A P

ractical Gu

ide

to Op

tical Metrology for T

hin

Films

Quinten

www.wiley-vch.de

This book presents a comprehensive overview of optical metrology for thin film thickness determination by optical means, from electrodyna-mic basics, and hardware components, to methods of measurement and evaluation. The author, an expert in the field with both academic and industrial experience, concentrates on the spectral reflectance measurement with miniaturized spectrometers, one of the most flexible techniques for inline and offline thickness determination.

From the contents:

● Propagation of Light and other Electromagnetic Waves● Spectral Refl ectance and Transmittance of a Layer Stack● The Optical Measurement● Thin Film Thickness Determination● The Color of Thin Films● Applications

Michael Quinten works as Head of R&D Sensors at FRT GmbH in Bergisch Gladbach, Ger-many. 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 for his habilitation. He then spent four years at several universities in Graz (Austria), Chemnitz, Aachen, Saarbruecken and Bochum. During his academic period from 1983 to 2000, he au-thored 50 scientific publications with topics in optical properties of nanoparticles, nanoparticle materials and aerosols. In 2001 he joined the ETA-Optik GmbH, Germany, where he first wor-ked in research and development of integrated optics components, and later became product manager in the Colour and Coatings Division. In 2007 he moved to FRT GmbH where he is responsible for the optical sensor technology division.

ISBN 978-3-527-41167-2

A Practical Guide to Optical Metrology for Thin Films

Michael Quinten

57268File AttachmentCover.jpg

Michael Quinten

A Practical Guide to Optical

Metrology for Thin Films

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Michael Quinten

A Practical Guide to Optical Metrologyfor Thin Films

The Authors

Dr. Michael QuintenMauritiusstr. 752457 Aldenhoven

CoverAn artifically oxidized bismuth crystalsuperimposed on a background of medieval glass.After a long period in soil alteration formed a thinnanometric film of layer silicates with locallydifferent thickness on the glass. The thicknessof the nanometric oxide film on the crystal islocally different too. (Photograph of crystalby U. Quinten; photograph of glass by G.Müller,www.mueller-mineralien.de).

All books published by Wiley-VCH are carefullyproduced. Nevertheless, authors, editors, andpublisher do not warrant the information containedin these books, including this book, to be free oferrors. Readers are advised to keep in mind thatstatements, data, illustrations, procedural details orother items may inadvertently be inaccurate.

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# 2013 Wiley-VCH Verlag & Co. KGaA,Boschstr. 12, 69469 Weinheim, Germany

All rights reserved (including those of translationinto other languages). No part of this book may bereproduced in any form – by photoprinting,microfilm, or any other means – nor transmitted ortranslated into a machine language without writtenpermission from the publishers. Registered names,trademarks, etc. used in this book, even when notspecifically marked as such, are not to be consideredunprotected by law.

Print ISBN: 978-3-527-41167-2ePDF ISBN: 978-3-527-66437-5ePub ISBN: 978-3-527-66435-1mobi ISBN: 978-3-527-66436-8oBook ISBN: 978-3-527-66434-4

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Printed in SingaporePrinted on acid-free paper

To my family

Contents

Preface XI

1 Introduction 1

2 Propagation of Light and Other Electromagnetic Waves 72.1 Properties of Electromagnetic Waves 72.2 Huygens–Fresnel Principle 142.3 Interference of Electromagnetic Waves 152.4 Reflection and Refraction 162.5 Diffraction 212.5.1 Transmission Gratings 272.5.1.1 Lamellar Transmission Gratings 272.5.1.2 Holographic Transmission Gratings 292.5.2 Reflection Gratings 312.5.2.1 Lamellar Reflection Gratings 312.5.2.2 Blazed Gratings 332.5.2.3 Holographic Gratings 342.6 Scattering 342.7 Dielectric Function and Refractive Index 352.7.1 Models for the Dielectric Function 352.7.2 Kramers–Kronig Analysis of Dielectric Functions 492.7.3 Empiric Formulas for the Refractive Index 502.7.4 EMA Models 53

