Light Scattering and Nanoscale Surface Roughness

Cover -- Contents -- Preface -- 1 Characterization of Surface Roughness -- 1.1. Introduction -- 1.1.1. Definition of Nanoscale Roughness -- 1.1.2. Early Beginnings: Visual Surface Inspection versus Quantitative Measurements -- 1.1.3. Beginnings of Quantitative Metrology in the 1940s -- 1.1.4. Metrology Advances in the 1950s and 1960s -- 1.1.5. Further Metrology Advances in the 1970s and 1980s -- 1.1.6. Recent Developments from the 1990s to the Present -- 1.2. Current Surface Metrology Techniques and Instruments -- 1.2.1. Questions to Answer Prior to Taking Measurements -- 1.2.2. Relations Between Surface Metrology Techniques -- 1.2.3. Surface Inspection and Imaging -- 1.2.4. Optical Profilers -- 1.2.5. Mechanical Profilers -- 1.2.6. Atomic Force Microscopes (AFM) -- 1.2.7. Total Integrated Scattering and Angle-Resolved Scattering -- 1.2.8. Surface Contamination and Cleaning -- 1.3. Current and Future Surface Metrology Requirements -- 1.3.1. General Comments -- 1.3.2. Metrology of Microcomponents -- 1.3.3. Metrology in the UV and Soft X-Ray Regions -- 1.3.4. Metrology of Steeply-Curved Spherical or Aspheric Surfaces -- 1.3.5. Polarization of Scattered Light for Target Discrimination -- 1.3.6. Automated, Rapid-Response Systems with Accept-Reject Capabilities -- 1.4. Summary -- 2 The Kirchhoff and Related Approximations -- 2.1. Introduction -- 2.2. The Helmholtz Formula -- 2.3. The Limit of the Observation Point Tending to the Surface -- 2.4. Kirchhoff Approximation for the Neumann Problem -- 2.5. Scattering Amplitude -- 2.6. The Tangent Plane Approximation -- 2.7. Scattering of Electromagnetic Waves from the Interface Between Dielectric Half-Spaces -- 2.8. The Stratton-Chu Formula -- 2.9. The Integral Equations for the Electromagnetic Case -- 2.10. Nonlocal Small-Slope Approximation -- 2.11. Relation to other Approaches -- 2.12. Conclusion -- 3 Scattering and the Spatial Frequency Representation -- 3.1. Introduction -- 3.2. Plane Waves -- 3.3. Scattering -- 3.4. Significance of the Three-Dimensional Spatial Frequencies -- 3.5. Polarization Effects -- 3.6. Random Surfaces -- 3.6.1. Statistics of Surface Scattering -- 3.6.2. Gaussian Autocorrelation Coefficient -- 3.6.3. Measurement of Surface Roughness -- 3.6.4. Imaging of Surface Roughness -- 3.6.5. Inversion of Scattering Data -- 3.6.6. Statistics of the Scattered Field -- 3.6.7. Limitations of the Kirchhoff Approximation -- 3.7. Fractal Surfaces with an Outer Scale -- 3.7.1. Scattering by a Fractal Surface with an Outer Scale -- 3.8. Total Integrated Scatter (TIS) -- 3.9. Dielectric Medium -- 3.10. Conclusions -- 4 Rayleigh Hypothesis -- 4.1. Introduction -- 4.2. Is the Representation Given by Eq. (7) Fundamentally Wrong? -- 4.3. Convergence of the Rayleigh Series -- 4.4. Rayleigh Hypothesis and the Perturbative Expansion of the SA -- 4.5. Application to Numerical Analysis -- 4.6. Conclusion -- 5 Small-Amplitude Perturbation Theory for One-Dimensionally Rough Surfaces -- 5.1. Introduction -- 5.2. Theory -- 5.3. Gaussian Roughness Spectrum -- 5.4. Enhanced Specular Peaks -- 5.4.1. Gaussian Spectra -- 5.4.2. Physical Origins -- 5.4.3. Rectangular Spectra -- 5.5. Comparisons with Experiments -- 5.5.1. The 2-2 Effect -- 5.5.2. The 4-4 Effect -- 5.6. Conclusions -- 6 Small-Amplitude Perturbation Theory for Two-Dimensional Surfaces -- 6.1. Int.