of the principal milestones and tasks in the development of SPM studies of ferroelectrics (Sect. 18.2). Specific features and properties of ferroelectrics are also explained here. The next two sections are devoted to different branches of SPM used in investigations of ferroelectric materials, and to modifications of this technique necessary to visualize ferroelectric domains. Section 18.3 deals with scanning force microscopy, while optical techniques, both in far and near field, are considered in a separate Sect. 18.4 due to a number of specific features inherent to optical microscopy. Section 18.5 reviews the main results obtained up to now with modern SPMs, and sets the principal areas of its application in current research.

18.2 Development of Scanning Probe Techniques for Ferroelectrics Ferroelectrics are materials possessing spontaneous electric polarization capable of being reoriented by an external electric field [1]. Although the history of their studies is approaching the century mark [2], the number of publications in this area is still continuing to grow rapidly. A large variety of applications is undoubtedly responsible for this interest. Ferroelectrics are traditionally used in electronics due to their high dielectric permittivity, while numerous sensors exploit their piezoelectric and pyroelectric effects as well [3]. Nonlinear optical and electrooptic properties make ferroelectrics of the lithium niobate family the basic medium

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for laser and optoelectronics technology [4]. The idea of ferroelectric random access memory (FeRAM) has given rise to extensive studies of ferroelectric thin films [5]. Ferroelectrics have much in common with ferromagnets, so that the same theoretical models are often applied to describe both kinds of materials. Spontaneous ordering below a certain temperature causes high values of polarization (magnetization) and permittivity. Switching between two (or more) stable orientations of the order parameter proceeds via nucleation and spreading of numerous domains, resulting in a nonlinear and history-dependent reversal curve (hysteresis loop). The spatially homogeneous state of both ferroelectrics and ferromagnets can be described using the phenomenological phase transition theory [6], while experimentally measured properties of real samples are dominated by extrinsic factors like domain structure kinetics. The similarity of cooperative phenomena in the two classes of materials supports the success of “spin” approaches (Ising model) describing the macroscopic behavior of ferroelectrics. Despite this apparent likeness, there are deep fundamental differences between ferroelectrics and ferromagnets. Three factors are worth mentioning. First, magnetic structure and magnetic ordering are determined by specific exchange interactions between adjacent spins. Large enhancement of the exchange energy makes sharp variations of the magnetization direction impossible, so that ferromagnetic domain walls acquire an effective thickness of the order of (A/K)1/2 , where A is the exchange constant and K is the anisotropy parameter. In ferroelectrics the exchange interaction is absent (A → 0) and domain walls are known to be extremely thin, comparable to a few lattice constants. The second factor is effective anisotropy. Magnetic spins are coupled to the crystal lattice via rather weak (relativistic) spinorbit interaction, and ordering forces inside the spin system itself are much stronger, so that phenomena like magnetostriction can be considered as a perturbation of a purely “magnetic” ground state. Contrary to this case, ferroelectric polarization is directly related to the lattice ion displacements, and elastic stress affects the domain structure as well as the electric field. Using the same description as before, one can say that not only A → 0 in ferroelectrics, but also K → ∞. Finally, the existence of free charge carriers like electrons or holes provides the opportunity of effective screening of the ferroelectric polarization, making thermodynamic rules less important for the ferroelectric domain structure compared with ferromagnetic materials. The difference mentioned above promotes ferroelectrics as a most prominent class of ordered materials in the field of nanotechnology. In ferromagnets, the “exchange length” limit of minimal reversal can be surpassed only by the physical separation of a magnetic phase from a nonmagnetic matrix (nanodots or nanoislands). In ferroelectrics, the situation is different. No such fundamental restriction exists for the minimum size of a region with reversed polarization, and calculations show that a ferroelectric material can be locally switched at the scale of a few lattice constants [7]. This promises, among other perspectives, potentially very high density of FeRAM, where bits of information can be represented by tiny reversed domains written by application of a local electric field. The technological perspectives coupled with further miniaturization of the rewritable area size provide the main drive for the current interest in ferroelectrics. In addition, traditional applications

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of ferroelectrics also gain from nanotechnology, because of the superior dielectric and piezoelectric properties of some nanoengineered materials. Optical applications also require spatial modification of the crystal properties at a scale comparable to light wavelength or less. The growing market of periodically poled lithium niobate (PPLN) is a good example of the evolution of modern materials from homogeneous substances, valuable due to their intrinsic macroscopic parameters, to artificial media with engineered domain structure. Being the tool of choice in nanotechnology, SPM has become indispensable for modern ferroelectrics science. It allows us, with some modifications, to address efficiently both principal tasks of interest: local characterization and local writing. The former problem was the central issue of early studies, starting from the pioneer work of Saurenbach and Terris, who succeeded to image for the first time the ferroelectric/ferroelastic domain wall in gadolinium molybdate single crystals [8] by means of a scanning probe technique named electrostatic force microscopy (Sect. 18.3). The following investigations involved quite nontrivial discussion concerning the origin of contrast in such technique [9–12]. As a result, a mere dozen of SPM varieties for ferroelectrics studies has been developed up to now [13–25], including piezoelectric force microscopy (Sect. 18.3) as an undoubted favorite among practical researchers due to its simplicity and well-defined phase contrast [17,26]. However, the necessity of working in contact mode and the non-local distribution of both electric field and mechanical stress around the tip impose some restrictions to the application of this method, so that the development of new techniques remains an actual issue. The modified near-field scanning optical microscopy (Sect. 18.4.3) is probably a hidden promise of this way. First efforts to modify the ferroelectric domain structure with SPM appeared very soon, even before principal aspects of SPM imaging in ferroelectrics had been established [27, 28]. The importance of the “nanowriting” step to develop ferroelectric memory was obvious, and the drawing of simple patterns on ferroelectric surfaces with a charged tip became common exercise during the next decade [29–38]. The stability of written information remains a problem, and transition to experiments with high voltage probes [39] appears to be a natural step to involve high coercivity materials. The nanowriting ideas seem to be even farther from exhaustive than SPM imaging; let us mention a few efforts to perform optical writing [40, 41] and a proposal to use optical pulses in ferroelectric channels to perform quantum computing operations as a brilliant example of hidden non-trivial applications [42]. Despite the fact that the progress of SPM in ferroelectrics is obviously driven by potential applications, there are still a lot of basic studies as well. Some of them are devoted to classical problems like the domain wall structure [14, 43–45] or phase transitions [14, 46–50]. However, we can expect (and observe) a gradual transition from the studying of traditional ferroelectric objects to somehow “exotic” materials. Spatially inhomogeneous ferroelectric thin films [34, 51–59], relaxors [60–62] and materials with composition close to the morphotropic phase boundary [63, 64] are the most popular examples. The properties of artificial nanostructured objects like multilayers or nanodots (nanoislands) are starting to be examined [65–72], although progress in sintering and optimization should attract the researchers’ attention. Once again, convergence of fundamental physics and industry is expected in this field.

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18.3 Scanning Force Microscopy Scanning force microscopy (SFM) found an ideal application for imaging of polarization domains on the surface of ferroelectric materials from 1990 [8]. Before then, surface maps of electrical polarization could be obtained by other methods, such as surface decoration [73], successive etching [74], scanning electron microscopy [75], and the nematic liquid crystal method [76], which however exhibit limited spatial resolution as well as high invasiveness. Instead, SFM is a non-destructive technique capable of monitoring the evolution of the ferroelectric domain structure with time intervals typical of scanning probe techniques (a few minutes per scan). Real time observation of polarization domains allows the investigation of relaxation dynamics, enlightening the phenomena of domain branching, coarsening, pinning, even during thermal treatments (annealing, thermal shocks, critical temperature crossing), and more generally on phase transitions at the sub-microscopic scale. Basically, SFM is sensitive to local forces exerted at the tip location. Shortrange forces such as attractive van der Waals and repulsive contact interactions, determine atomic resolution in the traditionally called atomic force microscope (AFM). In addition to atomic forces, electrostatic forces may appear when the tip/sample junction is biased. Such forces are due to capacitance and its space derivative, as well as to bound surface charges. The generic term to indicate SPM techniques sensitive to such electrostatic effects is electrostatic force microscopy (EFM). In the application of SFM to ferroelectric materials though, the surface charge and/or its discontinuity at the polarization domain walls is not the only quantity measurable by the probe. Other local effects like piezoelectricity can be used as indicators of the domain structure. In the converse piezoelectric effect, the electric field at the tip produces deformation in the material, which can be revealed by monitoring the atomic force that is sharply dependent on the tip/surface distance. In this respect, space resolution approaches the resolution of AFM. This technique is named Piezoresponse Force Microscopy (PFM). The detection of polarization domains can be accomplished in both non-contact and contact modes of SFM; nonetheless an electric potential may be applied in order to improve sensitivity to electrical properties of the sample. If the field is only applied to the sample and the tip is kept at fixed potential, only piezoresponse can be detected, while sensitivity to surface charge density is achieved by polarization of the tip. In such a case, a dc bias usually leads to convoluted images of topography and charge distribution, while ac voltage modulation and lock-in detection yield good separation between topography and the electrical signal. This will be clarified in the next paragraphs. 18.3.1 Non-Contact Mode Non-contact imaging of ferroelectric domains relies on the detection of the force gradient present at the domain boundary. Since non-contact mode SFM traces profiles of the constant force gradient [77], in order to measure the topography of homogeneous surfaces, electric force gradients are visualized as topographic features.

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Therefore, information on topography and domain boundaries are both contained in the topographic image. Different dc bias between tip and sample gives rise to the different contrasts in the detection of domain boundaries, with the appearance of their contours on the topographic image. Occasionally, evidence of domain contrast, i.e. of different uniform gray tones on the oppositely polarized regions, has been observed [78]. In general, however, contrast between domains in the non-contact mode under dc bias must be expected when the tip oscillation amplitude is high enough so that a detectable electrostatic force gradient is encountered by the tip even within the domain body. Such condition is better fulfilled when the spatial extension of a domain is small with respect to the tip radius. For instance, domains about 200 nm wide appear in Fig. 18.5 of [78], whereas only domain wall contrast is recorded on larger domains (e.g., 5 µm on [9], 20 µm on [11]). Clearly, the closer the tip to the surface, the more the electric field is to be considered uniform along the normal (z) direction, such as the one produced by an infinite charged plane. 18.3.2 Contact Mode In the contact mode, it has been shown that contrast due to ferroelectric domains can be detected on the topographic image [17], explained by the surface deformation caused by the converse piezoelectric effect. Also different friction coefficients measured in the lateral force mode have been attributed to the polarization domains [13], through the electrostatic effect of the stray electric field emerging from the sample surface on possible electric dipoles and/or bound charges present on the tip. In this case, the information on domains is contained in a separate measurement channel (lateral force, Sect. 18.3.5) and does not influence topography. In the general case, both piezoelectric and electrostatic effects can be anticipated, depending on the sample characteristics. For instance, on guanidinium aluminum sulfate hexahydrate [C(NH2 )3 Al(SO4 )2 · 6H2 O or GASH], where topographic domain contrast has been evidenced [17], friction effects similar to the ones found in [13] and [10,79] are also recorded [80]. Friction measurements are considered to be a well-established SFM method for the identification of ferroelectric domains [81], since they are presumably due to a side effect of the electrostatic force action. In order to explain the observed contrast, a couple of mechanisms have been put forward. In the first one [13], electric dipoles located on the tip, when interacting with the surface electric field, may exert a torque able to twist the cantilever, yielding a signal on the lateral force channel that may be interpreted as friction. This mechanism corresponds to space resolution similar to that of electrostatic force microscopy, since long-ranged surface electric fields are detected. The second explanation [10, 79] relies on direction-dependent surface potentials (that is, friction coefficients), which depend intrinsically on the surface atomic structure of the material under study. It has been shown, and demonstrated with scans along different orientations, that the dynamical friction coefficient may depend on the scan direction when measured by atomic resolution probes. Similarly, the friction coefficient might depend on the polarity of ferroelectric domains, since the structural composition and surface potentials of opposite domains can be different, and this could influence friction. Resolution in this case could approach the one of AFM, since local structural properties of the surface are involved. Besides peculiar

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friction mechanisms based on a priori assumptions, a more general explanation for the part of the frictional effect that can be ascribed to the surface electric field relies on the change of the normal contact force induced by the electrostatic interaction due to the tip/sample contact potential, net bound charges on the tip, or external biasing. Even when the friction coefficient is the same on oppositely charged domains, the change of the normal load, due to the electrostatic force between tip and sample, will cause change of the friction force. Such change is interpreted as a different friction coefficient that is defined as the slope of the lateral force versus load plot. Such an argument should be valid for a variety of materials, and in general when externally driven forces are applied to the tip. In fact, the AFM contact mode feedback loop, in the commonly used constant force mode, stabilizes the elastic force acting on the tip through the cantilever. Usually such a force is balanced merely by the atomic force exerted at the tip apical atoms. This contact force is the load responsible for friction. If the electrostatic force, which is long-ranged and thus acts on a more extended tip portion and not just on its apex, is present, there will be a variation of the contact force in order to achieve balance to the fixed elastic force. This will cause the variation of the friction force as well. Interaction of externally induced tip charges with surface charge of the sample must depend on the sign of the applied voltage. Experiments where this evidence is not confirmed [10] employed metal tips, with possible charge transfer between tip and sample and the related inhibition of the direct (Coulomb) interaction due to local neutralization of surface charges. More proper EFM is achieved with the use of heavily doped semiconducting tips, that combine high electrical conductivity due to the presence of a native oxide layer that reduces charge flow between tip and sample. 18.3.3 Voltage-Modulated SFM In order to minimize crosstalk of the electric signal into the topography, the technique of Voltage-Modulated Scanning Force Microscopy (VM-SFM) was introduced [8]. It consists of a sinusoidal polarization at frequency ω of the tip/sample junction, and relative detection of the ac cantilever bending at the same frequency, generally by means of lock-in techniques. This method is sensitive to both electrostatic and electromechanical (e.g. piezoelectric) contributions. Furthermore, measurements at the second harmonic of the excitation frequency provide information on dielectric permittivity and electrostriction effect [82, 83]. In the contact mode, sustained vibrations at the voltage-modulation frequency can still be recorded. The piezoelectric effect causes vibration of the sample surface and directly translates it into ac modulation of cantilever bending, by means of the atomic force. Electrostatic effects modulate the contact force (load) and translate in bending modulation through the viscoelastic response of the tip/sample junction. In other words, if the sample is compliant, the electrostatic force causes a surface deformation (yield) and thus cantilever vibration is still possible. VM-SFM operated in contact mode has been also named dynamic-contact electrostatic force microscopy (DC-EFM) [11]. The same effects as described above are considered to be responsible for domain contrast also in the dynamic non-contact EFM. There, by changing the tip/sample

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distance, the piezoelectric effect yields an oscillating force Fp cos ωt approximately given by the attractive force gradient dFint / dz multiplied by the displacement ∆z p of the surface. The Coulomb force is instead exerted directly on the tip. Both such forces cause cantilever bending through the spring constant k, that on the other hand is usually high for non-contact operation, and therefore yields rather small deflection signals. Nevertheless, the bending signal due to piezoelectric effect turns out to be independent of k, since dFint / dz = k/a, with a > 1 in the non-contact mode, so that the lever deflection becomes δp = ( dFint / dz∆z p )/k = (k/a)∆z p /k = ∆z p /a, independent on k. On the other hand, the electrostatic term is inversely proportional to k. Thus, it is expected that, depending on the cantilever spring constant used, the relative weight of the two effects may vary considerably. Sensitivity to the piezoelectric effect in the non-contact mode employing the slope detection method [77] can be further accessed in terms of the behavior of the cantilever oscillation at or near the mechanical excitation frequency ωres of the cantilever, when the sample surface undergoes a periodic displacement at frequency ω. Provided that ω is much greater than the distance regulation feedback cutoff frequency, ωcutoff , thereby preventing mixing to the topography, cantilever oscillation at ωres will be modulated in amplitude at frequency ω. The corresponding modulation depth depends on the cantilever quality factor Q, of the order of 100 in air for most commercial non-contact mode cantilevers. Namely, low Q means that the oscillation amplitude can change more rapidly, and effective amplitude modulation will be possible at frequencies lower than ωres /Q. In this respect, the most proper frequency range for dynamic non-contact EFM imaging exploiting the slope detection method would be ωcutoff < ω < ωres /Q. The upper frequency limitation is released when frequency modulation detection is employed [84], due to its peculiar release of bandwidth limit. A similar argumentation can also be applied to the case of the electrostatic effect. An example of non-contact EFM measurements on triglycine sulphate [(NH2 CH2 COOH)3 · H2 SO4 or TGS] is shown in Fig. 18.1. The domain images reveal oppositely polarized ferroelectric domains with sharp contrast, analogous to the one typical of DC-EFM, since the employment of stiff cantilevers reduces the possible tip/sample distance down to 1 nm, thereby increasing non-contact mode resolution. In addition, topography is better preserved than in contact mode, due to weaker mechanical interaction. Mixing between electric signal and topography is expected to be low, since no dc bias was employed (although a contact potential difference may exist between tip and sample) and the ac modulation is cut off by the distance stabilization feedback. Due to the rather high value of k used (40 N/m), here the piezoelectric effect should be dominant over the electrostatic force modulation. On the other hand, in the non-contact mode the two effects act in phase, thus imposing difficulties in their differentiation [83]. Nonetheless, their separate quantification would be of value especially for the assessment of absolute measurements of surface charge or piezoelectric deformation by means of the EFM signal. As is evident from the present state-of-the-art, there is still much to understand about contrast mechanisms in EFM. There are indirect indications on the diversity of domain contrast in TGS samples investigated by DC-EFM. Firstly, it has been verified in TGS that contrast of polarization domain images varies with temperature as (T − Tc }−γ with γ ≈ 0.23, rather than 0.5, which would be expected if only electrostatic

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Fig. 18.1. Non-contact topography (a), dynamic non-contact EFM amplitude (b) and phase (c) of lenticular ferroelectric domains in TGS. The modulation voltage used was 15 Vpp . Scan size 26 × 13 µm2 . (From [12], courtesy of APS)

terms contributed to domain contrast [47]. Therefore, thermodynamic arguments suggest that there is at least competition between electrostatic and electromechanical effects for domain contrast in TGS, since their contributions are expected to be of opposite sign in DC-EFM. Secondly, in such a mode contrast exhibits a strong frequency dependence [85], while the effect of electrostatic force should be frequency independent. Furthermore, frequency response of the electromechanical effects with features in the acoustic range have been excluded by dedicated experiments, pointing out the role of the cantilever resonance [12], as detailed in the following sections. 18.3.4 Resonance Modes of EFM Resonance modes of the AFM were pointed out, just after its invention in 1986, as being very effective for sensitivity enhancement of force detection. The most prominent example is non-contact AFM [77], which is performed by monitoring the shift of the resonance curve of the cantilever, regarded as a harmonic oscillator, due to the presence of a surface in close proximity to the tip. In particular, the resonance frequency depends upon the interaction force gradient. In such a case, the cantilever is made to oscillate at its resonance frequency, for instance by mechanical actuation, and the effect of sample proximity is recorded as a change of oscillation amplitude [77] or resonance frequency shift [84]. A different approach is exploited when the force exerted on the tip is due to direct, externally driven electrostatic interaction. For

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instance, “tapping-mode” AFM, i.e. a high-amplitude dynamic mode operated with the slope detection method, can be performed by exciting the dithering motion of the tip by the application of an ac potential to a conductive tip faced to a conductive sample [11]. Other forms of momentum transfer to the tip are, for instance, the ones employing light pressure [86, 87] and magnetic forces [88]. In general, convenient ways to detect small forces (down to the fN level) exploit a resonant effect, by tuning the frequency of the periodic excitation to the mechanical resonance of the AFM cantilever, that may exhibit rather high Q-factors, from about 100 in air to 105 in ultra-high vacuum (UHV). Resonant enhancement of force signal has been exploited in DC-EFM, to increase the measurement contrast in the imaging of oppositely polarized ferroelectric domains [85]. Such contrast [12] results from the amplification effect at the first flexural mode of the AFM cantilever in contact conditions. It is well-known that the cantilever exhibits a series of flexural [89], as well as torsional eigenmodes [90] and that the simple harmonic oscillator model is not sufficient to describe the cantilever motion for frequency higher than the fundamental one. Contact with the surface modifies the flexural modes of the free beam in such a way that the first mode is shifted to higher frequency, coming closer to the former second mode. It is observed that frequency dependence of EFM contrast is only present when operating close to the resonance frequency region of the cantilever. In the following, we analyze the latter mechanism in more detail and examine some related measurement techniques exploiting resonance effects in VM-SFM. The experimental setup used for the experiments reported here is basically a DCEFM [85], with the addition of the lateral force measurement channel [91]. Briefly, a contact-mode AFM is modified by applying an ac potential Vac between the conductive tip and the sample mounted on a flat metallic holder connected to the ground. Normal bending as well as lateral twisting of the cantilever beam are detected with the bidirectional optical lever method [92]. Forces exerted on the tip, arising from the electrostatic tip/sample interaction and piezoelectric displacement of the sample, are translated into cantilever deformations and detected, through the optical lever, as a modulated signal with peculiar amplitude R and phase ξ, or in-phase X = R cos ξ and out-of-phase Y = R sin ξ components, measurable by lock-in technique and carrying information on the interaction. The optical lever dc signal is proportional to the average contact force and is used for AFM distance stabilization, so that the scan can be performed in the constant force mode. The cantilevers used are of contact mode type (spring constant k ≈ 0.1 N/m, resonance frequency f res ≈ 15 kHz), except for the tapping mode operation experiment described in Sect. 18.3.8 that is carried out with non-contact mode type cantilevers (k ≈ 40 N/m, f res ≈ 300 kHz). The samples used are ferroelectric TGS uniaxial single crystals, grown from aqueous solution in the ferroelectric phase below the Curie temperature Tc = 49 ◦ C. The samples are cleaved in air along the (010) plane, perpendicular to the polar b-axis, in order to obtain on the inspected surface perpendicular sections of the typical 180◦ ferroelectric domains formed by the spontaneous electrical polarization. Such domains are comprised by opposite polarization regions in the bulk, and give rise to depolarization surface charges, accordingly distributed, on the cleaved region. Annealing above the Curie temperature and successive quenching was performed

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in situ by means of a temperature controlled stage mounted on the sample holder. Repeated annealing/quenching cycles are used to produce fine (sub-micron range) ferroelectric domains arranged in a lamellar structure, that is preferentially oriented along the polar c-axis. In this way, it is possible to easily locate a domain boundary even at the highest magnifications of the microscope. An example of the oscillation spectra of an AFM cantilever in contact, nearcontact and off-contact conditions, is shown in Fig. 18.2 (solid line). The resonant response is strongly dependent on whether the tip is located on a positive or negative polarization domain (Fig. 18.2a and b) owing to the different interaction with the surface charges. It should be noted that, although the tip motion is not pronounced, due to the contact constraint, cantilever vibrations at resonant modes are able to translate such a small motion, through the optical lever method, into an appreciable laser beam deflection, and therefore to be detected with high sensitivity. The drawback of all the resonance enhanced contrast techniques considered here is that the information on the phase of the signal with respect to the excitation is released, since the response function of the vibrating cantilever comes into play. However, charge polarity can still be determined by off-resonance operation, as well as by poling experiments [91].

Fig. 18.2. Oscillation amplitude spectra of the same cantilever in (a) contact situation on one TGS domain polarity, (b) on the other one, (c) near-contact and (d) off-contact. Modification of the fundamental resonance due to the tip contact is evident. Response of normal (solid line), as well as lateral (dotted line) channels is presented. The five frequencies marked by the dashed vertical lines are the ones at which images have been taken in this work. (From [94], courtesy of Springer)

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At the boundary between opposite polarization domains in TGS, VM-SFM typically records a rather smooth passage, within about 30 to 100 nm, between the signal levels pertinent to the two different polarities. Domain boundaries themselves are known to be much better defined, that is, less than 8 nm wide, as determined by friction force microscopy under UHV [78]. The higher values found by VM-SFM in air can be explained by several facts, among them the long-ranged electrostatic forces and related influence of the curvature radius of AFM tips, and the presence of screening by humidity and contamination layers adsorbed at the surface. In a simple picture, at the domain boundary the electric field should be parallel to the surface, while inside the domain it should be normal to it, as sketched in Fig. 18.3. This gives rise to a reduction of signal around the wall [93]. However, parallel fields could be capable of exciting resonant modes of the lateral as well as frontal cantilever motion, named twisting and buckling, respectively. The investigation of the modes reported here was carried out in [94].

Fig. 18.3. (a) Surface charge density σs across a domain wall (x = 0, dashed line). (b) Sketch of the electric field distribution outside the ferroelectric material near the domain wall. Parallel components appear in the vicinity of the boundary

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A sketch of the cantilever/sample system’s geometry is shown in Fig. 18.4. Forces in the z-direction are forces normal to the sample surface. Lateral forces in the y-direction (frontal forces, Fig. 18.4a) are parallel to the plane defined by the length axis of the cantilever and the tip axis, and produce buckling of the beam. Lateral forces in the x-direction (Fig. 18.4b) are perpendicular to the latter plane and instead produce twisting of the cantilever. The effect of the frontal force can get mixed into the normal channel of the optical lever, and it results indistinguishable from the bending signal if the bidirectional optical lever method is employed. Normal and frontal force contributions could be discriminated by implementing a more refined optical lever setup, composed of two different optical levers monitoring the bending at two different positions of the cantilever [95]. On the contrary, the effect of the lateral component of the parallel force, i.e. the one in direction x depicted in Fig. 18.4b, is straightforwardly monitored by the lateral channel of the optical lever detector. In the following, the twisting and buckling modes of an AFM cantilever are analyzed separately in relation to VM-SFM.

Fig. 18.4. Cantilever geometry and definition of force directions. The proportions are not respected in the sketch. (a) Lateral view, (b) frontal view. (From [94], courtesy of Springer)

18.3.5 Lateral Force The amplitude spectra recorded on the AFM lateral force channel are shown in Fig. 18.2 (dotted line). The spectra are acquired simultaneously to the ones of the normal force channel. A couple of features can be noticed. First, lateral motion is always observed in correspondence to normal motion. This is explained in terms of an inherent geometrical effect related to a small angle α between the tip axis and

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the sample normal axis (Fig. 18.4b), as well as to the asymmetric location of the tip on the cantilever beam [96]. A torque is always associated to a normal force exerted on the tip because of the arm b (Fig. 18.4b) with respect to the cantilever axis. Thus, normal motion translates to some extent into the lateral channel, when normal forces are exerted on the tip. The second feature is the resonance peak observable on both off-contact and contact situations, at about 76 kHz in this case (Fig. 18.2). Such a peak is assigned to the fundamental lateral resonance mode of the cantilever beam. Much weaker mixing of the lateral oscillation to the normal bending mode is detected, as can be anticipated from the system geometry. Let us now examine (Fig. 18.5) the frequency dependence of contrast, defined as the difference between signals recorded on ferroelectric domains with opposite polarity. As expected, no remarkable contrast enhancement is observed at the lateral resonance frequency, while the usual resonance on the normal channel is present [94], which also translates into a similar enhancement at the same frequency on the lateral channel. Nonetheless, the full exploitation of the lateral force channel is related to the detection of parallel fields [91] like the ones possibly present at ferroelectric domain walls. Indications of the possible influence on the normal channel of a lateral resonance excited while crossing a domain wall in TGS were given in [12].

Fig. 18.5. Contrast frequency response between oppositely polarized domains on the normal (solid line) and lateral (dotted line) channels. (a) Contrast on R, (b) amplitude (X 2 + Y 2 )1/2 , (c) X and (d) Y components. (From [94], courtesy of Springer)

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In order to investigate further the phenomenon, a set of scans around a domain wall of TGS have been taken, thereby acquiring both normal and lateral channels, with the microscope operated at a number of peculiar frequencies of the system, namely at or near the resonances of both modes, as well as off-resonance. The results are reported in Fig. 18.6. In the left column (Fig. 18.6a–e) the scans in the normal mode of VM-SFM are reported at five different frequencies. The first couple

Fig. 18.6. Series of scans around a domain boundary in TGS on both normal (a–e) and lateral (f–j) amplitude channels. The used frequencies are 64, 65, 70, 74.5, 80 kHz, respectively, for both channels. The dotted black line in (a) indicates the orientation of the cantilever longitudinal axis in this series of scans, while the black arrow indicates the expected direction of the in-plane polarization at the boundary. Scan size 1.7 µm × 1.7 µm. (From [94], courtesy of Springer)

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of frequencies (64 and 65 kHz) are located at the peak of the contrast function and on the slope of the same resonance curve, respectively (Fig. 18.5b). The third frequency (70 kHz) is an intermediate one, and the last couple (74.5 and 80 kHz) are on the peak and on the slope of the lateral resonance curve (Fig. 18.2a and b). The contrast between domains exhibits a clear dependence on frequency, and undergoes inversion at 80 kHz (Fig. 18.6e) and near nulling at 64 kHz (Fig. 18.6a) and 74.5 kHz (Fig. 18.6d). On the other hand, the domain boundary appears depleted, and the two values of the amplitude on the oppositely charged domains, which are expected to be equal, exhibit marked differences, and even undergo inversion as a function of voltage-modulation frequency. To explain some of these features, let us remind that a contact potential difference (CPD) is usually present at the interface between materials. This translates in the case of VM-SFM in a fixed dc polarization Vdc between tip and sample. Thus, the total normal force term modulated at frequency ω results [11]:  (18.1) Fel (t) ∼ = ( dC/ dz)Vdc + σC/2ε0 Vac cos(ωt)z , where C is the capacitance of the tip/sample system, and σ the bound surface charge density. As already pointed out in [93], when Vdc  = 0, the force exerted on the tip above the two domains (denoted by “+” and “−”) will assume two different values, namely:   ±  ±   F  ∼ (18.2) el = ( dC/ dz)Vdc + σ C/2ε0 Vac . Thus, the effect of CPD explains the inequality of amplitude levels recorded on oppositely charged domains. The experiments considered here have shown that response of the lateral channel (Fig. 18.6f–j) gives no clear indication of the presence of parallel electric fields at the surface. Indeed, at the frequency of the normal resonance (Fig. 18.6f,g) the same depletion effect at the boundary of Fig. 18.6a and b is found, indicating that the observed contrast pertains to the inherent coupling of the lateral mode to the normal one above described. When the frequency is increased towards the lateral resonance one, the measured contrast differentiates from the corresponding one found on the normal channel, and the signal reduction at the boundary disappears. Although the orientation of the cantilever longitudinal axis (Fig. 18.6a) with respect to the wall was not optimal, the expected lateral signal enhancement at the boundary has not shown up. Instead, as shown later, such enhancement has been verified for the frontal component. The more plausible explanation for the absence of signal on the lateral channel at domain boundaries resides in the low sensitivity of the lateral channel itself, noticeable from the spectra of Fig. 18.2, where the lateral mode resonance curve at 76 kHz has a similar intensity to the crosstalk term at 64 kHz. Moreover, the curve is significantly broader, indicating a highly dissipative mode. The lateral force mode is more effectively employed to reveal in-plane oriented domains by means of the frictional force induced by inverse piezoelectric effect that produces shear motion of the surface [31]. This will be detailed in Sect. 18.5.1.

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18.3.6 Frontal Force The possibility of mode excitation by parallel electric fields has prompted investigations on the effect of the frontal force component on the normal channel response. Unlike in friction force microscopy, where the scan direction determines the orientation of the kinetic friction force, in modulation techniques as the one used in DC-EFM, the parallel force can assume any direction on the plane, and thus, in general, may have a lateral as well as a frontal component. The tip motion associated to frontal forces has no constraints like in the case of the normal one, since the tip can slip on the surface, the only limitation being friction. Hence, frontal forces of electrostatic origin are expected to be more effectively translated into flexural motion of the cantilever, with respect to the normal ones. Also, the buckling modes may involve high amplitude motion of the cantilever beam even for a small force exerted at the tip, like for the bending case. Instead, twisting motion does not benefit from this enhancement effect, as is evident from the cantilever geometry. At ferroelectric domain walls, the physical orientation of the cantilever with respect to the wall direction determines the relative amount of lateral and frontal components. The issue of the proper force decomposition as regards the measurement of lateral force was analyzed in [96], where a rigorous treatment has been carried out. The same treatment has been reformulated for the present problem in [94]. It is observed that in a conventional AFM setup, the tip axis is inclined with respect to the sample normal by an angle ϕ, typically between 5 and 15◦ (Fig. 18.4a), for ensuring sufficient clearance during the tip approach. Additionally, the small lateral tilting α defined above might play a role. Local topography can affect force decomposition [96], but for cleaved crystals it is a good assumption to consider a flat surface. It can be concluded that, within the ferroelectric domain, cantilever bending and buckling modes can be excited by the modulated electrostatic/electromechanical interaction; lateral modes can be excited as well to a lesser extent, due to the unfavorable geometry of the cantilever, or due to crosstalk with the bending mode. On the contrary, bending and buckling modes are expected to be excited to a greater extent, due to the resonance enhancement favored by the cantilever geometry. At the domain boundary, assuming the presence of a parallel field, twisting modes may be excited, but buckling modes may become dominant even with respect to bending ones. By taking into account the latter results, a more thorough interpretation of VMSFM images becomes possible. As an example, let us consider the case of the force signal of (18.2). Such force translates in the cantilever bending/buckling angle to the extent:  (18.3) z ± (ω) = ±(Fel /k) (cos ϕ/leff,z )z + (lt sin ϕ/leff,x leff,z )y . Here a static decomposition of the system’s compliance in terms of bending and buckling has been applied according to [97], with l the cantilever length, lt the tip length, leff,z = 2l/3, leff,x = l/2. The actual cantilever oscillation will be related to such static deflection through its dynamic response, with possible excitation of resonant modes. Evidence of the influence of buckling modes on the VM-SFM

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signal are found on many amplitude images in the form of asymmetric response at domain walls of opposite orientation. An example is shown in Fig. 18.7a, where the walls on the left of negative (dark) domains exhibit pronounced depletion effect in the amplitude images, whereas walls on the right present much lower depletion. Such a feature is explained by the observation that the parallel fields at the two boundaries have opposite sign, so that (18.2) written for left (“L”) as well as right (“R”) boundaries becomes: P sin θ y , FL (ω) = ( dC/ dz)Vdc Vac x + Fel,y

(18.4)

F (ω) = ( dC/ dz)Vdc Vac x −

(18.5)

R

P Fel,y

sin θ y ,

P is the frontal force term induced by parallel fields at the surface. The line where Fel,y profile reported in Fig. 18.7b indeed shows the value at the left domain walls to be about five units below the one pertaining to the negative domains, whereas the right domain wall shows a depletion of about two units. Moreover, from the image of Fig. 18.7a, the clear dependence of the depletion effect on the domain wall direction yields further support to this explanation.

Fig. 18.7. VM-SFM amplitude image (a) of ferroelectric domains on TGS, taken at the contrast resonance frequency. Asymmetry of the response at the domain walls can be noticed. Line profile (b) taken at the position of the horizontal line on (a). The cantilever orientation is the same as in Fig. 18.4 of APA. Scan size 35 µm × 35 µm. (From [94], courtesy of Springer)

18.3.7 Second Harmonic Resonance enhancement of EFM signals can be successfully exploited for the detection of capacitive forces, whose quadratic dependence on the applied field leads to a response at twice the modulation frequency. Such a second harmonic response is related to local dielectric permittivity for a sample thickness much higher than the tip radius [82]. By tuning the excitation ac voltage to the half of the system’s resonance frequency, the second harmonic response is enhanced similarly to the first harmonic case. This technique is basically different from the one of [11], where the system was operated in tapping mode, and the voltage modulation was applied at half the

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fundamental flexural eigenmode frequency of a tapping-mode type cantilever. Here the tip is in permanent contact mode and the resonance exploited is the first flexural mode of a contact-mode type cantilever. An example of second harmonic imaging of a domain boundary of TGS is shown, along with the corresponding first harmonic one, in Fig. 18.8. The first harmonic image is shown in Fig. 18.8a. Domain boundary depletion is not visible, since the working frequency was 32 kHz, far below the resonance at 64 kHz. The corresponding second harmonic image of Fig. 18.8b shows a brighter region at the wall compared to the background level of both domain polarities. Since second harmonic response corresponds for thick samples to dielectric permittivity [82], enhanced capacitance can be inferred at the domain wall. Domains appear decorated by elongated structures not visible in the topography or in the first harmonic images, probably due to surface contamination modulating the local permittivity. Therefore, the second harmonic imaging mode at resonance provides a highly sensitive probe of surface dielectric properties.

