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Spie Press Book

Optical Scattering: Measurement and Analysis, Third Edition
Author(s): John C. Stover
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Book Description

The first edition of this book concentrated on relating scatter from optically smooth surfaces to the microroughness on those surfaces. After spending six years in the semiconductor industry, Dr. Stover has updated and expanded the third edition. Newly included are scatter models for pits and particles as well as the use of wafer scanners to locate and size isolated surface features. New sections cover the multimillion-dollar wafer scanner business, establishing that microroughness is the noise, not the signal, in these systems. Scatter measurements, now routinely used to determine whether small-surface features are pits or particles and inspiring new technology that provides information on particle material, are also discussed. These new capabilities are now supported by a series of international standards, and a new chapter reviews those documents.

New information on scatter from optically rough surfaces has also been added. Once the critical limit is exceeded, scatter cannot be used to determine surface-roughness statistics, but considerable information can still be obtained - especially when measurements are made on mass-produced products. Changes in measurement are covered, and the reader will find examples of scatter measurements made using a camera for a fraction of the cost and in a fraction of the time previously possible. The idea of relating scatter to surface appearance is also discussed, and appearance has its own short chapter. After all, beauty is in the eye of the beholder, and what we see is scattered light.


Book Details

Date Published: 30 July 2012
Pages: 330
ISBN: 9781628418408
Volume: PM224

Table of Contents
SHOW Table of Contents | HIDE Table of Contents
About the Third Edition
Preface to Second Edition
Preface to Third Edition

Chapter 1. Quantifying Light Scatter
1.1 The Scattering of Light
1.2 Scatter from a Smooth Sinusoidal Surface
1.3 Scatter from Other Surfaces
1.4 Scatter from Windows and Particulates
1.5 Bidirectional Scatter Distribution Functions
1.6 Total Integrated Scatter
1.7 Differential Scattering Cross Section
1.8 Summary

Chapter 2. Quantifying Surface Roughness
2.1 Profile Characterization
      2.1.1 Deterministic profiles
      2.1.2 Random profiles
      2.1.3 Sampled profiles
      2.1.4 Two-dimensional (area) profiles
2.2 The Surface Power Spectral Density and Autocovariance Functions
      2.2.1 The power spectral density function from the profile
      2.2.2 Extension to two-dimensional spectrums
      2.2.3 The autocorrelation function
2.3 The Effects of Profile Measurement Error
2.4 Summary

Chapter 3. Scatter Calculations and Diffraction Theory
3.1 Overview
3.2 Kirchhoff Diffraction Theory
3.3 The Rayleigh Approach
3.4 Comparison of Vector and Scalar Results
3.5 Calculating Scatter from Optically Rough Surfaces
      3.5.1 The Beckmann rough-surface result
      3.5.2 Other rough-surface calculations
3.6 Summary

Chapter 4. Using Rayleigh–Rice to Calculate Smooth-Surface Statistics from the BRDF
4.1 Practical Application of the Rayleigh–Rice Perturbation Theory
4.2 Roughness Statistics of Isotropic Surfaces
4.3 Roughness Statistics of One-Dimensional Surfaces
4.4 Roughness Statistics for the General Case
4.5 The ABC or K-Correlation Surface Power Spectrum Models
      4.5.1 The Lorentzian power spectrum
      4.5.2 Fractal surfaces
4.6 The TIS Derivation from the Rayleigh–Rice Perturbation Theory
4.7 Summary

Chapter 5. Polarization of Scattered Light
5.1 A Review of Polarization Concepts
5.2 The Polarization Factor Q
5.3 Scattering Vectors and Matrices
5.4 Summary

Chapter 6. Scatter Measurements and Instrumentation
6.1 Particle Scatter
6.2 Modeling Techniques and Accomplishments
6.3 Model Availability
6.4 Summary

