+Figure \ref{tcs_simple.pdf} shows a simplified schematic for the Total Current Spectroscopy experiments conducted during this study. Electrons are produced via thermionic emission by heating a cathode. A series of electrodes are used to accelerate and focus a current $I_1$ onto the target. The energy of primary electrons is controlled by adjusting the power supply $U$, which determines the potential between the cathode and target. The transmitted current $I$ to flow through an ammeter external to the chamber.
+
+\begin{center}
+ \includegraphics[scale=0.50]{figures/tcs_simple}
+ \captionof{figure}{Simplified Diagram of TCS Experiments}
+ \label{tcs_simple.pdf}
+\end{center}
+
+The goal of Total Current Spectroscopy is to measure variations in the secondary electron current $I_2$. It can easily be demonstrated that this can be accomplished by measurement of $I$. We will summarise the approach adopted by Komolov \cite{komolov}.
+
+From the above, it is obvious that $I = I_1 - I_2$. Assuming that $I$ is a constant, independent of primary electron energy $E_1$, we define the Total Current Spectrum (TCS) as:
+\begin{align*}
+ S(E_1) &= \der{I}{E_1} = - \der{I_2}{E_1}
+\end{align*}
+This result also assumes that $I$ does not vary during the time taken to perform a measurement of $S(E_1)$ for a range of $E_1$ values. This is generally valid in the period after the cathode reaches thermal equilibrium.
+
+RelThe energy of a single primary electron arriving at the sample is given by $E = e U + c$, where $e$ is the electron charge, $U$ is the potential difference between cathode and sample, and $c$ a constant including the contact potential between the cathode and sample.
+In reality, the cathode emits electrons with a distribution of energies, which is further altered by the focusing properties of the electrodes; as a result, the energy of the incident primary electrons is described by a distribution $f(E - E_1)$ about the mean value $E_1$, with the maximum of the distribution at $E = E_1$.
+
+The primary electron current $I_1$ for a mean energy $E_1 = e U$ can be written as:
+\begin{align*}
+ I_1(E_1) &= e A \int_{0}^{\infty} f(E - E_1) dE
+\end{align*}
+Where $A$ is the surface area irradiated by the beam.
+
+Introducing the secondary emission coefficient $\sigma(E)$, which gives the probability for secondary electron emission to occur due to a primary electron of energy $E$, we can write the secondary electron current as:
+\begin{align*}
+ I_2(E_1) &= e A \int_{-E_1}^{\infty} \sigma(E_1)f( E - E_1) dE
+\end{align*}
+
+The total current $I$ may then be written as:
+\begin{align*}
+ I(E_1) &= e A \left[ \int_{0}^{\infty} f(E - E_1) dE - \int_{-E_1}^{\infty} \sigma(E_1)f( E - E_1) dE \right]
+\end{align*}
+
+Differentiating, using the fundamental theorem of calculus, we can determine the total current spectrum:
+\begin{align*}
+ S(E_1) = \der{I}{E_1} &= e A \left\{ [ 1 - \sigma(0)] f(-E_1) - \int_{0}^{\infty} f(E - E_1) \der{\sigma(E_1)}{E_1} dE \right\}
+\end{align*}
+
+The first term in the above expression is determined solely by the distribution of primary electrons $f$. This term will be maximised when $E_1 = 0$; meaning that $U$ is equal to the contact potential $c$ between the cathode and sample.
+
+The second term contains all dependence of $S(E_1)$ on characteristics of the sample. At the threshold for a particular process, the secondary emission efficiency $\sigma(E_1)$ is expected to undergo a sharp change. This results in a well defined maxima or minima in the derivative $\der{\sigma(E_1)}{E_1}$, which can be seen as a corresponding maxima or minima in the total current spectrum $S(E_1)$. From the convolving function $f(E - E_1)$, it can be seen that the distribution of primary electron energy has the effect of broadening such a peak, and lowering its absolute height; the resolution of the method is determined by $f(E - E_1)$. It is desirable to achieve maximum resolution by accurate focusing of the electron gun.
