Spectroscopic Ellipsometry and Reflectometry A User's Guide

, by Tompkins, Harland G.; McGahan, William A.

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ISBN: 9780471181729 | 0471181722
Cover: Hardcover
Copyright: 3/18/1999

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While single wave ellipsometry has been around for years, spectroscopic ellipsometry is fast becoming the method of choice for measuring the thickness and optical properties of thin films. This book provides the first practical introduction to spectroscopic ellipsometry and the related techniques of reflectometry. A guide for practitioners and researchers in a variety of disciplines, it addresses a broad range of applications in physics, chemistry, electrical engineering, and materials science.

Preface

xiii

Perspective and History

(5)

Historical Aspects

(1)

Complementary Nature of the Techniques

(1)

Format and Purpose of the Book

(1)

References

(2)

Fundamentals

(17)

Description of an Electromagnetic Wave

(2)

The Effect of Matter on Electromagnetic Waves

(3)

The Complex Index of Refraction

(2)

Laws of Reflection and Refraction

(1)

Polarized Light

(3)

Sources

(1)

Linearly Polarized Light

(1)

Elliptically Polarized Light

(2)

Application of Elliptically Polarized Light

(1)

The Reflection of Light

(5)

Orientation

(1)

The Reflection Equations of Fresnel

(1)

The Brewster Angle

(3)

Reflections with Films

(1)

Ellipsometry and Reflectometry Definitions

(2)

Reflectance

(1)

Delta and Psi

(1)

The Fundamental Equation of Ellipsometry

(1)

References

(2)

Optical Properties of Materials and Layered Structures

(12)

The Physical Meaning of the Optical Constants

(1)

Conventions and More Basics

(2)

The Lorentz Oscillator

(2)

Insulators

(1)

Semiconductors

(2)

Metals

(2)

Kramers-Kronig Relations

(1)

Miscellaneous

(1)

References

(1)

Instrumentation

(19)

Introduction

(1)

Reflectometry in General

(1)

Reflectometer Hardware Configurations

(3)

Reflectometer Components

(1)

Sources

(1)

Beamsplitter

(1)

Lenses

(1)

Monochromators and Detectors

(1)

Ellipsometry in General

(1)

Optical Components Used in Ellipsometers

(4)

Sources

(1)

Polarizers

(1)

Compensators

(1)

Monochromators

(2)

Detectors

(1)

Ellipsometer Hardware Configurations

(5)

Null Ellipsometry

(1)

Rotating Element Photometric Ellipsometry

(3)

Modulation Ellipsometry

(1)

Single Wavelength Ellipsometers

(1)

Spectroscopic Ellipsometers

(1)

Instrument Parameter Characterization

(1)

Research vs. Production Ellipsometry

(2)

Errors in Reflectance and Ellipsometric Measurements

(1)

References

(1)

The Anatomy of a Reflectance Spectrum

(8)

General

(1)

Spectra for Substrates Only

(1)

With a Film: The Effect of Wavelength

(2)

Contribution of Film Thickness

(2)

Contribution of the Optical Constant Spectra of Film and Substrate

(2)

Summary

(1)

Aspects of Single-Wavelength Ellipsometry

(13)

General

(1)

Substrates: Delta and Psi and the Optical Constants

(4)

Calculating Delta/Psi Trajectories

(1)

Delta/Psi Trajectories for Transparent Films

(4)

Delta/Psi Trajectories for Absorbing Films

(1)

Trajectories for Two-Film Structures

(1)

Key Issues

(1)

References

(1)

The Anatomy of an Ellipsometric Spectrum

(10)

General

(1)

Typical Spectra

(2)

Spectra for Substrates Only

(1)

With a Film: Single-Wavelength Considerations

(2)

Effect of Wavelength

(2)

Contribution of the Optical Constant Spectra of Film and Substrate

(1)

Contribution of Film Thickness

(1)

Summary

(1)

References

(1)

Analytical Methods and Approach

(13)

General Approach

(1)

Sample Positioning

(1)

How Much Data?

(2)

Wavelength

(1)

Angle of Incidence

(1)

Analytical Methods

(9)

General

(1)

Tabulated Optical Constants

(1)

Simple Mixtures of Tabulated Optical Constants

(3)

Dispersion Relationships

(2)

Point-by-Point Optical Constants

(1)

Regression Process

(1)

Summary

(1)

References

(1)

Optical Data Analysis

(10)

Introduction

(1)

Direct Calculation

(2)

Regression Analysis Methods

101

(2)

The Problem

101

(1)

The Merit Function

101

(1)

The Regression Algorithm

102

(1)

Hybrid Methods

103

(1)

Goodness of Fit

103

(1)

Uniqueness

104

(1)

Combined Analysis of Multiple Data Types

105

(1)

Multiple Sample Analysis

106

(1)

