A Practical Guide to Optical Metrology for Thin Films

Description

A one-stop, concise guide on determining and measuring thin film thickness by optical methods.

This practical book covers the laws of electromagnetic radiation and interaction of light with matter, as well as the theory and practice of thickness measurement, and modern applications. In so doing, it shows the capabilities and opportunities of optical thickness determination and discusses the strengths and weaknesses of measurement devices along with their evaluation methods.

Following an introduction to the topic, Chapter 2 presents the basics of the propagation of light and other electromagnetic radiation in space and matter. The main topic of this book, the determination of the thickness of a layer in a layer stack by measuring the spectral reflectance or transmittance, is treated in the following three chapters. The color of thin layers is
discussed in chapter 6. Finally, in chapter 7, the author discusses several industrial applications of the layer thickness measurement, including high-reflection and anti-reflection coatings, photolithographic structuring of semiconductors, silicon on insulator, transparent conductive films, oxides and polymers, thin film photovoltaics, and heavily doped silicon.

Aimed at industrial and academic researchers, engineers, developers and manufacturers involved in all areas of optical layer and thin optical film measurement and metrology, process control, real-time monitoring, and applications.

Table of Contents

Preface

1 Introduction 1

2 Propagation of Light and Other Electromagnetic Waves 7
2.1 Properties of Electromagnetic Waves 7
2.2 Huygens–Fresnel Principle 14
2.3 Interference of Electromagnetic Waves 15
2.4 Reflection and Refraction 16
2.5 Diffraction 21
2.5.1 Transmission Gratings 27
2.5.1.1 Lamellar Transmission Gratings 27
2.5.1.2 Holographic Transmission Gratings 29
2.5.2 Reflection Gratings 31
2.5.2.1 Lamellar Reflection Gratings 31
2.5.2.2 Blazed Gratings 33
2.5.2.3 Holographic Gratings 34
2.6 Scattering 34
2.7 Dielectric Function and Refractive Index 35
2.7.1 Models for the Dielectric Function 35
2.7.2 Kramers–Kronig Analysis of Dielectric Functions 49
2.7.3 Empiric Formulas for the Refractive Index 50
2.7.4 EMA Models 53

3 Spectral Reflectance and Transmittance of a Layer Stack 59
3.1 Reflectance and Transmittance of a Single Layer 59
3.1.1 Coherent Superposition of Reflected Light 59
3.1.2 Influence of Absorption on the Layer 65
3.1.3 Partial Incoherence due to Thick Substrates 69
3.1.4 Partial Incoherence due to Roughness 72
3.1.5 Coherent Superposition of Transmitted Light 74
3.2 Propagating Wave Model for a Layer Stack 75
3.2.1 Coherent Reflectance and Transmittance of a Layer Stack 76
3.2.2 Consideration of Incoherent Substrates 78
3.2.3 Consideration of Surface Roughness 78
3.2.4 r-t-f Model for a Layer Stack 79

4 The Optical Measurement 81
4.1 Spectral Reflectance and Transmittance Measurement 81
4.2 Ellipsometric Measurement 85
4.3 Other Optical Methods 88
4.3.1 Prism Coupling 88
4.3.2 Chromatic Thickness Determination 92
4.4 Components for the Optical Measurement 94
4.4.1 Light Sources 94
4.4.1.1 Halogen Lamps 94
4.4.1.2 White Light LED 95
4.4.1.3 Superluminescence Diodes 96
4.4.1.4 Xenon High-Pressure Arc Lamps 97
4.4.1.5 Deuterium Lamps 97
4.4.2 Optical Components 99
4.4.2.1 Lenses and Mirrors 99
4.4.2.2 Polarizers and Analyzers 101
4.4.2.3 Optical Retarders 102
4.4.3 Optical Fibers 103
4.4.4 Miniaturized Spectrometers 107
4.4.4.1 Gratings 107
4.4.4.2 Detectors 110
4.4.4.3 System Properties 115

5 Thin-Film Thickness Determination 121
5.1 Fast Fourier Transform 122
5.1.1 Single Layer 122
5.1.2 Layer Stack 129
5.1.3 Accuracy, Resolution, Repeatability, and Reproducibility 130
5.2 Regression Analysis with 2-Test 131
5.2.1 Method of Thickness Determination 131
5.2.2 Accuracy, Resolution, Repeatability, and Reproducibility 137

6 The Color of Thin Films 141

7 Applications 149
7.1 High-Reflection and Antireflection Coatings 150
7.1.1 HR Coatings on Metallic Mirrors 151
7.1.2 AR Coatings on Glass 152
7.1.3 AR Coatings on Solar Wafers 153
7.2 Thin Single- and Double-Layer Coatings 156
7.2.1 SiO2 on Silicon Wafers 157
7.2.2 Si3N4 Hardcoat 157
7.2.3 Double-Layer System 158
7.2.4 Porous Silicon on Silicon 158
7.3 Photoresists and Photolithographic Structuring 160
7.4 Thickness of Wafers and Transparent Plastic Films 163
7.4.1 Thickness of Semiconductor, Glass, and Sapphire Wafers 163
7.4.2 Thickness of Transparent Plastic Films 167
7.4.3 Thickness of Doped Silicon 169
7.5 Silicon on Insulator 174
7.6 Thin-Film Photovoltaics 177
7.6.1 Inorganic Thin-Film Solar Cells 177
7.6.2 Organic Thin-Film Solar Cells 180
7.7 Measurement of Critical Dimensions 182

Numerics with Complex Numbers 187
Fourier Transform 191
Levenberg–Marquardt Algorithm 197
Downhill Simplex Algorithm 199
References 201
Index 209

Author Information

Dr. Michael Quinten works as Head of Research and Development Sensors at FRT GmbH in Bergisch Gladbach, Germany. Having obtained his diploma degree and Ph. D. in physics (1989) at the University of Saarland, Saarbruecken, Germany, he joined the Technical University RWTH Aachen in 1990 to work as a physics fessor. He then spent four years at several universities in Graz (Austria), Chemnitz, Aachen, Saarbruecken and Bochum (Germany). During his academic career, he authored 50 scientific publications on optical properties of nanoparticles, nanoparticle materials, and aerosols. In 2001, he joined the ETA-Optik GmbH, Germany, where he first worked in research and development of integrated optics components, and later became a product manager in the Colour and Coatings Division. During this period, he became expert in optical layer thickness determination. In 2007, he moved to FRT GmbH where he is responsible for the optical sensor technology division. He is the author of Optical Properties of Nanoparticle Systems: Mie and Beyond, Hardcover, 502 pages, Publisher: Wiley-VCH; 1 edition (March 15, 2011), ISBN10: 9783527410439, ISBN-13: 978-3527410439.