Fig. 18.8. Voltage modulation images at the first (a) and second (b) harmonics of a ferroelectric domain boundary in TGS. The frequency used is 32 kHz, for a resulting second harmonic of 64 kHz that coincides with the resonance peak of the main cantilever flexural mode in contact conditions. Scan size 4.2 µm × 4.2 µm. (From [94], courtesy of Springer)

18.3.8 Tapping Mode To conclude this set of examples of possible utilization of resonance techniques in VM-SFM, let us now discuss the implementation of an enhanced contrast technique in the AFM tapping mode, or intermittent contact mode. It is well-known that in the tapping mode, the fraction of time when the tip experiences contact with the sample may vary from 2% to 15% [98]. Thus, it is likely that both electrostatic and electromechanical interactions taking place in the contact mode may also affect the tapping mode oscillation, in the proper proportion. Nonetheless, in tapping mode, the mechanical vibration of the tip is adjusted by the distance control feedback loop to a constant amplitude value. Voltage modulation of the tip/sample junction, coherent with the tip vertical dithering, has been applied for the investigation of electrooptic

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contrast mechanism on TGS with an apertureless near-field microscope [99], which will be described in Sect. 18.4.3. In such experiments though, the effect of electric forces is expected to show up in the topographic image, while no evidence of such a phenomenon has been reported. A different approach is carried out by incoherent voltage modulation near the tapping-mode resonance. An example of domain imaging in tapping mode is shown in Fig. 18.9. The recorded topographic image was perfectly flat and is not shown here. The VM frequency was tuned at ∆ω = −600 Hz with respect to the tapping resonance, while the voltage modulation amplitude used was quite high (10 V) and the scan rate relatively low (10 Hz). The higher voltage required to achieve the shown contrast is due to the limited interaction time in tapping mode, whereas the low bandwidth is related to the low sensitivity of the system, composed by a high stiffness cantilever, added to the intrinsic noise level of the method that involves the incoherent beating term between the two close frequencies of tapping and voltage modulation. Indeed, the used frequency shift of 600 Hz resulted from the best compromise between resonant amplification and beating noise magnitude at ∆ω. By means of an integration time of 100 ms, such noise could be reasonably reduced. The main advantage of this method resides in the complete independence of topography and electric images, which is the main objective pursued by VM-SFM, at the expenses of a limited scan bandwidth. This mode may be helpful when delicate samples are investigated and contact mode is not easily applicable.

Fig. 18.9. Voltage modulation image of ferroelectric domains in TGS measured in the tapping mode. Scan size 20.5 µm × 20.5 µm. (From [94], courtesy of Springer)

18.4 Scanning Optical Microscopy 18.4.1 Pure Optical Microscopy The polarized light microscopy is a traditional tool of choice to investigate the ferroelectric domain structure [100]. The contrast between domains of different polarity is due to birefringence or, more rarely, spontaneous optical activity (rotation of the polarization plane). Optical microscopy provides direct observation of the

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phase transition kinetics, domain structure rearrangements with temperature and during the poling cycle. Reliable information about domain wall dynamics (that is, the relation between velocity and driving force, or amplitude-frequency spectra in the case of the ac field) is also courtesy of this technique. The popularity of optical microscopy and its important role among other techniques used to study ferroelectrics is due to many obvious advantages. Optical characterization is fast, non-destructive, non-contact, requires moderate surface quality, and provides clear and unambiguous images. Apparently there are only two factors seriously restricting its application to ferroelectrics: limited spatial resolution and the absence of optical contrast between antiparallel domains for some important crystal groups. Both these problems can be successfully overcome as shown below. The replacement of a conventional “analogous” polarized light microscope with a “digital” laser scanning system, where light is focused into the small spot and the image is formed by raster scanning similar to television, gives no obvious advantages at the first glance. In fact, the term “laser scanning microscopy” was initially related to the pyroelectric probe technique (see [101] and references therein). This method is based on local heating of the sample by a focused laser beam followed by the measurement of the induced macroscopic current, whose sign allows one to determine the direction of the probed ferroelectric polarization. Comparison of the optical picture from a laser scanning microscope with the simultaneously obtained pyroelectric image [101] shows that the former is less informative, giving only weak light scattering at grain boundaries, and no traces of ferroelectric domain structure (antiparallel domains in NaNO2 have identical optical properties). However, early works already demonstrated the main principle of scanning optical microscopy to be so effectively explored later: local illumination and detection provides the opportunity to measure additional physical parameters instead of mere “looking”. The human eye turns out to be supplied with a powerful army of electronic devices. The diffraction limit to spatial resolution was also attacked at approximately the same time. The old idea by Synge [102] to compete destructive interference by reducing both the light source aperture and distance to the object has been realized in scanning near-field optical microscopy (SNOM) [103]. In this case, the interaction of light with the object under study is realized in a very small spatial area well before the evanescent waves would decay. As a result, collected far-field light contains information about scattering at a sub-wavelength object. The typical SNOM setup explores the nanoscopic optical tip made of tapered glass fiber coated with a metal film to enhance light confinement. The tip aperture determines the spatial resolution of the technique. Narrower tips provide better resolution, but intensity becomes weak. Moreover, the metal cover must be thick enough to prevent light from escaping through the lateral sides. The practical spatial resolution of such SNOM setups is of the order of 100 nm. Better resolution can be obtained with non-fiber or apertureless SNOM exploiting light scattering from a small AFM tip; in this case, the main problem is to separate scattered light from the meddling background. First efforts to apply SNOM for the imaging of the domain structure in ferroelectric single crystals [23, 104] faced, once again, the problem of the absence of optical contrast between antiparallel domains. Figure 18.10 shows the picture of the triangular domain corner in a LiTaO3 crystal obtained by fiber SNOM in transmission

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Fig. 18.10. Image of the ferroelectric domain walls in a LiTaO3 single crystal obtained with conventional fiber SNOM. (From [23], courtesy of AIP)

mode. The contrasted areas correspond to strained regions with enhanced concentration of point defects in the vicinity of the domain walls. The picture is to some extent similar to optical images taken in dark field mode when only scattering at inhomogeneities can be seen due to elimination of the main optical beam [105]. The SNOM image shows practically no new important details compared to conventional optical microscopy, and the effective spatial resolution is still of the order of the diffraction limit. Although the quality of images was slightly improved in following works [106], the absence of direct coupling between probed ferroelectric polarization and optical signal still prevents the wide use of pure SNOM to study the ferroelectric domain structure even in single crystals; we know of only one effort [107] to apply this technique to ferroelectric thin films. Today it is occasionally applied to visualize the spatial distribution of light in ferroelectric optical waveguides [108, 109]. To make real progress in domain imaging, SNOM has to be adapted to couple optics with ferroelectric polarization. Different strategies will be described below, starting from their far-field implementations where necessary. 18.4.2 Scanning Electrooptic Microscopy The idea to induce artificial optical contrast between antiparallel domains with an external electric field has been known for decades [110]. For in-plane ferroelectric polarization, the transverse field rotates the initially parallel optical indicatrices within adjacent domains in opposite way, causing their disorientation and, therefore, difference in extinction conditions. Now the domain structure can be observed, as usual, by rotation of the sample between crossed polarizers [100]. For out-of-plane ferroelectric polarization, the contrast can be achieved by application of the longitudinal electric field to induce deformation of the optical ellipsoid–elongation for one kind of domain and suppression for the opposite one [111]. However, electrooptic visualization has not been widely-used in practice due to the relatively low value of

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induced contrast and necessity to apply strong bias fields, so that selective etching remained the main tool to distinguish antiparallel domains up to very recent times. The situation changed drastically with the development of scanning techniques. The opportunity to work in the modulation regime became a critical issue. Instead of applying large dc bias to induce noticeable optical contrast, a relatively small ac field can be applied to produce small intensity variations sufficient for sensitive lock-in electronics. Both amplitude and phase of the modulation response can be recorded at a given spot under the laser probe in addition to the light intensity, forming both optical and electrooptic images of the sample. The method is especially convenient for resolving phase transitions and other cases characterized by the coexistence of ferroelectric and paraelectric regions, because the symmetric high-temperature phase can be easily discriminated due to the absence of linear electrooptic effect [112]. Applications of the electrooptic modulation principle allowed one to obtain images of the ferroelectric (Ba, Sr)TiO3 thin films using confocal scanning optical microscopy (CSOM) in reflection mode [24]. The scheme of the experiment is shown in Fig. 18.11. The high numerical aperture of the objective and spatial filter cause good spatial resolution, close to the diffraction limit. The electric field is applied in plane (along the film surface) using a system of interdigitated golden electrodes sputtered on the film. The use of this approach succeeded to show that the structure of the ferroelectric film is highly inhomogeneous, apparently due to nonuniform stress, so that ferroelectric areas with high electrooptic response coexist with paraelectric ones for both nominally ferroelectric and nominally paraelectric compositions. The presence of local areas with broad spectrum of phase transition temperature seems to be the main reason for the abnormally wide (compared to single crystals) peaks of dielectric permittivity inherent to ferroelectric thin films. The principal properties and optimal conditions for modulated CSOM were established in [113] using single crystals of lithium niobate with well-known electrooptic properties. It was demonstrated that the output signal measured with electrooptic CSOM is strongly affected (up to several orders of magnitude) by the mutual orientation of the ferroelectric polarization, light polarization, and applied electric field. The

Fig. 18.11. Schematic for confocal scanning optical microscopy (CSOM) with electrooptic modulation. (From [113], courtesy of AIP)

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presence of a sinusoidal component of the reflected light is caused by the induced modulation of the refractive index due to the linear electrooptic effect: ∆(1/n 2 ) = rijk E k = r13 E cos θ sin2 ϕ + r33 E cos θ cos2 ϕ + 2r51 E sin θ sin ϕ cos ϕ . (18.6) Here rijk – electrooptic tensor, n – optical index, E – applied sinusoidal electric field. Components of the electrooptic tensor are written for the lithium niobate crystal (3 m symmetry group at room temperature). Angles θ and ϕ describe the deviation of the electric field and of the light polarization direction from the ferroelectric c axis lying in the plane of the sample (perpendicular to the incident light direction), respectively. The amplitude of the first harmonic of modulated light intensity is proportional to the expression above taken with opposite sign [114]. Its behavior in the case of an LiNbO3 crystal is shown in Fig. 18.12. Reversal of ferroelectric polarization leads to π-shift for both angles, so that the electrooptic response just changes its sign, and the CSOM contrast (the difference between the two signals in adjacent domains) is simply twice this value. It can be seen from Fig. 18.12 that maximal contrast is achieved when the field is applied perpendicular to the ferroelectric axis. Further, rotation of the polarization plane of the light leads to full extinction of the electrooptic image and then to its reappearance with reversed contrast. Contrary, no

Fig. 18.12. Anisotropic electrooptic CSOM response in a LiNbO3 single crystal: experiment (a) and theory (b). (From [113], courtesy of AIP)

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extinction should exist into LiNbO3 if the electric field is applied at small angles to the c axis, although the dependence on the light polarization angle remains periodic. All these features of the CSOM signal have been observed experimentally. Moreover, fitting of experimental light polarization curves to the electrooptic tensor allows one to determine the direction of the (presumably unknown) ferroelectric polarization axis with the accuracy of a few degrees [113]. We see that the variation of electrooptic response for different directions of applied fields is useful for extracting information about the crystal structure. Even more anisotropy is measured by CSOM for materials of the 4 mm symmetry group, like barium titanate. This case is important in view of the popular materials of the (Ba, Sr)TiO3 and Pb(Zr, Ti)O3 families. We have to mention here that highly anisotropic electrooptic response sometimes results in non-trivial effects like specific optical aberrations inherent to modulated images. The interested reader is referred to [114] for details. As has already been mentioned, the absence of linear electrooptic effect in the paraelectric state makes modulated CSOM very suitable for phase transitions studies. Thermal expansion causing both the laser spot drift and defocusing is a major problem. However, the evolution of the electrooptic image with temperature can be successfully traced within a temperature interval of the order of 300 K [57, 115]. Very useful information may be extracted by measuring local electrooptic loops with spatial resolution close to the diffraction limit. The dc bias field is applied to the sample in addition to the probing ac excitation, and the electrooptic response dependence on the bias field is investigated. Butterfly-like loops (similar to tuning curves for ferroelectric thin films) are common at temperatures below the local phase transition point, while the paraelectric state corresponds to no signal. The transformation from the former kind of response to the latter one has been found to proceed in the interval of a few degrees [57]. This confirms the hypothesis of stress-induced inhomogeneous widening of the phase transition in ferroelectric thin films, considering their abnormally broad maximum of the dielectric permittivity at a “phase transition” as the averaging of many usual narrow peaks with a wide distribution of local transition temperatures. Problems in interpretation of modulated CSOM data are posed by the absence of linear electrooptic response for a few specific orientations of ferroelectric polarization. This is the case, for example, for the important situation of out-of-plane polarization subjected to an in-plane field. The electrooptic analysis for the 4 mm symmetry group predicts no first harmonic intensity [115]. For to this reason, supplementary efforts are necessary to recognize the perpendicular ferroelectric polarization from the paraelectric state. First, the field produced by interdigitated electrodes on the surface has the out-of-plane component in a limited area near the electrode edge. Coincidence of this component with polarization direction induces the finite electrooptic response seen in the CSOM image as narrow stripes near the electrode edges having opposite sign at adjacent electrodes corresponding to “up” and “down” orientation of the normal field component. A more reliable method is the application of an additional dc bias field in the plane of the sample. Artificial deformation of the optical indicatrices due to the induced small in-plane component of polarization turns out to be sufficient to interact with the probing in-plane ac field resulting in finite electrooptic response throughout the film. The contrast is apparently proportio-

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nal to the applied field. This trick is similar to the old idea by Merz for conventional non-scanning electrooptic microscopy [110]. A detailed discussion of this problem can be found in [115]. Apart from being used in its initial form, electrooptic CSOM in the modulation mode can be modified to fit specific experimental tasks. Time-resolved CSOM is a good example of such adaptation [116]. This technique has been successfully applied to studies of the spatially resolved microwave properties of (Ba, Sr)TiO3 thin films [117, 118]. The continuous He–Ne laser in this case was replaced with a powerful mode-locked Ti:Sapphire laser producing a train of pulses with a repetition rate of 80 MHz. The pulses are locked to an electric microwave field applied to the sample. Variation of time delay between laser pulses and the microwave field phase allows one to “move” the illumination time along the electric field cycle and to perform observation of the ferroelectric structure in stroboscopic mode (Fig. 18.13). The time dependence of the electrooptic signal obtained in this way represents a mixture of first and second harmonics of the driving microwave field [116]. This was interpreted as an addition of linear and quadratic electrooptic effects inherent to ferroelectric and paraelectric states, correspondingly. Due to the similarity of the electrooptic response from out-of-plane polarization to the paraelectric response mentioned above, the second harmonic signal can be understood as a contribution from vertically polarized domains [117]. With this assumption, kinetics of the 90◦ switching after application of a large dc bias field can be investigated. The information obtained is useful for the characterization of ferroelectric films of different composition and growth conditions [117, 118].

Fig. 18.13. Time-resolved electrooptic images of the (Ba, Sr)TiO3 thin film at different delays between the optical pulse and microwave field. (From [116], courtesy of AIP)

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The results considered above provide evidence of the effectiveness of scanning electrooptic microscopy for the examination of the structure of ferroelectrics. However, its spatial resolution is limited to the micron and near sub-micron scale. To make this technique really useful for nanotechnology, it must be combined with near-field optics. 18.4.3 Near-Field Electrooptic Microscopy Electrooptic apertureless SNOM can be realized on the basis of a CSOM apparatus combined with AFM [25]. This simple principle faces serious complications to be overcome in the case of building a real setup. First, intensity of scattered light decreases by several orders of magnitude due to the small size of the AFM tip used as a scatterer. Second, multiple lock-in detection should be employed, since an ac vibration is applied to the tip for effective feedback while an ac electric field is used for modulation of the optical properties. Further, the proximity of the tip to the sample surface, necessary to enable the near-field imaging, makes the technique sensitive to surface topography. Intermittence of optical image with topographic artifacts poses serious problems, widely discussed in the context of near-field microscopy. Electrooptic modulation partially overcomes the difficulties related to interference with parasitic scattered light, but the signal/noise ratio remains the main issue. The possibility of separating the electrooptic image from the topographic artifacts has been demonstrated on (Ba, Sr)TiO3 thin film [25, 119]. A number of ways to rectify the useful signal has been applied. The first one is the interferometric principle of SNOM signal detection. Two separate spots were formed on the sample surface using a Nomarski prism, and interference of the two reflected beams was registered. Only one spot was affected by the vibrating tip near the surface to induce modulated optical signal in the output. Further, transformation of the in-phase and out-of-phase signals allowed one to eliminate effectively the surface-induced artifacts. Finally, superposition of images measured at different values of the electric field made it possible to extract information related to the ferroelectric structure. Special care was also taken to remove errors due to nonlinearity of the piezoelectric scanner. As a result, the change of the ferroelectric domain structure under applied electric field has been reliably observed [119]. A more traditional version of apertureless SNOM was applied to visualize the ferroelectric domain structure in TGS single crystal [99]. An optical beam was involved to get the near-field image using the light scattered from a dithering AFM tip, while the tip motion was controlled through a separate feedback circuit. It was found that the conventional SNOM image (similar to those described in Sect. 18.4.1 and reflecting very few features related to domains) transforms into a distinct picture of the ferroelectric domain structure when the electric field is applied to the tip (Fig. 18.14). The analysis showed that the registered SNOM signal had no correlation with motion and deformation of the tip itself, so that this experiment has to be ascribed to a family of electrooptic SNOM. However, mechanical contact of the tip with the sample surface and application of local electric field make this technique resemble PFM (see Sect. 18.3), with the essential difference that the main information is obtained from an induced change of optical properties.

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Fig. 18.14. The ferroelectric surface of a TGS single crystal imaged with apertureless SNOM in the presence (a) and absence (b) of the ac voltage at the tip. (From [99], courtesy of AIP)

An effort to converge piezoresponse-AFM and electrooptic SNOM into a new hybride technique was made recently [120]. The authors used the fiber SNOM in transmission mode simultaneously with the local application of a sinusoidal electric field. The field was applied to the BaTiO3 crystal surface through the ultrathin metal layer covering the tip. The obtained image (Fig. 18.15) resembles pictures of the domain structure taken with PFM. Simultaneous application of three highly inhomogeneous fields (optical, electric and elastic ones) should complicate the quantitative description of the effect; however, the relatively large size of the light spot allows one to consider the optical intensity as nearly homogeneous. In this sense, the new technique is similar to the previous one: a relatively large light spot probed with a small tip ensuring both nanoscopic near-field reflection/transmission and electric field supply. On the other hand, the apparently piezooptic origin of the observed contrast brings the new technique close to PFM with a coated optical fiber replacing the conventional AFM tip.

Fig. 18.15. Image of a BaTiO3 crystal surface taken with fiber SNOM with local illumination and local electric field. (From [120], courtesy of AIP)

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18.4.4 Micro-Spectroscopic Techniques Light scattered from the sample is characterized, in addition to its intensity level, by rich spectroscopic information. Investigation of its inelastic interaction with both optical (Raman scattering) and acoustic (Brillouin scattering) phonons is a classical tool to clarify the crystal structure and its changes during phase transitions. Being low-symmetric and, therefore, possessing manifold phonon spectra, ferroelectrics are traditional objects for infrared optical spectroscopy. The fingerprint of the ferroelectric phase transition is the presence of the so-called soft mode corresponding to a zero frequency instability of a definite branch of the phonon spectrum [121]. The soft mode concept happened to become so important for the theory of ferroelectrics that the whole system of classification of ferroelectric phase transitions is based on the type of the observed optical spectra [1]. The common problem complicating the comparison of theoretical predictions of ferroelectric properties with experimental data is their domain structure, whose typical size can be very small. Just like the measured hysteresis loop represents rather averaged ferroelectric polarization than the “theoretical” one (being, for example, the order parameter in a Ginzburg–Landau–Devonshire theory [122]), the measured infrared spectra often correspond to mixed state of different domain orientations and density. Recognition of this fact has resulted, on the one hand, in careful preliminary preparation of “single domain samples” for spectroscopic measurements; on the other one, in an intentional decrease of the laser spot to probe the local polarization state. The final stage in this evolution is the concept of a “spectroscopic microscope” [123], where variations of the Brillouin or Raman spectra along the sample allow one to estimate its spatial inhomogeneity. The micro-Raman studies have become common today in many areas, although the genuine microscopy (that is, mapping of the sample surface or bulk) is still more rare.

Fig. 18.16. Domain structure in a LiNbO3 single crystal imaged with luminescence microscopy. (From [131], courtesy of Springer)

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Studies of ferroelectrics with micro-Raman and micro-Brillouin scattering with a spatial resolution of 1–2 microns have been carried out [124–128]; near-field Raman spectroscopy has been also performed [129]. Problems start to arise when the technique is intended for spatial imaging. The first results show rather an absence of qualitative difference between the Raman spectra in separate domains [127, 130]. A reliable change of spectral characteristics has been registered only during scanning across isolated domain walls or other ferroelectric inhomogeneities [129, 130]. Application of luminescence spectroscopy for imaging of the ferroelectric domain structure seems currently more promising. It has turned out that the nearly stoichiometric LiNbO3 crystals doped with small amounts of Er3+ ions reveal a distinct contrast between opposite domains (Fig. 18.16), realizing in this way a genuine spectroscopic SPM [130, 131]. The origin of this contrast, as well as its conformity to the seed ions distribution and real ferroelectric structure are still to be examined. Perspectives of spectroscopic imaging in ferroelectrics are, therefore, an open question. 18.4.5 Second Harmonic Microscopy The role of the ferroelectric domain structure in producing higher optical harmonics was recognized forty years ago [132]. Optimization of second harmonic (SH) emission by domain structure engineering became the main issue of following studies, resulting in the vast nonlinear optics technology using quasi-phase-matched crystals [4]. After dielectric applications, optoelectronics and photonics remain the most important practical drive for exploring ferroelectrics. It was soon established that the impact of domain walls on SH generation could provide the new tool for investigating the domain structure itself. After an unavoidable period of initial studies using indirect macroscopic techniques, SH visualization of the antiparallel domain structure in TGS crystals marked the birth of a new kind of microscopy for exploring ferroelectric domains [133]. The need for high power lasers and the long time necessary for image acquisition inherent to SH imaging prevented its wide use; however, a number of efforts are worth mentioning [134–137]. The development of SPM revitalized SH imaging, as well as some other traditional techniques. The focusing of the laser beam into a small spot relieved requirements of both light intensity and exposition time compared with continuous illumination. For a period of time, optical microscopy in SH happened to become even more attractive to researchers than the usual signal at the fundamental frequency. The reason for this, apart from the obvious general drive of SH optics by promising applications, was, as has already been mentioned, the lack of direct coupling between ferroelectric polarization and the linear optical index. On the contrary, nonlinear optical properties inherent to ferroelectrics allow one to expect, in principle, a way to discriminate different polarization states. Nevertheless, first studies of ferroelectric domain structure using CSOM revealed no SH contrast between antiparallel domains in LiNbO3 and LiTaO3 single crystals [138–140]. The SH light intensity was found to be concentrated at domain walls, so they were distinctly visible on the homogeneous background [138]. The following studies revealed that, depending

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on the surface orientation under study and on the light polarization direction, the SH contrast could be reversed, that is, dark walls on the bright background are sometimes observed [139]. Ferroelectric films, contrary to single crystals, show high spatial inhomogeneity of SH during the polarization reversal cycle, so application of SH microscopy for domain structure kinetics examination is more reasonable in this case [141]. First efforts to investigate the structure of ferroelectric ceramics using second harmonic SNOM revealed a highly inhomogeneous spatial distribution of the SH signal throughout the sample with no visible correlation to the grain structure [142–144]. It was shown later [145] that the signal from areas with high SH activity could be varied by rotation of the polarization plane of incident light. There is also some difference between the SH response obtained from three orthogonal states of ferroelectric polarization in the case of a BaTiO3 single crystal. However, no pictures of the domain structure have been shown for single crystals, and the analysis gives no reasons to expect SH contrast between antiparallel domains. It is possible to observe non-collinear (90◦ ) domains with SH microscopy with sub-micron resolution [146], but this task can be achieved more easily with ordinary, fundamental wavelength SNOM. The tricks to artificially create SH contrast, similar to the addition of a crystal plate as in [136], may be not effective in SNOM experiments. However, this technique can be obviously be applied to a reasonable task. The boundaries of homogeneous domains are the most active in SH generation, so that highly inhomogeneous ferroelectric thin films and ceramics with high density of domain walls and grain boundaries can be successfully imaged with SH SNOM (Fig. 18.17). Otherwise, the technique is rather more useful for studies of spatial distribution of SH emission itself, than for characterization of the material. Of course, there is still

Fig. 18.17. Thin film of (Ba, Sr)TiO3 imaged with second harmonic SNOM. (From [145], courtesy of AIP)

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the possibility or working with single crystals by visualization of the domain walls versus the domain background [140], already known from confocal far-field studies.

18.5 Applications to Ferroelectrics After reviewing the techniques and their modifications to properly study the ferroelectric domain structure, we shall consider briefly the principal problems of ferroelectrics physics and technology where SPM approaches can be useful and even decisive. 18.5.1 Imaging of Domains and Domain Walls Visualization of the domain structure remains the main destination of SPM applied to ferroelectrics; that is clear even from the term “microscopy” in its name. Adequate representation of the spatial distribution of ferroelectric polarization is a principal goal of most improvements in the SPMs described above. It is natural that this oldest application is at the same time the most successful one. Numerous experiments with different SPM modes allowed one to identify ferroelectric polarization of any orientation to the surface (Fig. 18.18). However, there is still no universal tool to resolve details of the domain structure of any configuration in an arbitrary ferrolectirc and at nanoscopic scale. Every variety of SPM has its own restrictions, so choosing a proper technique is an important step towards achieving better quality images. The piezoelectric mode of SPM quickly became the favorite tool of researchers to reveal the out-of-plane component of ferroelectric polarization. It provides distinct and unambiguous patterns, especially accurate when the phase of the piezoelectric signal is used as output parameter. Taking into account that this technique is easily compatible with the “writing” mode (Sect. 18.5.2), and that perpendicular polarization is used in most FeRAM projects, being the main drive to study ferroelectrics today, the popularity of this technique is understandable. However, its application requires high piezoelectric coefficients, and sensitivity of the method decreases at

Fig. 18.18. Three-dimensional domain structure of BaTiO3 revealed in topographic mode (a), perpendicular (b) and shear (c) PFM. (From [31], courtesy of Springer)

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small sizes of the sample. It is still unclear whether the “disappearance” of ferroelectricity in ultrasmall grains [59] is a real effect, or whether the technique just becomes ineffective in such extreme conditions. Application of a local electric field combined with the global response also presents a problem that can be responsible for numerous quantitative disagreements. Visualization of in-plane components of the ferroelectric polarization (so-called a-domains) is more difficult for piezoelectric microscopy. The problem is that it is difficult to apply a local horizontal electric field, and the induced distribution of strain is three-dimensional and not compatible with simple models. Friction force microscopy can be successful in imaging the horizontal polarization [14] if there are no specific requirements to the quality of the surface. Fortunately enough, scanning electrooptic microscopy is not sensitive to such problems due to the absence of strong coupling between strain and optical response, so it can be used instead of piezoelectric SPM. Imaging of separate domain walls, instead of domains, is a much more complicated problem, despite the fact that historically it was this task that motivated first SPM application in ferroelectrics [8]. The obvious reason is the smaller width of a domain wall compared to domains. Further, the transient region from one polarization direction to another one is a powerful source of fields, strains, and diffraction (for optical techniques). As a result, many studies reveal extremely thick domain wall images, up to few microns [8, 44], so that special analysis is required to distinguish the real wall size from the apparent broadening due to emanated strains. In those cases where crystal properties and configuration of the experiment allow avoiding such complicated factors, the observed walls are extremely thin, as expected from theory, and free from topographic distortions at the surface [14,43]. Distortion of the wall image can be also exploited to image the domain structure in those cases where measured properties of adjacent domains are identical, like in second harmonic optical microscopy [138] or micro-Raman microscopy [131]. 18.5.2 Writing Patterns The most promising applications of ferroelectrics, like FeRAM, require domain structure engineering at a nanoscopic level. Optical devices based on PPLN and similar materials are also produced by means of submicron switching. The SPM setups are ideal for this purpose, providing both highly localized fields and reliable position control. The voltage sufficient for local switching is applied to the conductive probe, that is scanned along the surface according to a drawing path. The ease of change from the writing mode to subsequent imaging is also highly advantageous. All these factors caused the fast growth of experimental works devoted to nanoswitching and pattern writing using various kinds of SPM setups [27–41]. The minimal size of the switched area (considered as a potential information bit) was not far below one square micron in first experiments [17, 31], and the choice of materials to demonstrate SPM switching was initially not so wide. However, it was found very soon that manipulations of the value of the applied voltage and of its duration allow one to obtain a variety of sizes for the resulting written spots. In general, the size of the written domain grows with both voltage magnitude (up to

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Fig. 18.19. Two-dimensional array of circular domains written with a biased AFM tip and revealed by PFM. (From [148], courtesy of APS)

some saturation value) and pulse time [147]. As a rule, no switching was observed at all below some critical values of these parameters. An important issue is the stability of the written information. The switching process starts from forward spreading of the new ferroelectric domain from the tip to the opposite side followed by lateral expansion [1]. If the time of voltage application is too short or the voltage is too small, the new domain does not grow through the whole thickness, and the growth of a head-to-head domain wall (which has very high energy due to electrostatic fields) makes the written structure unstable, so that it disappears after some time. Otherwise, long voltage pulses cause spreading of the domain into a wide area due to domain wall creep [148] well outside the area immediately under the tip. Optimization of switching characteristics produces stable written bits of the order of a few tens of nanometers, depending on the material [31, 149, 150]. Writing on films looks more successful compared to experiments performed with single crystals due to a number of reasons. First, the films are just thinner, so that higher fields can be applied. Further, the complete breakthrough of the growing domain is also more likely to be due to the low thickness (there is simply no room to form head-to-head domain walls). Finally, the film structure is presumably more inhomogeneous than the one of a single crystal, resulting in lower spatial coherence of the switching process and more effective pinning of the lateral creep. Writing on single crystals is used mostly with optical crystals like lithium niobate where some waveguide application requires reversing of the polarization at the surface layer only [4]. 18.5.3 Phase Transitions The next step after the imaging of the ferroelectric domain structure itself is the investigation of its changes induced by external forces. Application of the bias electric field considered in a previous section is the most common case, definitely interesting in view of practical goals of domain structure engineering. Observations of domains kinetics made with high resolution SPM confirm the principal switching picture established in macroscopic and microscopic scale experiments at earlier stages of ferroelectrics studies [1]. Variation of temperature is another way to modify the domain structure, especially effective in the vicinity of the phase transition, where

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domains presumably have to disappear together with ferroelectric polarization itself. The practical value of such studies is less evident, but the phase transition anomalies remain a traditional problem of fundamental physics. The TGS crystal is the favorite model material to study ferroelectric phase transitions due to their growth simplicity, low switching voltage and convenient phase transition location not so far above room temperature (49 ◦ C). There is no optical contrast between ferroelectric domains of opposite polarity, so that the use of conventional optical microscopy is restricted, and SPM experiments provide relatively new information concerning the behavior of the domain structure in the vicinity of the phase transition. Scaling laws for domain size have been the purpose of a number of SPM investigations [46,47]; it was found that the experimental value of critical indices deviates from predictions of general thermodynamic models. This discrepancy is not very surprising, taking into account that the domain pattern in real ferroelectrics is determined by local imperfections rather than by cooperative ordering to minimize the stray field energy, because electrostatic interaction is relatively weak and partially screened by mobile charge carriers at the sample surface. The SPM investigation of the domain structure evolution at the phase transition in barium titanate crystals [14,48,50] mainly confirmed information obtained earlier with the use of other techniques. 18.5.4 Morphotropic Phase Boundary Materials in the vicinity of the phase transition look especially attractive for possible applications due to abnormal values of many useful physical properties, including high dielectric and piezoelectric coefficients. However, the temperature interval of such anomalies in common bulk materials is usually rather narrow. An interesting case is observed in complex perovskite systems, where structure, symmetry and properties depend on both temperature and concentration of the constituent atoms. It is well-known that small variations of concentration near the critical value are capable of changing the symmetry of the material. Strictly speaking, this structure difference should not be called phase transition, because the “driving force” (concentration) can not be applied externally. However, compositions near this so-called morphotropic phase boundary (MPB) combine abnormal physical properties, typical for phase transformations, with enhanced stability in temperature, which makes them attractive for technical applications. The development of some new models has caused a sharp growth of interest in this problem in the last few years. It was found that depending on external conditions, a narrow stripe of a stable monoclinic symmetry can exist at the boundary between well-known tetragonal and rhombohedral parts of the phase diagram [151]. The coexistence of different symmetry phases provides a rich variety of proposed mechanisms to explain the dielectric and piezoelectric response of MPB materials, from traditional domain wall displacement (enriched by the enormously high number of possible domain pair configurations) to the recently introduced exotic model of ferromagnetic-like polarization rotation [152]. The origin is still unclear due to the ambiguity of macroscopic data obtained from inhomogeneous materials with extremely strong sensitivity of the expected output to any fluctuations. It is very

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likely that SPM is destined to resolve this problem due to its fine spatial resolution and sensitivity to the local structure, including the existence and the sign of the piezoelectric or electrooptic effect. Indeed, first SPM experiments demonstrated the existence of an extremely fine domain structure with unusual behavior [63, 64]. 18.5.5 Relaxors Another example of “extended” phase transition where abnormal dielectric and piezoelectric properties are observed in a wide temperature interval is the so-called relaxor state. These materials have been known for a long time [153]. They are characterized by an extremely broad (up to hundred of Kelvins) width of the dielectric “peak” (which is a rather smeared maximum in this case) and by the pronounced dependence of both peak position and amplitude on the probe electric field frequency. This frequency dependence (relaxation) has given a name to the whole class of materials. Properties of relaxors are obviously similar to those of spin glasses, and some kind of structural disorder is involved in any explanation of the phenomenon. The first model [153] considered the coexistence of small regions of chemically different composition with spatial fluctuations of the local phase transition temperature. Superposition of numerous sharp peaks due to local phase transitions gives a wide maximum of the dielectric permittivity. The origin of the frequency dependence is less clear, so numerous efforts to improve the model were made in later works. It was argued also that even in the case of chemical homogeneity, a similar effect can be caused by “nanodomains” or “polar clusters” both below and above local transition temperature [154]; in this case, the frequency dependence could be simply due to dynamical properties of domain walls or thermoactivation. Estimation of the validity of such models, as well as the acquisition of new data requires spatial resolution at the nanoscopic scale. Once again, SPM seems to be the tool of choice to achieve significant progress in this field. Despite the fact that the idea of SPM studies of relaxors has already been realized in a number of investigations [60–62], little is still proved as to possible driving forces of relaxor properties. Coexistence of a coarse domain structure typical for crystalline ferroelectrics with extremely fine domains [62] provides some basis for the nanodomains model. Slow decay of the artificially written domains during heating above the dielectric maximum [60] may be an argument for the presence of polar clusters in the nominally paraelectric state. However, the presumed inhomogeneity of the samples reduces the “temperature of the relaxor phase transition” (determined by the peak of dielectric permittivity) to a merely formal parameter, depending on both sample inhomogeneity and frequency, so it is hard to say whether a material is in the ferroelectric or paraelectric state. It is clear that extensive and systematic SPM studies are still necessary to extract reliable information on the mechanisms of the relaxor state. 18.5.6 Thin Films The relation between properties of ferroelectric single crystals and films of the same composition remained an issue of ferroelectrics physics for many years [155]. Ma-

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croscopic dielectric and piezoelectric properties of films are usually worse compared to those of single crystals; the mechanisms responsible for this difference are important to improve thin film device performance. Recent boom in this field is obviously coupled to fast advances in film growth technology and numerous possible applications including FeRAM. It is not surprising that thin films quickly became one of the favorite objects in studies of ferroelectrics among researchers using SPM. We shall briefly note only the main results and directions of these vast investigations. The SPM study of ferroelectric thin films started soon after this technique was demonstrated on single crystals [28, 51]. Due to the grain structure typical for polycrystalline films, the obtained SPM images are usually mixed with topographic features, so that development of reliable methods to separate contrast inherent to ferroelectric domains from topographic background became the main issue of early works. One of the main problems of FeRAM development is the stability of the written information due to fatigue or ageing effects: properties of materials become gradually worse when numerous cycles of switching are performed. An irreversible change of domain structure is usually considered as the driving mechanism of fatigue, and experimental verification of this idea at nanoscopic level has been found using SPM [52]. Another important phenomenon is the decrease of the domain wall mobility known as freezing [54]. Kinetics of the polarization reversal has been found to depend on the initial domain structure, for example, on the presence of 90◦ domain walls [56]. Many features of films are due to spatial inhomogeneity of ferroelectric properties; it was demonstrated, for instance, that the broad maximum of dielectric permittivity, typical for most films, is due to significant variation of the local phase transition temperature along the film (tens of Kelvins), while the transition at a given point was relatively sharp and similar to that of single crystals [57]. A decrease of both the thickness and the lateral size of synthesized films poses the question of existence of ferroelectricity itself in very small objects. Ferroelectric ordering is a “bulk” phenomenon and can be suppressed when the surface contribution becomes stronger than the volume energy. For decades, this problem has been considered mainly in theoretical studies. Currently it can be addressed directly thanks to SPM. The first experiments in this direction were performed with ultrathin (few monolayers) ferroelectric polymer films [58] and ultrasmall ferroelectric grains [55,59]. It was observed that grains smaller than some critical value show no contrast in PFM. Additional experiments have to show whether the effect is fundamental or due to the lower performance of the experimental technique at the ultralow spatial scale. 18.5.7 Artificial Nanostructures The next logical step after examination of properties of ultrasmall ferroelectric objects is to create them artificially. The goal can be to achieve some combination of unusual material characteristics or to realize designed devices of the necessary size. Properties of nanodots, nanowires, nanolayers and other similar objects are the topic of studies in very different areas of science and technology. It is obvious that SPM is a tool of choice in the exploding field of nanoscience. Up to now ferroelectric nanostructures received less attention than similar objects of, say, magnetic nature. One of the reasons is the absence of exchange interaction,

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which determines properties of magnetic materials. One cannot expect significant variation of ferroelectric properties due to proximity effects. Further, the spatial scale necessary to achieve modifications of the ferroelectric state due to size effects is smaller, in general, than the critical size of other ordered systems. That simply means that more progress in the preparation of nanoobjects is necessary to achieve similar interest. Nevertheless, the smaller critical size scale makes ferroelectric nanostructures potentially more attractive for applications. Investigation of properties of artificial ferroelectric objects with SPM has made only first steps. It started, as it could be expected, from studies of nanoscopic size capacitors [65,66]. Then, ferroelectric nanowires [67,71,72] and nanotubes [68] were successfully imaged and switched using SPM. Assembling and SPM characterization of ferroelectric nanoislands [70] has been also reported.