Errors---Systematic and Random

106

(1)

References

107

(1)

Quality Assurance

108

(5)

General

108

(1)

Precision vs. Accuracy

108

(1)

Standards

109

(1)

Quality Assurance Measurements

110

(2)

References

112

(1)

Very Thin Films

113

(10)

Introduction

113

(1)

Determining Thickness

113

(4)

For Reflectance

113

(2)

For Ellipsometry

115

(2)

Determining Optical Constants

117

(1)

Distinguishing Between Materials

118

(4)

References

122

(1)

Roughness

123

(10)

Introduction

123

(1)

Roughness in General

123

(1)

Approximation of Surface Roughness as an Oxide Layer

124

(1)

Effective Medium Approximations (EMAs)

125

(1)

Examples

126

(4)

Polysilicon

126

(1)

Sensitivity in the Visible

127

(1)

Roughness Effects when Determining Optical Constants

128

(1)

SOI Interface Roughness

128

(2)

References

130

(3)

PROTOTYPICAL ANALYSES

Thermal Oxide, LPCVD Nitride, or Photoresist on Silicon

133

(5)

Salient Feature

133

(1)

Thinner Films

133

(2)

Intermediate Films

135

(1)

Thicker Films

136

(2)

Silicon Oxynitrides, PECVD Silicon Oxides, and Polysilicon

138

(9)

Salient Feature

138

(1)

Polysilicon

138

(3)

PECVD Silicon Oxides

141

(1)

Silicon Oxynitrides

142

(4)

References

146

(1)

PECVD Silicon Nitride, Silicon Dioxide, and Photoresist on Silicon

147

(8)

Salient Feature

147

(1)

Cauchy Modeling

147

(8)

LPCVD Polysilicon and Amorphous Silicon

155

(6)

Salient Feature

155

(1)

The Problem

155

(1)

The Optical Constants

155

(1)

Using the EMA Model

156

(1)

Using the Lorentz Oscillator Dispersion Model

156

(4)

References

160

(1)

Substrate Optical Constant Determination

161

(5)

Salient Feature

161

(1)

Aluminum

161

(2)

Glass

163

(3)

Analysis of Films on Transparent Substrates

166

(7)

Salient Feature

166

(1)

The Structure of the Example

166

(1)

Transmission

166

(1)

Reflection

167

(2)

Ellipsometry

169

(1)

Reverse Ellipsometry

170

(1)

Summary

171

(1)

References

172

(1)

Very Thick Films

173

(5)

Salient Feature

173

(1)

Thick Photoresist on Silicon---Reflectometry

173

(2)

Thick Photoresist on Glass---Ellipsometry

175

(1)

Conclusion

176

(2)

Compositional Analysis of Materials

178

(3)

Salient Feature

178

(1)

Background

178

(1)

GaAs/AlGaAs/GaAs

179

(1)

References

180

(1)

Thin Metal Films

181

(7)

Salient Feature

181

(1)

Background

181

(1)

Thin Titanium on Silicon

182

(1)

Thin Titanium Nitride on Oxide on Silicon

182

(2)

Using Multiple Films of Thin Metal

184

(3)

Comments and Summary

187

(1)

References

187

(1)

Photoresist Optical Constants

188

(7)

Salient Feature

188

(1)

Background

188

(1)

Photoresist on Silicon

189

(1)

Summary

190

(5)

Appendices

A Regression Algorithms

195

(1)

A.1 The Merit Function

195

(1)

A.2 The Analysis Procedure

195

(1)

A.3 The Algorithms

196

(1)

A.4 The Combination

197

(1)

A.5 References

198

(1)

B Maxwell's Equations and the Wave Equation

199

(1)

B.1 Introduction

199

(2)

B.2 Differential Equation Form of Maxwell's Equations

201

(1)

B.3 The Wave Equation

201

(1)

B.3.1 Dielectric Media

201

(3)

B.3.2 Including Conductors

204

(1)

B.3.3 The Magnetic Field Wave

205

(2)

B.4 References

207

(1)

B.5 Vector Calculus Notation Review

207

(1)

B.5.1 Vector Algebra

207

(1)

B.5.2 Scalar and Vector Fields

208

(1)

B.5.3 Vector Calculus

208

(4)

C Snell's Law, Fresnel's Equations, and the Total Reflection Coefficient Derivations and Historical Perspective

212

(1)

C.1 Introduction

212

(1)

C.2 Reflection and Refraction (Snell's Law)

212

(4)

C.3 Fresnel's Reflection and Transmission Coefficients

216

(4)

C.4 Using the Complex Index of Refraction

220

(1)

C.5 Total Reflection Coefficient for a Film on a Substrate

221

(3)

C.6 References

224

(1)

Index

225

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Spectroscopic Ellipsometry and Reflectometry A User's Guide

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Author Biography

Table of Contents

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