Light Scattering and Nanoscale Surface Roughness

Transcription

1 Light Scattering and Nanoscale Surface Roughness Alexei A. Maradudin Editor With 197 Figures lspri inger

2 Preface v 1 Characterization of Surface Roughness 1 Jean M. Bennett 1.1 Introduction Definition ofnanoscale Roughness Early Beginnings: Visual Surface Inspection versus Quantitative Measurements Beginnings of Quantitative Metrology in the 1940s Metrology Advances in the 1950s and 1960s Further Metrology Advances in the 1970s and 1980s Recent Developments from die 1990s to thepresent Current Surface Metrology Techniques and Instruments Questions to Answer Prior to Taking Measurements Relations Between Surface Metrology Techniques Surface Inspection and Imaging Optical Profilers Mechanical Profilers Atomic Force Microscopes (AFM) Total Integrated Scattering and Angle-Resolved Scattering Surface Contamination and Cleaning Current and Future Surface Metrology Requirements General Comments Metrology of Microcomponents Metrology in the UV and Soft X-Ray Regions Metrology of Steeply-Curved Spherical or Aspheric Surfaces 29 xiu

3 1.3.5 Polarization of Scattered Light for Target. Discrimination Automated, Rapid-Response Systems with Accept-Reject Capabilities Summary 30 The Kirchhoff and Related Approximations 35 A. G. Voronovich 2.1 Introduction The Helmholtz Formula The Limit of the Observation Point Tending to thesurface Kirchhoff Approximation for the Neumann Problem Scattering Amplitude The Tangent Plane Approximation Scattering of Electromagnetic Waves from the Interface Between Dielectric Half-Spaces The Stratton-Chu Formula The Integral Equations for the Electromagnetic Case Nonlocal Small-Slope Approximation Relation to other Approaches Conclusion 59 Scattering and the Spatial Frequency Representation 61 Colin J. R. Sheppard 3.1 Introduction Plane Waves Scattering Significance of the Three-Dimensional Spatial Frequencies Polarization Effects Random Surfaces Statistics of Surface Scattering Smooth Surface Rough Surface Gaussian Autocorrelation Coefficient Measurement of Surface Roughness Smooth Surface, n^ko = h 0 < Rough Surface, ÄO» 0.5 seca Fine Surface, Co <C 1/sina Coarse Surface, Co»1/sina Imaging of Surface Roughness Inversion of Scattering Data Statistics of the Scattered Field Limitations of the Kirchhoff Approximation 79

4 xv 3.7 Fractal Surfaces with an Outer Scale Scattering by a Fractal Surface with an Outer Scale Total Integrated Scatter (TIS) Dielectric Medium Conclusions 90 4 Rayleigh Hypothesis 93 A. G. Vownovich 4.1 Introduction Is the Representation Given by Eq. (7) Fundamentally Wrong? Convergence of the Rayleigh Series Rayleigh Hypothesis and the Perturbative Expansion ofthesa Application to Numerical Analysis Conclusion Small-amplitude Perturbation Theory for One-dimensionally Rough Surfaces 107 K. A. O'Donneil 5.1 Introduction Theory Gaussian Roughness Spectrum Enhanced Specular Peaks Gaussian Spectra Physical Origins Rectangular Spectra TheSpectrum Results Comparisons with Experiments The 2-2 Effect The 4-4 Effect Conclusions Small-amplitude Perturbation Theory for Two-dimensional Surfaces 127 Gerard Berginc 6.1 Introduction Derivation of the Reduced Rayleigh Equations Propagation Equations and Boundary Conditions Field Elimination The Reduced Rayleigh Equations The Diffusion Matrix.' 137

5 xvi Contents 6.4 A Perturbative Development Case of One Rough Surface A Rough Surface Separating Two Different Media A Slab with a Rough Surface on the Bottom Side A Slab with a Rough Surface on the Upper Side Case of Two Rough Surfaces The Mueller Matrix Cross-Section and the Surface Staüstics Case of One Randomly Rough Surface Case of Two Randomly Rough Surfaces Numerical Examples and Analysis of the Phenomena A Randomly Rough Surface Separating Two Different Semi-Infinite Media A Film with a Randomly Rough Surface on the Upper Side A Slab with Two Randomly Rough Surfaces Discussion 173 Appendix Computer Simulations of Rough Surface Scattering 181 Joel T. Johnson 7.1 Introduction Fundamental Issues One- and Two-Dimensional Surfaces Description of the Rough Surface Finite Size Surface Effects Other Physical Parameters Other "Numerical" Parameters Use of Approximate Theories Integral Equation Formulations Matrix Solution Methods Iterative Solution of Matrix Equations Preconditioning Physically Based Preconditioning Accelerating the Matrix-Vector Multiply Operation Canonical Grid Method Spectral Approach Parallelization Storage Issues Sample Results Conclusions and Recommendations for the Use of Numerical Methods 204

