The Handbook of Surface and Nanometrology

Table of Contents......Page 0
Handbook of Surface and Nanometrology......Page 1
Dedication......Page 3
Contents......Page 4
Preface......Page 13
Acknowledgments......Page 14
1.1 Where does surface metrology fit in general metrology, and what about nanometrology?......Page 16
1.2 Importance of surface metrology......Page 17
The nature of surfaces......Page 22
2.1 Surface roughness characterization......Page 23
2.1.1 Profile parameters......Page 28
2.1.1.1 Amplitude parameters......Page 31
2.1.1.2 Spacing parameters......Page 36
2.1.1.3 Hybrid parameters......Page 39
2.1.2 Reference lines......Page 41
2.1.2.1 Straight lines......Page 42
2.1.2.2 Polynomial fitting......Page 44
2.1.2.4 Filtering methods......Page 47
2.1.2.5 Envelope methods......Page 60
2.1.3 Statistical parameters of surface roughness......Page 64
2.1.3.2 Material ratio......Page 65
2.1.3.3 Autocorrelation function (ACF) and power spectral density (PSD)......Page 69
2.1.3.4 Power spectrum......Page 78
2.1.3.5 Peak and valley definitions and characteristics......Page 79
2.1.3.6 Cumulative distributions and peaks counts......Page 86
2.1.4.1 Direct methods of statistical assessment over an area......Page 93
2.1.4.2 Practical approach to areal (3D) measurement......Page 100
2.1.5.1 General......Page 104
2.1.5.2 Alternative discrete methods......Page 107
2.1.6 Assessment of isotropy and lay......Page 109
2.1.7.2 Skew and kurtosis......Page 112
2.1.7.3 Beta function [55]......Page 113
2.1.7.4 Chebychev function and log normal function......Page 116
2.1.7.5 Variations on material ratio curve......Page 117
2.1.7.6 Time series analysis methods of characterization—the characterization of spatial information......Page 124
2.1.7.7 Possible methods of classification based on a Fourier approach......Page 128
2.1.7.8 A general note about space-frequency functions......Page 129
2.1.8 Fractals......Page 138
2.1.9 Surface texture and non-linear dynamics in machines......Page 144
2.2 Waviness......Page 145
2.3.1 Introduction......Page 154
2.3.2 Straightness and related topics......Page 157
2.3.3 Generalized probe configurations for variable errors......Page 158
2.3.4 Assessments and classification......Page 159
2.3.5 Flatness......Page 161
2.3.6 Roundness......Page 167
2.3.6.1 Nature of departures from roundness......Page 168
2.3.6.2 Chordal methods......Page 172
2.3.6.3 Radial methods......Page 173
2.3.6.4 Nature of the signal produced by a radial departure instrument......Page 175
2.3.6.6 Effect of imperfect centring......Page 177
2.3.6.7 Assessment of radial, diametral and angular variations......Page 179
2.3.6.8 Roundness assessment......Page 182
2.3.6.9 Effect of imperfect centring on the minimum zone method......Page 186
2.3.6.10 Effect of angular distortion......Page 187
2.3.6.11 Equation of a reference line to fit a partial circular arc as seen by a roundness instrument [110]......Page 189
2.3.6.12 Lobing coefficients......Page 194
2.3.6.13 Roundness assessment without a formal datum......Page 196
2.3.6.14 Eccentricity, concentricity......Page 200
2.3.6.16 Curvature measurement from roundness data......Page 203
2.3.6.18 Estimation of radial slope......Page 211
2.3.6.19 Assessment of ovality and other shapes......Page 213
2.3.6.20 Three-dimensional measurement — sphericity......Page 216
2.3.6.21 Interpretation of results of equations (2.406)—(2.414)......Page 220
2.3.7 Cylindricity......Page 223
2.3.7.1 Methods of specifying cylindricity......Page 225
2.3.7.2 Assessment of cylindrical form......Page 226
2.3.7.3 Reference figures for cylinder measurement......Page 232
2.3.7.5 Limaçon cylindrical references......Page 235
2.4 Comparison of definitions for surface metrology and coordinate-measuring machines......Page 238