18.6 Conclusions Ferroelectrics still present significant interest for both contemporary science and technology, despite the already long history of their investigations. Improved dielectric, piezoelectric, optical, electrooptic and other properties provide the opportunity for numerous applications. The important feature of ferroelectrics is their possibility to reverse the polarization state of the material with external fields at very small spatial scale, making this class of materials one of the most prominent ones for information storage. The relatively low size of rewritable domains explains the significant role of nanoscopic techniques in the study of ferroelectrics. We have traced the history and evolution of scanning probe microscopy of ferroelectrics from the very first pioneering works up to its current use as a routine tool of materials science. We tried to show that traditional SPM setups using topographic or force modes happened to be not effective enough for reliable visualization of the ferroelectric polarization patterns. The specific nature of antiparallel domains, often showing no difference in both interaction force and optical index, impels development of new problemoriented techniques. The qualitative progress in SPM is as important for ferroelectrics science as for the investigation of materials’ properties themselves. The practice of the last decade has demonstrated that the most valuable information can be obtained by use of the modulation principle. Specific interactions of ferroelectrics with applied fields have been proved to be much more sensitive to the polarization direction. Among these techniques, the piezoelectric response microscopy currently takes the leading place due to its simplicity and unambiguity of the output values. Further progress can be achieved by coupling SPM to the blooming field of near-field optics. Although the few efforts to observe ferroelectric domains with near-field optical microscopy have not given any breaking news yet, the modulated scanning electrooptic microscopy looks at least as promising as the piezoelectric mode of “usual” SPM. We believe that the combined efforts of experts in optics, SPM, and traditional ferroelectrics would bring development of new experimental techniques capable of taking on the breathtaking challenge of modern ferroelectric materials and devices.

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Acknowledgements. Dr. Oleg Tikhomirov’s work at the INFM in Pisa is supported by the Marie Curie International Incoming Fellowship of the European Commission (project number MIF1CT-2004-002557). The authors are grateful to Prof. Jeremy Levy and to Dr. Vlassis Likodimos for critical reading of the manuscript and valuable remarks, and to the American Institute of Physics, the American Physical Society, and Springer for kind permission to reproduce the figures originally published in their journals.

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19 Morphological and Tribological Characterization of Rough Surfaces by Atomic Force Microscopy Renato Buzio · Ugo Valbusa

List of Abbreviations and Symbols a ac aL A A0 Ar Are Arp b C(q) d Df DT E fe fp Fadh Fc Fe Feff Ff Ffloc Fn Fnloc Fp f(ζ) G G(r) h

Contact spot area Critical contact spot area Largest contact spot area Sampled area of a surface Nominal area of contact Real area of contact Elastic component of the real contact area Plastically-deformed real contact area Scale parameter for self-affine transformations Power spectrum Distance between reference planes of rough surfaces Fractal dimension Topological dimension Young’s modulus of an interface Force sustained elastically by a single contact spot Force sustained plastically by a single contact spot Adhesive force acting on AFM tips Adhesive force in pull-off experiments Elastic component of normal reaction force Total force acting on an AFM tip Friction force Local friction force in MD simulations Externally applied normal load Local normal force in MD simulations Plastic component of normal reaction force Magnification function in Persson’s theory Roughness parameter for WM surfaces Height-height correlation function or structure function Height level

262

h0 H Hns-C HT6 k(a) K l L L1 n(a) N Nspots ns-C p(z) P(z) P(ε) P(ζ) Ppl (ζ) P(σ, ζ) q q q0 q1 qL r R R(a) s S T6 x y z u V w α δ ∆ ∆c ∆γ ε φ γ γeff (ζ) η λ

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Roughness parameter in Persson’s notation Indentation hardness Hardness of ns-C films Hardness of T6 films Curvature of a contact spot of area a Kurtosis Length scale System size Short distance cut-off for structure function G(r) Probability distribution of contact spot areas Number of AFM images Number of contact spots Nanostructured carbon Probability distribution of surface heights Cumulative probability distribution of surface heights Perimeter of island coastlines Normalized contact area Plastic component of normalized contact area Stress probability distribution at the contact interface Wave vector Modulus of wave vector Low-frequency cut-off for power spectrum High-frequency cut-off for power spectrum Smallest available wave vector of power spectrum Position vector Curvature radius of a single asperity Curvature radius of a single asperity of base area a Normalized surface height Skewness Sexithienyl thin films Spatial coordinate Spatial coordinate Surface height AFM probe displacement Sliding velocity Standard deviation for probability distribution Hurst coefficient or self-affine exponent Adhesion length Single asperity deformation Critical deformation of a single asperity for inception of plastic flow Interfacial energy Step length Material parameter Parameter for WM fractals Effective interfacial energy Density of surface asperities Length scale parameter

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Λ µ µn ν θ σ σ0 σa σY σa (ζ) τ ω ξ ψ ζ

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Topothesy Friction coefficient Central moments for height probability distribution Poisson ratio Local tilt of surface roughness Stress Uniform stress for smooth surfaces Constant detachment stress Materials yield stress Scale-dependent detachment stress Shear stress Probability distribution for asperity heights Lateral correlation length Plasticity index Magnification parameter

19.1 Characterization of Surface Roughness by Atomic Force Microscopy Investigations conducted in broad areas of materials science, on thin films and coatings, nanocomposites, nanostructured materials and biological systems, provide increasing evidence of the crucial role played by surface roughness on the functional performance of materials [1]. It has been shown that roughness can affect the electrical, magnetic and optical response of surfaces [2–6]; also wetting and biocompatibility are significantly influenced by morphology [7–10]. Friction, adhesion and wear are further examples of functional properties controlled, to some extent, by roughness [11, 12]. Despite their paramount importance in everyday life, they are still poorly understood: we note, as a matter of fact, that friction coefficients are still unpredictable quantities. On the contrary, we can appreciate the occurrence of robust friction laws, like Amontons’ law, governing macroscopic experiments: we believe that such laws exist for the interplay of general surface properties, roughness being one of them [12–14]. How does surface roughness influence tribology? The most intuitive picture assumes that morphology reduces contact between surfaces to a small fraction of the nominal contact area, formed by discrete spots randomly distributed at the interface (Fig. 19.1) [11, 15]. These spots, called asperities or junctions, support external load and adhesion, as well as friction forces at incipient and relative motion. The size and spatial distributions of the asperities depend on roughness, contact forces and the materials’ structure. The previous figure correctly suggests that a quantitative characterization of surface morphology from macroscopic to nanometer scale represents the first step for the investigation of roughness effects in tribology. In the following subsections, we focus on the statistical methods mostly used to describe rough surfaces, showing how to extract quantitative information from AFM images. This provides a conceptual framework for the development and validation of comprehensive tribological theories.

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Fig. 19.1. Schematic diagram of two rough surfaces in contact. Due to surface morphology, contact interface consists of multiple asperities supporting both normal and shear forces (white arrows and black arrows respectively)

19.1.1 Statistical Methods for Stationary Random Surfaces Solid surfaces can be formed by any of the following methods: film deposition, fracture of solids, surface machining and solidification of liquid fronts. It is found that most surfaces formed by these methods are rough, atomically-flat samples being quite rare in nature [16]. The randomness exhibited by real interfaces suggests that one must adopt statistical methods for topographical characterization. Let z(x, y) be the surface height at the location (x, y): we assume z to be a stochastic random process with respect to the spatial variables x and y, z ∈ (−∞, +∞). One of the most significant properties of a rough surface is given by the probability density p(z) for the distribution of heights (Fig. 19.2) [17]. The probability of a height lying in between z and z + dz is p(z) dz, and the cumulative probability distribution that a height will be below some level h is: h p(z) dz .

P(h) =

(19.1)

−∞

The distribution p(z) may be characterized by its central moments µn , defined as [17]: +∞ z n p(z) dz . µn =

(19.2)

−∞

The second moment µ2 is the variance of the height distribution. Because it is in √ units of height squared, it is customary to use the quantity w ≡ µ2 : this is called the surface roughness and describes the deviations of the surface from being ideally flat. The third central moment µ3 is the skewness, usually normalized as S ≡ µ3 /w3 (Fig. 19.2). Because it is an odd moment, it is a sensitive measure of the degree of asymmetry of the distribution. For a Gaussian distribution S = 0.

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Fig. 19.2. (a,b) Schematic diagram of a surface profile z(x) described by the height probability distribution p(z). (c,d) Symmetry and shape properties of p(z) are classified by skewness S and kurtosis K

The forth moment µ4 is called kurtosis, normalized as K ≡ µ4 /w4 (Fig. 19.2); it describes the overall shape of the distribution. A Gaussian distribution has K = 3, while distributions having a sharper central peak and longer tails have K > 3; the case of K < 3 occurs for flatter distributions. Experimental probability distributions can be extracted from digitized AFM images by collecting the relative frequencies of sampled heights in a histogram plot, then fitting it by analytical expressions; the central moments µn can be estimated from the digitized version of (19.2). It is often found that the experimental probability density p(z) has a Gaussian shape [15, 18], but non-normal distributions, like the inverted chi-squared distribution, have been reported [19]. Most machined surfaces tend to be at least slightly negatively skewed, because peaks are more easily removed than valleys [18]; this is also the case of road surfaces [20]. Low-adhesion polysilicon surfaces obtained by etch texturing (used in micro-electro-mechanicalsystems MEMS technology) have been reported to possess topographies with S > 0 and K > 3 [21]. Such an approach would in principle represent a powerful tool for rough surfaces classification [16, 22, 23], supporting, at the same time, tribological modeling and theoretical predictions through quantitative estimations of real specimens’ parameters. Unfortunately, a note of caution has to be made: we implicitly assumed z(x, y) to be a stationary random process [17], which means that the measured roughness sample represents a true statistical representation of the entire rough surface. In such a case, the probability distribution p(z) and the central moments µn are unique and well-defined quantities, which remain unchanged if the sample size or the location on the surface are altered. This condition can be satisfied by poorly

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sampling surface heights, so that they represent independent random variables. If on the contrary surface heights are densely sampled (as is usual in AFM imaging), memory effects influence neighbor heights and the probability distribution p(z) and its central moments become scale dependent, i.e., the probability distribution of a small region of the surface may be different from that of a larger region. When this happens, real surfaces have to be modeled by non-stationary random processes. Pioneering investigations performed by Sayles and Thomas [24] demonstrated that this was the case for several natural and man-made surfaces, their surface roughness scaling with the system size L as w ∝ L 1/2 on a wide range of wavelengths; also local slopes, curvatures and densities of maxima and minima were similarly affected [24–28]. Such behavior qualitatively reflects the multiscale nature of surface roughness and demands for scale-independent techniques of roughness characterization. 19.1.2 Statistical Methods for Fractal Surfaces The multiscale, self-repeating nature of surface roughness represents a peculiar feature of several objects found in nature. In his classical paper, Mandelbrot [29] drew attention to some earlier work by L.F. Richardson, who pointed out that a simple question such as, “how long is the coast of Great Britain?” has no answer, apart from an operational description of how one estimates the length of the coastline. In fact the coastline of Britain has self-similar features such that the more the coastline is magnified, the more features and wiggliness are observed. We can also say that it is a fractal object (Fig. 19.3). One can attempt to measure the length of the rugged coastline by striding around the coastline with steps ε to create a polygon whose perimeter P(ε) is an estimate of the coastline. However, if the estimate P(ε) is plotted with respect to ε on a graph having log–log scales, a straight line can fit data, that is the coastline of Britain is infinite if one can use smaller and smaller steps in the estimation. Richardson showed that this kind of paradox was inherent in the measurement of any type of coastline and pointed out that any estimate of any coastline should be linked with the statement of how that estimate was deduced. Mandelbrot demonstrated that the relationships P(ε) ∝ ε1−Df holds, where Df is the fractal dimension of the coastline, 1 ≤ Df ≤ 2. If Df = 1, the perimeter is independent of ε and the coastline belongs to a smooth one-dimensional object (like a circle) [29]. If on the contrary Df > 1, the power law P(ε) ∝ ε1−Df reflects the fractal nature of the coastline, that is the irregular and self-similar boundaries it possesses on a large range of length scales. We can also say that the fractal dimension Df is a scale-independent parameter summarizing the fractal nature of each specific coastline. Broadly speaking, the fractal dimension Df generalizes the mathematical concept of topological dimension DT to non-integer values and allows distinguishing among different self-similar objects [30–32]. The fractal description collects a broad class of systems, from naturally occurring patterns or geofractals (lakes, mountains, islands, rivers) to biological forms (cauliflower, ferns, felts, the crown of different types of trees) [30,31] and living objects (branched terminal elements in animals with hairy design of attachment pads,

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Fig. 19.3. The coastlines of Great Britain have self-similar properties when magnified on different length scales, being an example of fractal objects. Their perimeter P(ε) scales with the step ε according to the specific coastline fractal dimension Df , for the west coast of Britain and the land frontier of Portugal, while no fractal scaling is obviously expected for a circle

like beetles, flys, spiders and geckos) [33]. Fractal surfaces include thin films grown under non-equilibrium conditions (vapor- or beam-deposited atoms, molecules and clusters) [16, 34], fractures [35], manufactured metal surfaces and solidified liquid fronts [16, 20, 36]. Investigations originally reported by Sayles and Thomas pointed out the similarity of real surfaces with continuous non-differentiable processes like Brownian motion, hence emphasizing with implicit language the manifestation of self-similar fractal properties. A quantitative framework is needed to characterize fractal surfaces. We define a self-affine surface to be statistically invariant for the anisotropic scale transformation [16]: r → br , z(r) → bα z(r) ,

(19.3)

where α ∈ [0, 1] is called the Hurst coefficient or self-affine exponent. For α = 1, the surface is called self-similar (Fig. 19.4). From the value of the Hurst exponent, α we can estimate the fractal dimension Df , defined by the relation Df = 3 − α. Since 0 ≤ α ≤ 1, we have 2 ≤ Df ≤ 3, that is the fractal dimension is not smaller than the topological dimension of the surface DT = 2 and not larger than DT + 1. When applied to a unidimensional profile (DT = 1), the previous relation reduces to 1 ≤ Df ≤ 2. Several methods have been developed to estimate the values of fractal parameters. One of the most commonly used consists in the investigation of the height–height

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Fig. 19.4. Schematic diagram of self-affine profiles. (a) We can enlarge a portion of profile (1) laterally and vertically by factors b and bα , obtaining profile (2), then repeat anisotropic magnification to obtain profile (3). If all profiles have the same statistical properties, they are self-affine with Hurst coefficient α. (b) The parameter α controls the relative amplitude of high frequency to low-frequency wavelengths

correlation function G(r), often called structure function, defined as follows [15–18]:   2   2 1 G(r) ≡ z(r + r ) − z(r )  = z(r + r ) − z(r ) dr , (19.4) r A A

where z(r) is the surface height at the position r = (x, y) and A is the surface area. The structure function essentially measures the lateral correlation of the surface heights. For isotropic self-affine surfaces, G(r) depends only on the distance r = |r| and presents the following asymptotic behavior:  r 2α r  ξ (19.5) G(r) = 2w2 r ξ , where ξ is the lateral correlation length of the surface (Fig. 19.5a). Equation (19.5) demonstrates that self-affine fractal surfaces have a power-law structure function in the limit of small r values: therefore, one can expect that from the calculation of the structure function G(r) from experimental morphologies, the fractal parameters α and w can be extracted. A refined expression for the structure function of a 1D profile, in the limit r  ξ, is found to be [15, 28]: G(r) = Λ2(Df −1)r 2(2−Df )

(19.6)

The constant Λ, with dimensions of length, is called the topothesy and was introduced by Sayles and Thomas [24]. It appears to be an intrinsic property of fractal surfaces,

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Fig. 19.5. Asymptotic behavior of G(r) and C(q) functions for self-affine surfaces. (a) Parameters L 1 and ξ define, respectively the short-distance and large-distance cut-off for power-law region while L is the system size. (b) The same quantities are defined in the reciprocal space: q0 = 2π/ξ, q1 = 2π/L 1 , qL = 2π/L

controlling the amplitude of roughness over all length scales, redefined later by Berry as the horizontal separation of pairs of points on a surface corresponding to an average slope of one radian [37]. The topothesy naturally controls fractal roughness for some numerically generated surfaces, as in the case of Weierstrass–Mandelbrot (WM) random surfaces [38, 39]. Analytical expressions for the structure function of self-affine surfaces have been reported by Berry and Blackwell [40], Palasantzas [23] and others [16], mainly in the context of the stochastic equations governing surface growth under ballistic deposition. A different method used to characterize self-affine surfaces consists in the calculation of the power spectrum C(q), defined as [15–18]: 1 C(q) = (2π)2





2     −iqr  1  1 −iqr dr =  dr , z(r + r )z(r) r e z(r)e A (2π) 

(19.7) where q is the wave vector. The power spectrum can be obtained from a measured roughness profile by a simple fast Fourier transform routine. For isotropic self-affine surfaces, the power spectrum has the following asymptotic behavior:  q −2(1+α) (19.8) C(q) = (w/2π)2 , where q = |q| (Fig. 19.5b). Experimental estimates of the structure function or power spectrum have been reported for sputter-deposited, etched and ion-blasted surfaces, molecular-assembled and cluster-assembled thin films, machined surfaces, engineering coatings, surfaces of practical and technological interest [15, 16, 20].

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19.1.3 Estimation of Morphological Parameters from AFM Topographies We can efficiently estimate the values of fractal parameters for self-affine surfaces through morphological AFM investigations. The task consists of three basic steps: 1) acquiring a representative set of AFM topographies in a range from the nanometer up to several tens of microns; 2) computing the average structure function or power spectrum from digitized images; 3) comparing experimental findings with fractal scaling predicted by (19.5) or (19.8). The second step may eventually involve the implementation of other algorithms, like the Richardson plot [41], the variation method [42] or the variation-correlation analysis [43]. Actually, one routinely uses steps 1) and 2) for quantitative morphological characterization, without any explicit reference to fractal-like properties. Sucha procedure, despite its fundamental correctness, deserves some critical remarks, mostly related to the acquisition procedure of AFM images. The most significant of them are addressed through examples in the following. It is, first of all, necessary to acquire AFM topographies on an extended set of length scales, in order to sample all the relevant topographical features characterizing the studied interface. Such concept is clarified in Fig. 19.6, where we report AFM images of cluster-assembled carbon thin films [34]. These films have a cauliflower-like structure with sub-micrometric grains joined to form larger agglomerates. Figure 19.6a shows isolated units of few tens of nanometers in size, presumably containing the primeval deposited carbon clusters, joint into larger sub-micrometric domains. Figure 19.6b demonstrates that such domains are randomly distributed to form a uniform background. We emphasize that each figure carries out a specific morphological information: Fig. 19.6a reveals the presence of correlated structures below a length scale of about 1 µm, while from Fig. 19.6b

Fig. 19.6a,b. AFM topographies of cluster-assembled carbon films, scan size 1 × 1 µm2 and 15 × 15 µm2 , respectively. (c) Experimental structure functions for films of different thickness and mean cluster size: the self-affine scaling is satisfied with α ≈ 0.64 ÷ 0.68. (Reprinted with permission from Buzio R et al. (2000), Surf Sci 444:L1, Copyright (2000) by Elsevier)

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we conclude that no morphological correlations are present over a few micrometer lengths. A representative set of AFM images, therefore, consists of topographies sampling both the correlation and saturation length scales of surfaces [16]. Images should be acquired with the maximum available number of pixels (512 × 512 or higher), since it is has been established that poor sampling causes sensible discrepancies between the experimental and the “true” fractal parameters [44]. In Fig. 19.6c, we report the structure functions for carbon films: we clearly see a power-law scaling G(r) ≈ r 2α followed by a saturation region G(r) ≈ 2w2 , with α = 0.64 ÷ 0.68 and w ≈ 103 ÷ 104 nm. We note that damped oscillations can often appear in the saturation region and they have to be carefully treated: in fact they are unexpected for self-affine surfaces whereas, for the case of correlated rough surfaces, periodic cycles would actually reflect the occurrence of some periodic 3D features. To determine whether or not such cycles exist is, therefore, important, for it allows one to further derive the driving mechanisms for the corresponding morphology. Yang et al. have demonstrated that sampling-induced hidden cycles do exist even in self-affine fractal surfaces [45]. Such oscillatory behavior will, however, diminish when the image sampling size L is sufficiently large, approa ching zero to within an order of (ξ/L) DT , where ξ is the correlation length of the surface and DT is the topological dimensionality. This suggests that to distinguish mound-like surfaces from self-affine surfaces, the sampling condi tion ξ DT /N  1 and ensemble averaging of a large number N of images are required. Another important aspect to be mentioned is that the estimated structure function (or any other morphological function) can be substantially influenced by convolution

Fig. 19.7. (a) Morphology of a numerically generated fractal surface with α ≈ 0.5 and w = 5 nm. The white bar corresponds to 200 nm. (b,c) The same surface after being dilated with parabolic tips of curvature radius 10 nm and 120 nm, respectively. (d) Structure functions showing the effect of finite tip size on fractal scaling [48]

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effects due to the finite tip size [46]: non-ideal geometry of tips can considerably affect the reconstruction of nanoscale roughness during AFM imaging [47], finally conditioning its contribution to fractal scaling. We show in Fig. 19.7a,b,c the appearance of a numerically generated fractal surface after being dilated with tips of, respectively, 10 nm and 120 nm curvature radius. The relative structure functions are reported in Fig. 19.7d [48]. We observe that the finite linear dimensions of the tip change monofractal properties to multifractal ones, introducing a new scaling in the nanometer range. Similar arguments have been discussed in greater detail by Aué et al. [49] and more recently by Klapetek et al. [50]. We anticipate that multiple contact points between tip and sample prevent surface reconstruction by erosion algorithms, multifractal features being definitely unavoidable. The only practical solution to reduce tip convolution consists in using ultra-sharp or nanotube tips [51, 52].

19.2 Modeling Contact Mechanics for Rough Surfaces Early phenomenological theories of friction are due to investigations of Leonardo da Vinci, Amontons, Coulomb and Euler, and date back to the XVI–XVIII centuries [53]. In that period it was already accepted that the friction force Ff between two solid bodies in relative motion: 1) increases linearly with the externally applied load Fn , 2) does not depend on the nominal contact area A0 , 3) nor depends on the relative sliding velocity V . The first two laws are usually called the da Vinci–Amontons laws (or simply Amontons’ law), while the third law is attributed to Coulomb. They are synthetically expressed by means of the following equation: µ(A0 , V ) ≡

Ff = cost. , Fn

(19.9)

where µ is the friction coefficient for the two sliding materials and does not depend on A0 and V . The introduction of the quantity µ was motivated by the simple linear relationship occurring between friction force Ff and load Fn during macroscopic experiments. We observe that Amontons’ law was developed for non-adhering surfaces, with contacts mainly or totally controlled by the external load [54]. Such conditions were favored by poor control over surface finish, cleanliness and occurrence of wear effects; they led to a remarkable independence of friction coefficients from experimental conditions and sustained the idea that the friction coefficient could be considered a universal number (the Bélidor number) lying in the range 0.2 ÷ 0.3. Today we recognize that Amontons’ law remains surprisingly good at describing the majority of rubbing surfaces under load-controlled conditions. Relevant exceptions are represented by adhesive junctions, which give a friction force even for a vanishing external load. Solid-solid adhesion usually occurs between contacting asperities due to long-ranged van der Waals forces and capillary forces (caused by liquids adsorbed on solid surfaces), but more specific, short-ranged attractive forces can occur, due to metallic or covalent bonding or electrostatic interaction [55]. However, adhesion is not practically detected on macroscopic scale when stiff solids are pressed together, while it can have a substantial influence on the tribological

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performance of elastically soft solids. Since adhesion forces are proportional to the real area of contact Ar , we can generalize friction laws to the Amontons–Derjaguin equation: Ff = τAr + µFn ,

(19.10)

where τ is a critical shear strength. Equation (19.10) proves that friction force can be split up into separate and additive contributions, one internal due to adhesion (τAr ) and the other external due to the compressive force (µFn ). The former prevails on the latter for highly adhesive contacts, and we have Ff ≈ τAr : since Ar is a general function of the load Ar = Ar (Fn ), we can have deviations from Amontons’ law due to adhesion forces (which are indeed experimentally observed, see Sect. 19.3.2). On the contrary, for non-adhesive contacts, Ff ≈ µFn . Equation (19.10) applies both at the macroscopic and microscopic scale, being therefore scale-invariant. Such an observation is based on experimental findings, some of them being achieved only in the last decade by AFM and surface force apparatus (SFA) investigations on atomically smooth surfaces. Unfortunately, scale invariance does not necessarily reflect the occurrence of a single physical phenomenon governing friction at all scales: on the contrary, it seems that the robustness and widespread applicability of the Amontons–Derjaguin equation (or simply Amontons’ law for load-controlled friction) is due to the interplay of different factors. Two of them have been identified with surface roughness and third-body (mobile molecules, dust or debris particles) effects occurring at the sliding interface [13, 14]. We will devote subsequent subsections to describing the fundamental role attributed to surface roughness in contact mechanics modeling, providing at the same time an overview of the efforts spent to predict (19.9) and (19.1) on purely theoretical grounds. Due to the broadness of the subject, some topics will be merely mentioned or definitely skipped, like lubrication and wear phenomena, which are indeed actively studied by AFM and related techniques, but require a detailed treatment beyond the scope of the present chapter. 19.2.1 Early Phenomenological Contact Theories Coulomb was among the early scientists to recognize that surface roughness could have a prominent role in the contact mechanics phenomena. To explain (19.9), he suggested the possibility of purely geometrical interlocking of surface asperities. The main idea was that the top surface must be lifted up a typical slope tan θ, determined by the average roughness of the bottom surface, in order to slide laterally. In detail, at any coordinate x on the bottom surface, the lateral force Ff (x) to initiate sliding motion is related to the local slope tan θ(x) by the relation: Ff (x) = tan θ(x)Fn ,

(19.11)

and on the average Ff = tan θ Fn

(19.12)

There is no reference in (19.12) to the nominal contact area A0 or to the average sliding velocity V , and the linear relation between friction force and normal load

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is preserved: thus Coulomb’s geometrical model predicts (19.9) with µ = tan θ . Various arguments, both theoretical and experimental, were raised at the end of the XIX century against this simple interpretation [53]. At the beginning of the 1900s, Bowden and Tabor (B&T) developed some novel fundamental knowledge of friction origins. In a classical experiment reported in 1939, they observed that the electrical conduction across two metal surfaces was proportional to the external load Fn pressing surfaces together, both under stationary and sliding conditions [56]. Since electrical resistance depends on the electrical conductivity of the metals and on the size of the contact regions, electrical measurements indeed demonstrated that the real contact area Ar was proportional to the applied normal load Fn . The constant of proportionality was fixed assuming that only plastic deformations occurred during sliding, thus Ar = Fn /H ,

(19.13)

where H is the indentation hardness of solid surfaces [57]. Friction force Ff was then assumed proportional to Ar , the dissipation being physically related to the breaking of the cold-welded contact junctions. Introducing an average shear strength τ, B&T wrote: Ff = τAr , and obtained: τ Ff = FN = µFN . H

(19.14)

(19.15)

In this way, they predicted a friction law in agreement with (19.9), with a coefficient of friction µ related to the metal properties τ and H. Bowden and Tabor’s work shifted attention from the linearity between Ff and Fn , expressed by (19.9), to the linear relationship depicted by (19.13). The assumption of proportionality between the real contact area Ar and Fn had a strong impact on the development of all the following friction theories and led theoretical research to focus on equations of type Ar = Ar (Fn ), implicitly assuming Ff = τAr to be always true, even for non-adhesive junctions. For this reason, in what follows we will concentrate mainly on such functional relations. Despite the initial success of the B&T theory, some objections were soon raised: in fact plastic deformations occurring continuously on contacting interfaces would produce wear rates definitely higher than those experimentally observed and a quick failure of components. Following such ideas, Archard [58], and Greenwood and Williamson [59] separately developed theoretical models based on elastic deformations of contact spots. Both were capable of demonstrating that surface morphology, if suitably included into calculations, is sufficient to explain the linear dependence of the real contact area Ar on the normal load Fn , leading, however, to a non-destructive steady state contact between rough surfaces. Archard’s model is actually considered the precursor of the modern theories of contact between two fractal surfaces. It assumes a perfectly flat surface to be in contact with a nominally flat counterpart having a hierarchical distribution of

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Fig. 19.8. Schematic diagram of the randomly rough surface used by Archard: spherical protuberances are superimposed on larger ones in a hierarchical manner

spherical asperities (Fig. 19.8). Each asperity is deformed elastically according to Hertzian theory and load is redistributed on smaller protuberances. Archard showed that although the simple Hertzian theory does not predict the observed proportionality between the real contact area Ar and the load Fn , a generalized model like that shown in Fig. 19.8 can give successively closer approximations to the law Ar ∝ Fn as more stages are considered. He emphasized that for physically plausible surfaces any elastic model in which the number of contacts remains cons2/3 tant will give Ar ∝ Fn , but if the average size remains constant and the number increases, the area will be proportional to the load. In the Greenwood–Williamson (G&W) model, the authors considered the case of an ideally smooth surface pressed against a counterpart composed of hemispherical asperities with the same radius of curvature R. In such a case, they assumed the asperities to be randomly distributed on a reference plane according to a probability distribution of asperity heights ω(z) (Fig. 19.9). If the two surfaces come together until their reference planes are separated by a distance d, there will be contact at any asperity whose height was originally greater than d. Thus the probability of making contact will be: ∞ ω(z) dz .

Prob(z > d) = d

Fig. 19.9. Schematic diagram of the randomly rough surface used by Greenwood and Williamson: spherical protuberances, with curvature radius R, are randomly distributed on a reference plane

(19.16)

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The number of contact spots Nspots , the real area of contact Ar , and the total load Fn will be related to the separation d, density of asperities η, Young’s modulus E and nominal contact area A0 by the following expressions: ∞ Nspots = ηA0

ω(z) dz ,

(19.17)

d

∞ Ar = πηA0 R

(z − d )ω(z) dz ,

(19.18)

d

4 Fn = EηA0 R1/2 3

∞ (z − d )3/2 ω(z) dz .

(19.19)

d

These relations can be analytically integrated in the case of an exponential distribution of asperities’ heights, leading to: Ar = π(ηRw)A0 e−d/w , Fn = π

1/2

∗

(19.20)

(ηRw)E (w/R)

1/2

−d/w

A0 , e

(19.21)

where w is the standard deviation of the asperities’ height distribution. Results demonstrate that a linear relation is exactly verified between load and contact area, and that the real contact area does not depend on the nominal contact area, but only on the load. However, real surfaces often present a Gaussian distribution of asperities’ height. In such a case, previous equations are solved numerically and it is demonstrated that Amontons’ law (19.9) is satisfied. Following Tabor work on the ball indentation hardness test, G&W further observed that the onset of plastic flow is reached when the maximum Hertzian pressure between a ball and a plane reaches about 0.6 H [57]. With few simple calculations they demonstrated that the expected total area of contacts that become plastic, Arp , is: ∞ Arp = πηRwA0

(s − h)ω(s) ds ,

(19.22)

h+∆c

where s = z/w, h = d/w and ∆c = (R/w)(H/E)2 is the critical value of the normalized elastic displacement, at a single asperity, necessary for some plastic flow. If we define the limit of elastic contact to be when the area of plastic contact Arp becomes some specified fraction of the total contact area Ar , we can obtain a relation between the surface roughness, included in ∆c , and the critical value of the nominal pressure. For simplicity, the plasticity index is introduced:  (19.23) ψ ≡ (∆c )−1/2 = (E/H ) w/R , and the onset at which plastic flow becomes detectable is conventionally chosen as Arp /Ar = 0.02. In principle, the plasticity index ψ determines the critical load at

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which the deformation changes from elastic to plastic. Although it can in theory assume any value between 0 and ∞ (and it appears that real surfaces range from 0.1 to over 100), it is only in the narrow range 0.6 ÷ 1 that the mode of deformation is in doubt. When ψ < 0.6, elastic contact occurs, while when ψ > 1 plastic flow is expected even at the lightest loads. Based on the results of their model, G&W speculated that the origin of the laws of friction, and particularly of the proportionality between area and load, lies not in the particular surface model or deformation mode considered, but simply in the statistics of surface roughness. The G&W model has been extended to include refined plastic effects [60] and adhesion forces [61,62], compared to numerical and finite-element-modeling calculations [63] and used to interpolate experimental data [64] or predict the dynamics of MEMS devices [65]. The considerable drawback of the G&W model is that real surfaces are not formed by spherical asperities having the same curvature radius R and even the estimation of R from surface topographies is neither well defined nor straightforward [66]. This fact has forced contact mechanics modeling to develop theories based on more realistic, fractal-like, description of surfaces. 19.2.2 Contact Mechanics Theories for Fractal Roughness A model for contact between fractal surfaces was first developed by Majumdar and Bhushan (M&B) [67, 68]. They considered a WM profile, with power spectrum C(q): C(q) =

G 2(Df −1) −(5−2Df ) , q 2 ln γ

(19.24)

with the fixed scaling parameter γ = 1.5 [69]. The fractal dimension Df refers to a surface profile, hence 1 ≤ Df ≤ 2 in what follows. The constant G is simply proportional to the topothesy Λ [70]. To estimate the curvature of an asperity that makes a contact of length l, M&B assumed the curvature to be entirely due to the single component of the spectral density whose wavelength is l, z(x) = G Df −1l 2−Df cos(2πx/l). The height of the asperity, ∆, is then: ∆ = G (Df −1)l (2−Df ) = G (Df −1) a(2−Df )/2 ,

(19.25)

where a ≈ l 2 is the asperity base. The radius of curvature R for the asperity of base a is: R(a) =

a Df /2 . G (Df −1)

(19.26)

Thus the fractal surface can be imaged to be a collection of asperities where smaller ones are mounted on larger asperities in a hierarchical manner. It is then observed that for an asperity of radius R, deformed by a hard plane, the asperity will initially deform elastically, but beyond a critical deformation, ∆C ,

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the material will deform inelastically [57]. The critical deformation, similarly to that written above in the plastic G&W model, is:  ∆c =

πH 2E

2 R(a) = φR(a) ,

(19.27)

where φ is a material-dependent quantity. The criterion for inception of plastic flow for an asperity of base a is ∆ > ∆c . Since for a fractal surface ∆ = G (Df −1) a(2−Df )/2 and k(a) ≡ R−1 (a) = G (Df −1) /a Df /2 , there exists a critical contact area ac such that all spots smaller than ac deform plastically, while those larger than ac deform elastically. The expression for ac is given by: ac =

G2 1

φ Df −1

.