6 xvii 8 Overview of Rough Surface Scattering 211 John A. DeSanto 8.1 Introduction Coordinate-Space Methods Scalar Problems Electromagnetic Problems Spectral-Space Methods Scalar Problems Electromagnetic Problems, Infinite Surface Surface Inversion Solution Methods Discussion Experimental Studies of Scattering from Weakly Rough Metal Surfaces 237 K.A. O'Donnell 9.1 Introduction Experimental Methods Essential Couplings Rectangular Spectra Scattering Measurements Experimental Results Ideal Spectrum DetunedCase Second Harmonie Generation Roughness Spectrum Centered on A:^, Roughness Spectrum Centered on k p Angular Correlation Functions Conclusions Measuring Interfacial Roughness by Polarized Optical Scattering 259 Thomas A. Germer 10.1 Introduction Definitions Measurement Metiiods Roughness of a Single Interface Theory Limitations The Inverse Problem Example Roughness of Two Interfaces Theory The Inverse Problem Example Final Comments 281

7 xviii Contents 11 Scattering of Electromagnetic Waves from Nanostructured, Self-affine Fractal Surfaces: Near-fleld Enhancement 285 JoseA. Sänchez-Gil, Jose V. Garcia-Ramos, Vincenzo Giannini, and Eugenio R. Mendez 11.1 Introduction Scattering Model Scattering Geometry Scattering Equations NearField SurfaceField Self-Affine Fractals Near and Surface Field Surface Fields Near Field Map: Localized Surface-Plasmon Polaritons Surface Field Enhancement: Statistics Surface-Enhanced Raman Scattering Concluding Remarks Light Scattering by Particies on Substrates. Theory and Experiments 305 F. Moreno, J. M. Saiz, and F. Gonzalez 12.1 General Introduction Near Field of Particies on Substrates Introduction D Geometry D Geometry Concluding Remarks Far Field of Particies on Substrates Introduction Regulär Particies on Fiat Substrates Quasi-Regular Cases: Buried Particies and Surface Defects Buried Particies Particle with a Bumped Surface Nearby Many Particies: Polydispersity, Shadowing and Multiple Scattering Introduction Polydispersity Multiple Scattering and Shadowing Effect Light Scattering Statistics Concluding Remarks 337

8 xix 13 Multiple Scattering of Waves by Random Distribution of Particles for Applications in Light Scattering by Metal Nanoparticles 341 Ka-Ki Tse, heutig Tsang, Chi-Hou Chan and Kung-Hau Ding 13.1 Introduction Formulation for Foldy Lax Equations Extinction and Absorption Efficiency of Metal Nanoparticles and Plasmon Resonance Formulations Extinction Cross Section Absorption Cross Section Results and Discussions Convergence Test for Numerical Parameters Extinction and Absorption of Two Particles with Various Orientations Extinction and Absorption of Gold Nanoparticles with Various Fractional Volumes Extinction and Absorption of Silver Nanoparticles with Different Fractional Volume Energy Absorption of Each Particle in the Collection Phase Matrix of Light Scattering by Metal Nanoparticles Formulation of Phase Matrix Polarization Frame Scattering Cross Section Results and Discussion Phase Matrices of Single Realization and Average Realizations Phase Matrices ofl% and 5% Phase Matrix in Resonant Mode and Nonresonant Mode Optical Scattering of Nanoparticles Below or Above a Random Rough Surface Multiple-scattering Effects in Angular Intensity Correlation Functions 371 Tamara A. Leskova and Alexei A. Maradudin 14.1 Introduction The Correlation Function C(q, k\q', k') and Its Properties Determination ofc(q,k\q',k') Correlations in Single-Interface Systems 381

9 xx Contents The Correlation Function C m (q,k\q', k') The Correlation Function Ö w \q,k\q',k') The Transition from Complex Gaussian to Circular Complex Gaussian Statistics Correlations in Film Systems Frequency Correlation Functions Experimental Results Conclusions Speckle Pattern in the Near Field 409 Jean-Jacques Greffet and Remi Carminati 15.1 Introduction Role of Evanescent Waves in the Near Field Angular Spectrum Field and Intensity Correlations in the Near Field Speckle Patterns due to Random Thermal Fields Multiple Scattering Experimental Difficulties Nonuniversal Speckle Pattern Produced by a Slightly Rough Surface Statistical Description of a Random Rough Surface Amplitude of the Field Scattered by a Deterministic Slightly Rough Surface Speckle Pattern Generated by a Slightly Rough Surface in the Near Field, Detection of Optical Near Fields General Expression for the Near-Field Optical Signal Reciprocity Theorem Expression of the Detected Field Calculation of the Response Function Polarization Response Spectral Response Conclusion 427 Appendix: Reciprocity Theorem Inverse Problems in Optical Scattering 435 Eugenio R. Mendez and Demetrio Macias 16.1 Introduction The Scattering Amplitude The Thin Phase Screen Model Estimation of Statistical Properties of Surfaces Statistical Characterization of Random Surfaces The Random Field and Its Averages 441

10 xxi The Coherent Component The Incoherent Component Angular Correlations Estimation of the Surface Profile from Complex Amplitude Data Inversion Algorithm Numerical Example Estimation of the Surface Profile from Intensity Data Evolutionary Inversion Procedure Results of a Numerical Experiment Discussion and Conclusions The Design of Randomly Rough Surfaces that Scatter Waves ina Specified Manner 465 Alexei A. Maradudin 17.1 Introduction A Surface That Produces a Scattered Field with a Specified Angular Dependence of Its Mean Intensity A Surface That Synthesizes the Infrared Spectrum of a Known Compound Conclusions 486 Index 489