2.4.1 Other differences......Page 240
2.5.1 General......Page 241
2.5.3 Types of defect......Page 242
References......Page 244
3.1 Digital methods......Page 248
3.1.1 Sampling......Page 249
3.1.3 Numerical analysis—the digital model......Page 252
3.1.3.1 Differentiation......Page 253
3.1.3.2 Integration......Page 254
3.1.3.3 Interpolation, extrapolation......Page 256
3.2.3 Effect of quantization......Page 257
3.2.4 Effect of numerical model......Page 259
3.2.5 Effect of distance between samples on the peak density value......Page 261
3.2.6.1 Peak height measurement......Page 265
3.2.6.2 Peak curvature......Page 266
3.2.6.3 Profile slopes......Page 268
3.2.6.4 Summary......Page 271
3.2.7.1 General......Page 275
3.2.7.2 The expected summit density and the distributions of summit height and curvature......Page 276
3.2.7.3 The effect of the sampling interval and limiting results for the discrete surface......Page 279
3.2.8.2 Four-point sampling scheme in a plane......Page 282
3.2.8.3 The effect of sampling interval and limiting results [15] on sample patterns......Page 288
3.2.8.4 Discussion......Page 291
3.3.1 General properties of the Fourier transform......Page 295
3.3.2.1 Fast Fourier transform, analytic form......Page 297
3.3.3 A practical realization of the fast Fourier transform......Page 301
3.3.4 General considerations......Page 302
3.3.5.1 Use of Fourier transform for non-recursive filtering......Page 303
3.3.5.3 Correlation......Page 304
3.3.5.6 Other analysis......Page 305
3.4.1 Amplitude probability density function......Page 306
3.4.2 Statistical moments of the APDF......Page 307
3.4.3 Autocorrelation function (ACF)......Page 308
3.4.4 Autocorrelation measurement using FFT......Page 309
3.4.5 Measurement of power spectral density ( PSD )......Page 310
3.5.2.4 Frequency-limited signals......Page 312
3.5.2.10 Computation of DAF ( where n is restricted to 0, N—1, and N is even )......Page 313
3.5.3.1 Properties......Page 314
3.5.3.10 Total energy......Page 315
3.5.3.14 Moments......Page 316
3.5.4 Some examples of Wigner distribution: application to signals—waviness......Page 318
3.6.1 Numerical filtering methods for establishing mean lines for roughness and waviness profiles......Page 320
3.6.3 Standard filter......Page 321
3.6.4 Phase-corrected ( linear phase ) filters, other filters and filtering issues......Page 322
3.6.5 Gaussian filter......Page 324
3.6.6 Box functions......Page 327
3.6.7 Truncation......Page 328
3.6.8 Alternative methods of computation......Page 330
3.6.9 Equal-weight techniques......Page 331
3.6.11 The discrete transfer function......Page 333
3.6.12 The 2CR filter......Page 337
3.6.13 Use of the FFT in surface metrology filtering—areal case......Page 338
3.6.14 Examples of numerical problems in straightness and flatness......Page 339
3.6.15 Effect of computer word format......Page 341
3.7.1 Differences between surface and dimensional metrology algorithms: least-squares evaluation of geometric elements......Page 343
3.7.1.2 Linear least squares......Page 344
3.7.2.1 Best-fit plane......Page 345
3.7.2.2 Circles, spheres, etc......Page 346
3.7.2.3 Cylinders and cones......Page 348
3.7.3.1 Minimum zone method......Page 354
3.7.5 Simplex methods......Page 355
3.7.6.1 General......Page 358
3.7.6.3 Minimum radius circumscribing limaçon......Page 359
3.7.6.4 Minimum zone, straight lines and planes......Page 361
3.7.6.5 Minimax problems......Page 363
3.8.2 Hartley transform......Page 366
3.8.3 Square wave functions—Walsh functions......Page 367
3.8.4 Space—frequency functions......Page 369
3.8.5 Gabor transforms......Page 371
3.9.1 Profile generation......Page 373
3.9.2 Two-dimensional surface generation......Page 377
3.12 Summary......Page 380
