Automatic commit. Thu Aug 16 16:00:06 WST 2012

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

diff --git a/thesis/thesis.tex b/thesis/thesis.tex
index 113718c..e807997 100644 (file)
--- a/thesis/thesis.tex
+++ b/thesis/thesis.tex
@@ -122,8 +122,66 @@ Summarise the literature, refer to past research etc
 
 \subsection{Electron Spectra of Solids and Surface}
 
+\begin{itemize}
+       \item Overview of section
+\end{itemize}
+
+In this section, we will first introduce the basic concepts needed to describe the electron spectra of solids. A short description of methods for calculating the electron spectra will be given, and the results shown by these calculations. We will then discuss the electron spectra for the near surface region of solids, compared to the ``bulk'' spectra far from the surface.
+
+
+\subsubsection{Description of Matter in the Solid State}
+
+\begin{itemize}
+       \item Define and describe solid geometrically
+       \begin{itemize}
+               \item Basis + Lattice
+               \item Basis groups are assumed to be fixed relative to the lattice
+       \end{itemize}
+       \item Describe general properties of the potentials seen by electrons in solids
+\end{itemize}
+
+In the simplest models, a solid is represented by an infinite crystalline lattice; a geometrically repeated arrangement of some basis group of atoms. The nuclei of atoms are assumed to remain in fixed positions. 
+
+The potential seen by an electron in the lattice is periodic. For a single nuclei, the potential seen by an electron is 
 
+\subsubsection{Calculation of Electron Spectra}
+
+\begin{itemize}
+       \item Define electron spectra
+       \begin{enumerate}
+               \item 
+       \end{enumerate}
+       \item Free electron gas
+       \item Free electron entering a periodic potential
+       \item Potentials of real solids
+       \item Single vs Multiple electrons
+       \item Numerical calculations
+       \begin{itemize}
+               \item TODO: Actually research this
+               \item Find a comparison with a real experimental result
+       \end{itemize}
+       \item 
+\end{itemize}
+
+
+\subsubsection{The Near-Surface Region}
+
+\begin{itemize}
+       \item Real solids have surfaces
+       \item Differences between surface region and bulk
+       \begin{itemize}
+               \item Resulting differences in potential
+       \end{itemize}
+       \item How the electron spectra may differ from bulk values
+       \begin{itemize}
+               \item Surface states
+               \begin{itemize}
+                       \item Tamm & Shockley States
+               \end{itemize}
+       \end{itemize}
+\end{itemize}
 
+In the preceeding sections, solids were assumed to have infinite spatial extent. In practice, any real solid occupies a finite volume in space. Any interactions between a solid and its environment take place at the surface of the solid. As the volume of the solid is decreased, the role of the surface region in determining the behaviour of the solid in its environment is increased.