3 Spectral Reflectance and Transmittance of a Layer Stack 593.1 Reflectance and Transmittance of a Single Layer 593.1.1 Coherent Superposition of Reflected Light 593.1.2 Influence of Absorption on the Layer 653.1.3 Partial Incoherence due to Thick Substrates 693.1.4 Partial Incoherence due to Roughness 723.1.5 Coherent Superposition of Transmitted Light 743.2 Propagating Wave Model for a Layer Stack 753.2.1 Coherent Reflectance and Transmittance of a Layer Stack 76

VII

3.2.2 Consideration of Incoherent Substrates 783.2.3 Consideration of Surface Roughness 783.2.4 r-t-f Model for a Layer Stack 79

4 The Optical Measurement 814.1 Spectral Reflectance and Transmittance Measurement 814.2 Ellipsometric Measurement 854.3 Other Optical Methods 884.3.1 Prism Coupling 884.3.2 Chromatic Thickness Determination 924.4 Components for the Optical Measurement 944.4.1 Light Sources 944.4.1.1 Halogen Lamps 944.4.1.2 White Light LED 954.4.1.3 Superluminescence Diodes 964.4.1.4 Xenon High-Pressure Arc Lamps 974.4.1.5 Deuterium Lamps 974.4.2 Optical Components 994.4.2.1 Lenses and Mirrors 994.4.2.2 Polarizers and Analyzers 1014.4.2.3 Optical Retarders 1024.4.3 Optical Fibers 1034.4.4 Miniaturized Spectrometers 1074.4.4.1 Gratings 1074.4.4.2 Detectors 1104.4.4.3 System Properties 115

5 Thin-Film Thickness Determination 1215.1 Fast Fourier Transform 1225.1.1 Single Layer 1225.1.2 Layer Stack 1295.1.3 Accuracy, Resolution, Repeatability, and Reproducibility 1305.2 Regression Analysis with �2-Test 1315.2.1 Method of Thickness Determination 1315.2.2 Accuracy, Resolution, Repeatability, and Reproducibility 137

6 The Color of Thin Films 141

7 Applications 1497.1 High-Reflection and Antireflection Coatings 1507.1.1 HR Coatings on Metallic Mirrors 1517.1.2 AR Coatings on Glass 1527.1.3 AR Coatings on Solar Wafers 1537.2 Thin Single- and Double-Layer Coatings 1567.2.1 SiO2 on Silicon Wafers 157

VIII Contents

7.2.2 Si3N4 Hardcoat 1577.2.3 Double-Layer System 1587.2.4 Porous Silicon on Silicon 1587.3 Photoresists and Photolithographic Structuring 1607.4 Thickness of Wafers and Transparent Plastic Films 1637.4.1 Thickness of Semiconductor, Glass, and Sapphire Wafers 1637.4.2 Thickness of Transparent Plastic Films 1677.4.3 Thickness of Doped Silicon 1697.5 Silicon on Insulator 1747.6 Thin-Film Photovoltaics 1777.6.1 Inorganic Thin-Film Solar Cells 1777.6.2 Organic Thin-Film Solar Cells 1807.7 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

Contents IX

Preface

The optical response of a thin film is determined by several parameters: its thick-ness, its optical properties, and the surrounding (other layers, substrates). Amongthem, its thickness d is the most important. Compared to the vacuum wavelength oflight l, it must have a certain value to establish characteristic features in reflectance,transmittance, or ellipsometric parameters by interference. The size can be reducedby a factor n, with n being the refractive index of the film. The reason is that theoptical thickness t ¼ n�d is the intrinsic parameter that must be compared with l.

The measurement of reflectance, transmittance, or ellipsometric parameters hasbecome a major tool for in-line inspection, process control, and quality control ofthin films since it is fast, contactless, nondestructive, and even cheap compared toother methods.

During my successful stint with industry from 2001 till date, I have becomeacquainted with several aspects of optical thin-filmmetrology. It is a very fascinatingsubject since it connects electrodynamics with solid-state physics. The input para-meters of any evaluation algorithm are never constant but may vary from onemeasurement task to the next because the optical material functions strongly dependon film manufacturing, composition, and stochiometry. Film thickness determina-tion then becomes also a question of refractive index determination.

The purpose of this book is to introduce in optical metrology for thin filmthickness determination. It provides information on the electrodynamic basicsand methods of measurement and evaluation. Hence, it is directed at all peoplewho are involved in measuring film thickness by optical means, whether as man-ufacturer, in process and quality control, or in research and development. Hopefully,university lecturers and students of natural sciences and engineering will also findthis book beneficial.