References......Page 381
4.1.1 Historical details......Page 383
4.1.2 Some early dates of importance in the metrology and production of surfaces......Page 384
4.1.3 Specification......Page 386
4.1.5 Kinematics......Page 387
4.1.7 Mobility......Page 391
4.1.8 Linear hinge mechanisms......Page 393
4.1.9 Angular motion flexures......Page 396
4.1.10 Measurement and force loops......Page 397
4.1.11.1 Abbé offset......Page 407
4.1.12 Other mechanical considerations—balance of forces......Page 408
4.1.13 Systematic errors and non-linearities......Page 409
4.1.14 Material selection......Page 410
4.1.15 Drive systems......Page 413
4.2.1 Aspect of general stylus systems......Page 414
4.2.2.1 Tactile considerations......Page 415
4.2.2.2 Pick-up dynamics......Page 420
4.2.2.3 Conclusions about mechanical pick-ups of instruments using the conventional approach......Page 429
4.2.2.4 Relationship between static and dynamic forces......Page 431
4.2.2.5 Alternative stylus systems and effect on reaction/random surface (figure 4.61)......Page 436
4.2.2.6 Criteria for scanning surface instruments......Page 437
4.2.2.7 Forms of the pick-up equation......Page 438
4.2.2.8 Measurement systems (surface topography/atomic force measurement—loop considerations)......Page 442
4.2.2.9 Spatial domain instruments......Page 446
4.2.3 Scanning probe microscopes [48—51] ( SPM )......Page 449
4.2.3.1 Scanning tunnelling microscope (STM)......Page 452
4.2.3.2 Other scanning microscopes......Page 461
4.2.3.3 Operation and theory of the STM......Page 462
4.2.3.4 Spectroscopy......Page 465
4.2.3.5 Some simple scanning systems......Page 467
4.2.3.6 The atomic force microscope [50]......Page 470
4.2.4.5 Straight line generator......Page 471
4.2.4.7 Pick-up configuration......Page 472
4.2.4.8 Generation of the skid datum......Page 475
4.2.4.9 Stylus instruments where the stylus integrates......Page 483
4.2.4.10 Alignment of the stylus system......Page 485
4.2.4.11 Limitations of ‘references’ used in roundness measurement......Page 486
4.2.4.12 Other stylus methods......Page 488
4.2.4.13 Replication......Page 492
4.2.5.2 Mapping......Page 493
4.2.5.3 Criteria for areal mapping......Page 495
4.2.5.4 Movement positions on surface and sampling patterns......Page 498
4.2.5.5 Contour and other maps of surfaces......Page 503
4.2.5.6 High speed area tracking stylus [96]......Page 504
4.3.1 General......Page 505
4.3.2 Properties of the focused spot......Page 510
4.3.3 Optical followers......Page 511
4.3.4 Hybrid microscopes......Page 517
4.3.5 Oblique angle methods......Page 520
4.3.6.1 Spatial and temporal coherence......Page 522
4.3.6.2 Interferometry and surface metrology......Page 523
4.3.7.1 Phase detection......Page 529
4.3.7.2 Frequency-splitting method......Page 530
4.3.7.3 Other methods in interferometry comparable with heterodyne methods......Page 533
4.3.7.4 Relative merits of different nanometre instruments......Page 535
4.3.7.5 High-precision non-contacting metrology using short coherence interferometry—white light scanning interferometer......Page 538
4.3.8.1 General......Page 543
4.3.8.4 Shadow moiré......Page 545
4.3.8.5 Projection moiré......Page 546
4.3.9.1 Introduction......Page 547
4.3.10 Speckle methods......Page 552
4.3.11 Diffraction methods......Page 561
4.3.12 Scatterometers (glossmeters)......Page 574
4.3.13.1 General......Page 579
4.3.13.2 Transform plane methods......Page 580
4.3.13.3 Image plane detection......Page 584
4.3.13.4 ‘Whole-field’ measurement—flaw detection......Page 587
4.3.14 Comparison of optical techniques......Page 589
4.4.1 General......Page 590
4.4.2 Scanning capacitative microscopes......Page 593
4.7.1 General......Page 594
4.7.4 Liquid methods—water......Page 595
