The report will be organised as follows; first we will discuss literature relating to surface science and nanostructured thin films in particular. We will then give an overview of the primary experimental techniques employed during this project, before presenting experimental results. Finally, we will discuss stuff.
+\emph{NOTE: Introduction needs work}
+
\pagebreak
\section{Overview}
In this section we provide an overview of theoretical and experimental literature related to the properties of nanostructured thin films. We also include a summary of the past research which focuses on metallic-black films.
-\subsection{Secondary Electron Emission}
-% What is it?
-Secondary electron emission refers to the emission of electrons from a target surface caused by interactions with an incident electron, or more commonly a beam of electrons. Electrons from the incident beam are referred to as primary electons, whilst the term ``secondary electron'' applies to all electrons reflected or emitted from the surface under bombardment.
-% First mentions and early research
-% General description of secondary electron spectrum
-Figure \ref{se_dist.pdf} shows the general shape of an energy distribution of secondary electrons. for a primary electron energy of $E_p$. The narrow peak centred at $E = E_p$ is due to elastically scattered electrons; the width of this peak is determined by the distribution of primary electron energies, as well as the resolution of the detector. The broad peak in the low energy part of the spectrum is due to inelastically scattered electrons.
+\subsection{Electron Surface Interaction}
-\begin{center}
- \includegraphics[scale=0.40]{figures/se_dist.pdf}
- \captionof{figure}{{\bf Model of Secondary Electron Distribution}}
- \label{se_dist.pdf}
-\end{center}
-% How real secondary electron spectra depend upon the surface
+% Research of Komolov
-Real secondary electron distributions also show fine structure imposed upon the inelastic part of simplified spectrum described above. This fine structure is characteristic of the electron spectra of the target surface. Near to the elastic peak, fine structure is caused by energy loss to interband transitions and plasma vibration excitation. The central part of the distribution contains fine structure due to Auger electron emission, and energy losses due to excitation of inner electrons. Fine structure at low energies is due to the structure of empty states of the solid.
+\subsection{Electron Surface Interaction}
-% Research of Komolov
\subsection{Plasmons}
+\emph{NOTE: To be completely honest, I don't think I can say much about plasmons. The TCS experiment does not detect plasmonic behaviour. The Ellipsometer can be used to determine frequencies at which plasmons might occur. However, I have not seen any dips in $\epsilon$ which would indicate plasmon thresholds.}
+
% What are they?
A plasmon is a quasi-particle arising due to charge density oscillations in a solid.
+
+
% Early research
\subsection{Metallic-Black Films}
\subsection{Secondary Electron Spectroscopy}
-Secondary Electron Spectroscopy encompasses a large group of techniques which exploit secondary electron emission for studying the electron spectra of surfaces and solids. In these methods a beam of primary electrons is directed at a surface. The interactions between primary electrons and the surface give rise to an energy distribution of electrons elastically and inelastically scattered from the surface. Analysis of the distribution of the scattered ``secondary'' electrons gives information about the electron energy spectrum of the target surface.
+In this section, we will give a general overview of the basic concepts of Secondary Electron Spectroscopy. The next section will focus on low energy Total Current Spectroscopy, the particular technique which has been employed for this study.
+
+
+Secondary Electron Spectroscopy encompasses a large group of techniques used for studying the electron spectra of surfaces and solids, and processes of secondary electron emission. In these methods a beam of primary electrons is directed at a surface. The interactions between primary electrons and the surface give rise to an energy distribution of secondary electrons ejected from the surface.
+
+
+\begin{center}
+ \includegraphics[scale=0.40]{figures/se_dist.pdf}
+ \captionof{figure}{{\bf Model of Secondary Electron Distribution}}
+ \label{se_dist.pdf}
+\end{center}
+
+\emph{NOTE: I need to draw some fine structure on this curve somehow. Or find an actual spectrum to reproduce.}
+
+Figure \ref{se_dist.pdf} shows a simplified model of an energy distribution of secondary electrons.
+
+The spectrum shown in Figure \ref{se_dist.pdf} may be divided into several regions based upon the originating processes of the secondary electrons in each region. However, it is important to note that these processes are determined by the primary electron energy $E_p$; each process has a threshold energy, below which it cannot occur. For example, Auger electrons are only produced if the primary electrons have sufficient energy to excite an inner level electron to above the Fermi level.