To write this book required reading and evaluating many monographs and a stilllarger number of publications on this subject. To my surprise, a lot of work has beendone in ellipsometry, but spectral reflectance measurement for film thicknessdetermination is sparsely described in literature although it is a well-establishedmethod. The total amount of published work is, however, too immense to considerthem all in such a book. Therefore, I hope to have included the most relevant up todate, and apologize for all the contributions not considered here.

XI

Last but not least, I want to greatly acknowledge all the people who supported mewith data material, helpful information, and measurements, namely, Thomas Friesand Juergen Koglin from FRT GmbH, Anke Orth, Faiza Houta, and Bjoern Lewaldfrom FRT GmbH, Alexei Maznev from the Massachussetts Institute of Technology,and Leif J. Hoglund from Semilab AMS. Many thanks to Gerhard Mueller for thepicture of the glass on the cover, to my wife Ulrike for the picture of the oxidized Bicrystal on the cover, and finally to my family for their support and patience with meduring writing this book.

Aldenhoven, Michael QuintenFebruary 19, 2012

XII Preface

1Introduction

Thin films of transparent or semitransparent materials play an important role in ourlife. Avariety of colors in nature are caused by the interference of light reflected at thintransparent layers. Examples are the iridescent colors of a peacock feather, theimpressive colors of lustrous butterfly wings, or simply the play of colors of thin oilfilms on water.

Muchmoredemonstrative is,however, theuseof thinfilms in technicalapplications.Films with maximum thickness of a few hundred nanometers are used as protectivelayers, hard coatings, antireflection coatings, adhesion and antiadhesion coatings,decorativecoatings, transparent conductive layers, absorbing layers, inbiosensors, andfor tinted and annealed architectural glass. The combination of many thin films inmultilayer stackseven lead toopticalfilterswith sharpedges inreflectionand transmis-sion and almost 100% reflectivity in certain desired spectral ranges. The highestcommercial impact these films have in microelectronics. Most microelectronic parts(processors, RAMs, flat screens, CDs/DVDs, hard disks, and some more) are manu-factured with the help of thin-film technology. Thicker films of mainly transparentplastics arealmosteverywherepresentas foodpackaging,wrapping, foils,membranes,lamination, and in display technology and solar cells, to give some examples.

Hence, it is our attempt to get as much information as possible on the propertiesand composition of surfaces and surface coatings. The two main classes of thin-filmmeasurements are optical and stylus-based techniques. When measuring with a(mechanical) stylus, the thickness and roughness are obtained by monitoring thedeflections of the fine-tipped stylus as it is dragged along the surface of the film.Stylus instruments, however, require a step in the film to measure thickness, evenwhen using comparable optical sensors such as chromatic white light sensors. Theyare often the preferred method when measuring opaque films, such as metals.

Optical techniques determine the thin-film properties bymeasuring how the filmsinteract with light. They canmeasure the thickness, roughness, and optical constantsof a film. Optical techniques are usually the preferred method for measuring thinfilms because they are accurate, nondestructive, and require little or no samplepreparation. The two most common optical measurement types are the spectralreflectance measurement and the ellipsometry. They form themain subject of this book.Besides, there exist other nondestructive methods for film thickness determination

A Practical Guide to Optical Metrology for Thin Films, First Edition. Michael Quinten.� 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.

j1

with more or lower capabilities. Among them we find magnetoinductive andcapacitive methods and the eddy current method, as well as the indirect measure-ment by a vibrating quartz or the measurement with ultrasound. Optical methodscomprise light section, X-ray total reflection, photothermal deflection, and confocalchromatic measurement.