4.7.6 Pneumatic methods......Page 596
4.7.8 Ultrasonics......Page 597
4.8.1 General......Page 599
4.8.2 Reaction of electrons with solids......Page 602
4.8.3 Scanning electron microscope (SEM)......Page 604
4.8.5 Photon Tunnelling Microscopy (PTM)......Page 606
4.9 Merit of transducers......Page 608
4.9.1 Comparison of transducer systems......Page 609
4.9.2.1 Limitations......Page 611
4.9.3.1 General......Page 612
4.9.3.2 Variable resistance......Page 613
4.9.3.5 Voltage or current generators......Page 615
4.9.3.8 Photodetectors......Page 616
4.9.5.1 Inductive......Page 619
4.9.5.2 Capacitative......Page 620
4.9.5.3 Optical lateral positional sensor......Page 621
4.9.5.4 Optical area pattern photodiodes, transducer for lateral displacement......Page 622
4.9.6 Talystep......Page 623
4.9.7 Comparison of techniques—general summary......Page 627
References......Page 629
5.2 Nature of errors......Page 635
5.3 Deterministic or systematic error model......Page 636
5.4 Basic components of accuracy evaluation......Page 637
5.5 Basic error theory for a system......Page 638
5.6.1 Deterministic errors......Page 639
5.7 Some useful statistical tests for surface metrology......Page 641
5.7.2 Tests for the mean value of a surface—the student t test......Page 642
5.7.4 Goodness of fit......Page 644
5.7.6 Measurement of relevance—factorial design......Page 645
5.7.6.1 The interactions......Page 647
5.7.7 Lines of regression......Page 648
5.7.8 Methods of discrimination......Page 649
5.8 Uncertainty in instruments—calibration in general......Page 650
5.9 The calibration of stylus instruments......Page 652
5.9.1 Stylus calibration......Page 653
5.9.2 Calibration of amplification......Page 657
5.9.2.2 Calibration of SPM......Page 662
5.9.3 X-ray methods......Page 665
5.9.4 Practical standards......Page 671
5.9.5 Calibration of transmission characteristics......Page 673
5.9.6 Filter calibration standards......Page 675
5.10.1 Magnitude......Page 677
5.10.1.1 Magnitude of diametral change......Page 678
5.10.2 Separation of errors — calibration of roundness and form......Page 679
5.10.3 General errors due to motion......Page 686
5.10.3.1 Radial motion......Page 687
5.10.3.3 Error motion—general case......Page 688
5.10.3.4 Fundamental and residual error motion......Page 690
5.10.3.6 Fixed sensitive direction measurements......Page 691
5.10.3.7 Considerations on the use of the two-gaugehead system for a fixed sensitive direction......Page 692
5.10.3.8 Other radial error methods......Page 693
5.11 Variability of surface parameters......Page 694
5.12 General......Page 698
5.12.1 Geometrical Product Specification (GPS)......Page 699
5.12.3 Surface standardization......Page 701
5.12.4 Role of technical specification documents......Page 703
5.12.6 Selected list of international standards applicable to surface roughness measurement: methods; parameters; instruments; comparison specimens......Page 704
5.12.7 International (equivalents, identicals and similars)......Page 705
5.13.1 Surface roughness......Page 709
5.13.1.2 Reading the symbols......Page 712
5.13.1.4 Other points......Page 713
5.14 Summary......Page 714
References......Page 715
6.1 Introduction......Page 717
6.2.1 General......Page 718
6.3.1.1 General......Page 720
6.3.1.3 Effect of tool geometry—theoretical surface finish—secondary cutting edge [1]......Page 721
6.3.1.5 Fracture roughness [3]......Page 725
6.3.1.6 Built-up edge (BUE)......Page 726
6.3.1.7 Other surface roughness effects in finish machining......Page 727
6.3.1.8 Tool wear......Page 728
6.3.1.9 Chip formation and turning mechanisms......Page 731
6.3.2 Diamond turning......Page 732
6.3.3.1 General......Page 734
6.3.3.2 Roughness on the surface......Page 735
6.3.4.2 Mechanisms......Page 738
