Chapter
1 Introduction to Metrology for Advanced Manufacturing and Micro- and Nanotechnology
1.1 What is engineering nanometrology?
1.2 The contents of this book and differences to edition 1
2 Some Basics of Measurement
2.1 Introduction to measurement
2.2 Units of measurement and the SI
2.8 Accuracy, precision, resolution, error and uncertainty
2.8.1 Accuracy and precision
2.8.2 Resolution and error
2.8.3 Uncertainty in measurement
2.8.3.1 The propagation of probability distributions
2.8.3.2 The GUM uncertainty framework
2.8.3.3 A Monte Carlo method
2.9.1 Theory of the helium–neon laser
2.9.2 Single-mode laser wavelength stabilisation schemes
2.9.3 Laser frequency stabilisation using saturated absorption
2.9.3.1 Two-mode stabilisation
2.9.4 Zeeman-stabilised 633nm lasers
2.9.5 Frequency calibration of a (stabilised) 633nm laser
2.9.6 Modern and future laser frequency standards
3 Precision Measurement Instrumentation – Some Design Principles
3.1 Geometrical considerations
3.2.2 A single degree of freedom motion device
3.6.1 The structural loop
3.7.1 Minimising thermal inputs
3.7.2 Minimising mechanical inputs
3.9.1 Sources of vibration
3.9.2 Passive vibration isolation
3.9.4 Internal resonances
3.9.5 Active vibration isolation
4 Length Traceability Using Interferometry
4.1 Traceability in length
4.2 Gauge blocks – both a practical and traceable artefact
4.3 Introduction to interferometry
4.3.2 Beat measurement when ω1≠ω2
4.3.3 Visibility and contrast
4.3.4 White light interference and coherence length
4.4 Interferometer designs
4.4.1 The Michelson and Twyman–Green interferometer
4.4.1.1 The Twyman–Green modification
4.4.2 The Fizeau interferometer
4.4.3 The Jamin and Mach–Zehnder interferometers
4.4.4 The Fabry–Pérot interferometer
4.5 Measurement of gauge blocks by interferometry
4.5.1 Gauge blocks and interferometry
4.5.2 Gauge block interferometry
4.5.3 Operation of a gauge block interferometer
4.5.3.1 Fringe fraction measurement – phase stepping
4.5.3.2 Multiple wavelength interferometry analysis
4.5.3.3 Vacuum wavelength
4.5.3.5 Refractive index measurement
4.5.3.6 Aperture correction
4.5.3.7 Surface and phase change effects
4.5.4 Sources of error in gauge block interferometry
4.5.4.1 Fringe fraction determination uncertainty
4.5.4.2 Multi-wavelength interferometry uncertainty
4.5.4.3 Vacuum wavelength uncertainty
4.5.4.4 Temperature uncertainty
4.5.4.5 Refractive index uncertainty
4.5.4.6 Aperture correction uncertainty
4.5.4.7 Phase change uncertainty
4.5.5 Alternative approaches
5 Displacement Measurement
5.1 Introduction to displacement measurement
5.3 Displacement interferometry
5.3.1 Basics of displacement interferometry
5.3.2 Homodyne interferometry
5.3.3 Heterodyne interferometry
5.3.4 Fringe counting and subdivision
5.3.5 Double-pass interferometry
5.3.6 Differential interferometry
5.3.7 Swept-frequency absolute distance interferometry
5.3.8 Sources of error in displacement interferometry
5.3.8.1 Thermal expansion of the metrology frame
5.3.8.5 Heydemann correction
5.3.8.6 Random error sources
5.3.8.7 Other sources of error in displacement interferometers
5.3.9 Latest advances in displacement interferometry
5.3.10 Angular interferometers
5.5 Capacitive displacement sensors
5.6 Eddy current and inductive displacement sensors
5.8 Optical fibre sensors
5.9 Other optical displacement sensors
5.10 Calibration of displacement sensors
5.10.1 Calibration using optical interferometry
5.10.1.1 Calibration using a Fabry–Pérot interferometer
5.10.1.2 Calibration using a measuring laser
5.10.2 Calibration using X-ray interferometry
6 Surface Topography Measurement Instrumentation
6.1 Introduction to surface topography measurement
6.2 Spatial wavelength ranges
6.3 Historical background of classical surface texture measuring instrumentation
6.4 Surface profile measurement
6.5 Areal surface texture measurement
