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[matches/honours.git] / thesis / ellipsometry.tex~

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+\documentclass[10pt]{article}
+\usepackage{graphicx}
+\usepackage{caption}
+\usepackage{amsmath} % needed for math align
+\usepackage{bm} % needed for maths bold face
+ \usepackage{graphicx}    % needed for including graphics e.g. EPS, PS
+\usepackage{fancyhdr}  % needed for header
+%\usepackage{epstopdf} % Needed for eps graphics
+\usepackage{hyperref}
+\usepackage{lscape}  % Needed for landscaping stuff - when printing
+\usepackage{pdflscape} % Needed for landscaping - in pdf viewer
+ \topmargin -1.5cm        % read Lamport p.163
+ \oddsidemargin -0.04cm   % read Lamport p.163
+ \evensidemargin -0.04cm  % same as oddsidemargin but for left-hand pages
+ \textwidth 16.59cm
+ \textheight 21.94cm 
+ %\pagestyle{empty}       % Uncomment if don't want page numbers
+ \parskip 7.2pt           % sets spacing between paragraphs
+ %\renewcommand{\baselinestretch}{1.5}         % Uncomment for 1.5 spacing between lines
+ \parindent 0pt                  % sets leading space for paragraphs
+
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+\newcommand{\divg}[1]{\nabla \cdot #1} % divergence
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+\newcommand{\der}[3][ ]{\frac{d^{#1} #2}{d #3^{#1}}} %full derivative
+\newcommand{\phasor}[1]{\tilde{#1}} % make a phasor
+\newcommand{\laplacian}[1]{\nabla^2 {#1}} % The laplacian operator
+
+\usepackage{color}
+\usepackage{listings}
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+\lstset{language=Java}
+\lstset{backgroundcolor=\color{darkgray}}
+\lstset{numbers=left, numberstyle=\tiny, stepnumber=1, numbersep=5pt}
+\lstset{keywordstyle=\color{darkred}\bfseries}
+\lstset{commentstyle=\color{darkblue}}
+%\lstset{stringsyle=\color{red}}
+\lstset{showstringspaces=false}
+\lstset{basicstyle=\small}
+
+
+\begin{document}
+
+\pagestyle{fancy}
+\fancyhead{}
+\fancyfoot{}
+
+\fancyhead[LO, L]{}
+\fancyfoot[CO, C]{\thepage}
+
+%\title{\bf Characterisation of nanostructured thin films}
+%\author{Sam Moore\\ School of Physics, University of Western Australia}
+%\date{April 2012}
+%\maketitle
+
+\section{Ellipsometry}
+
+\subsection{Description of Method}
+
+Ellipsometry is a versatile optical technique commonly employed for determining the thickness of multilayered thin films \cite{}. In general, ellipsometry measures the parameters $\psi$ and $\Delta$, which are related to the complex Fresnel reflection coefficients $r_s$ and $r_p$:
+\begin{align*}
+       \tan \psi e^{i \Delta} &= \rho = \frac{r_p}{r_s}
+\end{align*}
+$r_s$ is the 
+
+
+For a bulk substrate (the simplest possible sample), $r_s$ and $r_p$ may be directly related to the optical constants of the material:
+\begin{align*}
+
+\end{align*}
+
+\emph{TODO: Multilayered thin films}.
+
+\section{Variable Angle Spectroscopic Ellipsometry}
+
+Traditional ellipsometers were limited to single measurements at a fixed wavelength and angle; the analysis of thin films involved \cite{}.
+
+With the 
+
+\subsection{Results}
+
+\subsubsection{Application of Ellipsometry to Multilayered Sample}
+
+\pagebreak
+\bibliographystyle{unsrt}
+\bibliography{thesis}
+ 
+\end{document}
+