6.4.1 General......Page 739
6.4.2 Types of grinding......Page 744
6.4.4.2 Factorial experiment......Page 746
6.4.5.1 General......Page 747
6.4.5.2 Important parameters for roughness and roundness......Page 748
6.4.5.3 Roundness considerations (figure 6.46)......Page 749
6.4.6.1 Spark-out......Page 751
6.4.6.2 Elastic effects......Page 753
6.4.6.3 Texture generated in grinding......Page 754
6.4.6.5 Other types of grinding......Page 756
6.4.7 General comments on grinding......Page 758
6.4.8 Nanogrinding......Page 759
6.4.9 General comments on roughness......Page 764
6.4.10 Honing......Page 770
6.4.11 Polishing (lapping)......Page 771
6.5.1 Ultrasonic machining......Page 775
6.5.3.1 Electrochemical machining (ECM)......Page 776
6.5.3.2 Electrolytic grinding......Page 777
6.5.3.3 Electrodischarge machining (EDM)......Page 778
6.5.4.1 Surface texture and the plastic deformation processes......Page 779
6.5.5.1 General......Page 786
6.5.5.2 Micropolishing......Page 787
6.5.5.3 Three dimensional micromachining......Page 791
6.5.6.2 Electron beam machining......Page 793
6.5.6.3 Ion beam machining......Page 796
6.5.6.4 General comment on atomic-type processes......Page 799
6.5.7 Structured surfaces—engineered surfaces......Page 801
6.6.1 General......Page 803
6.6.2 The interface......Page 804
6.6.2.1 Brittle/ductile transition in nanometric machining.......Page 805
6.6.3 General design points......Page 806
6.7.1 Surface effects resulting from the machining process......Page 807
6.7.2 Surface alterations......Page 808
6.7.3.1 General......Page 812
6.7.3.2 Grinding......Page 815
6.7.3.3 Turning......Page 817
6.7.3.6 General comment......Page 819
6.7.4.1 General......Page 820
6.7.4.2 Indirect methods......Page 821
6.7.4.3 Direct methods......Page 822
6.7.5.2 Influences of residual stress......Page 824
6.8.1 General......Page 827
6.8.2.1 On turned parts—single-point machining......Page 828
6.8.2.2 Abrasive machining......Page 830
6.8.3 Space-frequency functions (the Wigner function)......Page 832
6.8.4 Non-linear dynamics......Page 833
6.9 Summary......Page 837
References......Page 838
7.1. Introduction......Page 842
7.1.1 The function map......Page 843
7.1.2 Nature of interaction......Page 846
7.2.1 Contact......Page 848
7.2.1.1 Point contact......Page 850
7.2.2 Macroscopic behaviour......Page 851
7.2.2.1 Two spheres in contact......Page 852
7.2.2.2 Two cylinders in contact......Page 854
7.2.2.4 Sphere on a cylinder......Page 855
7.2.3.1 General......Page 856
7.2.3.2 Types of parameter......Page 857
7.2.3.3 Peak correlation—possible mechanisms......Page 858
7.2.3.4 Microcontact under load......Page 863
7.2.3.5 Elastic/plastic balance-plasticity index......Page 864
7.2.4 Effect of waviness on contact.......Page 877
7.2.5 Non-Gaussian surfaces and contact......Page 878
7.2.7 Coated contact......Page 880
7.3.1 General......Page 881
7.3.2 Stiffness......Page 882
7.3.3 Mechanical seals......Page 888
7.3.4 Adhesion......Page 889
7.3.5 Thermal conductivity......Page 893
7.3.6 Relationship between electrical and thermal conductivity......Page 897
7.4.2.1 Mechanisms—general......Page 901
7.4.3.1 Wear classification......Page 910
7.4.3.3 Wear prediction models......Page 914
7.9.4 Shakedown and surface texture......Page 916
7.4.5.1 General......Page 918
7.4.5.2 Hydrodynamic lubrication and surface geometry......Page 919
7.4.6.2 EHD lubrication and the influence of roughness......Page 932
7.4.7.1 General......Page 942
7.4.7.3 Breakdown of boundary lubrication......Page 945
7.5.1 Weibull and dual-frequency-space functions......Page 946
7.5.3 Surface roughness ‘one-number’ specification and running-in......Page 947
7.5.4 Designer surfaces—running-in......Page 949
7.5.5 Scuffing......Page 953
7.5.6.1 Rolling failure......Page 955