Spectral reflectancemeasurement or reflectometry uses the intensity of the light andmeasures the amount of light reflected from a thin film or a multilayer stack over arange of wavelengths, with the incident light normal (perpendicular) to the samplesurface. Spectral reflectance can also measure the thickness, roughness, and opticalconstants of a broad range of thinfilms.However, if thefilm is very thin so that there isless than one reflectance oscillation, there is insufficient information available todetermine the film parameters. Therefore, the number of film properties that may bedetermineddecreases for very thinfilms. If on the other hand one attempts to solve fortoomany parameters, a unique solution cannot be found, but more than one possiblecombination of parameter values may result in a calculated reflectance that matchesthe measured reflectance. Depending upon the film material and the wavelengthrange of themeasurement, theminimum single-film thickness that can bemeasuredusing spectral reflectance is in the 20–100nm range. Additional determination ofoptical constants increases this minimum thickness. Nevertheless, as spectral reflec-tance is much simpler and less expensive than the second most common opticalmeasurement – the ellipsometry – it is oftenused for quick and easy offline and in-linethickness determination in laboratories, production, and process control. To ourknowledge, no comprehensive book on reflectometry as it is being practiced existsexcept for the one by Tompkins and McGahan [1], published in 1999. Therefore, oneintention of this book is to bring the reflectometry closer to the practitioner.

In the late 1800s, Paul Drude [2] used the phase shift induced between theperpendicular components of polarized light to measure film thickness down to afew nanometers. This was the first study on film thickness measurement with amethod that was later called ellipsometry. When the perpendicular components ofpolarized light are out of phase, the light is said to be elliptically polarized, for whichthis technique came to be called ellipsometry. Ellipsometry measures reflectance atnonnormal incidence (typically around 75� from normal) and is rather sensitive tovery thin layers. The two different polarizationmeasurements provide twice asmuchinformation for analysis. Variable-angle ellipsometry can be used to take reflectancemeasurements atmany different incidence angles, thereby increasing the amount ofinformation available for analysis. In 1977, Azzam andBashara [3] authored the bookEllipsometry and Polarized Light, which has been the key source to be cited in mosttechnical writing on the subject. Later on, several handbooks were published [4–6]that cover the theory of ellipsometry, instrumentation, applications, and emergingareas, in which experts in the field contributed to various aspects of ellipsometry.Fundamental principles and applications of spectroscopic ellipsometry are to befound in the recently published work of Fujiwara [7].

This book starts with Chapter 2 with an introduction to the basics of thepropagation of light and other electromagnetic radiation in space andmatter. Beyondthe general properties of electromagnetic waves, we consider mainly the deviations

2j 1 Introduction

from the straightforward propagation by reflection, refraction, and diffraction sincethey are important for understanding the optical layer thickness determination andthe functioning of the optical measuring devices. Interference of electromagneticwaves is a key effect not only for the diffraction of light but also for the optical layerthickness determination as it causes characteristic deviations in the reflectancespectrum of a thin film. From this characteristic interference pattern, all the filmparameters are finally deduced.

Optical thickness determination is not only a question of electrodynamics but alsoa question of solid-state physics. The reason is that propagation inmatter alsomeansinteraction of the electromagnetic wave with the matter. This interaction can bedescribed with the complex dielectric function, while when discussing wave prop-agation in and through media the complex refractive index is appropriate. Both areconnected via Maxwells relation. In Chapter 2, we discuss physical models for thedielectric function and present empiric formulas for the refractive index.

Themain topics of this book, the determination of the thickness of a layer in a layerstack from measurement of the spectral reflectance or transmittance, is treated inChapters 3–5. The first step is taken in Chapter 3 with the modeling of the spectralreflectanceR and transmittanceTof a layer stack.Giving the thicknesses and complexrefractive indices of all layers and substrates of the layer stack as input parameters,two commonmodels – the propagatingwavemodel and the r-t-wmodel – can be usedto calculate R and T of the stack (see Figure 1.1). The models are introduced in

Layer Stack

Layers

Substrates

Thicknesses dj

Refractive Indices n + ij κj

Propagation Wave Model

r-t-φ-Model

Reflectance R(λ, d , n +ij j κj))

Transmittance T(λ, d , n +ij j κj))

Ellipsometric Parameters

Figure 1.1 Modeling the reflectance R and transmittance T or ellipsometric data of a layer stack.

1 Introduction j3

Chapter 3 and extensions on surface roughness and incoherent substrates arediscussed. Absorption of light in the layer restricts themeasurability of the thicknessto a material-dependent maximum thickness.

