David J. Whitehouse University of Warwick Coventry, UK Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business A TAYLOR & FRANCIS BOOK CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2011 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number: 978-1-4200-8201-2 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. 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CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Whitehouse, D. J. (David J.) Handbook of surface and nanometrology / by David J. Whitehouse. -- 2nd ed. p. cm. Rev. ed. of: Handbook of surface metrology. c1994. Includes bibliographical references and index. ISBN 978-1-4200-8201-2 1. Surfaces (Technology)--Measurement. I. Whitehouse, D. J. (David J.). Handbook of surface metrology. II. Title. TA418.7.W47 2011 620’.440287--dc22 2010014776 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com This book is dedicated to my wife Ruth who has steered me through many computer problems, mainly of my own making, and cajoled, encouraged, and threatened me in equal measure to carry on when my willpower flagged. Contents Preface........................................................................................................................................................................................xxi Acknowledgments ....................................................................................................................................................................xxiii Chapter 1 Introduction—Surface and Nanometrology ............................................................................................................1 1.1 General .........................................................................................................................................................1 1.2 Surface Metrology ........................................................................................................................................1 1.3 Background to Surface Metrology ...............................................................................................................1 1.4 Nanometrology .............................................................................................................................................2 1.5 Book Structure ..............................................................................................................................................2 Chapter 2 Characterization ......................................................................................................................................................5 2.1 The Nature of Surfaces .................................................................................................................................5 2.2 Surface Geometry Assessment and Parameters ...........................................................................................7 2.2.1 General—Roughness Review .........................................................................................................7 2.2.1.1 Profile Parameters (ISO 25178 Part 2 and 4278) .............................................................9 2.2.1.2 Reference Lines .............................................................................................................16 2.2.1.3 Filtering Methods for Surface Metrology ......................................................................21 2.2.1.4 Morphological Filtering .................................................................................................34 2.2.1.5 Intrinsic Filtering ...........................................................................................................41 2.2.1.6 Summary .......................................................................................................................41 2.2.2 Statistical Parameters and Random Process Analysis of Surface Roughness ..............................41 2.2.2.1 General...........................................................................................................................41 2.2.2.2 Amplitude Probability Density Function .......................................................................42 2.2.2.3 Random Process Analysis Applied to Surfaces ............................................................44 2.2.2.4 Areal Texture Parameters, Isotropy and Lay (Continuous) ...........................................59 2.2.2.5 Discrete Characterization ..............................................................................................65 2.2.2.6 Assessment of Isotropy and Lay ....................................................................................68 2.2.3 Methods of Characterization Using Amplitude Information ........................................................71 2.2.3.1 Amplitude and Hybrid Parameters ................................................................................71 2.2.3.2 Skew and Kurtosis .........................................................................................................71 2.2.3.3 Beta Function .................................................................................................................71 2.2.3.4 Fourier Characteristic Function .....................................................................................72 2.2.3.5 Chebychev Function and Log Normal Function............................................................73 2.2.3.6 Variations on Material Ratio Curve + Evaluation Procedures ......................................74 2.2.4 Characterization Using Lateral Spatial Information .....................................................................79 2.2.4.1 Time Series Analysis Methods of Characterization ......................................................79 2.2.4.2 Transform Methods Based on Fourier ...........................................................................81 2.2.4.3 Space–Frequency Transforms .......................................................................................82 2.2.4.4 Fractals...........................................................................................................................93 2.2.5 Surface Texture and Non-Linear Dynamics .................................................................................98 2.2.5.1 Poincare Model and Chaos ............................................................................................98 2.2.5.2 Stochastic Resonance .....................................................................................................99 2.3 Waviness ...................................................................................................................................................100 2.4 Errors of Form ..........................................................................................................................................106 2.4.1 Introduction .................................................................................................................................106 2.4.2 Straightness and Related Topics ..................................................................................................107 2.4.2.1 ISO /TS 12780-1, 2003, Vocabulary and Parameters of Straightness and 12780-2, 2003, Specification Operators, Give the International Standard Position Regarding Straightness and Its Measurement .............................................................107 2.4.2.2 Generalized Probe Configurations ..............................................................................108 2.4.2.3 Assessments and Classification ...................................................................................109 v vi Contents 2.4.3 Flatness .........................................................................................................................................110 2.4.3.1 ISO /TS 12781-1,2003, Vocabulary and Parameters of Flatness and ISO/TS 12781-2, 2003, Specification Operators Give the International Standards Position on Flatness ....................................................................................................................110 2.4.3.2 General..........................................................................................................................110 2.4.3.3 Assessment....................................................................................................................111 2.4.4 Roundness ....................................................................................................................................114 2.4.4.1 ISO/TS 12181-1, 2003, Vocabulary and Parameters and ISO/TS 12181-2, 2003, Specification Operators Give the International Standards Current Position on Roundness ...................................................................114 2.4.4.2 General..........................................................................................................................114 