+
+The narrow peak centred at $E = E_p$ is largely due to elastically scattered primary electrons\footnote{A typical width is $0.5-1.0$eV; as a result, small energy losses due to phonon excitations ($10-50$meV) can not resolved from truly elastic reflections \cite{komolov}}; the width of this peak is determined by the distribution of primary electron energies, as well as the resolution of the detector.
+
+Fine structure due to low energy losses can be observed just below the primary peak. These energy losses are due to transitions between the valence and conduction bands, and plasma vibration excitation. This part of the spectrum is the focus of Energy Electron Loss Spectroscopy (EELS).
-Techniques of Secondary Electron Spectroscopy can be divided into two classes. Energy-resolved methods are based upon observation of the secondary electron distribution at a fixed primary electron energy. These methods aim to examine specific secondary emission processes which occur within a selected energy interval. The angular distribution of emitted electrons is often also recorded.
+The central region of the distribution is mostly due to inelastically scattered (or ``rediffused'') primary electrons. If the energy of primary electrons is sufficient, this region may also contain fine structure due to Auger excitations.
-In contrast to Energy-resolved methods, Total Current (or Yield) methods measure the total current of secondary electrons as a function of primary electron energy. The focus of this project has been low energy Total Current Spectroscopy (TCS). While Total Current methods provide less detailed information about secondary emission processes within a solid, they are generally simpler to realise experimentally as they do not require energy analysers, and current measurement may be performed external to the vacuum chamber, using a conventional ammeter.
+The broad, asymetrical curve at low energy is due to inelastically scattered primary electrons which have undergone multiple scattering events. So called ``true'' secondary electrons, the direct result of secondary electron emission, also appear in this region for sufficiently large primary electron energies.
+For a more detailed discussion, refer to \cite{komolov}.
-\subsection{Total Current Spectroscopy}
-Figure \ref{} shows a simplified schematic for the Total Current Spectroscopy experiments conducted during this study. An electron gun is used to produce the beam of primary electrons. Electrons are emitted from a cathode held at negative potential relative to the target. These electrons are focused into a beam and accelerated onto the target through the electric field produced by a series of electrodes. A detector is used to measure the total current passing through the target.
+Techniques of Secondary Electron Spectroscopy can be divided into two classes. Energy-resolved methods are based upon observation of the secondary electron distribution at a fixed primary electron energy. The angular distribution of emitted electrons is often also recorded. These methods aim to examine the properties of secondary electrons emitted in a particular energy interval.
+In contrast to Energy-resolved methods, Total Current (or Yield) methods measure the total current of secondary electrons whilst varying the primary electron energy. As the primary electron energy reaches the threshold for a particular mechanism of secondary electron scattering, the analysis of the total secondary electron current as a function of energy can give information about the threshold energies for processes of interest.
-If the current incident upon the sample is $I_{\text{total}}$, and the current of secondary electrons scattered from the surface is $I_r$, then the transmitted current $I_t$ is given by:
+Total Current methods are generally simpler to realise experimentally compared with Energy-resolved methods, as they do not require energy analysers, and current measurement may be performed external to the vacuum chamber, using a conventional low current ammeter. It is also simple to combine a Total Current methods with existing Energy-resolved methods.
+
+\subsection{Low Energy Total Current Spectroscopy}
+
+As the name suggests, low energy Total Current Specroscopy is based upon measurement of the total secondary electron current at low primary electron energies, typically in the range of $0-15$eV. At low primary energies, the secondary electron current is predominantly composed of inelastically reflected primary electrons which have lost energy in causing interband transitions.
+
+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. 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.
+
+\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 $I$.
+
+In the following discussion, we will summarise the approach adopted by Komolov to relate measurement of $I(E_1)$ to characteristics of the sample under study \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*}
- I_t &= I_{\text{total}} - I_r
+ 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.
-Generally $I_{\text{total}}$ is assumed to be independent of initial energy $E$. This assumption is valid if the initial energy is small compared to the accelerating potential of the gun, and the distance of the sample from the gun is sufficiently large.
+The 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 $E = E_1$.
-In this case, differentiating with respect to $E$:
+The primary electron current $I_1$ for a mean energy $E_1 = e U$ can be written as:
\begin{align*}
- \der{I_t}{E} &= - \der{I_r}{E}
+ 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.
-Figure \ref{block_diagram.pdf} is a block diagram of the experimental setup including measurement and control systems external to the vacuum chamber.
-Note that the emission current ammeter is optional, and was used for testing purposes.