(19.28)

The total load f e supported elastically by an asperity of contact area a > ac is given by the Hertzian expression: fe =

4Ek(a)a3/2 , 3π 3/2

(19.29)

while an asperity under plastic conditions a < ac supports the total load f p : f p = Ha .

(19.30)

The total normal load supported at the fractal interface can be expressed as: ac Fn =

aL f p (a)n(a) da+

f e (a)n(a) da .

(19.31)

ac

0

where aL is the largest contact spot at the interface and n(a) is the distributions of contact spots under plastic or elastic conditions. Majumdar and Bhushan, following Mandelbrot studies on island patterns [71], postulated the size distribution n(a) to be: D /2

n(a) =

Df aL f . 2 a Df /2+1

(19.32)

The expression for the total load is finally given by: D /2 (2−Df )/2

Df HaL f ac Fn = 2 − Df

(3−D )/2

4Df EG Df −1 aL f + 3π 3/2 (3 − 2Df )

for Df  = 1.5 , 3/4

Fn = 3HaL ac1/4 +

3/4 EG 1/2 aL π 3/2

 ln

aL ac

 1−



ac aL

(3−Df )/2 

(19.33)

 ,

for Df = 1.5 .

(19.34)

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The real area of contact Ar is: aL Ar =

an(a) da = 0

Df aL . 2 − Df

(19.35)

The linear relationship between Ar and aL , together with (19.33) and (19.34), shows that under elasto-plastic conditions (aL > ac ), the elastic load scales as (3−D )/2 D /2 Fe ∝ Ar f , whereas the plastic load varies as Fp ∝ Ar f . Under fully plastic conditions (aL < ac ), the load varies linearly with area and Fn ∝ Ar . In Fig. 19.10a, we show model predictions for Df = 1.5 as a function of φ. The real contact area depends on normal load F as Ar ∝ F 1.25 for fully elastic (φ = 1) and elasto–plastic deformation modes (φ = 10−2 ), and the elastic component of contact area Are is very close to the real contact area Ar at the smallest values of applied normal load. For φ = 10−4 , plastic failure dominates incipient contact, Are ≈ 0 for a non-dimensional contact area below 10−4 and starts to grow at higher loads. The transition from plastic to elasto-plastic contact is reflected in the slope variation of the Ar vs. F curves. Majumdar and Bhushan have compared their theoretical predictions with experimental results reported by Yamanda et al. (for Pyrex glass surfaces) [72], and by Bhushan and Dugger for magnetic rigid disks [73], revealing a good agreement of experiment and theory (Fig. 19.10b).

Fig. 19.10. (a) Theoretical predictions of the M&B model. (b) Comparison of M&B theory with experimental results. (Reprinted with permission from Majumdar A and Bhushan B (1991) ASME J Trib 113:1, Copyright (1991) by ASME)

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Theories sharing common features with the M&B one were later developed by Yan and Komvopoulos [74], who considered in their analysis a WM surface with 2 ≤ Df ≤ 3 instead of a fractal profile, and Warren and Krajcinovic [75], describing the elastic-perfectly plastic deformation of a random Cantor set structure subject to the loading of a smooth rigid half-space. The model-independent aspects that emerge from such theories are that: 1) the real contact area Ar does not depend linearly on 3/4 3/4 normal load Fn (e.g., M&B theory predicts Fn ∝ Ar + Ar ln Ar for Df = 1.5), with the exception of fully-plastic contacts; 2) at incipient contact, according to the material parameters, one can have severe plastic failure. Both aspects are concrete manifestation of the role played by surface roughness, particularly the second one, which predicts plastic deformation of asperities even at the smallest available loads. This effect is due to the multiscale, self-repeating nature of roughness and it is not included in the G&W theory [66]. A definitely different approach to the contact of fractal surfaces has been developed by Persson [76]. His theory can be applied when both elastic and plastic deformations occur in the contact areas, adhesion forces and viscoelastic effects being also included [77, 78]; fully-analytical expressions are provided for the contact relationship Ar = Ar (Fn ), including material properties and the surface power spectrum C(q). The basic idea behind such contact theory is that it is very important not to a priori exclude any roughness length scale from the analysis. Thus, if A(λ) is the (apparent) area of contact on the length scale λ, the theory studies the function P(ξ) = A(λ)/A(L), which is the relative fraction of the surface area where contact occurs on the length scale λ = L/ζ (where ζ ≥ 1), with P(1) = 1. The quantity A(L) = A0 ≈ L 2 denotes the macroscopic contact area. The non-dimensional quantity ζ is the magnification at which we observe the contact interface (Fig. 19.11). We define qL = 2π/L and write q = qL ζ. Let P(σ, ζ) denote the stress distribuσ Y tion in the contact areas under the magnification ζ; we note that P(ζ) = P(σ, ζ)dσ, 0

where σY is material yield stress. The function P(σ, ζ) satisfies the differential equation [76]: ∂2 P ∂P = f(ζ) 2 , ∂ζ ∂σ

Fig. 19.11. An elastic ball squeezed against a rough hard substrate. Left: the contact interface at two different magnifications ζ = 1 and ζ = L/λ. Right: the contact area A(λ) is the real contact area when roughness on shorter length scales than λ has been removed

(19.36)

19 Morphological and Tribological Characterization of Rough Surfaces by AFM

where π f(ζ) = 4



E (1 − ν2 )

281

2 ζ 3 qL4 C(ζqL ) .

(19.37)

Equation (19.36) is a diffusion type of equation, where time is replaced by the magnification ζ, and the spatial coordinate with the stress σ (and where the “diffusion constant” depends on ζ). Hence, when we study P(σ, ζ) on shorter and shorter length scales (corresponding to increasing ζ), the P(σ, ζ) function will become broader and broader in σ-space. The physical meaning is as follows: when the system is studied at the lowest magnification ζ = 1, no surface roughness can be observed and the block makes (apparent) contact with the substrate everywhere in the nominal contact area. In this case, the stress at the interface will everywhere equal the applied stress σ0 , so that P(σ, 1) = δ(σ − σ0 ). When we increase the magnification we observe surface roughness with wavelength down to λ = L/ζ. In this case, one may observe partial contact, the stress going continuously to zero at the edges of the boundary between the contact and non-contact regions. It follows that the stress distribution P(σ, ζ) will have a tail extending the whole way down to the zero stress and a tail toward larger stresses σ > σ0 . Thus with increasing magnification, the stress distribution will broaden without limit. This is an analytical restatement of the B&T and M&B predictions: surface roughness at the contact interface increases local stresses and may eventually lead to significant plastic failure (Fig. 19.12a).

Fig. 19.12. (a) An elastic block in contact with a smooth surface at two different magnifications, ζ = 1 and ζ = 100. On increasing surface roughness, the corresponding stress distribution becomes broader in σ space. (b) Theoretical predictions for the elastic and plastic components of normalized contact area, Pel and Ppl , as a function of magnification ζ and normalized surface roughness q0 h 0 (in our notation h 20 = 2w2 ). (Reprinted with permission from Persson BNJ (2001) Phys Rev Lett 87:116101, Copyright (2001) by the American Physical Society)

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If we initially assume that only elastic deformations occur at the interface, ∞ σY → ∞ and P(ξ) = P(σ, ξ)dσ. We can solve (19.36) with the initial conditions 0

P(0, ζ) = 0 and P(∞, 0) = 0 and obtain, in the limit σ0  E, that P(ζ) ∝ σ0 , which means that the area of real contact Ar is proportional to the load Fn = σ0 A0 , in agreement with Amonton’s law. In Fig. 19.12b, we report more general results concerning both elastic and plastic deformations at the contact interface. We observe that by increasing the magnification ζ, the plastic component of Ar , Ppl dominates contact. Adhesion effects are included into the previous theory by solving (19.36) with the boundary condition P(−σ(ζ)a , ζ) = 0, where σa (ζ) is the scale-dependent detachment stress. For the simple case σa (ζ) ≈ σa , we immediately get P(ζ) ∝ σ0 +σa , in agreement with Amontons’ law: the adhesion force behaves as an offset added to the external load. Figure 19.13 (left) shows the effective interfacial energy γeff (1) and the normalized area of real contact, P(ζ1 ) = A(ζ1 )/A0 , as a function of normalized surface roughness q0 h 0 . The quantity γeff (1) is the macroscopic interfacial free energy that can be deduced, for example, from pull-off force experiments, using the expression Fc = (3π/2)Rγeff (1) [77]; ∆γ is, on the contrary, the macroscopic interfacial free

Fig. 19.13. Theoretical predictions for adhesive contacts: the normalized contact area P(ζ) and the interfacial free energy γeff (ζ) are studied as a function of roughness parameters q0 h 0 (a) and magnification ζ. (b) (Reprinted with permission from Persson BNJ (2002) Phys Rev Lett 89:245502, Copyright (2002) the by American Physical Society)0

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energy for perfectly smooth surfaces [79]. The quantity δ ≈ ∆γ/E, called adhesion length, takes into account the relative role of adhesion energy with respect to elastic energy and the product q0 δ predicts if the contact will be dominated by attractive adhesion or by repulsive elastic forces. As shown in Fig. 19.13 (left), for q0 δ = 0.3, 0.4 the effective interfacial energy γeff (1) first increases with increasing roughness amplitude h 0 and then decreases. The increase for small h 0 is due to the fact that the two solids are in complete contact, and, as expected, the complete contact remains as h 0 increases. Interfacial energy just decreases for q0 δ = 0.1, 0.2, that is, for stiffer and less adhesive surfaces. Note also that the contact area is nonzero even if γeff (1) is virtually zero: the fact that γeff (1) ≈ 0 (or Fc ≈ 0) implies that the elastic energy stored at the interface just balances the adhesion energy. Since it is the area of real contact that determines the sliding friction force, the adhesion interaction may strongly affect the friction force even when no adhesion can be detected in a pull-off experiment. This is a crucial point predicted by Persson’s theory in a straightforward manner. Previous graphs allow us to understand why roughness can prevent adhesion from being observed, in practice, between macroscopic bodies (this fact is referred to as the adhesion paradox). It simply happens that for elastically hard surfaces (e.g. q0 δ = 0.1, 0.2 in Fig. 19.13) the true contact between the solids at the interface is usually much smaller than the nominal contact area even at very small roughness amplitude (q0 h 0 > 0.4). In addition, the elastic energy stored in the solids in the vicinity of the contact regions is given back during pull-off (γeff (1) ≈ 0) and helps to break the interfacial bonds between bodies: as a result, adhesion forces are not detected. The variation of P(ζ) with the magnification ζ is shown in Fig. 19.13 (right) for q0 h 0 = 0.24. Results are reported both with and without the adhesion interaction. Without the adhesion, P(ζ) decreases monotonically with increasing magnification, and, without a short-distance cutoff, it vanishes. When adhesion is included, the apparent area of contact equals the area of real contact already at a rather small magnification ζ ≈ 10. However, this is only the case when the fractal dimension Df is close to 2, since for a large fractal dimension, e.g. Df ≈ 2.6, the area of contact decreases continuously with increasing magnification and, assuming no short-distance cutoff, it vanishes. The effective interfacial energy γeff (ζ) at first increases with decreasing the magnification ζ (until about ζ > 20). This effect results from the increase in the surface area because of the surface roughness. However, at long length scales (ζ < 10), γeff (ζ) decreases below ∆γ . This effect results from the contribution to the interfacial free energy from the elastic deformation energy induced by the substrate roughness. Persson’s theory shows good agreement with numerical and finite-element modeling calculations [80, 81], and appears to be a promising and flexible platform for future contact mechanics modeling. This can be recognized by its recent application to important technological fields, like automotive tire friction [82], sealing effects and adhesion in biology [83]. We finally note that Persson’s theory does not use the intuitive concept of contact asperities, thus any qualitative comparison with the assumptions made by the G&W or M&B theory is, at present, prevented, whereas model independent conclusions can be extracted from the comparison of theoretical predictions.

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To conclude this subsection, we note that all contact models discussed until now assume scale-independent mechanical properties E, σY and τ. Such an assumption has been recently discussed and revised by Bhushan and Nosonovsky [84, 85], providing scale-dependent estimations of interface contact properties based on the B&T equation Ff = τAr . 19.2.3 On the Molecular Origins of Amontons’ Law Despite the richness of details predicted by continuum contact mechanics for rough surfaces, this approach provides just a partial (average) picture of friction phenomena: in fact, it relates external load, bulk material properties (elasticity and plasticity) and surface effects (roughness and adhesion forces) to predict the real area of contact Ar , but the origins of the static and dynamic friction resistance are not addressed. They are embodied in the parameter τ and one writes Ff = τAr , but no estimate can be done on τ values; moreover we neither know which is the smallest junction still describable within continuum mechanics nor do we have a picture of friction dynamics on the molecular time scales. Molecular Dynamics (MD) computer simulations and a few analytical calculations have been used, in recent years, to gain further insight into these points. He et al. [86] and Muser et al. [87] have used MD simulations and analytical theories to access the role of third bodies (like hydrocarbons, water and other small airborne molecules) on the frictional resistance between (ordered and disordered) crystalline surfaces. He and coworkers have simulated the relative sliding of two bare crystalline surfaces, concluding that the mean friction vanishes between rigid surfaces, unless they happen to have the same periodicity and alignment. The same occurs between almost any pair of clean surfaces that deform elastically. On the contrary, MD simulations have shown that third bodies naturally give a nonzero static friction force: in detail, friction force produced by adsorbed layers of short molecules is consistent with Amontons’ law and does not vary substantially with thickness and chemistry of adsorbed layers. Muser et al. have developed a microscopic theory in which interactions between two surfaces are modeled by an energy penalty that increases exponentially with the degree of surface overlap. The resulting static friction is proportional to load but, in the case of bare surfaces, vanishes as the area of individual contacts grows. An area-independent friction coefficient is obtained when an adsorbed layer of mobile atoms is introduced between the surfaces. A considerable amount of experimental and theoretical work was recently proposed by Gao et al. [14], revealing the occurrence of Amontons’ law even at the molecular level. The authors demonstrate by experiments that for micrometric (and nanometric) non-adhering contacts, linearity between friction force and normal load occurs (see Fig. 19.17 in Sect. 19.3.2) and Ff ∝ Fn : this is shown both under dry or lubricated conditions. Moreover, friction coefficients measured with different techniques on the same systems are practically the same, even if tribological properties are tested on different length, pressure and area ranges. On the contrary, when adhesion-controlled junctions are studied, significant deviations from Ff ≈ µFn are reported: the real contact area is now a well-defined

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concept, Ff ∝ Ar and Ar can be related to external force and adhesion through Hertzian-like theories. Therefore, the condition of low-adhesion reduces friction dependence on the contact area. Since the load-controlled junctions are not plasticallydeformed, as suggested by B&T, and a statistical description (as the G&W model) invoking a randomly rough surface seems unlikely on the nanometer scale, the occurrence of Amontons’ law demands further theoretical investigations, including the role of periodic atomic-scale corrugation and eventually third-body effects. In order to gain theoretical insight on the molecular origins of Amontons’ law, Gao et al. considered large-scale Molecular Dynamics MD simulations of two gold shearing surfaces, separated by a thin film of hydrocarbon liquid between them. MD simulations always predict a linear dependence Ff ≈ µFn , with friction coefficients µ = 0.09 for non-adhesive junction and µ = 0.14 for the adhesive case. The two cases are seen to differ only in the limit of small loads, where friction force is still appreciably detected for the adhesive junction, while it is vanishing for the load-controlled junction. Interestingly, simulations reveal that at the local level Amontons’ law is not obeyed and tribological parameters fluctuate widely in uncorrelated manner: it is found that the local friction force Ffloc (averaged every ˚ 2 region) and the local normal load Fnloc are related by a non-linear 6 ps on a 6 × 6 A equation, whereas when local load and friction forces are time-averaged over longer periods, or space-averaged over larger distances, the friction force and normal load do obey Amontons’ law. The minimum time interval for an effective averaging is recognized to be of some nanoseconds, while the space-averaging length (related to the surface roughness) falls in the nanometers range. The tribological system can be said to be ergodic-like, but under dynamic conditions. Molecular dynamics simulations indicate, at the same time, that the concept largely used in macroscopic and mesoscopic contact mechanics, the real area of contact Ar , is individuated with difficulty in the course of systems dynamics and does not seem to enter directly the friction picture, at least at nanometer scale. The phenomenological observation of a clear separation of friction force into load-dependent and adhesion-dependent contributions, suggested by the Amontons–Dearjaguin equation (19.9), is not depicted by MD simulation. The number of interacting atoms and molecules is the microscopic relevant quantity: with respect to this observation, the real contact area can be used as a scaling parameter when it reflects the number of atoms or bonds formed at the sliding interface, which can be done for atomically-smooth surfaces. One can attempt to summarize previous observations as follows: 1) Amontons’ law is a robust macroscopic law requiring time- and space-averages over nanoseconds and nanometers, respectively; 2) beside the well-documented roughness effects, also third-body effects could significantly contribute to the scale-invariance of the Amontons–Dejaguin equation; 3) experimental and theoretical investigations on load-controlled junctions, even under conditions for which Ar is not well-defined (presence of lubricants and wear), provide evidences of the fact that the well-known B&T assumption Ar ∝ Fn is not strictly necessary to predict Ff ∝ Fn ; 4) the parameter Ar seems to control friction only for adhesive junctions. We underline that such conclusions, far from being definitive, emphasize the complexity of the subject and represent a challenge for experimental investigations.

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19.3 Investigations of Multi-Asperity Contacts by AFM 19.3.1 AFM Characterization of Surface Roughness for Tribological Purposes The morphological characterization of rough surfaces, from macroscopic down to the nanometer scale, represents the most direct route to support contact mechanics modeling and tribological investigations. The importance of such a step is recognized by past and present contact theories [57, 60, 67, 76]; Persson’s model, for example, predicts the normalized contact area P(ζ) to monotonically decrease towards zero for a magnification ζ 1 (see Fig. 19.13), both in the absence and presence of adhesion (the former for any Df ≥ 2, while the latter for Df > 2.5) [77]. This means that partial contact often occurs at the smaller wavelengths or, which is the same, nanoscale roughness may control the macroscopic contact interaction; a concrete manifestation of such an aspect, as has been mentioned before, is that nanoroughness can remove the adhesion between most hard solids, like metals and minerals. Therefore, in several cases, theoretical predictions require a preliminary and accurate estimation of the structure function, or power spectrum, of the involved surfaces. A number of AFM investigations are currently available describing the nanoscale roughness of MEMS devices [88–92]. These studies provide morphological details on micromachining processes and surface treatments, like hydrogen-termination and self-assembled monolayer coatings used to prevent stiction and high friction phenomena. Polysilicon and chemically modified silicon surfaces, diamondlike and silicon-carbide coatings are intensively studied, since they represent typical microdevice interfaces [92–94]. Single-asperity adhesion, friction and wear measurements are performed in dry and lubricated environments to mimic the actual operating conditions [95]. Figure 19.14 shows representative height maps of the various surfaces of a micromotor [96]. The rotor and stator topside have a roughness w ≈ 20 nm, while the rotor underside exhibits varying topography and a roughness w ≈ 10 nm. Such information is efficiently correlated to surface micromachining and micromotor operating conditions and provides at the same time a necessary input for predictive calculations of friction forces and wear phenomena. Similar studies are performed for the tribological characterization of the head disk interface in magnetic storage devices, AFM topographical data being directly coupled to analytical, numerical and finite element modeling calculations [97–104]. At present a great deal of attention is devoted to the morphological and tribological characterization of novel materials, like carbon-derived materials: nanotubes and fullerenes [105–110], bulk diamonds, chemical-vapor-deposited diamond, diamondlike and graphite-like carbon [111–118], boron carbide and carbon nitride [119–121]. The AFM, in conjunction with electron microscopy, explores materials’ microstructure and nanostructure to infer deposition mechanisms and assembling properties of primeval precursors [16]. An overwhelming variety of thin films and coatings display fractal-like features, studied by statistical methods and are useful, in principle, to predict materials performance through contact modeling. Morphological AFM investigations appear also to be an attractive tool to predict biocompatibility of artificial hip joints, surgical implants, prostheses of various kind

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Fig. 19.14. Typical AFM morphologies acquired on various component surfaces of a micromotor. Surface roughness σ (σ corresponds to w in the chapter notation) and peak-to-valley P–V values are given, demonstrating that the underside of the rotor exhibits different nanoroughness from the topside. A comparison provides information on surface micromachining and tribological operative conditions. (Reprinted with permission from Sundararajan S, Bhushan B (2001) J Vac Sci Technol A 19:1777)

and biological sensors [1,18,122]. Living cells can in fact sense, generate and support mechanical forces, as well as convert them to biological responses, and the capability to promote cells adhesion and activity by surface morphological control represents a hugely attractive vision. AFM metrology of biomaterials and force sensing of cells, proteins and DNA molecules appear, therefore, challenging to achieve fundamental knowledge in biomechanics. We finally note that an increasing number of reports involve the AFM coupled to optical or electron microscopy, to describe surface roughness on a wider range of length scales. Systems of actual interest consist in rock surfaces (basalt, granite), natural surfaces produced by crack propagation, machined surfaces, asphalt and con-

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crete road pavements [20]. These surfaces are actively studied in view of their impact on rubber friction and adhesion. In fact, according to the concepts developed above, any contact is easily influenced by uncontrolled impurities and moisture, so that predictive calculations of frictional forces for macroscopic interfaces are extraordinarily hard. However, if friction is not dominated by interfacial phenomena, but by material internal damping, as for rubber [123], one has some chance of controlling and predict friction phenomena under realistic conditions. Such an observation is stimulating a considerable theoretical and experimental activity on rubber friction and related subjects (design of car tires, rubber sealing effects, adhesion of soft matter and living organisms) [33, 82, 83, 124, 125]. 19.3.2 Contact Mechanics Investigations at the Nanometer Scale The contact behavior of an AFM probe sliding under wearless, purely elastic conditions has been extensively investigated in the past and a number of reviews are currently available describing the load and velocity dependence of friction forces [126–129], as well as the influence of topographical features on friction force measurements [130–132]. Despite the considerable progress done in this field in the last decade, we are still far from providing a comprehensive picture of contact mechanics at that scale. We describe in the following the main experimental achievements obtained using sharp (nanometric) AFM tips. Up until now experiments on friction between clean crystalline surfaces have been limited [133,134], but consistent with theoretical conclusions suggested by MD simulations [86]: small crystalline AFM tips, made of W or graphite, have shown substantial friction only in the case of commensurate alignment, while a vanishing friction force has been reported for incommensurate configurations. More frequently conventional Si or Si3 N4 tips have been used to test technologically relevant surfaces like carbon-based materials [105–121, 135, 136], mica [137–140] and layered compounds [141], metals [129], polymeric thin films, LB films and self-assembling monolayers [142–149]. In several cases a non-linear relationship has been found between friction force and external load [150–152], accompanied by the occurrence of a finite friction even at zero or negative (tensile) load. In Fig. 19.15, we report AFM friction curves showing the typical response of adhesive junctions. Friction data can be analyzed within continuum models for a perfectly elastic contact subject to compressive and adhesive forces, Fn and Fadh [152]. Such models predict the 2/3 Hertzian scaling FF ≈ Feff , where Feff = Feff (Fn , Fadh ): for example, in the case of the Derjaguin–Muller–Toporov theory, we simply have Feff = Fn + Fadh . The powerlaw scaling of these nanoscale contacts is consistent with the Amontons–Derjaguin 2/3 equation for adhesion-controlled elastic junctions, since Ff ≈ τAr with Ar ∝ Fn (see (19.10)). The experimental observation of the exponent 2/3 critically depends on the control achieved on the tip shape. Schwarz et al. [136] pointed out that even the smallest deviations of the tip apex from the spherical shape (observed by the transmission electron microscoscope) can destroy the 2/3 power-law, resulting in power-laws Ff ≈ Fnm with m in the range 0.5 ÷ 1. Similar conclusions have been reported by

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Fig. 19.15. Plot of Ff as a function of Fn for: (a) a GeS(001) substrate and a C60 thin film epitaxially grown on it (reprinted with permission from Schwarz UD et al. (1995) Phys Rev B 52:14976, Copyright 1995 by the American Physical Society); (b) amorphous carbon (a-C) film and a HOPG sample (reprinted with permission from Buzio R et al. (2002) Carbon 40:883, Copyright (2002) by Elsevier)

Carpick et al., who intentionally used blunt AFM tips [138]. Nevertheless, we can state that equations of the type Ff ≈ Fnm represent a quite robust feature of AFM experiments, being confirmed also for micrometric colloidal probes [153]. Despite the apparent clarity of the previous picture, exceptions to the non-linear behavior actually occur under interesting and quite general conditions and provide reasons for a lively scientific debate on the subject. In fact, we note that the mentioned models are based on continuum elasticity theory, hence they assume smooth surfaces with no plastic deformation and no viscoelasticity. It is first of all expected that the continuum description will break down on decreasing contact area to a few tens of atoms or less: actually, power-laws Ff ≈ Fnm with m > 1 have been recently reported by Socoliuc et al. [154] and by Fusco and Fasolino [155] (Fig. 19.16), revealing that atomically-sharp tips can show significant deviations from the Hertzian scaling. Qualitatively different exceptions have been reported by Putman et al. [156], demonstrating that a transition from the Hertzian scaling to Amontons’ law could be tuned (on mica and glass surfaces) by varying the value of the relative humidity, and by Cohen et al. [157], invoking tip nanoroughness to cause the appearance of Amontons’ law at the nanometer scale. In other words, the two studies have suggested that third-body effects and roughness could be responsible for the observation of Amontons’ law for elastic nanojunctions. Gao et al. have recently presented new results on experimental friction data obtained with the SFA and AFM on adhering and non-adhering surfaces, with the aim to test the range of applicability of the Amontons–Derjaguin equation for widely different systems and length scales [14]. The authors have observed that both the SFA and the AFM can measure friction forces at single-asperity contacts, but there is a considerable difference in the contact areas and pressures obtained with these two techniques [158]. However, when comparing the sliding of low-adhesion singleasperity contacts with each other, the friction force Ff is proportional to the load Fn , sometimes even with the same friction coefficient. On the contrary, when adhesion-

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Fig. 19.16. Plot of Ff as a function of Fn for: (a) an Si tip on a NaCl single crystal (reprinted with permission from Socoliuc A et al. (2004) Phys Rev Lett 92:134301, Copyright (2004) by the American Physical Society); (b) a simulated single-atom tip on a graphite surface (reprinted with permission from Fusco C and Fasolino A (2004) Appl Phys Lett 84:699, Copyright (2004) by the American Institute of Physics)

controlled contacts are studied, the friction force Ff is proportional to the real contact area Ar , and Hertzian scaling is recovered. In Fig. 19.17 we illustrate two examples of non-adhering nanojunctions and microjunctions following Amontons’ law. Figure 19.17a illustrates the case of two Si tips of different radii and spring constants sliding on Pyrex glass under ethanol; Fig. 19.17b shows SFA friction data for two molecularly smooth mica surfaces sliding in a 0.5 M KCl solution, where

Fig. 19.17. AFM and SFA friction measurements obeying Amonton’s law. (a) (Reprinted with permission from Ruth et al. (2003) J Phys Chem B 107:11149, Copyright 2003 by the American Chemical Society); (b) (reprinted with kind permission of Springer Science and Business Media from Berman A et al. (1998) Tribol Lett 4:95, Figure 2, Copyright (1998) by JC Baltzer AG, Science Publishers)

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intersurface forces are short-ranged and repulsive, providing a non-adhering system. The authors observe that in both cases, the chosen condition of low adhesion gives a purely load-dependent friction. Experimental results reviewed by Gao and coworkers qualitatively agree with the conclusions of Putman et al. and Cohen et al. [156, 157] and demonstrate that the Amontons–Derjaguin equation can describe both load-controlled and adhesion-controlled contacts. Unfortunately, a neat separation into load-dependent and adhesion-dependent terms seems more phenomenological than fundamental (see Sect. 19.2.3). We again note that the shear stress τ is treated as a fitting parameter and actually no theory or experiment on the nanometer scale has fully succeeded to relate such a quantity to the physically relevant dissipation channels [15, 159]. 19.3.3 Contact Mechanics Investigations on the Micrometer Scale Tribological AFM investigations on the micrometer scale are mainly performed by means of colloidal probes [160], intentionally blunt/worn tips or customdesigned probes. Several studies have been devoted to force sensing in air and liquid environments [161–165], single-asperity contact mechanics, adhesion and friction [166–169], liquids dynamics in confined geometries [170–173]. Buzio et al. have focused on multi-asperity contact mechanics studies performed with micrometric flat tips [174–176]. The first consequence of tip lateral extension is that the number of contact spots formed at the tip-sample interface is not constant, but varies according to the applied load and to the statistical properties of surface roughness; therefore, both structural and morphological properties become simultaneously accessible. Buzio et al. studied nanostructured carbon (ns-C) and sexithienyl (T6) thin films [177]. The ns-C and T6 fractal morphology was preliminarly characterized by AFM imaging with conventional sharp tips, fractal dimension and surface roughness being estimated from measured topographies; fractal parameters were partially tuned by local scratching (for ns-C films) or samples heating (for T6 films). Indentation and friction experiments were then performed with the flat probes to establish the role of fractal roughness. Figure 19.18 shows the average load-displacement curves, Fn vs. u, measured for ns-C and T6 films as a function of u/w (note that u/w < 1 during indentation experiments). The mechanical response of the films markedly depends on surface morphology. Within experimental resolution, samples with the same fractal dimension, but different roughness have the same load curve; moreover surface compliance increases with Df , because carbon samples with Df = 2.30 are more penetrable than those with Df = 2.10 or Df = 2.20. This suggests F to scale separately with the surface variables Df and u/w. The same occurs for T6 films. The origin of such behavior is qualitatively explained by invoking the redistribution of the external load on the multiple contact junctions. In fact, for a given displacement u, the rougher the film, the smaller the real contact area when pressed against a rigid flat punch (for fixed load Fn , rougher films display higher penetrability). Such arguments can be extended to any contact between rough solids, provided that adhesion is small enough that they are not pulled into direct contact over the whole nominal contact area. Experimental data agree with a perfectly plastic contact theory, with the average indentation hardness Hns-C = 45 MPa and

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Fig. 19.18. Load-displacement curves acquired on ns-C and T6 films by means of flat AFM tips. The curves significantly depend on the fractal parameters of surface roughness

HT6 = 18 MPa [175]. The condition HT6 < Hns-C implies that T6 films would appear softer than ns-C films for any conventional hardness tester working in the range u w, the real contact area being close to the nominal one. On the contrary, when u < w, surface effects become dominant and T6 samples can display a contact stiffness ∂Fn /∂u comparable to or larger than that of ns-C films. Figure 19.19 illustrates this aspect: the T6 film with Df = 2.15 and w = 36 nm has higher surface stiffness than the ns-C films with Df = 2.30 and w = 80 nm, whereas the T6 film with

Fig. 19.19. Contact stiffness numerically evaluated from experimental curves reported in Fig. 19.18. Note that T6 films can be stiffer than nsC films, even if their bulk hardness is smaller, due to surface effects

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Df = 2.26 and w = 160 nm has lower contact stiffness. Such an aspect emphasizes the crucial role of fractal surface geometry in conditioning the functional performance of materials: rougher solid surfaces are more compliant and penetrable, and their properties depend on surface morphological parameters. An increase of 10% in the fractal dimension causes the surface stiffness to decrease by more than one order of magnitude because of highly localized stresses and plastic deformations. Sliding friction experiments performed with the flat tips on ns-C films demonstrated, as expected, that frictional forces scale linearly with the normal load, recovering Amonton’s law. The coefficient of friction was estimated to be 0.24, independent of the fractal dimension Df and the surface roughness w [176]. It is clear from the foregoing discussion that experiments involving micrometric flat tips represent one possible approach for characterizing mesoscopic contacts: similar investigations could test fractal surfaces under elasto-plastic and fully-elastic deformation regimes, including adhesion effects due to meniscus and van der Waals forces [55]. Moreover, studies based on micrometric tips (beads, smooth punches or other well-controlled geometries) could be directly compared to tribological investigations using MEMS devices and related technologies [88, 90, 103, 178, 179], providing at the same time improved flexibility for sample choice and working conditions. Full control over tip size should allow studying scaling effects in nano/microtribology, as those recently modeled by Bhushan and Nosonovsky [84, 85]. The major technical challenge in a such field is surely related to the poor control over probe roughness, micrometric beads and punches usually having nanometric asperities protruding from their surface. These structures should be accurately taken into account in any experimental investigation requiring reliable and reproducible tribological data [158, 160, 180, 181].

19.4 Conclusions The most striking and impressive feature of AFM is probably related to its flexibility, with particular emphasis on detailed morphological, contact mechanics, friction and adhesion studies routinely performed under different environments. These capabilities have led the AFM to extend our fundamental knowledge on friction phenomena. Considerable progress has been made on friction laws and it appears wellestablished that the phenomenological Amontons–Dejaguin equation can safely be extended down to the nanoscale, describing both single-asperity and multi-asperity contacts. Therefore, a new challenging subject regards the characterization of the shear stress τ and its dependence on the physically relevant dissipation channels and sliding parameters. On the theoretical side, models have been developed treating the role of multiscale surface roughness, thus it is now possible to predict some of the most significant properties of solid bodies in contact. Acknowledgements. Renato Buzio acknowledges support by the INFM project FIRB 2003-2006 “Carbon-Based Micro- and Nano-structures” and COFIN project 2004-2006 “Nanotribology”. The authors wish to thank all the members of the European Science Foundation project NATRIBO for discussions.

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145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170.

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20 AFM Applications for Contact and Wear Simulation Nikolai K. Myshkin · Mark I. Petrokovets · Alexander V. Kovalev

20.1 Introduction The scanning probe microscopy (SPM) was invented more than twenty years ago as a method of surface analysis in a nanometer scale. The atomic force microscope (AFM) is one of the SPM techniques used in tribology as a basic device for studying the topography and surface properties [1–3]. When applying AFM, a probe moves over a surface registering the deflection and torsion of a cantilever. The deflection relates to the surface topography and torsion is dependent on friction between the probe and the surface. Thus, AFM has the possibility of simultaneous measurement of topography and friction force. Basic application of AFM provides a topography image of a surface with nanometer resolution in a real 3D presentation. It is possible to obtain the roughness parameters, morphological features, and texture. Quantitative parameters are calculated using the direct assessment of the AFM image. AFM image processing can simulate contact formation and determine the actual contact area at a given load [4, 5]. Using AFM it is possible to carry out experiments acquiring the force–distance curves when one body approaches another. The analysis of the curves allows us to carry out measurements of the elasticity modulus and the thickness of thin films. The mechanical properties of surface layers can be studied using the direct indentation of AFM tip. The scratch depth or wear volume can be calculated and displayed after acquiring the AFM-image.