6.6 Surface topography measuring instrumentation
6.7.1 Limitations of optical instruments
6.7.2 Scanning optical techniques
6.7.2.1 Triangulation instruments
6.7.2.2 Confocal instruments
6.7.2.2.1 Confocal chromatic probe instrument
6.7.2.3 Point autofocus profiling
6.7.3 Areal optical techniques
6.7.3.1 Focus variation instruments
6.7.3.2 Phase-shifting interferometry
6.7.3.3 Digital holographic microscopy
6.7.3.4 Coherence scanning interferometry
6.7.4 Scattering instruments
6.8 Capacitive instruments
6.9 Pneumatic instruments
6.10 Calibration of surface topography measuring instruments
6.10.1 Traceability of surface topography measurements
6.10.2 Material measures for profile measuring instruments
6.10.3 Material measures for areal surface texture measuring instruments
6.11 Uncertainties in surface topography measurement
6.12 Metrological characteristics
6.13 Comparisons of surface topography measuring instruments
6.14 Determination of the spatial frequency response
6.15 Software measurement standards
7 Scanning Probe and Particle Beam Microscopy
7.1 Scanning probe microscopy
7.2 Scanning tunnelling microscopy
7.3 Atomic force microscopy
7.3.1 Noise sources in atomic force microscopy
7.3.1.1 Static noise determination
7.3.1.2 Dynamic noise determination
7.3.1.3 Scanner xy noise determination
7.3.2 Some common artefacts in AFM imaging
7.3.2.1 Tip size and shape
7.3.2.2 Contaminated tips
7.3.2.3 Other common artefacts
7.3.3 Determining the coordinate system of an AFM
7.3.4 Traceability of atomic force microscopy
7.3.4.1 Calibration of AFMs
7.3.5 Force measurement with AFMs
7.3.6 AFM cantilever calibration
7.3.7 Inter- and intra-molecular force measurement using AFM
7.3.7.1 Tip functionalisation
7.3.8 Tip–sample distance measurement
7.3.9 Challenges and artefacts in AFM force measurements
7.4 Examples of physical properties measurement using AFM
7.4.1 Thermal measurement
7.4.2 Electrical resistivity measurement
7.5 Scanning probe microscopy of nanoparticles
7.6.1 Scanning electron microscopy
7.6.1.1 Choice of calibration specimen for scanning electron microscopy
7.6.2 Transmission electron microscopy
7.6.3 Traceability and calibration of TEMs
7.6.3.1 Choice of calibration specimen
7.6.3.2 Linear calibration
7.6.3.3 Localised calibration
7.6.3.4 Reference graticule
7.6.4 Electron microscopy of nanoparticles
7.6.4.1 Sources of uncertainties
7.7 Other particle beam microscopy techniques
8 Surface Topography Characterisation
8.1 Introduction to surface topography characterisation
8.2 Surface profile characterisation
8.2.2 Total traverse length
8.2.3.2 Roughness profile
8.2.4 Default values for profile characterisation
8.2.5 Profile characterisation and parameters
8.2.5.1 Profile parameter symbols
8.2.5.2 Profile parameter ambiguities
8.2.6 Amplitude profile parameters (peak to valley)
8.2.6.1 Maximum profile peak height, Rp
8.2.6.2 Maximum profile valley depth, Rv
8.2.6.3 Maximum height of the profile, Rz
8.2.6.4 Mean height of the profile elements, Rc
8.2.6.5 Total height of the surface, Rt
8.2.7 Amplitude parameters (average of ordinates)
8.2.7.1 Arithmetical mean deviation of the assessed profile, Ra
8.2.7.2 Root mean square deviation of the assessed profile, Rq
8.2.7.3 Skewness of the assessed profile, Rsk
8.2.7.4 Kurtosis of the assessed profile, Rku
8.2.8.1 Mean width of the profile elements, RSm
8.2.9 Curves and related parameters
8.2.9.1 Material ratio of the profile
8.2.9.2 Material ratio curve
8.2.9.3 Profile section height difference, Rδc
8.2.9.4 Relative material ratio, Rmr
8.2.9.5 Profile height amplitude curve
8.2.10 Profile specification standards
8.3 Areal surface texture characterisation
8.3.1 Scale-limited surface
8.3.3 Areal specification standards
8.3.4 Unified coordinate system for surface texture and form
8.3.6.1 Areal height parameters
8.3.6.1.1 Root mean square value of the ordinates, Sq
8.3.6.1.2 Arithmetic mean of the absolute height, Sa