+
+
+\subsubsection{The Secondary Emission Coefficient}
+
+Having established a means for measuring $\sigma(E_1)$
+
+
+
+
+Often, the conventional ammeter and DC power supply in Figure \ref{tcs_simple.pdf} are replaced with a lock-in amplifier and AC power supply, as in Komolov's description \cite{komolov}. The power supply can be set to a fixed frequency, and the lock-in amplifier used to remove all other frequencies from the detected signal; this can be used to eliminate . Lock-in amplifier techniques also have the advantage of measuring S(E) directly; without the amplifier, finite differences must be used to approximate S(E) from measurement of $I(E)$. For this study, the lock-in amplifier approach was inpractical due to the limitations on available equipment. For future studies, it is suggested that the lock-in amplifier approach be adopted.
+
+For a more detailed description of the experimental setup, Refer to Appendix B for a discussion of hardware to automate the measurement of $I$ and control of $U$. Refer to Appendix D for a discussion of the electron gun and its control circuit.
+
+
+
+\subsubsection{Automatic Data Acquisition}
+
+In order to collect data on the large number of planned samples for the study, some form of automation was required. The automated system needed to be able to set the initial energy by adjusting the potential of the cathode relative to the sample, and simultaneously record the total current through the sample.
+
+The available power supplies at CAMSP featured analogue inputs for external control. This meant that a Digital to Analogue Convertor (DAC) card was needed to interface between the control computer and the power supply. In addition, the available instruments for current measurement produced analogue outputs. As a result, Analogue to Digital Convertors (ADCs) were required to automate the recording of total current.
+
+Although an external DAC/ADC box was already available for these purposes, initial tests showed that the ADCs on the box did not function. The decision was made to design and construct a custom DAC/ADC box, rather than wait up to two months for a commercial box to arrive. The design of the custom DAC/ADC box is discussed in detail in Appendix B, and the software written for the on-board microprocessor and the controlling computer are included in Appendix D.
+
+
+\subsection{Ellipsometry}
+
+Ellipsometry is an optical technique most commonly used to determine the thickness of multilayered thin films. Ellipsometry can also be used to determine the optical constants and properties of unknown materials.
+
+Essentially, ellipsometry measures the change in polarisation of light reflected from a surface. This change in polarisation can be related to properties of the surface if knowledge of the surface is correctly applied. For a bulk sample, the change in polarisation can be directly related to the optical constants of the material.
+
+
+
+
+\subsubsection{Variable Angle Specroscopic Ellipsometry}
+A single ellipsometric measurement involves recording $r_p$ and $r_s$ at one angle and wavelength. The earliest ellipsometers were
+
+
+A Variable Angle Spectroscopic Ellipsometer at CAMSP has been used to perform a variety of measurements on metallic thin films.,
+
+The VASE
+
+It is also possible to conduct reflection and transmission spectroscopy experiments using the VASE.
+
+
+\subsection{Vacuum Techniques and Sample Preparation}
+
+Both the TCS experiments and the deposition of films must be performed in a vacuum. For convenience and simplicity, a single vacuum chamber at CAMSP has been repurposed to perform both of these tasks. The chamber can be pumped by a molecular turbo pump, backed by a rotaray pump, to a base pressure of $2\times10^{-8}$ mbar, or by the rotary pump alone to a base pressure of $1\times10^{-3}$ mbar. The pressure is monitored using either a pirani or ion gauge (for pressures greater than and less than $10^{-3}$ mbar respectively).
+
+%TODO: Insert graphs of pressure in chamber
+
+Figure \ref{} shows a diagram of the vacuum chamber used both for the creation of nanostructured thin films and their study using TCS. A rotatable sample holder is positioned in the centre of the chamber. One flange of the chamber houses the electron gun used for TCS measurements, whilst the opposite flange contains feedthroughs on which tungsten filament evaporators are mounted. This setup allows for almost immediate study of evaporated films by simple rotation of the sample holder to face the gun.
+
+
+The evaporators consist of a tungsten wire filament attached between two feedthroughs. A piece of a desired metal is folded over the apex of the tungsten wire. The metal can be heated by passing a current through the filament; near the metal's melting point it begins to evaporate. To clean the metal surface and ensure uniform evaporation, this procedure is first performed at low pressure (below $10^{-6}$ mbar) with no sample in the chamber, with the current increased until the metal piece begins to melt and forms a ball on the wire. Figure \ref{} shows an image of an evaporator that has been prepared for use.
+
+This study focused primarily on depositing Au films on an Si substrate, at both high and low pressures. The substrates and sample holders were cleaned in an acetone bath immediately prior to insertion in the vacuum chamber.
+
+