20.2 Scale Factor in Tribology The mainstream of tribology research goes from macroscopic models to current attempts of understanding the micro- and nanoscale processes of friction and wear. This transition gives a new insight into the basic problems, above of all the relation of deformation and adhesion at friction. Since asperities of different scale exhibit different behavior in frictional contact, it is reasonable that tribologists simulate the behavior of the smallest asperity using the most up-to-date SPM instruments. This reduction in scale of experiment reveals that mechanical properties of contacting materials become scale-dependent, and parameters such as Young’s modulus and hardness differ not only in magnitude

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but also in their physical meaning. In such a situation, the basic challenge is the physical interpretation of experimental data and their self-affinity in changing the scale factor [6]. Both the components of contact forces play a crucial role in friction and wear. Bearing the scale factor and friction dualism in mind, the mechanical wear modes may be ranked according to the deformation-to-adhesion relationship (Fig. 20.1) [7]. Given this, the adhesive and fatigue wear modes are in extreme positions, while the fatigue is mainly governed by deformation, whereas adhesion is dominant in adhesive wear. Such an approach to wear processes is, of course, very simplified. Friction always occurs in a certain environment, which produces a significant influence on the tribological processes through the chemical reactions. Although the reactions change the strain rate and interfacial junction strength, the dominant role of deformation and adhesion in wear processes remains intact. Because of this, hereinafter our consideration will be restricted by the mechanical wear. When considering the scale factor, SPM techniques can provide a lot of useful data at micro and nanometer range. First of all, surface topography and texture can be evaluated in 3D space. Second, the contact of surface elements can be simulated at the smallest scale of roughness. Third, the microscopic contact, friction, and wear events can be modeled by tip indentation and scratching.

Fig. 20.1. Combination of factors affecting friction and wear

20.3 AFM as a Tool of Contact Simulation 20.3.1 Contact of Rough Surfaces A real surface is composed of several roughness scales, which are superimposed on each other. Four scale levels can be distinguished: the atomic and molecular one resulting in material surface texture at nanoscale, conventional roughness formed in

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machining, waviness as a result of periodical effects of tool, and errors in form of a given part. The accuracy of traditional contact (probing) as well as non-contact techniques was perfected to a level allowing measurement of roughness in the nanometer range (Fig. 20.2). The most accurate profilometer probes allow measurement of nanometer heights [8]; optical instruments have the same ultimate vertical resolutions [9, 10]. Yet, the comparatively poor lateral (horizontal) resolution significantly limits application of these techniques to the nanometer topographies when the distance between asperities is much less than the resolution or 0.1–1 µm. The development of techniques using probes smaller than the radius of the stylus or the light wavelength makes it possible to extend the spectrum of surfaces studied. The electron beam in the scanning electron microscope (SEM) is an example of such a probe. By interpreting the emission intensity of the secondary electrons, the topographic pattern can be restored, and the SEM technique can be used to gauge topography with a comparable resolution both vertically and laterally [11]. A still finer probe is the electron flux tunneled between the target surface and the tip in STM. In this case, the surface topography resolution is 0.01 and 0.1 nm in the

Fig. 20.2. Diagram of the height and spacing parameters and ranges of vertical–lateral resolution for different methods of roughness measurement

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vertical and lateral directions, respectively [12]. Significant prospects are connected with the application of AFM [13]. Although scanning probe microscopy is widely used for studying the surfaces of solids, there is a basic drawback of the technique related to the small size of scanning area. Therefore, the problem of combination of nano/microscale data with data obtained on the macroscopic area needs more thorough investigation. The real contact area (RCA) is one of the basic notions adopted in tribology. This notion was introduced because a contact of rough surfaces occurs in a small part of the apparent contact area of the same surfaces considered smooth and flat. One of the specific features of the modern mechanics of friction relates to intensive use of the probabilistic methods for calculating a contact between rough surfaces. The whole set of contact models can be illustrated by the general scheme given in Fig. 20.3. Calculation of RCA is based on two groups of characteristics, physicalmechanical and geometrical ones. The former involves Young’s modulus, Poisson’s ratio, surface energy, and so on; the latter describes real geometry of contacting

Fig. 20.3. Calculation scheme of rough and multilevel contact

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surfaces using the distribution of asperity heights. The probability distribution for asperity parameters is determined using the measurement data or/and theories of roughness. As a rule, the asperity is replaced with a body having a simple geometrical shape (e.g. sphere, elliptic paraboloid, cone, etc.). Then, the solution to the contact problem for interaction of a single asperity with a counterbody is found, and the averaging of load and contact area over a whole set of asperities is produced. An elegant model of elastic contact advanced first by Greenwood and Williamson (GW model) awakened great interest in simulation of real contact by statistical methods [14]. This model is based on the contact problem for smooth sphere modeling of a single asperity. There is no way of listing every modification of the GW model, which opened a wide avenue for simulation of the real contact. It should be mentioned that this work was concerned with using various statistics of surface topography, deformation modes, shape of single asperity, and other factors. As applied to AFM data on the description of real surfaces, the following two approaches should be mentioned. When a single asperity is simulated by a sphere being in adhesion contact with counterbody, then the Johnson, Kendall, and Roberts [15] and Deryagin, Muller, and Toporov [16] theories can be used. The development of a single asperity contact problem with adhesion to the rough contact problem was done within the framework of the model of Tabor and Fuller [17, 18]. The GW approach proved to be efficient at developing the so-called two-level model [19]. The combination of two levels, roughness and subroughness, was examined. To take into account the subroughness on the larger asperities (roughness), the solution of Greenwood and Tripp [20] for contact of rough spheres was used as the governing equation for a single asperity. The above models may be described within the framework of Winkler’s assumption, which gives some simplification in calculation [5]. From the contact models modified with the aim of considering the surface (molecular) and/or capillary forces as well as the two-level roughness, it follows that an additional contact area between the surfaces appears due to action of surface forces. Even with adsorbed films on the working surfaces, the adhesion in the contact remains strong. The features of the real contact formation were revealed, which depend on geometric parameters of rough surfaces, the mechanical behavior of contacting materials, normal load, and surface forces including the capillary force. 20.3.2 Rough Contact with Adhesion As mentioned above, the theories of adhesion contact between sphere and flat surface were formulated by Johnson, Kendall and Roberts (JKR model) [15] and Deryaguin, Muller and Toporov (DMT model) [16]. The former considers the adhesion as a change in surface energy only where the two bodies are in contact (that is, the attractive forces are infinitely short-range). The latter takes into account the interaction outside the contact zone (the Lennard–Jones potential). Analysis shows that each of these models is correct for certain combinations of physical-mechanical and geometrical characteristics and both of the theories were used in simulation of rough contact with adhesion [21] based on the GW model.

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Tentative assessment of the effect of intermolecular forces can be made using the adhesion parameter [17] 1 ∆c = 3σ



9π β 2 ∆γ 8 K

2/3 ,

(20.1)

where σ is the mean quadratic deviation of the height; β is the mean radius of rounding of asperities; ∆γ = γ1 +γ2 −γ12 ; K = 4/3[(1−ν12 )/E 1 +(1−ν22 /E 2 )]−1 ; γi , νi , E i (i = 1, 2) are the specific surface energy, Poisson’s ratio and Young’s modulus of contacting bodies; γ12 is the interface energy of the contact zone. Estimation of the adhesion forces shows that the discrete contact is highly sensitive to its adhesion ability. So, larger magnitudes of ∆C can increase the RCA more than 100 times. The relation ∆C < 0.1 can occur only in the case when at least one of the contacting bodies is completely elastic. Theoretical and experimental studies show that contact is formed by adhesion and surface forces are dominant when ∆C > 0.1. Since physical-mechanical properties of mating materials are introduced into (20.1) in addition to the roughness parameter, the condition ∆C ≥ 1 can determine the ultimate mean arithmetic deviations of the equivalent roughness Ra = (Ra1 + Ra2 )1/2 , below which the degree of adhesion in the contact should be taken into account (Fig. 20.4). A transition region exists above this level when condition ∆C > 0.1 is fulfilled only at a certain combination of properties of contact materials; hence each specific case needs validation. This analysis indicates that it is impossible to study contact of any materials at nanoscale, unless the atomic and molecular interactions between the surfaces are taken into account. There were a lot of attempts to measure adhesion, but the main problem was its rapid increase with decreasing the distance between the test specimens. Hence, the measurements should be carried out at a very small speed that cannot be done using the design of the common balance. Deryaguin et al. proposed to solve the problem [22] by applying the principle of a feedback balance. This design with modification was used later in a number of

Fig. 20.4. Interrelation of roughness, mechanical properties and surface forces in a contact of solids

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experiments intended to measure molecular attraction forces. In particular, Israelachvili’s surface force apparatus (SFA) measures the surface separation by a multiple beam interferometer with an accuracy of ±0.1 nm. The surface or interfacial energy can be measured with accuracy of about 10−3 mJ m−2 [23]. Nowadays, the molecular forces are measured with AFM using a special technique [24, 25], even bearing in mind that the AFM measurement of attraction has a basic problem related to the quasi-static character of the probe motion. The evident example of this problem is a “jump to contact” caused by dynamic movement of probe under the action of attractive forces. Correct measurement of adhesion can be carried out under the condition of controlled and quasi-stationary probe-to-surface movement. Solving this problem, the contact adhesion meter was developed by MPRI researchers Komkov and Dubravin [26]. When designing the apparatus, a vertical torsion balance with the negative feedback as a basic design scheme was chosen (Fig. 20.5). This design eliminates the problems with balancing and errors caused by friction in the balance support. The device consists of a ball probe with a diameter of 0.5–10 mm, fixed on the arm of a highly sensitive electromagnetic balance with negative feedback. The test sample is brought up to the ball with a predefined contact force (10–10,000 µN). The dependence of adhesion forces vs. distance between the ball probe and the sample is measured during both approach and pull-off of the sample from the ball. The interface forces, which tended to rotate the arm with the ball, are compensated by an electromagnet located on the opposite arm of the balance. The measurement

Fig. 20.5. Principal scheme of contact adhesion meter: 1 – frame; 2 – string; 3 – holder. 4 – movable coil; 5 – mirror; 6 – laser; 7 – expander of optical base; 8 – photodetector; 9 – coil; 10 – specimen; 11 – table; 12 – stepping motor; 13 – system of fine positioning driven by piezodrive

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of a compensating current in the electromagnet allows us to determine the acting interface forces. The sample movement proceeds by a piezo-stack and could be varied from 0.1 to 10 nm/s in the range up to 10 µm. The contact adhesion meter (CAM) allows one to measure the force interaction of surfaces in two regimes. When the surfaces are separated the rupture of bonds (pull off force) is fixed. On the other hand, approaching and contact of surfaces with formation of strong forces is also studied. The latter process is shown in Fig. 20.6, which presents the force–distance curve [27]. Here point A shows the beginning of interaction of approaching surfaces, and the portion AB corresponds to pure attraction without formation of the real mechanical contact between the solids. After the point B, the force interaction and elastic deformation occur simultaneously. At the point C, the elastic force of resistance to penetration becomes dominant. The point D corresponds to the moment when the elastic force of resistance to penetration equals to the adhesive force of mutual attraction. Using CAM, we measured the surface energy of coating on silicon plate (crystal structure (111), homeopolar semiconductor). Materials of coatings were OTS (octadecyltrichlorsilane) of 3 nm in thickness, SEBS (poly[styrene-b-(ethyleneco-butylene)-b-styrene of 8 nm in thickness, and epoxysilane of 1 nm in thickness [28, 29]. Also, the organic SAMs (self-assembled monolayers) of ODPO4 and DDPO4 ) of 2 nm in thickness were studied with titanium and its oxide as underlayers [30, 31]. The typical dependence of the adhesion force during approaching and retracting of the silicon ball obtained by CAM is shown in Fig. 20.7. Our measurements have demonstrated that the specific surface energy of the test coatings depends on materials of the coating and the probe, as well as on the probe radius. The energy is equal to 0.004 J/m2 for OTS and epoxilane (probe radius 1 mm) and 0.003 J/m2 for epoxysilane and 0.002 J/m2 for SEBS (probe radius 1.5 mm). The following results were obtained for SAMs: 0.007 J/m2 for Si + TiOx + ODPO4 , 0.011 for Si + Ti + ODPO4 , and 0.002 for Si + Ti + DDPO4 (1 mm), as well as 0.004 J/m2 for ODPO4 (1.5 mm). According to the test data, the adhesion force is two orders of magnitude less than the calculated one [32]. Such deviation was also mentioned by other researchers,

Fig. 20.6. Stages of contact formation and main points on the force–distance curve: h AC is the effective radius of surface forces, h BC corresponds to the tensile elastic deformation of the surface, h CD corresponds to the elastic mutual penetration with account for adhesive attraction between solids

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Fig. 20.7. Force–distance curve for OTS samples and silicon ball. 1 – approaching; 2 – retraction

most of whom agree that these deviations probably stem from the ambiguity of the contact area of real rough surfaces. A supposition was made that the value of the probe radius should be treated as the radius of asperity. To verify this supposition, we examined the surface topography of the test objects. Figure 20.8 represents their AFM surface images and cross-section profiles. The analysis of the obtained data led us to the conclusion that the following modes of contact occur. In the first case (Fig. 20.8a), the contact corresponds to the sphere-on-sphere contact with the radii of about 10 µm. Contact of the steel surface most likely occurs over a single sphere/asperity 2 µm in size (Fig. 20.8b). As for the surface presented in Fig. 20.8c, multiple contact of asperities about 80 nm in size is most probable. In this case, the asperity radius of the surface (Fig. 20.8c) is considerably less than the asperity radius for the silicon ball, therefore, the sphere-on-flat geometry can be used. According to the evaluation of the contact spot, a diameter of up to 500 such asperities may come into contact with the probing surface. The results of calculations proceeding from the above considerations agree quite well with the theoretical estimations [32]. 20.3.3 Multilevel Contact Models For considering the effect of two-level roughness on contact characteristics, the model of discrete contact was developed [5]. The geometric and mechanical difficulties were obviated by considering either level of roughness as an object in its own geometry and mechanical behavior; in so doing the combined deformation of asperities

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of different levels is incorporated. The calculation procedure is a modification of the conventional scheme, for example, the GW model. However, at the first stage, in lieu of the Hertz problem for smooth spherical asperity, we use a solution to the problem of contact of a rough sphere and plane [20]. On examination of combination – roughness (level 1) plus subroughness (level 2) – the rough sphere serves as a model of a real asperity carrying subroughness. Solution of the problem gives relationships between the contact parameters. Based on the data on computer simulation, we estimated the limit values of rms roughness, below which the surfaces can be treated as perfectly smooth ones, that is, they form a continuous physical contact with separation that does not exceed an interatomic spacing. Those values are about 1 nm for metals, 1–3 nm for rigid polymers, and about 10 nm for elastomers. The subroughness below these values exerts no influence on the real contact. Calculation shows that the highest asperities of the first level come into contact and form the elementary real contact spots. Yet, contrary to traditional view, the spots are not continuous but multiply-connected, that is, each of the spots consists of a set of subspots whose total area was conditionally named “physical contact area”. This area results from the contact of nanometer-scale asperities (subroughness). Calculation of physical contact area is shown in Fig. 20.9 (here Aa is the apparent contact area and A stands for RCA or physical contact area; E  is the reduced modulus of elasticity). Here, the real contact area A as a function of the load is presented for comparison. The RCA is plotted for a rough surface with the following roughness parameters: root-mean-square roughness σ1 = 0.50 µm, radius of peak curvature R1 = 13.3 µm and bandwidth parameter α = 6.3 (subroughness is assumed to be absent). The remaining curves present the cases when the same roughness “carries” subroughness with σ2 = 0.1 µm and α = 6.3, but different values of surface density of asperities D2 (µm−2 ), curvature radius at asperity peak R2 (µm) and complex parameter of topography µs , respectively.

Fig.20.8.AFM-images of surfaces: (a) silicon plate (50×50 µm); (b) steel specimen (27×27 µm); (c) silicon surface covered with titanium (2 × 2 µm)

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Fig. 20.9. Real (dotted line) and physical (solid lines) contact areas vs. load: (1) σ1 = 0.50 µm, R1 = 13.3 µm; (2) σ2 = 0.1 µm, R2 = 0.20 µm, D2 = 3.2 µm−2 , µs = 0.2; (3) σ2 = 0.1 µm, R2 = 0.10 µm, D2 = 25 µm−2 , µs = 1.0

Calculation shows that the physical contact area is less than the RCA by one-two orders of magnitude (Fig. 20.9). The strong interaction between the mating surfaces may occur within the physical contact area. Its contribution to the friction force may be very significant [5]. Thus, the physical contact area previously known as a qualitative characteristic gains its quantitative measure due to the two-level model. The two-level model with adhesion is of interest for precision engineering. It can be developed in the same manner as for the above model. A rough sphere modeled an asperity of the first level. The load-contact radius relation for a single microscopic asperity was assumed to result from JKR or DMT theory. Without going into the details of the calculation procedure, which is described elsewhere [5], we simply present some results dealing with the physical contact area. Numerical experiment shows that for polymers, the physical contact area increases several times due to the surface forces. This rise can be of about 1.5 times for high-density polyethylene, 3 times for low-density polyethylene, and 2 times for nylon. Under the same conditions, a rise in the real contact area is substantially less. For example, for high-density polyethylene the RCA increases by 10% when the root-mean-square roughness σ is 0.5 µm and by 30% when σ = 0.08 µm. 20.3.4 Simulation of Contact Using AFM Images The point that friction of solids is substantially conditioned by roughness of rubbing surfaces and their free energy was understood adequately by the founders of tribology. Let us recall the well-known discussion on the relation between the mechanical (deformation) and molecular (adhesion) components of friction. Although scanning probe microscopy is widely used for studying the surfaces of solids, the problem of measuring the average parameters on the nanoscale needs more thorough investigation. The problem to determine the average dimensions of topographical elements forming the surfaces of solids at the molecular level can be solved only by providing a sufficient bank of statistically valid representative data. As has been noted, the STM and AFM can produce the necessary degree of resolution. The problem remains how to combine the data based on SPM measurements at the small area of scanning with the real engineering quality control requirements.

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Basically we have the following principal problems: erratic arrangement of surface asperities and random distribution of their parameters (height, slope, summit curvature); multiscale character of roughness (size of asperities can vary from the length of the sample to the atomic scale); and non-stationarity, dependence of roughness parameters on the scale of measurement. These properties are not independent, for example, non-stationarity owes its origin to the multiscale topography, all other things being the same. As mentioned before, real surfaces have roughness of different scale. Archard first perceived the important implication of this fact for tribology and proposed the well-known multilevel model [19]. Non-stationarity of surface topography was first identified by Sayles and Thomas [33]. In this connection, we proposed a crude method to separate a real topography measured by AFM into two levels, roughness and subroughness. This method provides the fulfillment of at least one of two conditions for stationarity, namely, zero mean of random process. The procedure is as follows. Preliminary analysis of the AFM-image of a rough surface (Fig. 20.10a) revealed that the profile contains long-wave component relating to roughness rather than subroughness. To eliminate the component, we used the procedure of repeated median filtration of the image. After each application of the procedure, utmost points on the perimeter of the images where the heights were deformed most of all as a result of edge effects were cropped. The filtration procedure was carried out up to seven times. Computational experiment has shown that, for the images, it was enough to filter out subroughness components of the relief. A greater number of filtration repetitions do not change significantly the spectral function for appropriate profile sections of the image. At the following stage the filtered image (B) was subtracted from the initial image (A) to obtain the resultant image (C) reflecting a surface subroughness (Fig. 20.10). Parameters for the submicrorelief were determined on the basis of the C-type images.

Fig. 20.10. Image processing procedure for separation of roughness scale levels. A = B + C, where A is the initial image, B is its long-wave component, and C is the subroughness image

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The proximity of spacing parameters obtained from image C (Fig. 20.10) and that measured by Talystep on the same sample may be good indirect evidence that the above procedure is acceptable. There is a great diversity of mathematical theories of roughness from simplest deterministic models (which describe a rough surface as a regular array of bodies with simple geometry) to complex models based on the theory of probability and fractal geometry. Here it is pertinent to note that computer simulation of roughness with prescribed properties may be useful [34, 35]. Application of computing power allows simulating rough contact based on 3D images of surface topography. The topography is represented as a matrix of surface and may be generated by special algorithms or measured by scanning technique (stylus and optical profilers, as well as STM and AFM). Aside from pictorial rendition, this approach has a number of other advantages. It offers freedom of replacing asperities by simple geometry bodies (as is done by models of the GW-type) and does not set limits on statistics of surface (as contrasted to fractal approach). Computer simulation permits one to consider any factor of interest to tribologists (surface forces, boundary films, anisotropy of roughness and mechanical properties, and so on). So far, the stationary contact was modeled. Hopefully, the computer simulation will provide a way of studying the movable contact or at least the transition from static to dynamic friction. Some progress in using the computer simulation of real contact has been achieved [36–38]. Computer simulation is very adaptable technique, which can be combined with other methods. Such an example is presented below where computer simulation is applied in conjunction with the GW model to the examination of a two-level contact model. Real topography was measured by AFM, and subsequent analysis showed that the topography involves two levels of roughness (Fig. 20.10). It is believed that the contact is formed by deformation of both the levels of roughness due to external load and surface forces. It is well known that RCA is a set of separated contact spots. Within the framework of the two-level model, it was shown that the RCA has a multiply-connected pattern. In other words, each of the real spots consists of a set of smaller spots, the total area of which was conditionally named physical contact area. This area is formed by contact of nanometer-scale asperities (subroughness). The physical contact area is less than the RCA by one-two orders of magnitude. It has a clear meaning when comparing contact areas bearing the load and those conducting the electric current. Figure 20.11 can be an illustration of this concept presenting the AFM data processing with extraction of subroughness by median filtration of a digital image. Here it is pertinent to make some points. As was shown in [11], the traditional averaging of surface height and spacing parameters applied to profile measurements cannot adequately present the surfaces with various spatial structures. First, the contact problems with consideration of roughness are usually solved under the implicit assumption that the asperities coming in contact have little or no effect on each other. This is true for mild load, and yet there are situations where such an effect should be taken into account. In these cases, information on the mutual arrangement of the asperities (surface texture) should be available. Second, theoretical and experimental study has indicated that the arrangement of contact spots exerts an effect on the

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Fig. 20.11. Visualization of contact spots at various scales: (a) AFM-image of an analyzed area (scan 15×15 µm); (b) actual contact spots at microlevel; (c) actual contact spots at submicrolevel (physical contact area)

contact conductance. These two examples demonstrate the importance of surface texture research for tribological practice. One of the directions of such research is the visualization of contact area in micro and nanoscale, which provides the data on spatial 3D arrangement of surface features. Dealing with nanoinstruments such as AFM, we obtain 3D digital images that need novel techniques of processing. Such methods were developed in the pattern recognition area for many years. Scaling from macro to nanoscale can be related to transition from bulk properties of material to surface layer properties, local Young’s modulus and nanoindentation. New promising results are expected in the application of SPM methods to evaluation of mechanical properties. The basic problem here is the physical interpretation of experimental data and their self-affinity in changing the scale factor. 20.3.5 Nanomechanical Probing of Soft Layers The ability to probe surface mechanical properties with nanometer-scale lateral and vertical resolutions is critical for many emerging applications involving nanoscale (1–100 nm) compliant coatings for microelectromechanical and microfluidic devices, where nanoscale details of surface deformations and shearing play a critical role in the overall performance [39–41]. Usually, a nanomechanical probing experiment exploits either AFM or microindentation techniques [42, 43]. Despite numerous technical issues associated with the AFM nanoprobing (e.g., non-axial loading, jump-into contact, high local pressure, and topographical contributions), a number of successful applications have recently been demonstrated,

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including nanomechanical probing of spin-coated and cast polymer films, organic lubricants, self-assembled monolayers, polymer brushes, biological tissues, and individual tethered macromolecules [44–46]. Absolute values of the elastic modulus have been measured for polymer surfaces in the range from 0.01 MPa to 30 GPa. Spatial resolution unachievable by any other probing technique makes AFM nanomechancial probing a unique experimental tool [47]. We believe that a further expansion of the AFM-based probing of ultrathin (below 10 nm) polymer films in the contact mode will rely on solving several fundamental issues including the evaluation of the substrate effect in elastic response for multilayered coatings. In papers [48–50] an approach is described for the analysis of microindentation experiments for layered solids in AFM experiments. General relationships between the normal load and the elastic indentation are suggested in classical Hertzian and Sneddon theories, with more complex cases analyzed with the JKR approach, as described elsewhere [51–53]. As considered, indentation depth is a function of the applied force (normal load) P, tip geometry (radius R or parabolic focus distance c), as well as the mechanical and adhesion properties of the contacting bodies. The normal load for AFM nanomechanical probing experiments conducted as depicted in Fig. 20.12 is calculated as P = kn z defl , where kn is the vertical spring constant of the cantilever deflected in vertical direction by z defl .

Fig. 20.12. (a) Two-spring model for the analysis of the loading curve for the parabolic tip–plane surface contact. (b) AFM cantilever deflection and indentation in the course of force–distance measurements

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Fig. 20.13. Simultaneous deformation of several elastic layers

There are several methods for the evaluation of the elastic modulus of thin films on solid substrates, which include microindentation and bending experiments [54, 55]. As suggested in these approaches, the compression of the layered elastic solids (e.g. a compliant film on a stiff substrate) results in concurrent deformations of two or more interfaces with local deformation depending on the mechanical properties of layers and a load transfer between adjacent layers (Fig. 20.13). A more sophisticated model, which considered the elastic deformation of the layered solids with a certain transfer of the mechanical load between adjacent layers, was proposed for the analysis of the microindentation data and was reported elsewhere [56]. Another approach starts from the presentation of the nonuniform depth profile in an analytical form as a function of indentation depth h [57]. These approaches provided a good analytic tool for a variety of specific cases of the layered solids [58]. The comprehensive analysis conducted in this study demonstrated a reasonably good agreement of different approaches with the best fits and suggested some practical routines in implementing both experimental procedures and data treatment. In paper [48], a generalized approach was described that starts with a simple definition of the depth profile as a smooth function with gradual localized changes providing the means for the “visualisation” of the transfer function and its concise interpretation for complex layered solids with two- and tri-layer architectures. Any variation of the elastic modulus along the vertical coordinate h (indentation depth) can be represented as a constant level superimposed with a combination of positive and negative local deviations: E  (h + ∆h) = E  (h) + m · E  (h)∆h − n · E  (h)∆h .

(20.2)

This equation represents a change in the current value of the elastic modulus in the ∆h range as the previous value, E  (h), plus a combination of increasing m E  (h)h and decreasing n E  (h)∆h contributions. After the same mathematical substitutions, integration is possible to obtain an equation that describes the elasticity change between two layers of the E 1 and E 0 elasticity modulus. E =

E1 − E0 , 1 + exp(−α · (E 1 − E 0 ) · (h − h 0 ))

where α is a transition parameter and h 0 is the thickness of top layer.

(20.3)

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The depth profile of the elastic modulus is described as the superposition of the initial level and variable contribution: E (h) = E 0 + E  (h) .

(20.4)

The proposed description is based on simple initial assumptions and basic arguments. It shows all major features of the many approaches discussed above, and suggests a relatively simple equation for describing the elastic modulus gradient for layered systems. For the important case of thin film on substrate, only two variables can be varied to fit the test data (elastic modulus of top layer and parameter α) assuming that the elastic properties of the substrate are known. Experimental data for ultrathin, layered surface polymer coatings with different microstructures were obtained with Dimension 3000 and Multimode Nanoscope III (Digital Instruments, Santa Barbara, CA) AFM. Experiments were done in a dry environment according to experimental procedures described elsewhere [59]. Experimental force–distance data (cantilever deflection versus piezoelement displacement) were collected in the force–volume mode. A polymer “sandwich” system was prepared by grafting a rubber polymer interlayer of 10-nm thickness to a self-assembled monolayer on a silicon wafer and capping this interlayer with a photopolymerized stiff polymer topmost layer with a thickness between 10–30 nm [60]. This model represents a complex tri-layer system with elastic modulus changing from 2000 MPa for the topmost layer to 5– 10 MPa for the rubber interlayer and to 1000 MPa for underlying organic layer on 160,000 MPa silicon substrate as was independently measured for these materials. In fact, the force–distance curves collected on different surface locations clearly demonstrated a non-monotonic character with three different local slopes. This non-monotonic character became more visible on the loading curve, which showed a pronounced S-shaped behavior (Fig. 20.14). Attempts to fit the experimental data with the Hertzian model failed: significant deviations were observed in the range of either low or high deformation, depending on the selection of the elastic modulus.

Fig. 20.14. The depth distribution of the elastic modulus for the tri-layer polymer system (circles) and fitting with the tri-layer model (solid line). (b) Fitting of the experimental loading curve (circles) by the tri-layer model (solid black line, almost completely screened by experimental data points) and the best fit with Hertzian curve (dotted line)

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The best fit has been achieved with the tri-layer model composed of the 5nm thick topmost stiff layer with an elastic modulus of 2 GPa, a central interlayer 20-nm thick with the apparent elastic modulus of 0.8 GPa, and the solid substrate with the elastic modulus of 160 GPa (Fig. 20.14). The ultimate indentation of the tri-layer film was about 35 nm, which was close to the total thickness of the tri-layer film and indicated virtually complete compression under very high mechanical load. The thickness of the transition zone does not exceed 10 nm, which indicates modest gradient distribution between layers within the layered coatings. Complex shapes of the loading curves and the elastic modulus depth profiles obtained from experimental data were successfully fitted by the graded model with nanomechanical parameters (elastic moduli and transition zones) closely matching microstructural parameters of layered elastic materials known independently. The approach has limitations related to its eligibility only for purely elastic, completely reversible deformations without any contribution from plastic deformation, the viscoelastic phenomenon, strong adhesion, and high friction.

20.4 AFM in Wear Simulation Atomic force microscopy has opened up the possibility of investigating a wide range of surface characteristics, especially when used in conjunction with nanoindentation [61]. The modern AFM instrument is well-suited to investigation of surface coatings. Surface roughness and various physical properties such as hardness and elastic modulus can be determined. A characteristic feature of the technique is that the depth of sampling is very small, typically ranging from around 50 nm to 1 µm. Scanning probe microscopy methods are successfully used to obtain images of topography and local micromechanical heterogeneity of surfaces (lateral force, phase shift images). There are also SPM methods for a quantitative micromechanical characterization of a sample surface by destructive effect of the probe (nanoindentation, nanowear). A possibility of direct measurement of mechanical properties of the surfaces analyzing force-on-distance curves was for the first time pointed out by Burnham and Colton [61]. Using the scanning probes made of diamond and fullerit, one can estimate micromechanical properties of hard materials like natural diamond [62]. Commercially available SPM silicon probes (spring constant of cantilevers < 100 N/m) cannot provide a high enough indentation load to realize deformations at which the sublayer contribution becomes noticeable if the outer layers have a thickness above 100 nm. The use of cantilevers with higher stiffness can result in plastic deformations of hard materials. Moreover, such cantilevers do not deflect enough to allow estimation of the applied load. SPM can also combine the destructive effect on the surface by hard tip (nanoindentation, micro- and nanoscratching) and stage-by-stage monitoring of the effect results (scanning of the sample with the same tip). This feature enables study of local microwear of relatively hard materials (Mn–Zn ferrite [63]; carbon films [64]; Si 100 [63, 65]).

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In study [66], we used an SPM technique for microscratching and microwear testing of sample surfaces by a stiff piezoelectric cantilever in dynamic mode. It is possible to scratch a surface estimating a scratching resistance, the development of cracks, and so on. Repeated scratching or indentation can also provide the fatigue characteristics of a surface. Thin hard coatings based on transition metal compounds such as TIN, Ti, TiAlN, and CrN are in widespread industrial use. Applications vary considerably and range from cutting and forming tools to medical implants. For many years, there has been a desire to find materials that can be applied to surfaces to produce a reduced friction coefficient, while at the same time improving wear resistance. Such materials are needed especially in situations where liquid lubricants cannot be used, for example, for devices used in satellites and in food processing equipment. Of the available materials that can be used as self-lubricating coatings, carbon and MoS2 have seen significant recent developments. Initially these materials proved problematic and gave variable performance, owing to poor adhesion in combination with undesirable internal defects. Teer Coatings Ltd, (UK) developed a new range of magnetron-sputtered coatings based on MoS2 and known as MoST. These coatings comprise alternating layers of MoS2 and Ti, each layer being only a few tens of nanometers thick. The company has also developed a carbon-based coating known as Graphit-ic [67, 68]. It was published that the coefficient of friction of MoST and Graphit-ic coatings can be as low as 0.03 or 0.07, respectively, when sliding against the bearing steel with a maximum contact pressure of 3–5 GPa. It proved to be possible to deposit these coatings whilst retaining the very low friction characteristics and to combine them with high hardness. The samples were investigated using a multifunctional AFM instrument (Nanotop 203, Metal-Polymer Research Institute, Belarus). We used a sensitive cantilever with an attached indentor. The indentor was used in two modes, imaging and nanoindentation. The former mode was done at a low contact force, whilst the latter at a higher contact force. The measuring cantilever, with a stiffness of 1400 N/m, is of a novel design. It is possible to control the amplitude and frequency of the cantilever and hence the sensing probe oscillations during the surface scanning. This allows us to get the topographical images, as well as changes in physical properties. A bimorph piezoceramic resonator made as a cantilever beam served as a sensitive part of the probe. The driving voltage was applied to the metallized sides of the cantilever. The resonator was switched into the self-exciting oscillator circuit as a frequency-driving element. The self-exciting oscillator circuit supported constant resonance frequency of the cantilever oscillations (about 10–30 kHz). In contact with the sample surface, amplitude and resonance frequency of the cantilever oscillations change. Procedures of AFM calibrations and execution indentation, scratching, wear tests have been described elsewhere [66]. 20.4.1 Nanoscratching and Nanowear with AFM Tip Apart from measuring hardness, the nanoindentation mode of the AFM technique can be adapted to determine the scratch resistance of a surface. Information concerning

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the propensity for crack propagation during scratching can also be obtained. It is furthermore possible to carry out repetitive scratching at the same location and to determine the fatigue characteristics of a surface. To obtain reliable data, it is essential to calibrate the sensing tip so that an adequate interpretation of the measured data [69] can be applied. In our studies, we used the tip made in the shape of a triangular based (trihedral) pyramid. In the present design, the apex angle was 85 + 5◦ and the tip radius was 50 nm. This was confirmed by AFM imaging (Fig. 20.15). Indentation and scratching was carried out in the following scheme. Initially, the surface of the samples was scanned to obtain the topography image and select a place for testing. Then the tip was positioned in the selected point and the probe was moved over the surface by the piezoceramic tube scanner. Knowing the scanner expansion and stiffness of the cantilever, it is possible to calculate the load with which the tip acts on the surface. In the experiments, a series of indentations was conducted with maximum loads of 1.4, 1.8, 2.1, 2.8 mN. Once the indentation or scratching has been made, the surface was scanned again to obtain an AFM-image of a surface place after the tip penetration. Each measurement was repeated not less than five times in different areas of a sample and the results obtained were averaged. The wear tests of surfaces were conducted according to the following scheme [65, 66]. The surface was initially scanned to receive its AFM-image. Within the scanned site we selected a smaller area where the nanowear procedure was then performed. The selected area was scratched in a raster way (along the parallel lines) with a tip under load. The load on the tip at nanowear tests was 2.1, 1.8, and 1.4 mN. The scratching was performed along the lines close together. Because the number of lines was 128, the spacing between them accounts for 24 nm. The spacing is small in comparison with the worn region dimension (3000 × 3000 nm) and the curvature radius of the tip (50 nm). Upon completion of the nanowear procedure, the AFMimage of the whole initial field was received to visualize the test results. Each test was repeated not less than five times in different areas and the results were averaged. Figure 20.16 shows the data on the wear test of a silicon wafer. The reference grooves were obtained at one-pass scratching under a load of 0.5, 0.2, and 0.1 mN. The test grooves were formed after 200 cycles of reciprocal tip movement in trans-

Fig. 20.15. Image of the diamond tip reconstructed after scanning the TGT01 (NT-MDT Ltd.) test sample

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Fig. 20.16. Multicycle scratching of a silicon plate by the AFM tip: (a) 3D-image of the test area (scan size 14 × 14 micron, height amplitude is 412 nm; (b) profiles of the deepest groove after a different number of scratching cycles n

verse direction. While scratching the surface, the profile of the groove bottom was recorded during each pass. Figure 20.16a shows changes of groove profile after a different number of scratching cycles n. One can see the different wear of the initially flat areas and the pit slopes. Wear is irregular in time and, in some cases, it might be negative due to material transfer. Analyzing the curves in Fig. 20.16b it is seen that wear rate tends to stabilize with the number of cycles. The samples were chosen with fine surface roughness and a wide range of tribological characteristics. They were smooth silicon plate and lubricious coatings MoST (MoS2 -Ti) and carbon based Graphit-ic. A series of hardened and tempered low alloy steels (Vickers hardness ≈ 300 kg mm−2 ) were coated with MoST and Graphit-ic by Teer Coatings Ltd. The coatings were approximately 2 µm thick. MoST and Graphit-ic, both hexagonal layer lattice materials, have self-lubrication properties. The macroscopic mechanical and tribological properties of these coatings

Fig. 20.17. AFM-images of samples with MoST coating (a): 1 – pit produced at load 2.8 mN, depth – 79 nm; 2 – pit at load 2.1 mN, depth – 64 nm; and with Graphit-ic coating (b): 1 – pit at load 2.8 mN, depth – 111 nm; 2 – pit at load 2.1 mN, depth – 97 nm

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Fig. 20.18. Influence of load on nanoindentation hardness

have been studied elsewhere [67, 68]. Figure 20.17 shows AFM-images of pits on samples of MoST and Graphit-ic coatings using loads of 2.8 and 2.1 mN. The images were obtained immediately after completion of the indentation procedure. The indentation depth was greater for the Graphit-ic coating (111 nm and 97 nm correspondingly) than for the MoST coating (79 nm and 64 nm). The hardness data (Fig. 20.18) indicate that MoST coatings were harder than Graphit-ic coatings. In both cases, the measured hardness decreased with increasing test load. This may in part be a result of deviations from the ideal tip geometry that occur at low contact loads, where much of the indentation is due to contact between the surface and the tip radius. Accordingly, the hardness data obtained at the highest test load of 2.8 mN are probably the most reliable. These indicate a hardness of 33.2 + 3.6 GPa for the MoST coating and 16.4 + 0.8 GPa for the Graphit-ic coating. 20.4.2 Wear Simulation in AFM Contact Mode A silicon sample was used to test for definition of wear resistance of a material in a cyclic wear process depending on the increased external load. Tests were carried out under the following conditions: in the initially scanned area the field of the smaller area (10 × 10 µm) was selected; raster scanning with the increased external loading (1.4 mN) was carried out; in the worn area the field of the smaller area (5 × 5 µm) was again selected; raster scanning with the same increased external loading (1.4 mN) was carried out; the field of 2 × 2 µm has finally been chosen and scanned at the same loading 1.4 mN. The experimental result for silicon plate wear testing is shown in Fig. 20.19. Results of tests have shown that the average depth of the first worn area (10×10 µm) is 160 nm; the average depth of the second worn area (5 × 5 µm) is 200 nm; and the average depth of the third worn area (2 × 2 µm) is 230 nm. It is obvious, that with increase in distance from a surface, wear resistance decreases.