2.4.4.3 Measurement and Characterization ..............................................................................115 2.4.4.4 General Comments on Radial, Diametral, and Angular Variations............................124 2.4.4.5 Roundness Assessment ................................................................................................126 2.4.4.6 Roundness Filtering and Other Topics ........................................................................133 2.4.4.7 Roundness Assessment Using Intrinsic Datum ...........................................................135 2.4.4.8 Eccentricity and Concentricity ....................................................................................138 2.4.4.9 Squareness ...................................................................................................................139 2.4.4.10 Curvature Assessment Measurement from Roundness Data ......................................139 2.4.4.11 Radial Slope Estimation ..............................................................................................144 2.4.4.12 Assessment of Ovality and Other Shapes ....................................................................145 2.4.5 Three-Dimensional Shape Assessment .......................................................................................146 2.4.5.1 Sphericity .....................................................................................................................146 2.4.6 Cylindricity and Conicity ............................................................................................................150 2.4.6.1 Standards ISO/TS 1280-1, 2003, Vocabulary and Parameters of Cylindrical Form, ISO/TS 1280-2, 2003, Specification Operators ................................................150 2.4.6.2 General.........................................................................................................................150 2.4.6.3 Methods of Specifying Cylindricity ............................................................................151 2.4.6.4 Reference Figures for Cylinder Measurement .............................................................156 2.4.6.5 Conicity ........................................................................................................................160 2.4.7 Complex Surfaces .........................................................................................................................161 2.4.7.1 Aspherics ......................................................................................................................161 2.4.7.2 Free-Form Geometry ....................................................................................................161 2.5 Characterization of Defects on the Surface ..............................................................................................164 2.5.1 General ISO 8785 Surface Defects .............................................................................................164 2.5.2 Dimensional Characteristics of Defects ......................................................................................165 2.5.3 Type Shapes of Defect .................................................................................................................165 2.6 Discussion .................................................................................................................................................165 References ...........................................................................................................................................................167 Chapter 3 Processing, Operations, and Simulations .............................................................................................................171 Comment ..............................................................................................................................................................171 3.1 Digital Methods .........................................................................................................................................171 3.1.1 Sampling .......................................................................................................................................171 3.1.2 Quantization .................................................................................................................................173 3.1.3 Effect of Computer Word Length .................................................................................................174 3.1.4 Numerical Analysis—The Digital Model ....................................................................................175 3.1.4.1 Differentiation...............................................................................................................175 3.1.4.2 Integration .....................................................................................................................176 3.1.4.3 Interpolation and Extrapolation ....................................................................................176 3.2 Discrete (Digital) Properties of Random Surfaces ...................................................................................177 3.2.1 Some Numerical Problems Encountered in Surface Metrology .................................................177 3.2.2 Definitions of a Peak and Density of Peaks ................................................................................177 3.2.3 Effect of Quantization on Peak Parameters .................................................................................178 3.2.4 Effect of Numerical Analysis on Peak Parameters ......................................................................178 Contents vii 3.2.5 Effect of Sample Interval on the Peak Density Value .................................................................180 3.2.6 Digital Evaluation of Other Profile Peak Parameters .................................................................182 3.2.6.1 Peak Height Measurement ...........................................................................................182 3.2.6.2 Peak Curvature ............................................................................................................183 3.2.6.3 Profile Slopes ...............................................................................................................184 3.2.7 Summary of Profile Digital Analysis Problems ..........................................................................186 3.2.8 Areal (3D) Filtering and Parameters ...........................................................................................186 3.2.9 Digital Areal (3D) Measurement of Surface Roughness Parameters ..........................................188 3.2.9.1 General.........................................................................................................................188 3.2.9.2 The Expected Summit Density and the Distributions of Summit Height and Curvature .....................................................................................................................189 3.2.9.3 The Effect of the Sample Interval and Limiting Results .............................................190 3.2.10 Patterns of Sampling and Their Effect on Discrete Properties (Comparison of Three-, Four-, Five- and Seven-Point Analysis of Surfaces) ....................................................................192 3.2.10.1 Four-Point Sampling Scheme in a Plane .....................................................................192 3.2.10.2 The Hexagonal Grid in the Trigonal Symmetry Case .................................................193 3.2.10.3 The Effect of Sampling Interval and Limiting Results on Sample Patterns ...........................................................................................................195 3.2.11 Discussion....................................................................................................................................198 3.3 Digital Form of Statistical Analysis Parameters ......................................................................................199 3.3.1 Amplitude Probability Density Function ....................................................................................199 3.3.2 Moments of the Amplitude Probability Density Function ..........................................................201 3.3.3 Autocorrelation Function ............................................................................................................201 3.3.4 Autocorrelation Measurement Using the Fast Fourier Transform ..............................................202 3.3.5 Power Spectral Density ...............................................................................................................202 3.4 Digital Estimation