In Chapter 4, we introduce the reflectometric and ellipsometricmeasurement andfurther optical methods, and discuss the optical components needed for the mea-surements. In all setups for optical thickness determination, the sample getsilluminated. Hence, light sources and their spectral distribution play a key role inthe layer thickness determination, as well as the second key component, spectro-meters. With the spectrometer, the reflected light modulated by the thicknessinterference gets spectrally resolved and analyzed.

Reflectometric and ellipsometric measurements do not measure the physicalproperties themselves but the optical response of the system caused by the physicalproperties. Hence, one needs to solve an inverse problem in order to find the value ofactual physical properties of interest, such as thicknesses of the layers and opticalproperties of thematerials. This inverse problem is solved numerically byfinding thebest fit between measured and calculated data, and physical properties are inferredfrom the model that gives the best fit (see Figure 1.2). To get reliable results, it isimportant to check the validity of the usedmodel and to understand the sensitivity ofthe measured data to parameters of interest. In Chapter 5, we present and discussnumericalmethods for determination of layer thickness and determination of opticalconstants of the layer material.

Chapter 6 is devoted to the apparent color of thin films. As the photographs on thecover of this book demonstrate, the interference in thin films leads to various colorsdepending on the thickness and refractive index of the film. However, not all colors

Measured R, T

Measured Ellipsometric Parameters

Model R, T

Model Ellipsometric Parameters

Regression Analysis

Adjust dj, nj + iκj

Final Result dj, nj + iκj

Figure 1.2 Fit procedure when analyzing measured R, T, or ellipsometric data for film thickness.

4j 1 Introduction

are available from one single layer. Instead, multilayer systems are needed to cover acertain color gamut.

Finally, inChapter 7we present several technical applicationswherefilm thicknessmeasurement is important. They are accompanied by corresponding measuringresults. The applications can be classified into the following:

. Applications with a single unsupported layer, for example, glass, sapphire, orsemiconductor wafers, and transparent polymer films.

. Applications with one layer on a substrate, for example, protective layers (hardcoats), broadband antireflection coatings, photoresists, and transparent conduc-tive layers (TCF and TCO).

. Applications with two layers on a substrate. Examples of two layers on a substrateare photoresists on silica on a wafer, bonded wafers, and SOI wafers (SOI, siliconon insulator).

. Multilayer applications, for example, high reflective (HR) and antireflective (AR)coatings, beam splitter coatings, dielectric mirrors, optical filters, thin-film solarcells, and OLEDs (organic light emitting diodes).

We want to point out that all calculations of reflectance and transmittance spectra,the evaluation of thickness parameters and color, and the determination of opticalconstants were carried out with self-made software packages, MQLayer, MQNandK,and MQColor [8].

1 Introduction j5

2Propagation of Light and Other Electromagnetic Waves

This chapter introduces the basics of the propagation of light and other electromag-netic radiation in space andmatter. Beyond the general properties of electromagneticwaves, we consider mainly the deviations from the straightforward propagation byreflection, refraction, and diffraction since they are important for understanding theoptical layer thickness determination and the functioning of the optical measuringdevices. Last but not least, propagation in matter also means interaction of theelectromagnetic wave with thematter for what we also discuss the dielectric functionand the refractive index in this chapter.

2.1Properties of Electromagnetic Waves

When discussing the properties of electromagnetic waves, it seems appropriate togive first a definition of a wave. A wave generally is a process that is periodic in timeand space. Thatmeans there exists a periodicity T in time after that thewave looks thesame as at a certain time point t, and a periodicityR in space where the wave looks thesame as at a certain point r:

AðrþR; tþTÞ ¼ Aðr; tÞ: ð2:1Þ

Mathematically, A(r,t) fulfills the wave equation (in Cartesian coordinates):

q2

qx2þ q

2

qy2þ q

2

qz2� 1c2

q2

qt2

� �Aðr; tÞ ¼ 0; ð2:2Þ

with c being the propagation velocity. That means, in general, we search for a vectorwith its second derivative in time being proportional to its second derivative in space.The actual solution, however, is additionally determined by the boundary conditionsof this differential equation.