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Fig. 20.19. Test for wear resistance of a silicon plate by the AFM tip: (a) 3D-image of the initial surface (scan size 14.3 × 15.4 µm, height amplitude is 2.6 µm); (b) silicon surface after wear test (scan size 14.3 × 9.5 µm, height amplitude is 3.2 µm), the image has been cut off especially for the best representation of the worn areas

The Graphit-ic and MoST coatings were investigated for wear resistance. Examples of the images obtained are shown in Fig. 20.20. A series of identical tests was conducted with both coatings. Subsequent imaging of the surface allowed us to determine the depth of worn areas. In keeping with their great hardness, the maximum scratch depths for the MoST coating were lower than those for the Graphit-ic coating. The depth of the worn area gradually increased in the direction of scratching and then stabilized at the same maximum value. Short displacement (up to 7 µm) multiple track scratch test results for loads 1.4, 1.8, and 2.1 mN are summarized in Fig. 20.21. The depths of the multiple track scratches gradually increased in the direction of scratching and then stabilized at

Fig. 20.20. AFM-images of a surface with MoST coating (a) and Graphit-ic coating (b) after realization of the wear test. The load is 2.1 mN, the depth of the penetration indenter is 790 and 990 nm, correspondingly. The arrow indicates the direction of the motion of indenter

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Fig. 20.21. Influence of the scratching load on the wear depth

some maximum value (these values are plotted in Fig. 20.21). This effect can be seen in the AFM images of typical multiple track scratches shown in Fig. 20.20. The stabilized depths were always deeper than the hardness indentation produced when using the same indentation load. This fact may be connected with the way in which the scratches were generated by multiple passes only 24 nm apart. During such tests, most of the individual scratches are produced via asymmetric loading of the coated test surface, and increasing pressure on the front side of the moving indentor. There was no evidence of the coating material being pushed ahead of the indentor during scratching (ploughing). Hence, material removal probably resulted via cutting (abrasion). In this respect, the MoST coating was more resistant to abrasion than the Graphit-ic coating [66]. The DLC coating (Belarus Railroad University, Gomel) was deposited using a pulsed vacuum arc deposition system. A thin titanium nitride and titanium intermediate layer was deposited on the substrate using a metal plasma source. The thickness of the DLC coating was 300–400 nm, as measured by the quartz oscillation technique. The thickness of the TiN sublayer was 150 nm and of the Ti sublayer

Fig. 20.22. AFM images of the DLC coating before (a) Rq = 19.8 nm, and after the wear test, (b) the average wear depth is 61.37 nm. Scan size 9.4 × 9.4 µm

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Fig. 20.23. Wear depth versus load for DLC coatings with different sublayers

20 nm. The DLC coating hardness measured using a microhardness system (CSEM) with a load of 100 mN was approximately 65 GPa. Wear resistance was determined by modeling the abrasive wear of the surface. For this purpose, we chose a test area within the scanned site of the sample surface and wore it by the normally pressed diamond tip moving in a usual scanning regime. The test area was set within the AFM control software. The worn area depth was determined from the AFM image of the whole site including the test area that was obtained directly after the wear test and done under minimum load on the tip. Figure 20.23 shows the dependence of the wear depth on the loading force for the three types of coatings. In the loading range from 0.3 to 1.4 mN, the wear depth is directly proportional to the applied loads for all the samples. The DLC coating without sublayers was worn most of all. The coating with the TiN sublayer underwent lower wear. Presence of second sublayer of Ti promoted even more decreased wear. Analysis of the results obtained at measurements of microhardness and wear resistance shows that harder surfaces have higher wear resistance. The effect of sublayers on microhardness and wear resistance of the DLC coating can be explained by the smooth transition of the elastic properties in the DLC coating/silicon substrate boundary. That results in lower internal stress in the coating and increases its strength. Nevertheless, the mechanism of effective strengthening of ultrahard DLC coatings demands additional study.

20.5 Conclusions At present, there is a strong trend towards a transition from macro to micro and nanoscale that may give a new insight into the basic problems of tribology, such as the influence of deformation and adhesion mechanisms on friction and wear. The atomic force microscope provides a unique opportunity to obtain the 3D surface topography at nanoscale, to simulate the contact interaction of rough surfaces,

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to measure the micro-mechanical properties of materials in the thin surface layers, and to model the elementary acts of wear. AFM can be efficiently used in the development of multilevel models of surface roughness and contact simulation based on these models. There are certain drawbacks of AFM related to the dynamics of probe-to-surface interaction and effects of probe shape and hardness on the test data. These drawbacks can be overcome by using precise quasi-static devices and microtribometers in combination with AFM. It is clear that progress in engineering will provide a lot of new fields in applications of AFM, but micro- and nanotribology continue to be fascinating and fruitful areas for such applications. Acknowledgements. This chapter is partially based on the results of collaboration with Iowa State University, USA; ETH-Zurich, Switzerland; and the University of Leeds, UK. The authors would like to thank Prof. V. Tsukruk (ISU), Prof. N. Spencer (ETH), and Dr. P. Dearnley (LU) for test samples and fruitful discussions. We wish to thank also the INTAS program (grants 99-0671 and 03-51-4206), and the SCOPES program (grant 7BYPJ065579) for partial support of the research.

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24. Gibson CT, Watson GS, Mapledoram LD, Kondo H, Myhra S (1999) Appl Surf Sci 144– 145:618 25. Israelachvili JN (1992) Surf Sci Rep 14:109 26. Myshkin NK, Grigoriev AYa, Dubravin AM, Komkov OYu, Spencer ND, Tosatti M (2004) 14th Int Colloquium Tribology. Esslingen, Germany 27. Myshkin NK, Kovalev AV, Kovaleva IN, Grigoriev AYa (2004) Proc of 4th Int Tribology Conference. Prague, Czech Republic 28. Luzinov I, Julthongpiput D, Tsukruk VV (2000) Macromolecules 33:7629 29. Tsukruk VV, Luzinov I, Julthongpiput D (1999) Langmuir 15:3029 30. Hofer R, Textor M, Spencer ND (2001) Langmuir 17:4014 31. Textor M, Ruiz L, Hofer R, Rossi A, Feldman K, Hähner G, Spencer ND (2000) Langmuir 16:3257 32. Myshkin NK, Goryacheva IG, Dearnley PA, Grigoriev AYa, Dubravin AM, Komkov OYu, Kovaleva IN (2003) Interfaces in advanced materials IAM’03. Chernogolovka, Russia 33. Sayles RS, Thomas TR (1978) Nature 271:431 34. Patir N (1978) Wear 47:263 35. Hu YZ, Tonder K (1992) Int J Mach Tool Manufact 32:82 36. Webster MN, Sayles RS (1986) ASME J Trib 108:314 37. Ren N, Lee SiC (1993) ASME J Trib 115:597 38. Tian X, Bhushan B (1996) ASME J Trib 118:33 39. Mate CM, Wu J (2000) In: Tsukruk VV, Wahl K (eds) Microstructure and microtribology of polymer surfaces. ACS Symposium Series 741, p 405 40. Muller RS (1997) In: Bhushan B (ed) Micro/nanotribology and its applications. Kluwer, Dordrecht, p 579 41. Bhushan B (1997) (ed) Micro/nanotribology and its applications. Kluwer, Dordrecht 42. Chen X, Vlassak J (2001) J Mater Res 16:2974 43. Tsukruk VV (2001) Adv Mater 13:95 44. Bliznyuk VN, Everson MP, Tsukruk VV (1998) J Tribol 120:489 45. Gorbunov V, Fuchigami N, Stone M, Grace M, Tsukruk VV (2002) Biomacromolecules 3:106 46. Tsukruk VV, Shulha H, Zhai X (2003) Appl Phys Lett 82:907 47. Tsukruk VV, Gorbunov VV (2001) Microsc Today 1:8 48. Kovalev A, Shulha H, Lemieux M, Myshkin N, Tsukruk VV (2004) J Mater Res 19:716 49. Shulga H, Kovalev A, Myshkin N, Tsukruk V (2004) Eur Polym J 40:949 50. LeMieux M, Shulha H, Kovalev A, Minko S, Tsukruk VV (2004) Polym Mater Sci Eng 90:207 51. Oliver W, Pharr G (1992) J Mater Res 7:1564 52. Sneddon N (1965) Int J Eng Sci 3:47 53. Johnson KL (1985) Contact mechanics. Cambridge University Press 54. Nix WD (1989) Metal Trans 20A:2217 55. Pharr GM, Oliver WC (1992) MRS Bull 17:28 56. Doerner MF, Nix WD (1986) J Mater Res 1:601 57. Gao H, Chiu CH, Lee J (1992) Int J Solids Struct 29:2471 58. Mencik J, Munz D, Quandt E, Weppelmann ER, Swain MV (1997) J Mater Res 12:2475 59. Tsukruk VV, Gorbunov VV (2002) Probe Microsc 3-4:241 60. Tsukruk VV, Ahn H, Kim D, Sidorenko A (2002) Appl Phys Lett 80:4825 61. Burnham N, Colton RJ (1989) Vac Sci Technol A7:2906 62. Blank V, Popov M, Lvova N, Gogolinsky K, Reshetov V (1997) J Mat Res 12:3109 63. Jiang Z, Lu C-J, Bogy DB, Miyamoto T (1995) Trans ASME J Tribol 117:328 64. Martinu L, Raveh A, Boutard D, Houle S, Poitras D, Vella N, Wertheimer MR (1993) Diamond Relat Mater 2:673

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21 AFM Applications for Analysis of Fullerene-Like Nanoparticles Lev Rapoport · Armen Verdyan

21.1 Introduction The advent of nanoscale science and technology has stimulated an almost unprecedented effort to develop new strategies for the synthesis of nanomaterials of a controlled size and shape at affordable prices. Probably the most important nanotechnology belonging to the latter category is the future integrated nanocircuits, which in the relatively distant future may replace silicon-based integrated circuit technology. In the same context, another driving force is the desire to combine nanotechnology and biotechnology, e.g. in gene manipulation, molecular biomotors, or for on-line health monitoring. However, nanomaterials are likely to also find important niches in more mundane technologies, like ultra-strong nanocomposites, and as additives to various phases. In the present work, the behavior of a novel brand of nanomaterials – inorganic fullerene-like nanoparticles with substantial technological potential as a solid lubricant – is briefly outlined. The stimulus for the formation of carbon fullerenes [1] and carbon nanotubes [2] stems from the abundant reactive atoms on the periphery of the quasi two-dimensional graphitic nanostructure. Recently, the tribological properties of C60 and C70 fullerenes were described [3–5]. It was speculated that the nearly spherical fullerenes may behave as nanoscale ball bearings. Intuitively, the fullerene molecules are thought to be too small to separate between asperities of the mating metal surfaces and, therefore, they tend to enter into crevices or valleys. Experiments by Campbell et al. with C60 molecules dissolved in dry toluene tend to substantiate this hypothesis [6], but comparison of this result with macroscopic friction measurements is not obvious. Further work of this group has demonstrated that, whereas the adhesion energy of smooth C60 films is very low, the friction coefficient is rather high in this case. The average value of the friction coefficient for a freshly cleaved mica surface with C60 molecular layers was found to be equal to 0.1 [7]. The tendency of the fullerene powders to clump and compress into a high shear strength layer was demonstrated to be a main cause of the high friction coefficient [8]. Recent experiments showed a possibility of obtaining a low friction coefficient of 0.012 for thin C60 films deposited by molecular beam epitaxy [9]. The initial discovery of inorganic fullerene materials elicited a substantial effort of many groups, which has been recently reviewed by a number of authors [10, 11]. These nanomaterials were termed under the generic name inorganic fullerene-like materials, IF. Using the reasoning of carbon fullerenes, it has been proposed [12–14] that the formation of fullerenes and nanotubes is not unique to carbon and is in fact

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a genuine property of 2-D (layered) compounds, like WS2 and MoS2 . In contrast to graphite, each molecular sheet consists of multiple layers of different atoms chemically bonded to each other. As a consequence of their atomic-scale structure involving strong covalent bonds and non-compact space filling, these materials have been identified as strong candidates for tribological applications such as solid lubricants [15, 16]. The main advantages of IF over their crystalline platelet (2H) particles are their spherical shape and the absence of dangling bonds (edge effects). The absence of dangling bonds (edge effects) makes the IF powder chemically inert, so the nanoparticles have a lower tendency to stick either to the substrate, or to one another. It was shown that the frictional and wear properties of MoS2 thin films deposited by ablating a solid MoS2 target can be improved by the incorporation of fullerene-like nanoparticles [17]. IF-MoS2 nanoparticles tested under boundary lubrication and ultra-high vacuum (UHV) were found to give an ultra-low friction coefficient in both cases, compared to hexagonal 2H-MoS2 material [18]. Recent experiments have shown a new possibility for obtaining fullerene-like MoS2 and WS2 nanoparticles by arc discharge in water [19]. Detailed analysis of the nanoparticles’ properties is essential to gain understanding of the complex physical behavior of this nanopowder at the interface during a friction test. There are some theoretical works attempting to characterize individual fullerene-like nanoparticles (see, e.g. [20,21]). Understanding the complex interplay between the chemical and structural properties of the lubricant film and the mating surfaces; the mechanical behavior of friction pairs under different contact conditions and the tribology induced chemical processes, requires a multidisciplinary approach. To elucidate the friction mechanisms of IF nanoparticles, a careful analysis of the mating surfaces and the lubricating medium by a number of experimental techniques was carried out. In the present work, the main attention has been devoted to the study of friction and wear of inorganic fullerene-like solid lubricant nanoparticles of WS2 and MoS2 , mainly by atomic force microscopy (AFM). The obvious advantage of the tribological SFM is that it allows imaging of the surface that is being tribo-tested with near-atomic resolution. SPM is widely used in the analysis of different materials at nanoscale level [e.g. 22, 23]. Kinetics of the formation and destruction of the films with IF nanoparticles using SFM has been considered in recent years [24–26]. Based on the AFM, scanning electron microscopy (SEM); transmission electron microscopy (TEM); X-ray photoelectron spectroscopy (XPS), and X-ray powder diffraction (XRD), the mechanisms of IF self-lubrication are discussed in this work.

21.2 Instrumentation 21.2.1 Friction Experiment Friction of WS2 and MoS2 solid lubricant films, as well as the behavior of IF nanoparticles as additives to oil are considered in this work. In order to assess the behavior of the IF nanoparticles with oil, ring-block tests of steel pairs at a wide range of sliding velocities and loads have been performed [27]. To simulate typical industrial

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conditions, only 1 wt % of the solid lubricants (IF or 2H-WS2 ) were dispersed in oil. Another set of the experiments has been carried out in order to analyze the behavior of the IF nanoparticles under high contact pressure. Consequently, the friction tests were performed using a ball-on-flat device. A silicon nitride ball was slid against an alumina wafer with maximum contact pressure close to 2 GPa and a reciprocal sliding velocity of 0.2 mm/s. The roughness parameter Rz of alumina samples was close to 1 nm. The alumina flat and silicon nitride ball were rinsed in hexane and acetone using an ultrasonic bath and then dried before and after the test. Paraffin oil with a viscosity of 60 cSt at 20 ◦ C was used as a base oil. The friction test was stopped periodically after different numbers of cycles and the rubbed surfaces were analyzed using different surface analysis devices. 21.2.2 AFM Experiment Two types of AFM experiments have been performed. In the first one, the nanotribological properties of type-II (0001) oriented WS2 and MoS2 thin films were studied [28]. For the nanotribological evaluation of solid lubricant films, a Topometrix TMX2010 Discoverer scanning force microscope SFM equipped with Si microfabricated cantilevers with integrated tips Nanoprobe, Singlefen, Germany, was used. The instrument was modified to allow 20× amplification of the lateral force signal without changing the normal force signal. The friction experiments consisted of contacting the tip to the surface, measuring a force–distance curve from which the absolute load was determined, then measuring friction at varying loads while scanning the sample perpendicular to the long axis of the cantilever, over distances of 100–200 nm. The dynamic friction for each load is equivalent to half the height of the friction “loop” obtained by plotting friction signal vs. lateral distance, while scanning back and forth across a line. In order to avoid cross-talk between normal and lateral signals, only flat regions of the surface, which were atomically smooth as evidenced by the SFM, were used. Calibration of normal and lateral signals was deduced from known geometry of the SFM detection system by recording the signal change for a known movement of the adjustment screws for normal and lateral signals. This method was compared to calibration of the normal force signal by deflecting a hard sample in contact with the tip by a known amount with the z-piezo through the Topometrix software, and was found to be comparable. The lateral force signal was collected and averaged on a digital scope Nicolet 410. In a typical experiment, after achieving contact between tip and sample, a topographical image of the sample was made over a scale of 500–1000 nm. Subsequently, the friction experiment was performed in the middle of the region, using increasing loads. After achieving the highest loads under the instrumental limitations, the load was reduced in order to check for hysteresis in the friction. At the end of the set of friction measurements, an additional topography image was generated to check for wear. In addition to the WS2 , and MoS2 films, a polished Si wafer and mica were tested and are reported below for the sake of comparison. Another test has been carried out in order to evaluate the topography and roughness after microtribological tests with IF nanoparticles added to oil. The surface topography of the samples before and after the friction tests was studied with SPM

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DI Dimension 3100. Tapping mode was used in order to diminish the effects of high roughness and a presence of the oil’s film on the friction surfaces. The silicon tips OTESPA-70 (DI production) with a resonance frequency of 320–380 Hz were used. For better resolution of the tested surfaces, the amplitude setpoint value was chosen to be 25% lower than the RMS amplitude voltage at the moment when a tip touched the surface. All the measurements were carried out in ambient conditions at 25 ◦ C and ca. 60% humidity.

21.3 Characterization of Fullerene-Like Solid Lubricant Nanoparticles The analysis of the IF nanoparticles showed that most, if not all nanoparticles were closed and hollow, having nearly spherical shape. The hollow cage structure of the IF imparts a high elasticity, which augments their resilience in a specific loading range [29]. Dislocations, which have a deleterious influence on the chemical stability and the tribological behavior, were abundant in these nanoparticles. The AFM image of an IF-WS2 nanoparticle is shown in Fig. 21.1. The ratio between the height and the diameter of nanoparticles was close to 0.3 for nanoparticles of different sizes. The tilting of the samples in the TEM suggests that the IF-WS2 nanoparticles have a near spherical shape, Fig. 21.2. The number of molecular layers in a pristine WS2 nanoparticle was close to 15–20 with an interlayer distance of c/2 = 0.62 nm. Van der Waals bonds between IF nanoparticles usually led to their agglomerations. Agglomerates with sizes of 1–5 µm were sometimes observed after the sintering. The size of the pristine IF-WS2 nanoparticles was varied from 50 to 300 nm. The average size of the IF-WS2 particles was close to 120 nm, while it was about 50 nm for IF-MoS2 . Although the structure of IF-WS2 nanoparticles

Fig. 21.1. AFM image of quasi-spherical IF-WS2 nanoparticles

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Fig. 21.2. TEM image of typical IF-WS2 nanoparticles at different tilt angles. The results demonstrate the quasi-spherical shape of these nanoparticles

is more strained than that of the WS2 nanotubes [29], they were able to withstand a high hydrostatic pressure under compression without suffering heavy damage. It was found that these nanoparticles are capable of withstanding severe hydrostatic pressure, caused by compression. Detailed structural studies revealed that no phase changes were observed during compression. Frequently observed defects are associated with a deformation of the IF nanoparticles and breakage of the outer shells of the nanoparticles under compression. The layer to layer distance of 0.62 nm has been preserved in the broken sheets. The inner layers of these nanoparticles seem to remain intact. The broken outer layers are expected to be transferred to friction surfaces providing superior tribological properties of rubbed surfaces. The 2H-WS2 particles with platelet shape suffered severe damage under the same loading conditions.

21.4 Friction of Solid Lubricant Films The WS2 film consisted of a continuous film with predominantly hexagonal terraces. Atomic resolution was accomplished with the SFM essentially on the entire surface area of the film. This observation indicated that the film is suitable for tribological applications, since it exposes only the low energy vdW surface (type II texture). The MoS2 film was expected to exhibit inferior tribological properties, since the film is discontinuous and the crystallites are smaller. Thus, reaction of the prismatic edges with the humid atmosphere could not be averted in this case. Typical SFM curves of normal load vs. lateral force for WS2 (a) and MoS2 (b) films are shown in Fig. 21.3. The friction coefficient, which was calculated from the slope of the curves, was 0.035 and 0.040(±0.005) for the WS2 and MoS2 films, respectively. The two lowest points in a WS2 were taken after the highest force was applied to the film. The small deviation of these two points from the straight line is indicative of the absence of tip-induced damage to the film as a result of the measurement. It should be noted that because of coupling between normal and lateral force constants in the SFM, measurement of extremely low friction coefficients is problematic, and these values are at the lower range of reliability for

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Fig. 21.3. Typical normal load vs. shear force dependence for (a) WS2 and (b) MoS2 films, obtained with the help of the SFM. The two lowest points in (a (shown by arrows) were taken after the highest force was applied to the film

the SFM [31]. We also note that, for a single asperity Hertzian contact, linear friction vs. load behavior is not expected, rather it arises due to the relatively narrow range of forces that can be applied by a single cantilever. By using different cantilevers with lower normal and torsional force constants, we observe somewhat different friction coefficients. For ideal Hertzian single asperity contact, the frictional force is proportional to the 2/3 of the power of the load. In this case, we would expect a “friction coefficient” that is about two times greater for loads in the range 5–50 nN when compared to loads in the range 50–500 nN. This effect is indicated by the nonzero y-intercept of the plots. The friction coefficients are, therefore, included for comparison with measurements made under similar conditions only, and not for comparison with macroscopic measurements. Under similar conditions, much higher friction coefficients were measured by the SFM for gold (0.3–0.4), polished Si wafer (0.9) and mica (0.25–0.6). On the basis of these results, it may be concluded that friction of the films with type II orientation is more than an order of magnitude lower on these films than on the reference substrates Si, mica, and Au; (0001) planes exhibit enhanced tribological

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behavior as opposed to type I films, whose performance degrades considerably in the ambient as compared with vacuum; using the imaging mode of the SFM, no wear track could be resolved on either of the above films after the tribological measurements (in contrast, extensive wear occurred on the gold, Si, and mica surfaces following the nanotribological tests). These results clearly indicate the favorable tribological properties of the highly textured type II films of metal dichalcogenides. The improved tribological properties of the present films can be attributed to the negligible exposure of dangling bonds that usually occur on the prismatic (1120) face (||c) of the crystallites.

21.5 Friction and Wear of the Surfaces Lubricated with Oil + IF Nanoparticles In order to evaluate the effect of IF nanoparticles under friction with oil, the main attention was given to preparation and analysis of the surfaces after lubrication. The surfaces were carefully rinsed in an ultrasonic bath with acetone and hexane, and subsequently dried. All stages of the sample preparation (virgin state, state after lubrication and friction) were checked by AFM. After evaluation of dry virgin surfaces, some drops of paraffin oil with IF nanoparticles were dripped on the surface of alumina wafer. Following the sedimentation of the IF nanoparticles on the surface of alumina wafer for ten–twenty minutes, the lubricant was rinsed and the surface was again studied by AFM. The IF nanoparticles, as well as thin films of paraffin oil were found to be preserved on the surface of alumina after rinsing, Fig. 21.4. The thickness of the oil films was close to 10 nm. Only careful rinsing allowed decreasing the oil content on the surface of the alumina, Fig. 21.5. Generally, a shearing of the IF nanoparticles in the interface under friction led to the formation of island films

Fig. 21.4. AFM image of the IF-WS2 nanoparticles and oil films on the surface of alumina

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Fig. 21.5. IF-WS2 nanoparticles on the surface of alumina wafer after careful rinsing off the oil

Fig. 21.6. The islands of the IF nanoparticles on the surface of an alumina wafer

on the contact surfaces after some cycles of friction, Fig. 21.6. The size and the shape of the islands depend on the contact conditions. Under low loads, a mixture of practically non-damaged IF nanoparticles with oil are observed at the interface. With load increase thin sheets of destroyed IF nanoparticles are observed on the rubbed surfaces.

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Mixed lubrication is an extremely important regime of liquid lubrication when both fluid film and boundary lubrication take place [32, 33]. The effect of the IF in oil under friction of steel samples was studied using a pin-on-disk tester. Interaction between full film and the asperity contact fractions was considered and the evolution of the friction force with time was evaluated. In this experiment, the lubricant feeding was interrupted in a steady state friction regime and the time interval to a friction force jump was assessed. It was found that the friction force increased after five minutes for the pair lubricated with oil, while it was more than thirty-five minutes for the pair with oil + IF nanoparticles, Fig. 21.7. The surface of the disk and the pin rubbed with oil + IF was found to be covered with the layers of destroyed IF nanoparticles mixed with oil, Fig. 21.8. The thickness of the layers was close to 10 nm. Formation of thin nanosheets of delaminated IF are confirmed by high resolution SEM both on the surface of the pin and the disk. XPS analysis revealed that this film consisted mainly of WS2 . Together with thin nanosheets in the contact spots, pristine IF nanoparticles are also observed in the grooves of rough friction surface. These nanosheets and IF nanoparticles preserve the rubbed surfaces from straight contact and thus decrease the wear. The wear of the rubbed samples with oil + IF lubricant was lower in comparison to the pair lubricated with pure oil at all studied loads. This effect becomes more predominant with load increase, suggesting the favorable role of IF with the load. It was concluded that the transfer of thin sheets of destroyed IF nanoparticles is probably responsible for their self-lubrication effect under mixed lubrication. The amount of the oxide was found to be substantially larger on the surface of the wear track in contact with the 2H-WS2 platelets as compared to IF nanoparticles. The absence of dangling bonds may, therefore, be one of the prime advantages of IF nanoparticles over the crystalline platelet (2H) particles for the reduction of friction and wear. 9 8.5

paraffin oil

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Fig. 21.8. AFM image of IF layers mixed with oil on the surface of the pin after the test in a condition of mixed lubrication

Based on the AFM, TEM SEM and XPS studies, it may be seen that the islands of thin sheets of destroyed IF nanoparticles provide low friction and wear under different contact conditions.

21.6 Friction of IF Nanoparticles Under Severe Contact Conditions Friction test of an alumina wafer-silicon nitride ball with IF nanoparticles showed a friction coefficient of less than 0.04 under high contact pressure, while it was appreciably higher for the pure oil. No damage was observed for the alumina plate and the silicon nitride ball after friction with oil + IF lubricant. The friction track was found to be covered with IF nanoparticles and delaminated thin sheets of IF nanoparticles. A smooth surface without large agglomerates of the IF nanoparticles was observed in the middle area of the friction track, Fig. 21.9. The thickness of the thin sheets of destroyed IF nanoparticles on the surface of the alumina wafer was close to 7 nm. A typical small aggregate of IF nanoparticles near the middle area of the contact is shown in Fig. 21.10. The aggregates were tightly stuck to the surface of the alumina and could not be removed from the contact area after careful rinsing. The greater the distance from the center to the edge of the track, the larger the number and the size of IF agglomerates, Fig. 21.11. Based on AFM study, a discontinuous film consisting of uniformly distributed islands with thickness of about 5–20 nm was observed. It is seen that already after a few cycles the thickness of these layers is smaller than the size of pristine IF nanoparticles. The thickness of these layers was further reduced to 5–6 nm after 10–15 cycles and remained unchanged over a time. Given the interlayer distance of 0.62 nm, the number of molecular WS2 layers in the film can be evaluated. It was typically found that islands made of 8–10 molecular

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Fig. 21.9. AFM image of the islands of the IF films in the middle part of the friction track on the surface of the alumina after 5 cycles

layers of broken solid lubricant nanoparticles were adhered to the middle area of friction track. In addition to the analysis of the thickness of IF-WS2 films, the damage of the solid lubricant nanoparticles during a friction test was studied. The damage of IF nanoparticles varied with the distance from the middle area to the edge of the contact in a systematic manner. The aggregates of the IF nanoparticles suffered severe deformation. The greatest damage of the IF nanoparticles was exhibited in the center of the track, where the contact pressure was maximum. Small flakes that

Fig. 21.10. SEM micrograph of a small aggregate of IF-WS2 nanoparticles in the friction track on the surface of the alumina

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Fig. 21.11. Large agglomerates of IF nanoparticles close to the edge of friction track

were separated from the nanoparticles were found to cover a contact surface of alumina in the middle area of the contact, Fig. 21.12. Aggregated and compressed IF nanoparticles and their shells around the contact spot were able to support the load and decrease thus the real contact pressure. Thus, it may be concluded that thin sheets of destroyed IF nanoparticles in the interface provide improved tribological properties under severe contact conditions.

Fig. 21.12. The IF thin layers on the surface of alumina in the area of high contact pressure

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21.7 Mechanisms of Friction of the IF Nanoparticles A definite relation between the height and the diameter of pristine IF-WS2 nanoparticles of about 0.33 has been found by AFM. One of the causes of this effect could be a strong adhesion between fullerene-like nanoparticles and the substrate due to the van der Waals interaction [19, 20]. The lateral size of nanoparticles is close to the curvature of the radius of the tip that may be also the cause of this deviation. However, the error in the measurement of height and diameter of the nanoparticle cannot be so large. Therefore, it may be expected that the main cause for the reduced height is the adhesion between IF nanoparticles and the substrate. Strong adhesion of the nanoparticles apparently limits the rolling friction as had been expected previously [15,26,28]. The adhesion between the IF nanoparticles can be also attributed to the van der Waals interaction, leading to the formation of the agglomerates of the IF nanoparticles. In order to better understand the adhesion of the IF nanoparticles to the underlying substrate further investigation is needed. The measurement of the thickness of the solid lubricant layer in the gap between ceramic surfaces showed that this thickness is remarkably smaller than the size of pristine IF-WS2 nanoparticles (the average size of a quasi-spherical nanoparticle is close to 120 nm). Since thin layers of the broken nanoparticles are observed in the interface after few cycles of the friction test, it may be assumed that some of the small pristine nanoparticles with strongly faceted structure are entrapped in the inlet of the contact. High contact pressure leads to a squeezing out of the oil and tight sticking of broken shells of destroyed IF nanoparticles on the surface of the alumina flat. Thin shells gradually cover the middle range of the contact surface. Aggregated and compressed IF nanoparticles and their shells around the contact spot support the load and thus decrease the real contact pressure. Furthermore, if one takes into account that no damage is observed for the ceramic ball and the flat, it may be concluded that the friction and wear of the ceramic pair can be attributed to deformation and destruction of the solid lubricant layers in the interface alone. It is expected that the small friction is associated with sliding between outer shells

Fig. 21.13. The IF nanoparticles in the grooves of the surface of a disk under mixed lubrication

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Fig. 21.14. AFM images of the contact region in the mica surfaces following a friction experiment carried out in the SFA with (a) IF-WS2 in tetradecane, (b) 2H-WS2 platelets (non-fullerene) in tetradecane. The scan size is 0.8 µm × 0.8 µm for both images [24] (with permission Elsevier Science)

of the pristine nanoparticles at the edge of the friction track and the basal planes of molecular sheets of the IF nanoparticles in the middle area of the contact. The tightly stuck thin IF sheets and the aggregates preserve the rubbed bodies from a direct contact. The mechanical properties of ceramic materials are remarkably higher than those of steel samples. While IF nanoparticles are destroyed in the inlet of the contact with ceramic samples, stiff IF nanoparticles plough the contact surfaces and penetrate into the interface, Fig. 21.13. The similarity in the behavior of steel and ceramic pairs seems to be in the filling of the valleys, grooves and gaps of rubbed surfaces with the IF nanoparticles and their layers. Thus, it may be concluded that if IF nanoparticles could increase the contact area, this would decrease a direct contact between rubbed bodies and thus improve the tribological properties of the contact under severe contact conditions. Using the surface force apparatus, the friction behavior of the IF nanoparticles was investigated in some detail [23–25]. It was revealed that the IF nanoparticles are gradually exfoliated, leaving molecular sheets of WS2 on the mica surface, thereby reducing the shear resistance of the mating pairs in tetradecane suspension, Fig. 21.14 [25]. Ultra-thin WS2 islands are found produce small and uniform defor-

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mation in comparison to a significantly rougher and disordered surface rubbed with 2H-WS2 nanoparticles. 2H-WS2 nanoparticles added in tetradecane showed a very high friction coefficient (up to 0.8). It was concluded that slow exfoliation seems to play an important role in the self-lubrication of mating tribological surfaces with IF.