7.5.6.2 Roughness effects on 3D body motion......Page 958
7.5.6.3 Rough surfaces and rolling......Page 964
7.5.6.4 Pitting due to debris and subsequent surface effects......Page 966
7.5.7.1 Dynamic effects......Page 967
7.5.8 Squeeze films and roughness......Page 968
7.5.9 Fretting and fretting fatigue......Page 969
7.6.1 General......Page 972
7.6.2 Fatigue......Page 973
7.6.3 Corrosion fatigue-general......Page 978
7.6.4.1 General......Page 979
7.6.4.3 Heterogeneities......Page 982
7.6.4.4 Localized attack-electrochemical......Page 983
7.7.1.1 Models......Page 984
7.7.2 General optical......Page 985
7.7.3 Smooth random surface......Page 989
7.7.4 Geometric ray-tracing criterion—rough random surfaces......Page 990
7.7.4.1 Effect of surface curvature......Page 991
7.7.5 Scatter from deterministic surfaces......Page 993
7.7.7 Geometric ray condition, rough deterministic surfaces......Page 994
7.7.8 Summary of results, scalar and geometrical......Page 995
7.7.9 Mixtures of two random components......Page 996
7.7.10.1 Angle effects......Page 997
7.7.10.2 Multiple reflections......Page 999
7.7.10.3 Shadowing......Page 1003
7.7.11.1 Fresnel scattering......Page 1008
7.7.11.3 Fractal surfaces......Page 1010
7.7.11.4 Fractal slopes: Subfractal model......Page 1015
7.7.12 Aspherics......Page 1016
7.8.1.1 Electromagnetic waves......Page 1019
7.8.3 Bragg scattering......Page 1020
7.8.3.1 Non-elastic scattering......Page 1021
7.8.3.2 Influence of roughness—thin-film measurement......Page 1022
7.9.2 Tolerances......Page 1024
7.10.1 Profile parameters......Page 1028
7.10.2 Functional types of parameter......Page 1029
7.10.3 Areal (3D) parameters......Page 1030
7.10.4 Function maps and surface parameters......Page 1035
7.10.5 System approach......Page 1037
7.11 Conclusions......Page 1041
References......Page 1042
8.1.2 Nanotechnology and engineering......Page 1051
8.1.3 Nanometrology......Page 1053
8.2.1 Machineability......Page 1054
8.2.2 Dynamic considerations—how force balance depends on scale......Page 1057
8.2.3 Structural considerations—how stiffness and resonance change with scale of size......Page 1058
8.2.4 Functional dependence on scale of size......Page 1060
8.3.2 Geometric features and the scale of size......Page 1061
8.3.3 How roughness depends on scale......Page 1062
8.3.4 Surface and bulk properties dependence on scale......Page 1064
8.3.5.1 Engineering shape......Page 1065
8.5.3.2 Molecular shape and scale of size......Page 1066
8.3.5.3 Molecular and biological shape considerations......Page 1067
8.3.5.5 Simulation and scaling up of molecular machine elements......Page 1068
8.4.1 Length......Page 1069
8.4.2 Nano position sensing......Page 1071
8.5.2 Length and position calibration and measurement at the nanoscale......Page 1072
8.5.3 The probe......Page 1074
8.5.4 Height measurement calibration at the nanometre scale of size......Page 1076
8.6.1 Signal limitations......Page 1078
8.7 Calibration artefacts......Page 1079
8.8 Dynamics of calibration at nanometre level......Page 1082
8.9 Software correction......Page 1083
8.10.1 Scanning force microscope—nanometrology version......Page 1084
8.10.2 Traceability......Page 1085
8.11.2 Heterodyne......Page 1086
8.11.3 Frequency tracking—Fabry-Perot etalons (FPE)......Page 1087
8.11.4 Capacitative methods......Page 1088
8.11.5 Stylus instruments......Page 1089
8.12 Summary......Page 1090
References......Page 1093
9.1 General......Page 1095
9.2 Characterization......Page 1096
9.3 Data processing......Page 1099
9.4 Instrumentation......Page 1100
9.5 Calibration......Page 1104
9.6 Manufacture......Page 1105
9.7 Surfaces and function......Page 1106
9.8 Nanometrology......Page 1110
9.9 Overview......Page 1113
Glossary......Page 1116