+Introducing the secondary emission coefficient $\sigma(E)$, which gives the probability for a primary electron of energy $E$ to give rise to a secondary electron, 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*}
-\begin{center}
- \includegraphics[scale=0.60]{figures/block_diagram.pdf} \label{block_diagram.pdf}
-\end{center}
+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*}
-\subsubsection{Electron Optics}
+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 electron gun used for this experiment was repurposed from an old Cathode-Ray Oscilloscope (CRO). Figure \ref{} shows a simplified diagram of the electron gun, whilst Figure \ref{} shows a photograph of the gun.
+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 full circuit diagram for the electron gun control circuit is shown in Appendix A. %\cite{}
+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 determines the degree to which $\der{\sigma(E_1)}{E_1}$ may be resolved from measurement of $S(E_1)$.
-\subsubsection{Automatic Data Acquisition}
+The total current spectrum $S(E_1) = \der{I}{E_1}$ can be obtained from measurement of $I(E_1)$ using a finite difference approximation. 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}. Lock-in amplifier techniques have the advantage of measuring $S(E)$ directly. The lock-in amplifier also eliminates unwanted sources of noise. 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.
-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.
+\subsubsection{The Secondary Emission Coefficient}
-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 presented in Appendix D.
+$\sigma(E)$ can be written as the sum of two components, representing the probability for secondary electrons arrising due to elastic reflections or any mechanism involving primary electron energy loss.
-\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.
-A
-\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.,
+\subsection{Ellipsometry}
-The VASE
+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.
-It is also possible to conduct reflection and transmission spectroscopy experiments using the VASE.
+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.
\subsection{Vacuum Techniques and Sample Preparation}
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.
-
+\pagebreak
\section{Experimental Results and Discussion}
\subsection{TCS Measurements}
+This study has focused on the evolution of the TCS of Au deposited on Si with increasing thickness of Au film. A general dependence of TCS curves on time has also been observed; it is likely that this time dependence is due to oxidation of the surface of the sample.
+
+
+
+\subsubsection{TCS of Si Substrate}
+
+Figure \ref{} shows the TCS
+
+Figure \ref{} shows the TCS of Si in the (111) and (100) orientations as presented by Komolov \cite{komolov}
+
\subsection{Ellipsometric Measurements}
Using the VASE and a commercial spectrometer (OceanOptics) in independent experiments, we obtained transmission spectra for metallic-black and some other metallic films.
+\pagebreak
+
+\section{Conclusions}
+\pagebreak
+\bibliographystyle{unsrt}
+\bibliography{thesis}
-\section{Achievements}
\pagebreak
-\section*{Appendix A - Electron Gun Control and Current Measurement Circuit}
+\section*{List of Student Achievements}
-Figure \ref{} shows the complete electron gun control circuit. The circuit was designed and constructed as part of this project. The design is based upon examples found in \cite{komolov} and \cite{Moore}.
+\pagebreak
-\subsection*{Electron Optics}
-The electron gun has been recycled from a Cathode Ray Oscilloscope. Figure \ref{} shows a diagram and photograph of the gun. The gun contains a total of 9 electrodes; several electrodes are held at the same potential, as shown in the figure. As shown in figure \ref{}, the electrode potentials are referenced to the cathode, not signal ground. Because of the relatively large distance between the gun and sample (held at ground), this ensures that changes in initial energy do not significantly effect the focusing properties of the gun.
+\section*{Appendix A - Electron Optics for Total Current Spectroscopy}
-The optimum potentials of the gun electrodes were determined manually by focusing the gun on an Au film (deposited on Si). I-V curves obtained by measuring current through the sample as a function of initial energy were obtained. The electrode potentials were systematically altered to ensure the curves were as close as possible to the ideal model.
-\subsection*{Model of I-V curves}
-The current detected through the sample is due to electrons which have sufficient energy to overcome the potential barrier between the surface and vacuum, entering the conduction band
+Figure \ref{electron_gun.pdf} shows the complete electron gun control circuit. The circuit was designed and constructed as part of this project. The design is based upon examples found in \cite{komolov} and \cite{Moore}.
+The electron gun has been recycled from a Cathode Ray Oscilloscope. The gun contains a total of 9 electrodes; several electrodes are held at the same potential, as shown in the figure. As shown in figure \ref{electron_gun.pdf}, the electrode potentials are referenced to the cathode, not signal ground; this ensures that the focusing properties of the gun are not affected with changing potential between the cathode and ground.