of Reference Lines for Surface Metrology ................................................................203 3.4.1 General ........................................................................................................................................203 3.4.2 Convolution Filtering ..................................................................................................................204 3.4.2.1 Repeated Convolutions ................................................................................................205 3.4.3 Box Functions ..............................................................................................................................206 3.4.4 Effect of Truncation ....................................................................................................................207 3.4.5 Alternative Methods of Computation ..........................................................................................208 3.4.5.1 Overlap Methods..........................................................................................................208 3.4.5.2 Equal-Weight Methods ................................................................................................208 3.4.6 Recursive Filters ..........................................................................................................................209 3.4.6.1 The Discrete Transfer Function ...................................................................................209 3.4.6.2 An Example ..................................................................................................................211 3.4.7 Use of the Fast Fourier Transform in Surface Metrology Filtering ............................................212 3.4.7.1 Areal Case ...................................................................................................................212 3.5 Examples of Numerical Problems In Straightness and Flatness ..............................................................213 3.6 Algorithms .................................................................................................................................................214 3.6.1 Differences between Surface and Dimensional Metrology and Related Subjects .......................214 3.6.1.1 Least-Squares Evaluation of Geometric Elements .......................................................214 3.6.1.2 Optimization ................................................................................................................215 3.6.1.3 Linear Least Squares ...................................................................................................215 3.6.1.4 Eigenvectors and Singular Value Decomposition........................................................215 3.6.2 Best-Fit Shapes ............................................................................................................................215 3.6.2.1 Planes ...........................................................................................................................215 3.6.2.2 Circles and Spheres .......................................................................................................216 3.6.2.3 Cylinders and Cones .....................................................................................................217 3.6.3 Other Methods .............................................................................................................................221 3.6.3.1 Minimum Zone Method ..............................................................................................221 3.6.3.2 Minimax Methods—Constrained Optimization .........................................................221 3.6.3.3 Simplex Methods .........................................................................................................222 3.7 Basic Concepts In Linear Programing .....................................................................................................223 3.7.1 General ........................................................................................................................................223 viii Contents 3.7.2 Dual Linear Programs in Surface Metrology .............................................................................223 3.7.2.1 Minimum Radius Circumscribing Limaçon ...............................................................224 3.7.3 Minimum Zone, Straight Lines, and Planes ...............................................................................225 3.7.4 Minimax Problems ......................................................................................................................227 3.7.4.1 General Algorithmic Approach ...................................................................................227 3.7.4.2 Definitions....................................................................................................................227 3.8 Fourier Transforms and the Fast Fourier Transform ................................................................................228 3.8.1 General Properties .......................................................................................................................228 3.8.2 Fast Fourier Transform ................................................................................................................229 3.8.2.1 Analytic Form ..............................................................................................................229 3.8.2.2 Practical Realization ....................................................................................................231 3.8.3 General Considerations of Properties .........................................................................................232 3.8.3.1 Fourier Series of Real Data .........................................................................................233 3.8.4 Applications of Fourier Transforms in Surface Metrology .........................................................233 3.8.4.1 Fourier Transform for Non-Recursive Filtering ..........................................................233 3.8.4.2 Power Spectral Analysis ..............................................................................................234 3.8.4.3 Correlation ...................................................................................................................234 3.8.4.4 Other Convolutions ......................................................................................................234 3.8.4.5 Interpolation.................................................................................................................234 3.8.4.6 Other Analysis in Roughness ......................................................................................234 3.8.4.7 Roundness Analysis .....................................................................................................234 3.9 Transformations In Surface Metrology ....................................................................................................235 3.9.1 General ........................................................................................................................................235 3.9.2 Hartley Transform .......................................................................................................................235 3.9.3 Walsh Functions–Square Wave Functions–Hadamard ...............................................................236 3.10 Space–Frequency Functions .....................................................................................................................237 3.10.1 General ........................................................................................................................................237 3.10.2 Ambiguity Function ....................................................................................................................237 3.10.3 Discrete Ambiguity Function (DAF) ..........................................................................................238 3.10.3.1 Discrete Ambiguity Function Computation ................................................................238 3.10.4 Wigner Distribution Function W(x, ω) .......................................................................................239 3.10.4.1 Properties .....................................................................................................................239 3.10.4.2 Analytic Signals ...........................................................................................................239 3.10.4.3 Moments ......................................................................................................................239 3.10.4.4 Digital Wigner Distribution Applied to Surfaces ........................................................240 3.10.4.5 Examples of Wigner