21.8 Conclusions 1. Friction and wear of quasi-spherical fullerene-like solid lubricant nanoparticles of WS2 and MoS2 have been studied. 2. It was shown that these nanoparticles are capable of withstanding high hydrostatic pressure, caused by compression without suffering heavy damage. 3. The IF nanoparticles added to oil improve the tribological properties of the steel and ceramic pair mainly under severe contact conditions in comparison to layered solid lubricant powder and a pure oil. 4. Based on the AFM, TEM and SEM study it was shown that the islands of thin sheets of destroyed IF nanoparticles provide low friction and wear under high contact pressure. 5. With load increasing, the IF nanoparticles penetrate into the interface, protecting the rubbed surfaces from a direct contact and thus increase the wearability of friction pairs. Molecular sheets of WS2 from the delaminated IF nanoparticles, which reside in the valleys of the rough surfaces cover the contact spots and thus decrease the number of adhered spots under friction. Acknowledgements. We are grateful to Prof. V. Leshchinsky, Prof. Ya. Soifer, Dr. M. Lvovsky, Dr. O. Nepomnyashchy, Dr. Yu. Volovik, Dr. I. Lapsker, all from the Holon Academic Institute of Technology; Prof. R. Tenne, Dr. S.R. Cohen, Dr. Y. Feldman, Dr. R. Popovitz-Biro all from the Weizmann Institute of Science. The support of the Israeli Ministry of Science (Tashtiot) and Bi-National Science Foundation (BSF) are greatly acknowledged. We are grateful to Dr. R. Rosentsveig form Weizmann Institute for the synthesis of the IF-WS2 nanoparticles, and to NanoMaterials, Ltd. (www.apnano.com) for the support of this research and for assistance with regards to the inorganic fullerene materials.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Kroto HW, Heath JR, O’Brein SC, Curl RF, Smalley RE (1985) Nature 318:162 Iijima S, (1991) Nature 354:56 Bhushan B, Gupta BK, Van Cleef GW, Capp C, Coe JV (1993) Appl Phys Lett 62:3253 Bhushan B, Gupta BK, Van Cleef GW, Capp C, Coe JV (1993) Tribol Trans 36:573 Schwarz UD, Allers W, Gensterblum G, Wiesendanger R (1995) Phys Rev B 52:14976 Campbell SE, Luengo G, Srdanov VI, Wudi F, Israelachvili JN (1996) Nature 382:520 Thundat T, Warmack RJ, Ding D, Compton RN (1993) Appl Phys Lett 63:891 Blau PJ, Haberlin CE (1992) Thin Solid Films 219:129 Nakagawa H, Kibi S, Tagawa M, Umeno M, Ohmae N (2000) Wear 238:45 Tenne R (2001) In: Kenneth D (ed) Progress in inorganic chemistry. Wiley, New York, p 269 Nath M, Rao CNR (2003) Dalton Trans 1:1 Tenne R, Margulis L, Genut M, Hodes G (1992) Nature 360:444

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13. 14. 15. 16.

Margulis L, Salitra G, Tenne R, Talianker M (1993) Nature 365:113 Feldman Y, Wasserman E, Srolovitz DJ, Tenne R (1995) Science 267:222 Rapoport L, Bilik Yu, Homyonfer M, Cohen SR, Tenne R (1997) Nature 387:791 Rapoport L, Feldman Y, Homyonfer M, Cohen H, Sloan J, Hutchison JL, Tenne R (1999) Wear 225-229:975 Chhowalla M, Amaratunga GAJ (2000) Nature 407:164 Cizaire L, Vacher B, Le-Mogne T, Martin JM, Rapoport L, Margolin A, Tenne R (2002) Surf Coat Technol 160:282 Hu JJ, Bultman JE, Zabinski JS (2004) Tribol Lett 17:543 Schwarz US, Komura S, Safran SA (2000) Europhys Lett 50:762 Srolovitz DJ, Safran SA Homyonfer M, Tenne R (1995) Phys Rev Let 74:1779 Bhushan B (1999) (ed) Handbook of micro/nano tribology. CRC, New York B Bhushan (2003) (ed) Springer handbook of nanotechnology. Springer, Berlin Heidelberg New York Golan Y, Drummond C, Homyonfer M, Feldman Y, Tenne R, Israelachvili J (1999) Adv Mater 11:934 Golan Y, Drummond C, Israelashvili J, Tenne R (2000) Wear 245:190 Drummond C, Alcantar NA, Israelachvili J, Tenne R, Golan Y (2001) Adv Funct Mater 11: 348 Rapoport L, Leshchinsky V, Lapsker I, Volovik Yu, Nepomnyashchy O, Lvovsky M, Popovitz-Biro R, Feldman Y, Tenne R (2003) Wear 255:785 Cohen SR, Rapoport L, Ponomarev EA, Cohen H, Tsirlina T, Tenne R, Levy-Clement C (1998) Thin Solid films 324:190 Leshchinsky V, Popovitz-Biro R, Gartsman K, Rosentsveig R, Rosenberg Yu, Tenne R, Rapoport L (2004) J Mater Sci 39:4119 Zhu Q, Sekine T, Brigatti KS, Firth S, Tenne R, Krotto HW, Walton DRM (2003) J Am Chem Soc 125:1329 Schwarz UD, Köster P, Wiesendanger R (1996) Rev Sci Instr 67:2560 Cameron A (1966) Principles of lubrication. Longmans, New York Spikes HA, Olver AV (2002) In: Bartz WJ (ed) Lubricants, materials, and lubrication engineering. Proceedings of 13th international colloquium on tribology, vol 1, Ostfildern, p 19

17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

22 Scanning Probe Methods in the Magnetic Tape Industry James K. Knudsen

22.1 Introduction For over 50 years, magnetic recording tape has been an important medium for storage of information. The recording tape is constructed with a flexible substrate, most commonly polyethylene terephthalate (PET) or polyethylene naphthalate (PEN). The recording layer is a magnetic coating that most commonly consists of very fine single-domain magnetic particles dispersed in a polymeric matrix. The earliest tapes employed iron oxide magnetic particles, and subsequent materials have included chromium dioxide and barium ferrite. Most common in recent tapes are particles made from metallic alloys, predominantly of iron and cobalt. For some applications, the magnetic coating is a metallic thin film applied by a sputtering or evaporation process. It is common for magnetic tapes to have a non-magnetic coating on the opposite surface of the tape. The surface texture and electrical conductivity of the backside coating allow control of friction and static charge buildup, thus improving tape-handling performance. Recording of information is accomplished by passing the tape over a recording head, as shown schematically in Fig. 22.1. This head is a ring-shaped magnetic material wound with wires that conduct the signal current, which establishes a magnetic circuit. At the surface facing the tape there is a gap that allows some of the magnetic flux to escape the confines of the head. This alternating “fringing field” from the gap magnetizes the moving tape to create a recorded pattern corresponding to the signal current applied to the head. Early heads were built from laminations of magnetic metals. Improved highfrequency response and wear properties were achieved with the introduction of ferrite head materials. Higher write fields were achieved by metal-in-gap (MIG) heads, which employ a thin film of magnetic metallic alloy with higher saturation magnetization, applied to one or both of the gap faces of a ferrite head. For a head that is only used for tape motion in one direction, the metal only needs to be applied to the trailing-edge gap face. Modern data-storage tape drives employ thin-film heads, which achieve high write fields with excellent high-frequency response, and allow finer dimensions for narrow, tightly spaced track locations. In thin-film heads, the magnetic elements, conductors, and various insulating and bonding elements are applied in a sequence of thin-film depositions [1]. Playback can be accomplished in the opposite process, in which fringing fields from the magnetic pattern on the tape are transmitted through the magnetic head

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Fig. 22.1. Schematic view of recording head and tape. (a) Signal curent creates a time-varying magnetic circuit in the head, resulting in a spatially varying pattern on the tape moving with velocity V. (b) Close-up view showing magnetic field lines in the recording gap region. Head-tape spacing can arise from surface roughness and air bearing effects. Adapted from [5]

structure. In inductive heads, the same magnetic element used for writing can also be used for reading: the magnetic flux that is transmitted through the head induces a voltage in the windings. More common in modern heads, however, is the use of a magnetoresistive (MR) element in the playback head, which provides greater sensitivity than inductive playback. Recent advances in MR elements for heads have been a key driving force for dramatic increases in the data density and speed of magnetic recording media. In contrast to hard disk heads, which are supported by a layer of air that maintains head-disk separation, magnetic tape operates in contact with the head. The tape is not in perfect contact with the magnetic structure of the head, however, due to surface irregularities in the tape and head, which will be discussed below. In addition, air that is carried along with the moving tape creates a partial air bearing, thus reducing the head-tape contact force. These all become important factors in the design of heads and tapes for high recording density, which require extremely good conformity between head and tape [2]. Several books are available for a tutorial review of magnetic recording technology [3–5] and tribology [6, 7]. Over the years, advances in both head and tape technology have enabled a remarkable increase in recording density. As shown in Fig. 22.2, the areal density (product of linear bit density and track density) of recorded data in data-storage tapes has increased by a factor of about 250,000 over 50 years. Both linear recording density and track density improvements have contributed to this growth, although in recent years the trend in track density has accelerated, due to advances in head technology and track-following capabilities [8]. Another important factor in bit density growth has been the development of advanced error-correction capabilities, which introduce a degree of redundancy to the data to enable reliable recording at very high density amid the inevitable imperfections of physical media.

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Fig. 22.2. Areal recording density for IBM tape systems [8]. © 1998 IEEE. More recent data added, courtesy of MP Sharrock, Imation Corp

Increased recording density has required coatings with smaller magnetic particles, smoother surfaces and reduced thickness, as well as improved magnetic properties. Over the 50 years represented in Fig. 22.2, magnetic particle sizes have been reduced from 1 µm to about 50 nm in length. As a result, the dramatically higher concentration of particles per unit volume has reduced the noise level in recorded signals [3]. Smooth surfaces are achieved with a calendering process, in which the tape is compressed between polished metal rolls at elevated temperature and pressure. As the magnetic layer thickness has decreased, a dual-layer coating process that applies a very thin magnetic layer over a thicker nonmagnetic sublayer has enhanced the effectiveness of the calendering process [9, 10] and constitutes a key enabling technology for data density growth. The shrinking of recorded features has brought requirements of tight dimensional tolerances and vanishingly small surface roughness to the manufacture of heads and tapes in order to achieve ever-closer head-tape contact. Atomic force microscopy and magnetic force microscopy have become valuable tools in the analysis of the very fine features of magnetic tapes and heads.

22.2 Atomic Force Microscopy 22.2.1 Topographic Characterization of the Magnetic Tape The surface topography of the magnetic tape has important implications for the recording performance and mechanical reliability of the tape. Surface texture contributes to unwanted noise in recorded signals, and by increasing the effective spacing between head and tape, it reduces the signal level and hinders the resolution of closely-spaced recorded features. On the other hand, a certain amount of surface texture is beneficial for reducing friction and wear of the tape. As a result, designers of magnetic tape formulations are presented with tradeoffs between recording performance and reliability, often requiring specialized surface textures to meet these goals. AFM is a useful method for characterizing surface roughness and the nature of any defects or wear on the surface.

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As recording density has increased, the roughness of the magnetic surface has correspondingly decreased. Figure 22.3 shows AFM images for a data-storage tape, showing both the magnetic and backside surface. This tape is a second-generation UltriumTM tape1 designed for high-density recording of data: 230 Mbits per square inch (2.3 × 108 bits/square inch). As is typical in magnetic tapes, the backside surface is much rougher than the magnetic surface, for improved tape-handling characteristics in the tape drive. Figure 22.4 shows AFM images of a tape for TravanTM Data Cartridges2 , designed for 65 Mbits per square inch. To achieve superior tape handling in the drive, the backside coating for this tape has higher roughness, which enables improved layerto-layer contact to counter the effects of entrapped air during high-speed winding. While tape is wound in roll form, some of this backside roughness can be embossed or transferred to the magnetic coating of the adjacent layer of the tape in the roll, especially under conditions of high temperature and high radial pressure in the roll. While this roughness transfer can be significant, advanced error correction in the drive, as well as lower recording density relative to the previous example, assure the required data reliability in this system. This type of imprinting of features from the backside to the magnetic surface is also common with isolated features. Figure 22.5 shows the effect of very large asperities in the backside coating, which cause corresponding pits in the magnetic coating while wound in a roll and stored at high temperature. In most cases, such pits

Fig. 22.3. AFM images of a data-storage tape designed for 230 Mbits/sq. in. (a) Magnetic surface, Ra = 4.5 nm. (b) Backside surface, Ra = 16.6 nm 1 2

Ultrium is a trademark of Certance, Hewlett-Packard, and IBM. Travan is a trademark of Imation Corp.

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Fig. 22.4. AFM images of a data-storage tape designed for 65 Mbits/sq. in. (a) Magnetic surface, Ra = 8.4 nm. (b) Backside surface, Ra = 76.4 nm. The long-wavelength roughness in the magnetic surface is a result of layer-to-layer contact in roll form, imprinting roughness from the backside coating

Fig. 22.5. (a) AFM image of the backside coating of a magnetic tape. Three very large asperities are seen as white spots and numbered for reference. (b) AFM image of the magnetic surface of this tape, from adjacent wrap on the roll. The large asperities in the backside coating caused corresponding pits in the magnetic coating, in a mirror-image pattern

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are very small and do not have a significant effect on tape performance. However, as the pit diameters approach a significant fraction of the track width, error rates are adversely impacted. In this particular case, the largest asperity in the backside was 9 µm in diameter and 320 nm in height; the corresponding pit in the magnetic surface was 4 µm in diameter and 130 nm in depth. Some additional examples of coating defects are illustrated in Fig. 22.6. A large defect is embedded in the coating in Fig. 22.6a. Wear that occurred during operation in the tape drive is evident on the surface of the defect. This is an indication that the defect is an agglomeration of small particles rather than one very large particle. Another class of defect is illustrated in Fig. 22.6b. The calendering process is designed to impart the smooth surface of the calender rolls to the tape, but in this case, damage to one of the calender rolls has caused a pattern to be imprinted on the tape surface. In most cases, the calender rolls impart no discernible pattern to the tape. However, as tape surfaces continue to get smoother to accommodate ever-higher data densities, the microstructure from the calender rolls, whether it be microcracks or finishing scratches, is visible on the tape surface, as seen in Fig. 22.7. In addition to the magnetic particles in a magnetic tape coating, various other particles are included to contribute to properties such as electrical conductivity, wear resistance and abrasivity [11]. AFM imaging allows visualization of particles on the tape surface. Because some of the latest data-storage tapes employ particles as small as 50 nm in length, high-resolution probes are required. In addition, the surrounding polymeric matrix obscures much of the detail of the individual particles. It is, therefore, advantageous to obtain phase-angle contrast images in intermittent-

Fig. 22.6. Tape defects: (a) Large coated-in defect, subjected to subsequent wear during operation. (b) Impression from damaged calender roll

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Fig. 22.7. Calender marks in a smooth tape, Ra = 2.3 nm. Microcracks from the calender roll are embossed onto the magnetic surface as 3 nm high ridges, which are noticeable only on extremely smooth tape surfaces

contact AFM. This technique is commonly used to enable visualization of polymer structures [12,13]. Damping of the tip oscillation is dependent on the surface viscoelastic and adhesion properties of the material being imaged. In particulate magnetic tapes, this allows one to distinguish particles from the surrounding polymeric matrix. Figure 22.8 is a phase-angle contrast image of a data-storage tape, and reveals the generally acicular particle shape of the magnetic particles in the coating. Kasai et al. [14] demonstrated more detailed phase-angle contrast images using a torsional resonance mode as opposed to an intermittent-contact technique.

Fig. 22.8. AFM phase image of a magnetic tape. Phase-angle contrast reveals hard particles in a polymeric matrix. The generally acicular shape of magnetic particles is evident

22.2.2 Topographic Characterization of Heads In a head for writing and reading information on magnetic tape for data storage, the magnetic transducers are typically embedded in a ceramic structure that is designed to provide minimal wear and optimal contact with the active region of the head. The overall structure is typically that of several rails contoured to a curved shape,

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Fig. 22.9. Head for an Ultrium tape drive. Multiple read/write transducers are positioned in a narrow band on two of the rails. In the drive the head is translated to allow access to the full tape width. The curved surface and transverse slots provide optimal contact between head and tape. Courtesy of R Tapani, Imation Corp.

as for the Ultrium head in Fig. 22.9. The slots between the various rails serve to improve head-tape conformity by reducing the development of an air bearing in the head-tape interface. Multiple read/write transducers are positioned on the head to enable simultaneous writing or reading of as many as 16 tracks on the tape. Figure 22.10 shows an AFM image of an Ultrium head in the region of one of the transducers. Writing is done at the gap between the pole pieces a and b of the magnetic element. Reading is done with a magnetoresistive transducer positioned between pole b and shield c. The region surrounding the magnetic elements is an insulating material, such as Al2 O3 , which is deposited in thin-film form along with the magnetic structure and electrical conductors. The surrounding structure is made from Al2 O3 -TiC, and shows evidence of surface grains of TiC pulled out of the Al2 O3 matrix [15]. Grain pullouts occur in the polishing process during head fabrication, and can continue as part of wear processes during head-tape operation. The loose grains and other debris [16] can abrade the magnetic poles as they are carried across the head, contributing to pole-tip recession (PTR), the amount by which the active magnetic element is recessed below the surface that contacts the tape. Delicate finishing processes are used to provide a uniform surface, although some deviations from the ideal profile are inevitable due to differential wear of various materials with differing hardness.

Fig. 22.10. AFM image of a read/write transducer in an Ultrium tape head. Transducers are built up by thin-film deposition on the Al2 O3 -TiC substrate, followed by bonding to another Al2 O3 -TiC structure. The magnetic poles a and b define the write gap. An MR sensor is deposited in the gap between pole b and magnetic shield c

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Figure 22.11 shows an AFM image of a head that has undergone extended usage in a tape drive. On the alumina surrounding the pole tips, there is evidence of deposits that may have originated in the tape, head, or external environment. With a crosssectional view as in Fig. 22.11b, one can readily measure the size of such deposits, as well as PTR and the grain pullouts in the Al2 O3 -TiC surface. For most tape heads, the surface curvature is very large compared to the surface deviations one wishes to measure. For properly measuring the PTR and other features, care must be exercised in plane-fitting or flattening, so as not to distort the shape. For example, it may be preferable to use only part of the image to determine the surface flattening.

Fig. 22.11. (a) AFM image of an MR head after significant usage. Deposits are evident, especially in the regions surrounding the write gap. (b) Cross-sectional view of the head. Pole-tip recession is 25 nm, measured from the Al2 O3 -TiC surface. The gaps between the magnetic poles are elevated because they are filled with a harder material that is less subject to wear than the poles

22.2.3 Tape Roughness Analysis 22.2.3.1 Sampling Considerations The magnetic tape is coated on a very thin polymeric substrate of only a few microns thickness, and has a surface roughness of only a few nanometers. Unless the tape is mounted very flat, distortions in the tape surface can be a significant fraction of the measured surface roughness. A double-adhesive tape on polymer film provides better

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flatness than one mounted on a paper carrier, which in general is too non-uniform in its thickness. Using a thin liquid adhesive would also achieve the desired flatness. Even with the most careful of mounting, some residual distortion may exist in the sample. This can be corrected with the plane-fitting and/or flattening routines in the AFM software. Plane-fitting corrects the curvature of the overall image, while flattening corrects each individual scan line. For either type of correction, features such as very large peaks or very deep pits that are well beyond the extremes of the main portion of the surface should be excluded from the region used to compute the flattening correction, to avoid distortion of the image. In plane-fitting or flattening an image, some judgments are necessary concerning the appropriate order of fit to be used and what features are properly considered as characteristic of the surface (as opposed to a distortion from mounting the sample). Also, the likely effect of such distortions on the head-tape spacing needs to be considered. For example, a tape may be seriously distorted due to wound-in debris. Since this is a “real” feature rather than a mounting artifact, the analyst might choose not to filter it out of the image. On the other hand, knowledge of the particular headtape interface may suggest that such distortions would be flattened out by the head, and thus would cause no functional problem. In such a case, the analyst interested in effects on head-tape spacing may prefer to remove the distortion from the AFM image, even if it is “real”. Distortions in this category would include those with a long wavelength relative to the thickness of the tape. The size of the contact zone of the head relative to the wavelength of the distortion would be another consideration. Meaningful roughness statistics require a scan size large enough to representatively include sparse features. For example, if a magnetic tape surface includes some isolated large asperities, a scan that only includes one or two of these asperities may provide roughness statistics that are not representative of the tape surface. This is especially true in the case of kurtosis, which will be discussed below. If these isolated features are too sparse even for the largest available scan size, averaging of multiple measurements is necessary. 22.2.3.2 Amplitude Parameters Surface roughness can broadly be characterized by amplitude parameters, which describe deviations from an ideally smooth surface, and texture parameters, which describe the spatial frequency content of the surface. High-density recording of information on magnetic tape requires very close head-tape spacing. Although a magnetic tape may be considered to be in contact with the head, the effective spacing is limited by the surface roughness. This effective spacing is determined by the roughness of the tape surface, which in general is much rougher than the head surface. This contact is illustrated in Fig. 22.12, which shows a smooth surface forced with load W against a rough surface. For the light load in this example, the smooth surface is supported by the highest peaks in the height distribution. Several amplitude parameters are useful for characterizing the surface roughness and its effect on head-tape spacing. The extreme-value parameters measure the total extent of the surface. For example, the height difference between the highest peak

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Fig. 22.12. Schematic representation of the contact between a rough surface and a smooth surface [7]

and the lowest valley is designated as Rt [17]. This is not particularly useful or representative of the surface, so it is more common to use Rz , which is the height difference between the average of the five highest peaks and the average of the five lowest valleys. A related parameter, Rpm , is the height difference between the average of the five highest peaks and the mean surface. Even with the use of five separate peaks and valleys, extreme-value parameters are rather unrepresentative of the surface as a whole, and numerous measurements are required to provide useful results. Furthermore, some ambiguity exists in the definition of a peak. Whether small local maxima are counted as peaks depends on the sampling interval and quantization level. Thus great care is needed in interpreting extreme-value roughness measurements. Parameters that are much more representative and repeatable are average parameters, such as Ra and Rq . The arithmetic average roughness Ra is given by Ra =

n 1 |Z i − Z M | , n i=1

(22.1)

where the summation is over both x and y directions, n is the total number of data points in the AFM image, Z i is the height of each data point, and Z M is the height of the mean plane. The rms roughness Rq is given by  n 1 (Z i − Z M )2 . (22.2) Rq = ! n i=1 Rq or Ra is commonly used to describe the surface roughness with a single number, but use of various distribution parameters provides additional information that provides a better understanding of the surfaces and their effect on recording performance and the head-tape interface.

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Consider the distribution of point heights about the mean surface. For many surfaces, the point-height distribution approximates the Gaussian distribution  2 −z 1 p(z) = √ exp , (22.3) 2σ 2 σ 2π where the standard deviation σ is identical to the rms roughness Rq . Figure 22.13 shows the point-height distribution for an AFM image of a magnetic tape surface that is very close to a Gaussian distribution. The highest points on the surface with appreciable probability density are at about three to four times the standard deviation σ or Rq . In a Gaussian distribution only 0.3% of points are above 3σ, and 0.003% of points are above 4σ. Because of the very light contact forces between head and tape, head-tape spacing is determined by the highest peaks that represent an extremely small fraction of the surface area, and is often in the range of three to four times Rq . However, quite small deviations from the ideal Gaussian distribution, e.g. a few large asperities, can have dominant effects on the head-tape spacing, so Rq alone should not be used to predict the spacing. Deviations from a Gaussian distribution are seen in skewness and kurtosis. They quantify observations of pits, peaks and defects that stand out from the general surface in the AFM image. The skewness is given by Rsk =

n 1  (Z i − Z M )3 . n Rq3 i=1

(22.4)

For a Gaussian or other symmetric surface distribution, Rsk = 0. An otherwise symmetric surface with a number of deep pits will have negative skewness, and an otherwise symmetric surface with a number of large asperities will have positive skewness. The kurtosis is given by Rku

n 1  = (Z i − Z M )4 . n Rq4 i=1

Fig. 22.13. Histogram of point heights from AFM of the tape surface, compared with Gaussian distribution

(22.5)

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For a Gaussian distribution, Rku = 3. Because of the fourth-order dependence, a small number of asperities that are very high compared to Rq (or pits that are very deep compared to Rq ) can greatly increase the kurtosis. In fact, a single deep pit or tall asperity can result in large kurtosis. As a result, a large scan size or a large number of scans is necessary for a representative value of kurtosis. Incomplete dispersion of the particles during the preparation of the magnetic coating can give rise to occasional large asperities that contribute to high kurtosis, and more importantly, increased head-tape spacing. It is also common in some magnetic tape surfaces to have high kurtosis by design. For example, a small quantity of rather large particles can be incorporated into an otherwise smooth coating to optimize other properties such as friction. These sparse particles act as load-bearing particles, and reduce the real area of contact and thus the friction. This is illustrated in Fig. 22.14, which shows an AFM image of a floppy disk coating, for which skewness and kurtosis were 0.4 and 4.3, respectively. The large asperities (white regions) reduce the friction between head and medium, thus reducing the motor torque required to spin the disk. To understand the suitability of the tape surface as a bearing surface, such as wear resistance, friction, and head-tape spacing, it is useful to perform bearing analysis on the topographical data. The bearing ratio is the fraction of material that intersects a plane at a given height. The bearing ratio curve, a plot of bearing ratio vs. the height of the intersecting plane, is shown in Fig. 22.15. This curve has a relatively straight section in the center, with deviations on the far left due to peaks, and on the far right due to valleys. The bearing ratio is an approximation to the percent contact area between head and tape for a given head-tape separation [18]. Contact between head and tape is very light, resulting in very small contact area represented by the extreme left end of the curve. For example, one might pick a value for bearing ratio, and compare the height of the intersecting plane for various tapes as a measure of the head-tape spacing one would expect in those tapes. The bearing ratio curve can be quantified with the parameters Rk , Rpk and Rvk , which describe the core roughness, peak height, and valley depth, respectively [17, 19]. Although the various topographic parameters have utility in predicting head-tape spacing and real area of contact, they are necessarily approximate. Bearing analysis

Fig. 22.14. Load-bearing particles in a floppy-disk coating. Lightest (highest) spots are due to large particles incorporated into the coating to reduce head-medium friction

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Fig. 22.15. Bearing ratio curve for a magnetic tape surface

only looks at slices of the surface. A more thorough analysis must take into account the material deformation, employing various models of contact mechanics [20]. For example, a model for surface contact that has proven to be very useful is that of Greenwood and Williamson [21], who extended the single-contact Hertzian equations to include many contacts. This model views the surface as comprising a large number of asperities, all with the same radius of curvature at the summit, with heights that vary randomly with a Gaussian distribution. Despite its highly simplified representation of the surface, it has provided good insights into countless contact problems. For example, it has been used to compute the relationship between contact pressure and the mean separation between surfaces, as shown in Fig. 22.16, as well as the real area of contact, which relates to surface friction [22]. The Greenwood–

Fig. 22.16. Relation between head-tape separation and apparent contact pressure, computed from the Greenwood–Williamson contact model [22]

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Williamson model has been used in computer models of the head-tape interface to include contact forces along with air-bearing and tape deflection equations [23]. Other numerical approaches have employed more generalized models for the surface without the simplifying assumptions of Greenwood and Williamson [24]. To complement this theoretical approach, an experimental method for determining the head-tape spacing as a function of the normal applied pressure is the measurement of “asperity compliance”. The tape is forced against a glass plate with known values of pneumatic pressure, and spacing between the glass and the mean tape surface is measured using optical interferometry [25]. Such measurements have provided a link between tape surface roughness, contact pressure, and head-tape spacing [26]. Asperity compliance measurements have been correlated to experimental head-tape spacing measurements over a range of tape surface roughnesses measured by AFM [27]. 22.2.3.3 Texture Parameters Analysis of the spectral content of the surface topography is useful in determining its effect on signal fluctuations, or noise, in the magnetic recording tape. Applying the autocorrelation function (ACF) to AFM data is useful in relating noise in magnetic recording to surface topography. In addition to the roughness amplitude, a parameter that is found to be important in determining the contribution of surface texture to the noise is the correlation length [28], which is defined as the length over which the ACF decays to some fraction (commonly 0.1 or 1/e) of its initial value. The correlation length provides a measure of the spatial frequency content of the surface. Topographic factors that contribute to the noise are surface roughness (with short correlation length) and surface asperities (with long correlation length). Even nonmagnetic asperities can make a significant contribution to tape noise, by causing intermittent separation or “tenting” of the surrounding region of the tape as it passes over the head [29–31]. This causes a fluctuation in the depth of recording, which can result in undesirable variations in signal amplitude or timing. Surface texture parameters are also important in understanding contact mechanics between the head and tape. For example, the Greenwood–Williamson model mentioned above employs a value for the radius of the curvature of summits in a given surface. However, for real surfaces, the summit radius is highly dependent on the scale of measurement, and does not have a unique value [32]. It is, therefore, useful to employ fractal analysis of topographical data [33, 34]. Fractal surfaces have the property of self-similarity; i.e. they have similar appearance at any scale of magnification, as seen in Fig. 22.17. However, this self-similarity is over a finite range of scales. Furthermore, surfaces subjected to wear or multiple processes will be multi-fractal [35], with a transition point called a corner frequency [36]. This can be useful in analyzing the various manufacturing and wear processes that a magnetic tape is subjected to. The amplitude and texture parameters derived from AFM images of magnetic and backside surfaces provide useful criteria for the quality of the magnetic tape. Parameters such as rms roughness, skewness, kurtosis, and correlation length provide measurable criteria for optimizing a tape formulation for head-tape spacing and real

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Fig. 22.17. Self-similarity of a surface at various scales of magnification [7]

area of contact [37]. In the case of tapes made by thin-film deposition (e.g. evaporation or sputtering), the required surface texture can be achieved by incorporation of protrusions in the base film [38]. From the initial product design to maintenance of manufacturing consistency and evaluation of product defects, AFM roughness data is of critical importance.

22.3 Magnetic Force Microscopy 22.3.1 Methodology Since the early 1990’s magnetic force microscopy (MFM) has developed into a widely-used method for the characterization of magnetic materials and devices, with important applications in the magnetic recording industry [39]. Continued development of MFM methodology, particularly in the area of probe preparation, has achieved resolution of the order of 20 nm [40]. Some of the methods for highresolution probes include electron beam deposition of “spike tips” [41–43], ion beam modification of tips [44, 45], and attachment of carbon nanotubes [46]. MFM uses a tip that is coated with a thin film of magnetic material, and typically employs methods such as TappingModeTM and LiftModeTM techniques3 to provide both topographic and magnetic images from interleaved scans of the region under investigation. After each tapping-mode pass, the probe is lifted just above the sample surface, and the topography is replayed while being monitored for magnetic forces on the tip. Ideally, the topographic and magnetic images are independent of one another, but topographic features can interfere with the magnetic image, for example on weakly magnetized samples. This interference also increases as the lift height is lowered to improve lateral resolution. MFM tips are available with high coercivity (e.g. CoCr, CoCrPt) and low coercivity (e.g. FeNi, FeCoNi) materials. Common values of coercivity are 300–400 Oe for CoCr tips and 1–5 Oe or less for low-coercivity tips. There are also reports of superparamagnetic [47, 48], paramagnetic [49], and antiferromagnetic [50] MFM tips. The proper tip choice depends upon the requirements of a given study. In most 3

TappingMode and LiftMode are trademarks of Veeco Instruments Inc.

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cases, a standard high-coercivity CoCr-coated tip is suitable for MFM investigations of magnetic tapes. Interaction of the magnetic tip with the sample is quite complex, and this complexity extends to the interpretation of MFM images. The magnetic force is not simply proportional to the stray field resulting from the sample magnetization, but is also sensitive to higher spatial derivatives of the field components. When imaging recorded tracks on a magnetic tape, the first step is to locate the magnetic features of interest. If the track format is known, one often only needs to move a known distance from the tape edge to locate the track in question. Alternatively, the recorded tracks can be revealed with a colloidal suspension of small magnetic particles called a Bitter solution [51]. When the solution is applied to the tape sample, the particles are attracted to locations of high magnetic field gradient (i.e. recorded transitions) and remain in place when the solution dries, providing a visible magnetic pattern. The Bitter solution allows rapid large-scale examination of recorded features, which can then be examined more closely and quantitatively with MFM. The Bitter technique locates the transitions, but provides no quantitative intensity information. MFM provides a measure of intensity as well as higher lateral resolution. Figure 22.18 shows a low-power optical image of a Bitter pattern of recorded tracks on a magnetic tape. The angular orientation alternates from track to track in this particular tape format in order to minimize signal interference due to track misregistration. If the playback head is positioned partially on an adjacent track, the angular mismatch attenuates the interfering signal.

Fig. 22.18. Bitter pattern of tracks recorded on a magnetic tape. Courtesy of TD Depuydt, Imation Corp.

22.3.2 Characterization of the Magnetic Tape with MFM There is a wide range of information available in an MFM image of a data track. Figure 22.19a shows the edge of a relatively low-density data track. One can clearly see the transitions between bits as either light or dark vertical lines. If one closely looks at the edge of the track, one can see additional low-level magnetic features

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beyond the track edge. This is written by the fringe field of the magnetic head, and is sometimes called side writing. The size and amplitude of side writing will depend on the physical geometry of the edge of the trailing pole of the head, the current used to write, and the coercivity and orientation of the media. Also clearly evident in this MFM image is a grainy background pattern. This is due to the discrete structure of the media, and is exhibited in the playback signal as noise. The graininess has very different levels of in the areas within the track and outside the track, which relates to different levels of noise in recorded data. This can be quantified by a “surface roughness” of the phase image: the variation in phase within a given region. Comparing the phase variation in the two rectangular regions in Fig. 22.19a, the rms variation in the on-track region is 1.4 times as great as that in the off-track region. This difference arises because the area outside the track is in an AC-erased (“degaussed”) magnetic state, while the region inside the track is in a DC-saturated state.

Fig. 22.19. (a) MFM phase image at the edge of the recorded track. White boxes indicate regions for measurement of variation in the MFM phase. Variation (noise) in the on-track region was 1.4 times as great as in the off-track region. (b) Cross-sectional view of this MFM image along a single line gives a very noisy signal. (c) Averaging of this cross-sectional view over a 12 mm width reduces the noise level in the same manner as a wide read head width reduces noise

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Fig. 22.20. AFM topography and MFM phase-angle images of a DC-saturated magnetic tape. Light and dark domains in the MFM image are evidence of magnetic clustering of particles, which contributes to noise in recording systems

A cross-sectional view of the recorded track is shown in Fig. 22.19b for a single scan line, which gives a very noisy signal. Averaging over a 12 µm width as in Fig. 22.19c significantly reduces the noise level, as would a read head of this width. Another way to quantify the graininess in the MFM image is through the cluster size of magnetic aggregates in the coating. Chen et al. [52] and Takahashi et al. [53] related such cluster sizes to medium noise in thin-film recording media. In the particulate magnetic tape, Ozawa et al. [54] used the number of magnetic aggregates above 0.5 µm in size as a criterion for the uniformity of dispersion of magnetic particles. This magnetic aggregation can be studied for particular magnetic states of a magnetic tape, as a part of understanding their effects on tape noise. Figures 22.20, 22.21, and 22.22 show AFM and MFM images of the same tape in three different magnetization states. In the DC-saturated state, the sample is magnetized with a strong magnetic field in the longitudinal (tape motion) direction. In the DC-demagnetized state, the sample is first DC saturated, and then a field is applied in the opposite direction, just strong enough to reduce the remanent magnetization to zero. In the AC-demagnetized state, the sample is subjected to an alternating field that is initially strong enough to saturate the sample magnetization, and which is gradually reduced to zero. Distinct magnetic aggregation is observed in the DC-saturated sample, and to a lesser degree in the DC-demagnetized sample. In the AC-demagnetized sample, there is less evidence of magnetic aggregation, owing to the finer-scale demagnetiza-

Fig. 22.21. AFM and MFM images of a DCdemagnetized magnetic tape. Less magnetic clustering is evident than in the saturated state

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Fig. 22.22. AFM and MFM images of an ACdemagnetized magnetic tape. No significant magnetic clustering is evident, due to the thorough demagnetization. Significant interference of topographic data is evident in the MFM image due to weakness of the magnetic forces

tion that results from a decaying alternating field. In addition, the effect of topography is more evident in this MFM image. With the weaker magnetic effect of this sample, it becomes more difficult to separate the magnetic and topographic effects. In thin-film recording media, as opposed to particulate media, the fluctuations contributing to the noise are concentrated near the recorded transitions. Analysis of such transitions has yielded good correlation between MFM image data and signal-to-noise ratio in thin-film recording media [55]. Another important use of the MFM in the magnetic tape industry is the analysis of servo tracks that enable reliable tracking at the high track densities of modern datastorage tapes. Early magnetic tapes had a very low track density, and referencing the data track locations to the edge of the tape provided sufficient accuracy. With the high track density of modern data-storage tapes, a pre-recorded servo pattern is written on the tape to provide a more precise means of locating data. On the head, in addition to transducers for writing and reading data tracks are special elements called servo readers, which are designed to read the servo pattern. The head is on an actuator that moves transverse to the tape motion direction. The servo pattern is constructed in such a way as to allow determination of the transverse location of the servo reader. A schematic of an amplitude-based servo pattern is shown is Fig. 22.23. It consists of recorded and erased regions. The relative amplitude of the two regions is an indicator of the position of the head relative to the tape. In this example, the signal alternates between 100% and 20% of full amplitude when the servo reader is at position 1, between 100% and 50% at position 2, and between 100% and 80% at position 3. There are many other approaches to servo pattern design, some of which rely on the timing rather than the amplitude of recorded pulses in the servo pattern. The servo tracks need to be written very precisely, since any defect or unexpected change in the pattern will cause tracking problems for the tape drive. Specifications for the physical dimensions and amplitude of the recorded and erased regions assure an operating window in which deviations from the ideal do not introduce excessive tracking errors. An example of an MFM image of part of a servo track is shown in Fig. 22.24. A residual signal in the erased region of the track is clearly evident. The peak-to-peak phase signal in the erased region is about 8% of the original written signal. This incomplete erasure could introduce a slight error in the track position if the servo system is not designed for it.