8.3.6.1.3 Skewness of topography height distribution, Ssk
8.3.6.1.4 Kurtosis of topography height distribution, Sku
8.3.6.1.5 Maximum surface peak height, Sp
8.3.6.1.6 Maximum pit height of the surface, Sv
8.3.6.1.7 Maximum height of the surface, Sz
8.3.6.2 Areal spacing parameters
8.3.6.2.1 Auto-correlation length, Sal
8.3.6.2.2 Texture aspect ratio of the surface, Str
8.3.6.3 Areal hybrid parameters
8.3.6.3.1 Root mean square gradient of the scale-limited surface, Sdq
8.3.6.3.2 Developed interfacial area ratio of the scale-limited surface, Sdr
8.3.6.4 Functions and related parameters
8.3.6.4.1 Areal material ratio of the scale-limited surface
8.3.6.4.2 Areal material ratio of the scale-limited surface, Smc(c)
8.3.6.4.3 Inverse areal material ratio of the scale-limited surface, Sdc(mr)
8.3.6.4.4 Areal parameters for stratified functional surfaces of scale-limited surfaces
8.3.6.4.5 Void volume, Vv(mr)
8.3.6.4.6 Material volume, Vm(mr)
8.3.6.4.7 Peak extreme height, Sxp
8.3.6.4.8 Gradient density function
8.3.6.5 Miscellaneous parameters
8.3.6.5.1 Texture direction of the scale-limited surface, Std
8.3.7 Feature characterisation
8.3.7.1 Step 1 – Texture feature selection
8.3.7.2 Step 2 – Segmentation
8.3.7.3 Step 3 – Significant features
8.3.7.4 Step 4 – Selection of feature attributes
8.3.7.5 Step 5 – Quantification of feature attribute statistics
8.3.7.6 Feature parameters
8.3.7.6.1 Density of peaks, Spd
8.3.7.6.2 Arithmetic mean peak curvature, Spc
8.3.7.6.3 Ten point height of surface, S10z
8.3.7.6.4 Five point peak height, S5p
8.3.7.6.5 Five point pit height, S5v
8.3.7.6.6 Closed dale area, Sda(c)
8.3.7.6.7 Closed hill area, Sha(c)
8.3.7.6.8 Closed dale volume, Sdc(c)
8.3.7.6.9 Closed hill volume, Shv(c)
8.4.1 Linear fractal methods
8.4.2 Areal fractal analysis
8.4.2.1 Volume-scale analysis
8.4.2.2 Area-scale analysis
8.5 Comparison of profile and areal characterisation
9.1.1 CMM probing systems
9.1.5 Prismatic against free form
9.2 Sources of error on CMMs
9.3 Traceability, calibration and performance verification of CMMs
9.3.1 Traceability of CMMs
9.4.1 Stand-alone micro-CMMs
9.4.1.1 A linescale-based micro-CMM
9.4.1.2 A laser interferometer-based micro-CMM
9.4.1.3 A laser interferometer-based nano-CMM
9.5.1 Mechanical micro-CMM probes
9.5.2 Silicon-based probes
9.5.3 Optomechanical probes
9.6 Verification and calibration of micro-CMMs
9.6.1 Calibration of laser interferometer-based micro-CMMs
9.6.2 Calibration of linescale-based micro-CMMs
10 Mass and Force Measurement
10.1 Traceability of traditional mass measurement
10.1.1 Manufacture of the kilogram weight and the original copies
10.1.2 Surface texture of mass standards
10.1.3 Dissemination of the kilogram
10.1.4 Post nettoyage–lavage stability
10.1.5 Limitations of the current definition of the kilogram
10.1.6 Investigations into an alternative definition of the kilogram
10.1.6.1 The Watt balance approach
10.1.6.2 The Avogadro approach
10.1.6.3 The ion accumulation approach
10.1.6.4 Levitated superconductor approach
10.1.7 Mass comparator technology
10.1.7.1 The modern two-pan mechanical balance
10.1.7.2 Electronic balances
10.2 Low-mass measurement
10.2.1 Weighing by subdivision
10.3 Low-force measurement
10.3.1 Relative magnitude of low forces
10.3.2 Traceability of low-force measurements
10.3.3 Primary low-force balances
10.3.4 Low-force transfer artefacts
10.3.4.1 Deadweight force production
10.3.4.2 Elastic element methods
10.3.4.3 Miniature electrostatic balance methods
10.3.4.4 Resonant methods
10.3.4.5 Further methods and summary
Appendix A: SI Units of Measurement and Their Realisation at NPL
Appendix B: SI Derived Units
Examples of SI derived units expressed in terms of base units
SI derived units with special names and symbols
Fundamental Principles of Engineering Nanometrology
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