Chapter 7. Instrumentation and Measurement Issues
7.1 Scatterometer Components
7.2 Instrument Signature
7.3 Aperture Effects on the Measured BSDF
7.4 Signature Reduction and Near-Specular Measurements
      7.4.1 Reflective versus refractive focusing optics
      7.4.2 Minimizing the near-angle/far-angle boundary θN
      7.4.3 Scatter measurements inside θN
7.5 Scatter Screens
7.6 The Noise-Equivalent BSDF
7.7 Measurement of Scatter from Discrete Surface Features in DSC Units
7.8 Measurement of Pi and Instrument Calibration
7.9 Measurement of Curved Optics
7.10 Coordinate Systems and Out-of-Plane Measurements
7.11 Camera-based Systems
7.12 Raster Scans
7.13 Measurement of Retroreflection
7.14 Alternative TIS Devices
7.15 Error Analysis of the Measured BSDF
7.16 Obtaining Appriopriate PSD Measurements
7.17 Summary

Chapter 8. Predicting Scatter from Roughness
8.1 Optical Surfaces: Using the Rayleigh–Rice Equation
      8.1.1 The general case
      8.1.2 Isotropic samples
      8.1.3 One-dimensional samples
8.2 Optically Rough Front-Surface Reflectors
      8.2.1 Stretching the Rayleigh smooth-surface limit
      8.2.2 Predicting rough-surface scatter from the PSD
      8.2.3 TIS measurements and rough surfaces
8.3 Partial Data Sets
      8.3.1 Fractral surfaces
      8.3.2 Curve fitting
8.4 Scatter from Diffuse Samples
      8.4.1 Lambertian samples
      8.4.2 Non-Lambertian samples and material signatures
8.5 BRDF Standard Surfaces
8.6 Software for Prediction of Stray Light in Optical Systems
8.7 Summary

Chapter 9. Detection of Discrete Defects
9.1 Polarization Effects Associated with Defect Scatter
9.2 Bulk Defects in Transparent Optics
9.3 Near-Point-Scatter Sources
9.4 Nontopographic Defects in Opaque Materials
9.5 Summary

Chapter 10. Appearance and Scattered Light
10.1 Beauty is in The Eye of the Beholder—And What We See is Scattered Light
10.2 Practical Appearance Monitoring
10.3 Other Examples
10.4 Summary

Chapter 11. Industrial Applications
11.1 Semiconductor Applications
      11.1.1 Finding small particulates and point defects on polished surfaces
      11.1.2 Scattering and roughness characterization of silicon
      11.1.3 Particle scanner inspection of wafers
11.2 Computer Disks
11.3 Contamination Measurement by Wavelength Discrimination
11.4 Solar Energy Applications
      11.4.1 Photovoltaic collectors
11.5 General Manufacturing Examples
      11.5.1 Detection of paper flaws
      11.5.2 Noncontact monitoring of emissivity and temperature
      11.5.3 Ball bearings
11.6 Summary

Chapter 12. Published Scatter Standards
12.1 Integrated Scatter Standards
12.2 Angle-Resolved Scatter Standards
12.3 The PSD Standard
12.4 Standards for Semiconductor Particle Scanners
      12.4.1 SEMI M52: Scanner specifications
      12.4.2 M50: Capture rate
      12.4.3 M58: Scanner calibration
      12.4.4 M58: Particle deposition confirmation
      12.6.3 Ball bearings
12.5 Summary

Chapter 13. Scatter Specifications
13.1 Generic Specifications
13.2 Application-Specific Specifications
      13.2.1 Example 1: Scatterometer-focusing mirrors
      13.2.2 Example 2: Imaging optics
      13.2.3 Example 3: Laser resonator losses
      13.2.4 Example 4: Diffraction from precision-machined turning mirrors
      13.2.5 Example 5: Scatter in a laser range finder
      13.2.6 Example 6: Roughness specifications for semiconductor components
13.3 Empirical Scatter Specifications
13.4 Summary

Appendix A. Review of Electromagnetic Wave Propagation
A.1 The Wave Equation
A.2 Electromagnetic Plane Waves in Free Space
A.3 Plane Waves in a Dielectric
A.4 Plane Waves in a Conducting Medium

Appendix B. Kirchhoff Diffraction from Sinusoidal Gratings

Appendix C. BSDF Data

Appendix D. Units



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