+Here we give a general discussion of aspects of the electron gun:
+\begin{enumerate}
+ \item Cathode
-\subsection*{}
+A high yield $\text{Ba}\text{O}^2$ filament was used as the cathode. This type of filament consists of a straight piece of tungsten wire bent at the centre into a sharp kink. A $\text{Ba}\text{O}^2$ disc is attached to the apex of the kink. A heating current (between 1.1 and 1.2A) is applied across the filament. Electrons near the surface of the disc recieve thermal energy as the filament is heated; once an electron has recieved enough energy, it is able to leave the surface of the disc through thermionic emission.
-The filament is surrounded by a conducting cylindrical electrode commonly called the ``Venault''. The potential of the venault has little effect on the focusing properties of the gun, but is largely responsible for determining the current leaving the gun. Figure \ref{} shows I-V curves for several venault settings, including the optimum setting.
+By applying Kirchoff's Laws to the circuit shown in Figure \ref{electron_gun.pdf}, it can be seen that the ammeter labelled ``Emission Current'' measures the total current in all loops passing through an electrode or the sample, and the cathode. This measured current does not include electrons which pass directly through the the vacuum chamber to ground; however, due to the large distance between the gun and the chamber walls, this current can be neglected.
-\subsection*{Einzel Lens}
-%Electrodes passing through the aperture of the venault are accelerated towards the target through six electrodes. The first and last pair of electrodes are at the same potential; the central pair are held at a different potential. Such an arrangement can be considered as an ``Einzel'' or ``zoom'' lens. It can be shown \ref{Moore} that the
+ Figure \ref{} shows the measured cathode emission current as a function of time, starting several seconds prior to heating the cathode. From this graph, it can be estimated that at least $10$ minutes should be allowed for the filament to come to thermal equilibrium before commencing measurements.
+
-\pagebreak
+ \item Primary Energy - The potential difference between the sample and the cathode $U$. Primary electrons arriving at the sample have energy $E = eU + \text{constant}$.
+
+ For obvious reasons, it is impractical to directly attach a wire to the emitting surface of the cathode. Instead, two equal resistors are placed in series with the cathode, with the primary energy set point connected to the middle of the resistors. By applying Kirchoff's Voltage Law, making the (reasonable) assumption that both halves of the filament have equal resistance, the potential of the filament tip will be equal to that of the primary energy set point.
+
+
+ \item Wenhault
+
+ The Wenhault is a small cylindrical electrode which surrounds and houses the filament.
+
+ \item Einzel Lens
+
+ \item Deflection Plates
+
+ \item Final Electrode
+\end{enumerate}
+
+As discussed in Section \ref{}, the resolution of total current spectroscopy (and energy resolved secondary electron spectroscopy) is intrinsically linked to the distribution in energies of electrons arriving at the sample. Although the dist
+
+A two dimensional electron gun simulator has also been written in order to help produce figures for qualitative purposes; results of some simulations are shown in Figure \ref{}.
+
+
+
+
+\subsection*{Primary Energy Control and Current Measurement}
+
+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 primary 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.
+
+Figure \ref{block_diagram.pdf} shows a block diagram including all aspects of the Total Current Spectroscopy experiments. The emission current measurement point was included to allow for monitoring the behaviour of the filament, and confirm the assumptions of constant emission current. After the malfunctioning of one of the two available ammeters, it was only possible to measure sample current. However, earlier tests suggested that for short time periods (several minutes at most) the emission current's dependence upon time was negligable.
+
+\begin{center}
+ \includegraphics[scale=0.80]{figures/block_diagram}
+ \captionof{figure}{Block Diagram for TCS Experiments}
+ \label{block_diagram.pdf}
+\end{center}
+
+
+\begin{landscape}
+
+
+ \includegraphics[scale=0.85]{figures/electron_gun.pdf}
+ \captionof{figure}{Electron Gun and Control Circuit}
+ \label{electron_gun.pdf}
+
+
+\end{landscape}
\section*{Appendix B - DAC/ADC Box - Hardware}
Although the RS-232 is relatively simple to implement, which makes it ideal for non-proprietry microprocessor applications, most modern computers no longer feature RS-232 COM ports. Although a computer with COM ports was available at CAMSP, due to the extreme unreliability of this computer, it was quickly replaced with a laptop that did not possess COM ports, and a commercial RS-232 to USB converter was used to interface with the laptop.
-
+\pagebreak
\section*{Appendix C - Pressure Monitoring}
No really, you don't want to know
-\pagebreak
-\bibliographystyle{unsrt}
-\bibliography{thesis}
+
\end{document}
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