A Practical Guide to Optical Metrology for Thin Films, First Edition. Michael Quinten.� 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.

j7

When talking about electromagnetic waves, we often find, though it is notmandatory, that solutions of the wave equation are harmonic functions in time andspace like

Aðr; tÞ ¼ A0 � expðiðkr�v tþwÞÞ; ð2:3Þwith k¼ |k|¼ 2p/|R|, v¼ 2p/T, and w an arbitrary constant. The length |R| is calledwavelength l and describes the distance between two successive identical phases ofthewave in space, for example, the distance between twomaxima or twominima. Thepropagation velocity corresponds to the vacuum velocity of light c¼ 299 792 458m/s.k and v fulfill the dispersion relation

k2 ¼ v2

c2: ð2:4Þ

Note that in (2.3)we used the notationwith complex numbers, with i ¼ ffiffiffiffiffiffiffi�1p beingthe complex unit. This notationwill be used throughout the book. For an introductionto the numerics with complex numbers, we refer to Appendix A.

For electromagnetic waves, we have to consider an electric field E(r,t) and amagnetic field H(r,t) that must fulfill on the one hand the above conditions for A(r,t) and on the other hand Maxwells equations:

divðDÞ ¼ r; ð2:5Þ

divðBÞ ¼ 0; ð2:6Þ

curl E ¼ � qBqt

; ð2:7Þ

curlH ¼ Jþ qDqt

: ð2:8Þ

These equations, however, contain three more vectors, the current density J, theelectrical flux density or displacement D, and the magnetic induction B. To resolveMaxwells equations for E and H, it is therefore necessary to supplement them byrelations that connect J, D, and B with E and H.

When applying an electric field E on anymaterial, the electric field forces unboundcharge carriers to move, resulting in a current with density J. The current isproportional to the applied field, with the conductivity s being the proportionalityconstant:

J ¼ sE: ð2:9ÞFor bound charge carriers, the situation is different. They cannot move but aredisplaced. Inside the body of condensed matter the electric field usually displacesonly the electrons while the ions are too inert as to follow the electric field. Thereby,each atom becomes an electric dipole with dipole moment p. These dipole momentsadd up to amacroscopic net polarization P of thematerial that is related to the electric

8j 2 Propagation of Light and Other Electromagnetic Waves

field E by the general equation

P ¼ e0xE: ð2:10ÞThe factor x is the macroscopic susceptibility of the matter. The polarization P

contributes to the electrical flux density or displacement D:

D ¼ e0EþP ¼ e0ð1þ xÞE ð2:11Þdefining the dielectric constant or permittivity e as

e ¼ 1þ x: ð2:12ÞSusceptibility x and dielectric constant e are the optical material functions. In theframework of Maxwells theory, they enter the field relations as constants that arevalid for the bulk material under consideration.

Applying a time harmonic electric field, the dipoles oscillate with the samefrequency as the applied field. That means the center of gravity of the displacedelectrons changes fromone side to the other side, resulting in a displacement currentqD/qt.

Similar to the electric field E, the magnetic fieldH also causes two reactions of thematerial on the applied field, a magnetizationM, and a current displacement qD/qt.The latter is the result of the Lorentz force on bound and free electrons. Themagnetization M contributes to the magnetic induction B in the material

B ¼ m0Hþ m0M ¼ mm0H ð2:13Þdue to reorientation of permanent magnetic dipoles in the applied field. Looking atfrequencies of electromagnetic waves, permanentmagnetic dipoles are too inert as tofollow a rapidly oscillating magnetic field. This holds true for frequencies rangingfrom the far infrared to infinity. Therefore, the relative permeability m can be assumedto be 1 throughout the above frequency range, even for magnetic materials.

Finally, we point to the fact that when dealing with electromagnetic waves, staticcharges are absent, that is, r¼ 0. If we further restrict only to timeharmonicfields forthe sake of simplification, the time dependence of thefields can be separatedwith theansatz

E ¼ EðrÞ � exp �ivtð Þ and H ¼ HðrÞ � exp �ivtð Þ ð2:14Þand the corresponding Maxwell equations for the unknown parts E(r) andH(r) nowread

divðEÞ ¼ 0; ð2:15Þ

divðHÞ ¼ 0; ð2:16Þ

curlðEÞ ¼ ivm0H; ð2:17Þ

curlðHÞ ¼ ð�iee0vþ sÞE: ð2:18Þ

2.1 Properties of Electromagnetic Waves j9