\chapter*{Electron Optics}


There are two goals of electron optics as applied to total current spectroscopy (and other forms of electron scattering experiments): firstly, to produce the narrowest possible distribution $f(E - E_1)$ of primary electron energies at the sample, and secondly, to ensure that 

The electron gun used for this study contains a total of ten electrodes, with six independently adjustable groups. Figure \ref{egun_simulation1.pdf} illustrates a cross section of the gun, using colour coding to indicate groups of electrodes which are kept at the same potential.


The important electrode groups are, in order from left to right:
\begin{enumerate}
	\item {\bf Wenhalt Cylindar}

	The first electrode, which houses the cathode, providing a narrow apparture for electrons to exit. A positive potential (of the order of $10V$ applied to the Wenhalt causes electrons leaving the cathode to be accelerated into a narrow beam.

	It is difficult to control the focusing properties of the gun using the Wenhalt alone; the main purpose of the Wenhalt is to create a high current, narrow beam of electrons, which can be focused by the other electrodes in the gun. If the potential applied to the Wenhalt is too high, electrons will be drawn into its surface. If the Wenhalt potential is too low, then the 

	\item {\bf Einzel Lens }

	The six central electrodes are an example of an Einzel lens, used for acceleration and focusing of the electron beam.
	The first and last pair of electrodes are held at a large positive potential, causing electrons to accelerate. A smaller potential (often negative, but not necessarily) applied to the central pair of electrodes has the effect of altering the angular dispersion of the beam.

	\item {\bf Deflection Plates}

	Unequal potentials applied to the deflection plates can be used to bend the direction of the electron beam. To ensure the accelerating potential seen by the electrons is as uniform as possible, the deflection plates are biased at potentials of $\frac{V_d}{2} \pm V_a$, with $V_d$ determined by the controlling power supply. When $V_d = 0$, the beam is undeflected.

	\item {\bf Final Electrode}

	The electron gun was originally designed for use in a Cathode Ray Oscilloscope (CRO). This electrode is held just in front of a flurescent screen, but is not electrically connected to the screen. When accellerated electrons strike the screen, they are 

	In the total current spectroscopy experiments, this electrode is typically at a much higher potential than the surface under bombardment. As a result, low energy primary electrons may be deflected or even turned back towards the gun, rather than striking the surface. This effect can be exploited to narrow the energy distribution of primary electrons at the surface, but also has the effect of greatly reducing the current of primary electrons reaching the surface.
\end{enumerate}

In preparation for Total Current Spectroscopy experiments, the effect of each of the controllable potentials was investigated by focusing the electron gun on its original flurescent screen. However, when repurposed for total current spectroscopy, the gun needed to be refocused several times (with changing sample holder design).

From \ref{tcs_theory1}, it is apparent that the electron gun should be focused to achieve the maximum possible resolution by producing the narrowest possible primary energy distribution at the target. In addition, to increase the energy range (relative to the target), it 

The gun was focused using an iterative process, by which each potential was altered in turn to maximise the current.


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\section{A two dimensional electron gun simulation}

The below figures \ref{egun_simulation1.pdf} and \ref{egun_simulation2.pdf} are the results of a simplistic electron gun simulation. The results of this simulation were not used to focus the actual electron gun; the images shown here are purely presented as a visual aid.

\begin{center}
	\includegraphics[scale=0.45, angle=270]{/home/sam/Documents/University/honours/thesis/figures/egun_simulation1.pdf} 
	
	\captionof{figure}{{\bf 2D Simulation of trajectories of electrons accelerated through an electron gun}}
	\label{egun_simulation1.pdf}
	\includegraphics[scale=0.45, angle=270]{/home/sam/Documents/University/honours/thesis/figures/egun_simulation2.pdf} 
	\captionof{figure}{{\bf 2D Simulation of the electrostatic potential produced by the electron gun}}\label{egun_simulation2.pdf}
	
\end{center}

\pagebreak