Distribution: Application to Signals—Waviness .......................241 3.10.5 Comparison of the Fourier Transform, the Ambiguity Function, and the Wigner Distribution ..................................................................................................................................242 3.10.6 Gabor Transform .........................................................................................................................243 3.10.7 Wavelets in Surface Metrology ...................................................................................................244 3.11 Surface Generation ...................................................................................................................................244 3.11.1 Profile Generation .......................................................................................................................244 3.11.2 Areal Surface Generation ............................................................................................................246 3.12 Atomistic Considerations and Simulations...............................................................................................248 3.12.1 General ........................................................................................................................................248 3.12.1.1 Microscopic Mechanics ...............................................................................................248 3.12.1.2 Macroscopic Propagating Surfaces .............................................................................248 3.12.2 Mobile Cellular Automata MCA .................................................................................................249 3.12.3 Simulation Considerations...........................................................................................................251 3.12.4 Molecular Dynamics ...................................................................................................................251 3.13 Summary ..................................................................................................................................................252 References ...........................................................................................................................................................253 Contents ix Chapter 4 Measurement Techniques ....................................................................................................................................255 4.1 Background ...............................................................................................................................................255 4.1.1 Some Early Dates of Importance in the Metrology and Production of Surfaces ........................255 4.1.2 Specification ................................................................................................................................257 4.2 Measurement Systems Stylus—Micro .....................................................................................................257 4.2.1 The System ..................................................................................................................................257 4.2.1.1 Stylus Characteristics ..................................................................................................258 4.2.2 Tactile Considerations .................................................................................................................258 4.2.2.1 General.........................................................................................................................258 4.2.2.2 Tip Dimension .............................................................................................................258 4.2.2.3 Stylus Angle .................................................................................................................260 4.2.2.4 Stylus Pressure-Static Case, Compliance, Stiffness, and Maximum Pressure ...........260 4.2.2.5 Elastic/Plastic Behavior ...............................................................................................261 4.2.2.6 Stylus and Skid Damage Prevention Index ..................................................................262 4.2.2.7 Pick-Up Dynamics and “Trackability” ........................................................................263 4.2.2.8 Unwanted Resonances in Metrology Instruments .......................................................265 4.2.2.9 Conclusions about Mechanical Pick-Ups of Instruments Using the Conventional Approach ......................................................................................................................267 4.2.3 Relationship between Static and Dynamic Forces for Different Types of Surface .....................268 4.2.3.1 Reaction due to Periodic Surface .................................................................................268 4.2.3.2 Reaction due to Random Surfaces ...............................................................................268 4.2.3.3 Statistical Properties of the Reaction and Their Significance: Autocorrelation Function and Power Spectrum of R(t) ..........................................................................269 4.2.3.4 System Properties and Their Relationship to the Surface: Damping and Energy Loss ..............................................................................................................................270 4.2.3.5 Integrated Damping: System Optimization for Random Surface ...............................270 4.2.3.6 Alternative Stylus Systems and Effect on Reaction/Random Surface ........................271 4.2.3.7 Criteria for Scanning Surface Instruments ..................................................................272 4.2.3.8 Forms of the Pick-Up Equation ...................................................................................272 4.2.4 Mode of Measurement.................................................................................................................274 4.2.4.1 Topography Measurement ...........................................................................................274 4.2.4.2 Force Measurement .....................................................................................................275 4.2.4.3 Open- and Closed-Loop Considerations......................................................................276 4.2.4.4 Spatial Domain Instruments ........................................................................................277 4.2.5 Other Stylus Configurations ........................................................................................................278 4.2.5.1 High-Speed Area Tracking Stylus (a Micro Equivalent of the Atomic Scanning Probe Family) ..............................................................................................................278 4.2.5.2 Multi-Function Stylus Systems ....................................................................................279 4.2.5.3 Pick-Up and Transducer System ..................................................................................280 4.2.6 Metrology and Various Mechanical Issues .................................................................................281 4.2.6.1 Generation of Reference Surface .................................................................................282 4.2.6.2 Intrinsic Datum—Generation and Properties of the Skid Datum ...............................284 4.2.6.3 Stylus Instruments Where the Stylus Is Used as an Integrating Filter ........................289 4.2.6.4 Space Limitations of “References” Used in Roundness Measurement .......................290 4.2.7 Areal (3D) Mapping of Surfaces Using Stylus Methods .............................................................294 4.2.7.1 General Problem ..........................................................................................................294 4.2.7.2 Mapping .......................................................................................................................295 4.2.7.3 Criteria for Areal Mapping ..........................................................................................295 4.2.7.4 Contour and Other Maps of Surfaces ..........................................................................301 4.3 Measuring Instruments Stylus—Nano/Atomic Scale ..............................................................................301 4.3.1 Scanning Probe Microscopes (SPM) [or (SXM) for Wider Variants] ........................................301 4.3.1.1 History .........................................................................................................................301 4.3.1.2 Background ..................................................................................................................303