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Fig. 22.23. Schematic of servo track, showing servo signals for 3 positions of the servo reader. This type of servo system uses the relative amplitude of the full and partially recorded regions as a measure of servo reader position

Another type of defect in the servo pattern can occasionally occur when some debris collects on the head that writes the servo track. This causes a small region of low amplitude in the servo track. This is referred to as an unrecorded line in the servo track. Figure 22.25 is an MFM image of an unrecorded line, which shows a 50% drop in the MFM phase signal, and is about 5 µm wide. This defect can significantly affect the amplitude of the servo signal in this region, with the result that the servo reader will improperly position the head. MFM has been useful in the study of magnetization and erasure processes in recording media. Jander et al. [56] used successive MFM images of recording media

Fig. 22.24. (a) MFM image of a portion of a servo track. (b) Cross-sectional view showing residual signal in the erased region

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Fig. 22.25. Unrecorded line defect in the servo track, due to deposit on the servo-writing head that caused local spacing loss. Such a defect can result in tracking errors

after the application of increasing magnetic fields to reveal (a) micromagnetic structure underlying various states of remanent magnetization and (b) demagnetization of a recorded transition. Proksch et al. [57] and Kuo et al. [58] applied in-situ magnetic fields in an MFM to study the erasure process. As the magnetic field was increased, the degradation and eventual erasure of recorded patterns on magnetic recording media were observed. Walsh et al. [59] used MFM to image the slow dynamics of the micromagnetic structure in magnetic media in an applied field. In the presence of external applied fields, it is desirable for the coating on the MFM tip to have much higher coercivity than the sample for minimal influence by the applied field, or much lower coercivity than the sample, so the tip is always aligned with the applied field. MFM offers a high-resolution method of analyzing recorded tracks on magnetic media. Liu et al. [60] used MFM to quantify curvature in recorded transitions to nanometer accuracy. This provides an improvement over attempts to study this curvature with a read sensor, which is much larger than the MFM tip dimension. Li et al. [61] achieved similar accuracy using MFM to measure written track distortions induced by stray fields from the media. 22.3.3 Characterization of Heads with MFM MFM has also proven to be very useful in the imaging of magnetic fields from recording heads. High recording density requires recording heads that can produce high magnetic fields with a sharp gradient and good high-frequency response, so the high resolution capability of MFM is critical in measuring the lateral extent of head fields. Figures 22.26 and 22.27 illustrate some of the capabilities of MFM for analysis of head fields [62]. Figure 22.26a shows an MFM image of a MIG head, with metal on the right side of the gap and ferrite on the left side. Peaks resulting from the magnetic field in the head are seen on both sides of the gap. On the ferrite side, the peak gradually decreases toward the track edge, due to degradation of the magnetic field at the edge of the ferrite. MFM is useful for directly observing the onset of saturation of the magnetic structure. As the write current is increased, saturation begins at the corners of the gap. Analysis of read-write data in a drive provides only a coarse approximation to

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Fig. 22.26. MFM images of recording heads [62], © 1991 IEEE. (a) MFM image of an MIG head, coil current IC = 20 mA dc. The peak height gradually decreases toward the track edge on the ferrite side, while it drops sharply on the metal side. (b) Coil current dependence of the MFM image of the MIG head. Saturation is seen on the ferrite side. A small peak is also seen at the metal-ferrite interface

the onset of saturation, since it is the result of integration over the whole magnetic structure. MFM, on the other hand, is capable of quantifying saturation with high lateral resolution [63]. It is particularly useful for heterogeneous head constructions, such as MIG heads, in analysis of magnetic effects at the material interfaces. Figure 22.26b shows the dc current dependence of the MFM image of a MIG head, measured at the center of the track, with no scanning in the y direction. At low current, the peaks for the ferrite and metal side are about equal, but at currents of 30 mA and above, saturation on the ferrite side is observed, while the peaks on the metal side continue to grow, due to the higher saturation magnetic flux density of the metal. MFM is capable of imaging the spatial dependence of head fields, not only for heads energized with a static current (DC), but at the high frequencies used in recording as well. Figure 22.27a shows the dependence of the MFM image on coil current frequency for a MIG head. At 5 to 10 MHz, the image is very similar

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Fig. 22.27. MFM images of recording heads [62], © 1991 IEEE. (a) Coil current frequency dependence of the MFM image of the MIG head. IC = 40 mA p–p. This head cannot excite an ac magnetic field beyond 30 MHz. Large peaks around 20 MHz are considered to be caused by electrical resonance. (b) The coil current frequency dependence of the MFM image of a thin-film head. IC = 40 mA p–p

to the dc case. Large peaks are observed in the range of 15 to 20 MHz, due to an electrical resonance. At higher frequency, the peaks begin to decrease, disappearing completely at about 30 MHz, which is beyond the write capability of this head. By contrast, a thin-film head, seen in Fig. 22.27b, shows a slowly decreasing peak height out to 50 MHz. This curve is consistent with earlier measurements of the frequency dependence of thin-film heads [64], which is evidence that the MFM technique is useful up to at least 50 MHz, and thus able to identify recording frequency limitations that are inherent in head constructions such as the MIG head. More recent work has pushed this capability to higher frequency [65–67]. The above analysis used the response of an MFM probe to applied current in a head. It is also possible to invert this analysis, using the MFM probe as a magnetic

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source and measuring the signal induced in the head. This allows analysis of heads in a read rather than write mode. Gibson et al. [68] used MFM to spatially map the sensitivity of read heads, both inductive and magnetoresistive.

22.4 Conclusions In the magnetic tape industry, AFM is an important tool for routine, as well as nonroutine analysis. The routine measurement of roughness by AFM is an indispensable part of developing new magnetic tape products and in maintaining quality control on existing products. Optical profiling methods provide greater measurement speed, which is useful for high-volume roughness data in a factory environment. The AFM, however, offers superior lateral resolution, which is required for surfaces with features that are too fine for the optical profiler [7]. On a routine basis, statistics like Ra , Rq , skewness and kurtosis provide an overview of the surface roughness that lends itself well to a database for product development or production control purposes. Measurements of kurtosis, and to a lesser degree, skewness, can be greatly affected by outliers in the sample, i.e. a small number of large asperities or deep pits. Thus, care is needed to assure that the scan size and number of images measured per sample is sufficient to provide representative data. The ability of AFM to provide accurate quantitative measurement of extremely small features makes it ideally-suited for analysis of defects and wear in tape and heads, which contribute to increased noise and errors in recorded data. At the very high recording density that is common today, defects of only a few nanometers in height can cause significant error problems. The capabilities of MFM continue to grow, and provide a tool that is useful for the tape and heads. In the tape, the detail that MFM provides in the study of recorded features has allowed a greater understanding of the recording process, e.g. in the shape of transitions and in underlying noise levels. In heads, the high-resolution imaging of head fields has provided deeper understanding of the write and read process, and guidance in the design of advanced heads. Acknowledgements. The author wishes to acknowledge the support of Imation Corp. while he was employed there until retirement. Excellent collaboration with fellow members of the Analytical Laboratory at Imation and helpful discussions with Paul Iverson and Chris Merton of Imation are gratefully acknowledged.

References 1. Jones RE, Mee CD, Tsang C (1996) Recording heads. In: Mee CD, Daniel ED (eds) Magnetic recording technology, 2nd edn. McGraw-Hill, New York 2. Bhushan B (1996) Tribology of the head-medium interface. In: Mee CD, Daniel ED (eds) Magnetic recording technology, 2nd edn. McGraw-Hill, New York 3. Mallinson JC (1993) The foundations of magnetic recording, 2nd edn. Academic Press, San Diego 4. Jorgensen F (1995) The complete handbook of magnetic recording, 4th edn. TAB Books, Blue Ridge Summit, PA

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5. Mee CD, Daniel ED (1996) (eds) Magnetic recording technology, 2nd edn. McGraw-Hill, New York 6. Bhushan B (1990) Tribology and mechanics of magnetic storage devices. Springer, Berlin Heidelberg New York 7. Bhushan B (1999) Principles and applications of tribology. Wiley, New York 8. Richards DB, Sharrock MP (1998) IEEE Trans Magn 34:1878 9. Inaba H, Ejiri K, Abe N, Masaki K, Araki H (1993) IEEE Trans Magn 29:3607 10. Saitoh S, Inaba H, Kashiwagi A (1995) IEEE Trans Magn 31:2859 11. Bhushan B, Khatavkar DV (1995) Wear 190:16 12. Magonov SN, Reneker DH (1997) Annu Rev Mater Sci 27:175 13. Magonov S (2004) Visualization of polymer structures with atomic force microscopy. In: Bhushan B, Fuchs H, Hosaka S (eds) Applied scanning probe methods. Springer, Berlin Heidelberg New York 14. Kasai T, Bhushan B, Huang L, Su C (2004) Nanotechnology 15:731 15. Sourty E, Sullivan JL, De Jong LAM (2003) IEEE Trans Magn 39:1859 16. Tsuchiya T, Bhushan B (1995) Tribol Trans 38:941 17. Thomas TR (1999) Rough surfaces, 2nd edn. Imperial College Press, London 18. Greenwood JA (1967) ASME J Lub Technol 89:81 19. Mummery L (1990) Surface texture analysis: the handbook. Hommelwerke, Mulhausen 20. Johnson KL (1985) Contact mechanics. Cambridge University Press 21. Greenwood JA, Williamson JBP (1966) Proc R Soc London Ser A 295:300 22. Bhushan B (1984) ASME J Trib 106:26 23. Wu Y, Talke FE (1996) IEEE Trans Magn 32:160 24. Bhushan B (1998) Tribol Lett 4:1 25. Lacey C, Talke FE (1992) ASME J Trib 114:646 26. Tan S, Talke FE (1999) IEEE Trans Magn 35:770 27. Tan S, Talke FE (1999) IEEE Trans Magn 35:2382 28. Lin GH, Xing X, Johnson KE, Bertram HN (1997) IEEE Trans Magn 33:950 29. Bertram HN (1994) Theory of magnetic recording. Cambridge University Press 30. Coutellier J-M, Bertram HN (1987) IEEE Trans Magn 23:195 31. Roesler A, Zhu J-G (2001) IEEE Trans Magn 37:1059 32. Ganti S, Bhushan B (1995) Wear 180:17 33. Majumdar A, Bhushan B (1991) ASME J Trib 113:1 34. Khamesee MR, Kurosaki Y, Matsui M, Murai K (2004) Mater Trans 45:469 35. Russ JC (1994) Fractal surfaces. Plenum Press, New York 36. Majumdar A, Tien CL (1990) Wear 136:313 37. Bhushan B (1996) IEEE Trans Magn 32:1819 38. Sato S, Arisaka Y, Matsumura S (1999) IEEE Trans Magn 35:2760 39. Rugar D, Mamin HJ, Guenther P, Lambert SE, Stern JE, McFryden I, Yogi T (1990) J Appl Phys 68:1169 40. Koblischa MR, Hartmann U (2003) Ultramicroscopy 97:103 41. Ruhrig M, Porthun S, Lodder JC, McVitie S, Heyderman LJ, Johnston AB, Chapman JN (1996) J Appl Phys 79:2913 42. Ruhrig M, Prothun S, Loder JC (1994) Rev Sci Instrum 65:3224 43. Skidmore GD, Dahlberg ED (1997) Appl Phys Lett 71:3293 44. Phillips GN, Siekman MH, Abelmann L, Lodder JC (2002) Appl Phys Lett 81:865 45. Liu Z, Dan Y, Jinjun Q, Wu Y (2002) J Appl Phys 91:8843 46. Wastlbauer G, Skidmore GD, Merton C, Schmidt J, Dahlberg ED, Skorjanec J (2000) Appl Phys Lett 76:619 47. Hopkins PF, Moreland J, Malhotra SS, Liou SH (1996) J Appl Phys 79:6448 48. Liou SH, Malhotra SS, Moreland J, Hopkins PF (1997) Appl Phys Lett 70:135

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49. Teschke O (2001) Appl Phys Lett 79:2773 50. Wu Y, Shen Y, Liu Z, Li K, Qiu J (2003) Appl Phys Lett 82:1748 51. Craik DJ (1994) The observation of magnetic domains. In: Coleman RV (ed) Methods of experimental physics, vol 11. Academic Press, New York 52. Chen J, Saito H, Ishio S, Kobayashi K (1999) J Appl Phys 85:1037 53. Takahashi M, Kikuchi A, Hara H, Shoji H (1998) IEEE Trans Magn 34:1573 54. Ozawa T, Doushita H, Harasawa T (2004) US patent 6,713,171 55. Svedberg EB, Khizroev S, Litvinov D (2002) J Appl Phys 91:5365 56. Jander A, Dhagat RS, Indeck RS, Muller MW (1998) IEEE Trans Magn 34:1657 57. Proksch R, Runge E, Hansma PK, Foss S, Walsh B (1995) J Appl Phys 78:3303 58. Kuo HV, Merton C, Dahlberg ED (2001) J Magn Magn Mater 226:2046 59. Walsh B, Austvold S, Proksch R (1998) J Appl Phys 84:5709 60. Liu F, Li S, Liu Y, Gray G, Schultz A (2002) J Appl Phys 91:6842 61. Li S, Zhu W, Wang L, Palmer D (2003) J Appl Phys 93:8531 62. Wago K, Sueoka K, Sai F (1991) IEEE Trans Magn 27:5178 63. Bailey W, Wang SX, Cain WC (1995) IEEE Trans Magn 31:3120 64. Hoyt RF, Helm DE, Best JS, Horng CT, Horne DE (1984) J Appl Phys 55:2241 65. Proksch R, Neilson P, Austvold S, Schmidt JJ (1999) Appl Phys Lett 74:1308 66. Abe M, Tanaka Y (2001) J Appl Phys 98:6766 67. Abe M, Tanaka Y (2002) IEEE Trans Magn 38:45 68. Gibson GA, Schultz S, Carr T, Jagielinski T (1992) IEEE Trans Magn 28:2310

Subject Index

abalone nacre, II 110 activation energy, III 89 active near-field optical probes, II 178 actuation, IV 251 adhesion, III 272, III 282, III 300, III 303–305, III 309, III 313, III 316, III 323 adhesion corrected, III 99 adhesion length, III 283 adhesion meter (CAM), III 306 adhesion paradox, III 283 adhesives, III 31 adsorbed layers, III 284 Al2 O3 , III 42 alkane derivative, IV 170, IV 171 n-alkane derivatives, IV 167 amino acid, IV 174 Amontons’ law, III 272 amplitude modulation, II 1 analytical technique, II 381 anharmonic signals, II 23 antenna structures, II 177 aperture, III 236 aperture-based near-field optical probes, II 175 apertureless near-field microscope, III 235 apertureless SNOM, III 236, III 242 array of silicon cantilever, II 169 artifacts, III 242 artificial hip joints, III 286 asperity, III 346–348, III 352, III 354–357, III 367 asphalt, III 287 atom orbitals, III 45 atomic force microscopy (AFM), II 1, II 143–147, II 149, II 152, II 155, II 158, II 159, II 161, II 165, III 28, IV 251 AFM tips, III 288 AFM topographies, III 270 AFM based lithography, IV 105

blunt AFM tips, III 289 dynamic AFM, II 1 α atoms, III 41 β atoms, III 41 autocorrelation function (ACF), III 357 auxiliary electrode, II 187 average, III 353 barium titanate, III 240, III 250 barrier-hopping fluctuations, III 100 basic principles of STM and STS, III 185 bearing ratio, III 355 benthic, III 30 bias-induced nanofabrication, IV 107 bidirectional optical lever, III 225 binary mixture, IV 170 biochemical sensors, II 185 biocompatibility, III 286 biology, III 283 biomineralization, II 109 biomolecules, II 183 bipyridyl, IV 167 bitter pattern, III 359 blind friction calibration, III 93 boron carbide, III 286 boundary conditions, II 6 bow-tie antenna, II 177 BSE, III 34 buckling, III 227 calender, III 348 calendering, III 345, III 348 calibration of lateral forces, III 93 calix[8]arene, IV 163 calorimetry, IV 252 CAM, III 306 canticlever concept, II 195 cantilever bending, III 222 dynamics, II 33

372 probes, II 165 cantor set, III 280 capacitance, III 231 capacitive forces, III 233 capillary neck, III 103 carbon, II 170 clusters, III 270, III 272 nanotube, II 170 nitride, III 286 thin films, III 270 carrier lifetime, II 181 cavity model of elastic-plastic indentation, III 117 cells, III 287 in vivo, III 28 channelling contrast, II 367 chaperones, III 34 characterization of the magnetic tape with MFM, III 359 charge carrier transport, III 109 chemical force mapping, II 183 chemical force microscopy (CFM), II 183 chemical functionalization, II 183 chemical mapping, II 184 chromatic aberration, II 364 cluster-assembled, III 269 co-adsorbed, IV 167 collocated systems, II 6 colloidal probes, III 291 commensurate, III 288 compliance, II 167 confined polymer systems, III 85 confocal scanning optical microscopy (CSOM), III 238, III 245 time-resolved CSOM, III 241 contact area, III 299, III 302, III 308, III 309, III 311 junctions, III 274 mechanics, III 90 mode, III 220, III 221, III 225 potential, III 222 potential difference (CPD), III 223, III 231 pressure, III 117 problem, III 303 stiffness, II 8 contamination needles, II 193 continuum models, III 288 contrast, III 229 mechanisms, II 367 converse piezoelectric effect, III 220

Subject Index cooperative molecular motion, III 107 cooperatively rearranging regions (CRRs), III 103 cooperatively rearranging regions (CRRs), III 85 coronene, IV 162 correlation length, III 357 corrosion phenomena, II 189 Coulomb explosion, III 43 creep models, III 100 Creutzfeldt-Jakob disease, III 33 vCJD, III 34 critical wavelength, II 193 cryoelectron microscopy, III 35 current vs. distance (IZ) curve, II 97, II 101 cut-off effect, II 175 data storage devices, II 169 Deborah number, III 105 decacyclene, IV 162 defect characterization, II 388 deformation, III 300, III 306, III 309, III 316, III 323 dendrimers, IV 23 Derjaguin–Muller–Toporov (DMT), II 7 detachment stress, III 282 detection of higher eigenmodes, II 20 device fabrication, II 395 device under test (DUT), II 179 dewetting kinetics, III 110 diamond, II 167 probes, II 171 diamondlike, III 286 diatoms, III 28 dielectric permittivity, III 233 diffusional shielding, II 188 dimensional constraints, III 109 dip-pen nanolithography (DPN), IV 2, IV 105, IV 251 Dirac’s delta function, II 181 direct writing, IV 8 directional diffusion, IV 176 disentanglement barriers, III 111 dissipation, III 274 lengths, III 108 dissipative, III 231 distribution of heights, III 264 DLC coating, III 322, III 323 DMT model, III 303 DNA, IV 8 domains, III 229

Subject Index boundary, III 227, III 234 contrast, III 221–223, III 225, III 235–237, III 239, III 245, III 250 structure, III 218, III 235–237, III 242, III 244, III 245, III 247, III 251 walls, III 218, III 219, III 221, III 230, III 236, III 237, III 245, III 246, III 248, III 249, III 251 dual beam systems, II 365 dynamic force microscopy (DFM), II 143–147, II 158 dynamic-contact electrostatic force microscopy, III 222 eigenfrequency, II 167 eigenmode, II 3, II 5 eigenvector, II 3 elastic–plastic materials, III 120 elasto–plastic deformation, III 279 electrocatalysis, II 189 electrochemical DPN (E DPN), IV 22 electrochemical microscopy, II 166 electrode, II 96 electron beam deposited tips, II 170, II 193 electrooptic contrast, III 234 modulation, III 238 electrostatic force, III 222 interaction, II 8 electrostatic force microscopy (EFM), III 219, III 220 energy barrier, II 152–155 ergodic, III 285 errors, III 367 correction, III 344, III 346 rates, III 348 Escherichia coli, III 35 etched, III 269 Eunotia sudetica, III 31 evanescent, II 175 waves, II 174 Eyring model, III 99 far-field optics, II 174 ferroelectric, III 217, III 238, III 240, III 241, III 244, III 251 ferroelectric random access memory (FeRAM), III 218, III 252 films, III 246, III 249 finite element modeling, II 99

373 flat tips, III 291 flexural mode, III 225 focused ion beam (FIB), II 194, II 361 force spectroscopy, II 143, II 144, II 149, II 152, II 153, II 155, II 156, II 158, II 161 force–distance curve, II 185 force-induced nanofabrication, IV 108 Fourier coefficient, II 1 Fourier optics, II 174 fractal, III 266, III 357 dimension, III 266 morphology, III 291 surfaces, III 277 fractures, III 267 free volume, III 88 free cantilever, II 2 friction, III 221, III 227, III 248 coefficient, III 104, III 272 force, III 272 friction-velocity analyses, III 104 internal, III 103 monomeric, III 103 theories, III 274 friction force microscopy (FFM), III 85, III 98 frictional dissipation, III 103 fullerenes, III 286 functional head group, II 183 functionalized probes for biological applications, II 166 functionalized tips, II 182 gallium arsenide, II 167, II 173 gas-assisted deposition, II 377 GASH, III 221 Gaussian distribution, III 354–356 geofractals, III 266 glass transition, III 85 graphite, III 41 GroEL, III 35 GroEL GroES complex, III 35 GroES, III 35 guest-host interactions, IV 160 GW model, III 303, III 308, III 311 hard disk recording, II 194 hardness tester, III 292 harmonic, II 1, II 3 signal, II 18 head-tape interface, III 350, III 352, III 353, III 357

374 spacing, III 352, III 354, III 355, III 357 Heaviside function Θ(t − t0 ), II 181 height–height correlation function, III 267 Hertzian, III 275, III 288 hetero epitaxial nucleation, II 110 heterogeneous dynamics, III 85 glass formers, III 103 heterogeneous molecular arrays, IV 166 high coercivity tip, II 194 high spatial frequencies, II 193 high spatial frequency near-field components, II 175 high-speed imaging, IV 252 higher harmonic images, II 25 higher harmonics, II 16 highly oriented pyrolytic graphite (HOPG), III 38 hollow atoms, III 41 host network, IV 160 hydrocarbons, III 284 hydrogen bond, IV 160 IC diagnostics: destructive and nondestructive analysis, II 394 IC failure mode analysis, II 391 immobilization of peptides, IV 14 implants, III 286 in situ polymerization, IV 22 in-plane gate (IPG) transistor, II 397 inclusion effect, IV 162 indentation, III 291 hardness, III 274 indirect patterning, IV 8 inorganic materials, IV 25 inorganic overlayers, III 188 instability, II 16 insulating surfaces, III 38 interfacial boundaries, III 109 constraints, III 84 energy, III 282 glass transition profiles, III 113 plasticization, III 109 reactions, II 186 Tg profile, III 125 intermittent contact mode, II 1, III 234 intermolecular forces, II 149 intralayer array, IV 168 intramolecular forces, II 143, II 149, II 156, II 158, II 161 ion

Subject Index bombardment, III 38 column, II 362 current, II 97 optics, II 364 ion beam, II 408 ion beam lithography, II 379 ion-blasted, III 269 JKR model, III 303 Kelvin probe force microscopy, II 3 kinetic sputtering, III 38 kurtosis, III 265, III 352, III 354, III 355, III 357, III 367 kuru, III 34 lamella templates, IV 174 lamella-type structure, IV 167 Langevin equation, III 101 Laplace transformation, II 13 large organic molecules, III 33 Larmor frequency, III 47 laser scanning microscopy, III 236 lateral contact stiffness calibration, III 93 forces, III 228 twisting, III 225 lateral force microscopy (LFM), IV 18 layered compounds, III 288 LB films, III 288 leakage current, II 93 light lever detection, II 22 light lever readout, II 20 light-emitting diodes, III 109 linear creep model, III 100 linker molecule, II 183 lithium niobate, III 219, III 238, III 249 living cells, III 27 LMIS, II 362 lock-in, III 225 low moment tip, II 194 low temperature grown (LT) GaAs, II 179 luminescence spectroscopy, III 245 machined, III 269 magnetic charges, II 192 material, II 195, IV 27 microscopy, II 166 particles, III 343, III 345, III 348, III 349, III 359, III 361 recording tape, III 343

Subject Index resonance, III 48 resonance imaging, III 48 storage devices, III 286 tape, III 343 magnetic force microscopy (MFM), II 192, III 345, III 358–367, IV 27 magnetic resonance force microscopy, III 48 magnetization, II 192 magnetoresistive, III 344, III 350 magnetoresistive head (MRH), II 380 manufactured metal surfaces, III 267 mask defects, IV 28 material aspects, II 166 material characterization, II 386 material contrast, II 367 mediator, II 188 meniscus force nanografting (MFN), IV 9 mesoscopic contacts, III 293 metal, III 274, III 288 metal-in-gap (MIG), III 343 method of reduced variables, III 104 mica, III 288 micro-Brillouin, III 245 micro-Raman, III 245, III 248 microarrays, IV 7 microcontact Printing (µCP), IV 28 microelectromechanical systems (MEMS), II 167, III 265 micromachining, II 401, III 286 micromechanical properties, III 30 micromotor, III 286 MIG, III 364, III 365 head, III 365, III 366 milling, II 361, II 407 millions of nanometric oscillators, II 169 millipede project, II 169 mineral bridges, II 110 mixed monolayer, IV 19 mobile atoms, III 284 modal harmonic distortion, II 32 modulated contacts, III 92 modulus-matched interface, III 124 molecular assembled, III 269 dynamics (MD), III 284 electronic devices, III 109 friction, III 102 mobility, III 84, III 85 networks, IV 160 overlayers, III 201 recognition, II 149, II 156, II 161

375 relaxations, III 85 templates, IV 159 molecular recognition force spectroscopy, II 158 monolayer protected clusters, IV 177 monomers, IV 22 morphology, III 263, III 274 morphotropic phase boundary (MPB), III 219, III 250 mother of pearl, II 109 multiple degree of freedom (MDOF), II 9 multiply charged ions, III 38 multiscale, III 266 nacre, II 109 nanodefects, III 37 nanoelectromechanical systems (NEMS), III 85, III 103 nanofabrication, IV 103 nanografting, IV 105, IV 109 nanoimpact studies, III 123 nanoindentation, III 312, III 316, III 317 nanomanipulation, II 409 nanometric oscillators, II 169 nanoparticle inks, IV 25 NanoPen Reader and Writer (NPRW), IV 19, IV 109 nanopipette, II 95 nanoroughness, III 286 nanoscience technology, II 165 nanoscopic constraints, III 85 nanoscratching, III 316, III 317 nanoshaving, IV 109 nanostructuring, III 45 nanotube tips, III 272 nanotubes, III 286 nanowear, III 316–318 Navicula seminulum, III 31 near-field electrooptic microscopy, III 242 near-field optics, II 166, II 174 near-field scanning optical microscopy, III 219 noise, III 345, III 357, III 360–362, III 367 nominal contact area, III 272 non-Markovian behavior, III 102 noncollocated systems, II 6 noncontact, III 220, III 223 nonlinearity, II 16 nonminimum phase, II 6 nonspecific tip modification, II 182 object spatial frequencies, II 174

376 oligonucleotides, IV 8 optical aberrations, III 240 optical microscopy, III 235 order–disorder transitions, III 87 organic thin film transistors, III 109 output feedback, II 11 matrix, II 10 2D overlayers, III 208 paraelectric, III 238, III 240, III 241, III 251 parametric excitation, II 33 patch clamp technique, II 107 PEG, II 151, II 158 pentacene, IV 162 phase separation, IV 167 phase transition, III 219, III 236, III 238, III 240, III 244, III 249, III 251, III 252 photoconductive switch, II 179 phthalocyanine, IV 163, IV 168 physicochemical parameters, II 186 piezoelectric force microscopy, III 219 piezoelectric SPM, III 247 piezoresistive cantilevers, IV 252 piezoresistive Wheatstone bridge, II 169 piezoresponse, III 243 piezoresponse force microscopy (PFM), III 220 plastic, III 274 failure, III 280, III 281 flow, III 117 yield, III 116 plasticity index ψ, III 276 pointed tapered metal-coated waveguide, II 175 poisson equation, II 99 polarized light microscopy, III 235 pole zero, II 13 pole-tip recession (PTR), III 350, III 351 poly(ethylene glycol) (PEG), II 150 poly(styrol) (PS), II 28 polyelectrolytes, IV 23 polymer, IV 21 coatings, III 315 polymeric, III 288 polysilicon, III 286 polystyrene, III 103 porous sample, II 94 porphyrins, IV 163 potential barrier, III 102 potential sputtering, III 38

Subject Index power spectrum, III 269 preferential adsorption, IV 160 projection mask technique, II 172 prostheses, III 286 proteins, IV 10 arrays, IV 127 immobilization, IV 129 nanoarrays, IV 11 nanopatterns, IV 128 unfolding, II 157 pull-off force, III 282 pump/probe experiment, II 179 pyroelectric probe, III 236 quality factor, III 223 quantum computing, III 47 quartz microbalance, III 43 ramped creep model, III 100 randomness, III 264 Rayleigh’s criterion, II 175 reactive ion plasma etching, II 177 real area of contact, III 273, III 355, III 356, III 358 recognition image, II 143, II 159–161 reconstruction, II 33 3D, II 382 recording head, III 343, III 344, III 364 redox couple, II 187 relaxation, III 102, III 104 relaxor, III 219, III 251 resolving, II 175 power, II 174 resonance modes, III 224 resonant frequencies, II 5 resonant modes, III 232 rheological boundary layers, III 109 rheological gradients, III 119 rim formation during indentation, III 120 rms roughness, III 353, III 354, III 357 road pavements, III 288 rock surfaces, III 287 root locus map, II 13, II 15 roughness, III 264, III 299–301, III 303, III 304, III 309–311, III 316, III 324, III 344–347, III 351–353, III 355, III 357, III 358, III 360, III 367 rubber, III 288 saturation, III 364, III 365 scanning electrochemical microscopy, II 186 scanning electron microscope (SEM), II 366

Subject Index scanning electrooptic microscopy, III 237, III 248 scanning force spectroscopy (SFS), II 183, II 184 scanning ion conductance microscope (SICM), II 91 scanning near-field optical microscopy (SNOM), II 174, III 236 scanning probe lithography, IV 103 scanning thermal microscopy, IV 251 scanning tunneling microscopy, II 165, III 28 sealing effects, III 283 second harmonic, III 233, III 245, III 248 secondary ion mass spectroscopy (SIMS), II 367 self-affine surface, III 267 self-assembled monolayers (SAMs), III 288, III 306, III 313, III 315, IV 162 self-lubricating coatings, III 317 self-similar, III 266 semiconductor device characterization and nanofabrication, II 166 semiconductor industry, II 389 shear bands, III 120 shear force microscopy, II 111 shear modulation force microscopy (SM FM), III 85, III 97 shear strength, III 274 silanes, IV 19 silazanes, IV 19 silicon, II 167, II 168 silicon (111)-(7 × 7) surface, III 46 silicon-carbide, III 286 silver/silver chloride electrode, II 96 single degree of freedom (SDOF), II 3 single electron spin, III 48 detection, III 47 single molecular array, IV 169 single molecule level, III 34 single molecules, IV 163 single-crystalline diamond, II 171 site-selective adsorption, IV 172 skewness, III 264, III 354, III 355, III 357, III 367 slope-detection method, III 223 small cantilever, III 35 solid-state materials, IV 26 specific tip modification, II 183 spectrum, II 27 spherical aberration, II 365 sputter-deposited, III 269

377 squeezing effect, II 92, II 100 standalone cantilever probes, II 169 state space, II 4, II 9 static contacts, III 90 static friction, III 284 statistics, III 277 steady-state diffusion-limited reaction, II 187 stearic acid, IV 167, IV 173 stiffness, III 292 strain hardening, III 121 rate effects, III 123 shielding, III 124 softening, III 120 stress distribution, III 280 stroboscopic mode, III 241 structural analysis, II 388 structural anisotropy, III 125 structural heterogeneity, III 105 structure function, III 268 structures 1D, III 188, III 202 2D, III 196 subatomic features, III 45 subatomic range, III 27 subharmonics, II 19 substrate constraints, III 122 subwavelength aperture, II 175 superposition of friction-velocity isotherms, III 104 supramolecular architectures, IV 159 compounds, IV 24 surface charge density, III 231 surface energy, III 306 surface force apparatus (SFA), III 273 surface forces, III 309 switching, III 241, III 248, III 249, III 252 system matrix, II 9 tape drive, III 343, III 346, III 348, III 351, III 362 tape roughness analysis, III 351 tapping-mode, II 1, II 108, III 225, III 234 TEM -SEM sample preparation, II 384 template, IV 168 texture, III 299, III 300 TGS, III 223, III 225, III 242, III 245, III 250 the glass transition, III 85 thermogravimetry, IV 252

378 thermomechanical data storage (TDS), III 115 thin films, III 218, III 219, III 237, III 238, III 240, III 251, III 267 head, III 343, III 366 recording, III 362 recording media, III 361, III 362 thiol, IV 167 third-body, III 273, III 284 tip modification, II 182 tip–sample interaction, II 7, II 12 tips, II 193 tire friction, III 283 top-to-bottom nanostructure fabrication, II 176 topographic characterization of heads, III 349 topographic characterization of the magnetic tape, III 345 topographic contrast, II 367 topography, III 299, III 301, III 307, III 318, III 323 topothesy, III 268 total harmonic, II 32 total harmonic distortion (THD), II 17 transfer function, II 13, II 22 transmission electron microscopy (TEM), II 371 transmission minima, II 5, II 12 transmission zeros, II 13 transport phenomena, II 186 transport properties of DPN, IV 4 tribological models for FFM, III 99

Subject Index tribology, III 263 truncated, II 5 model, II 15 twisting, III 227 two-level model, III 303 two-level roughness, III 303, III 307 ultrafast electrical field sampling, II 166 ultrafast scanning probe microscopy, II 179 ultrahigh vacuum, III 42 ultramicroelectrode (UME), II 186 unbinding force, II 149, II 151–154 van der Waals interaction, II 7, IV 163 VCSEL, II 178 virus, IV 15 viscoelastic materials, III 121 vitrification, III 106 voltage modulation, III 220 voltage-modulated scanning force microscopy (VM SFM), III 222 water, III 284 waveguide properties, II 175 wet-chemical surface modification, II 186 Williams–Lendel–Ferry (WLF), III 89 WLF behavior, III 104 writing, III 219, III 248 X ray crystallography, III 35 yield stress, III 280 Young’s modulus, III 276