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thesis.pdf : thesis.tex
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+[LATEX]
+master-filename = ../thesis.tex
+
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+[LATEX]
+master-filename = ../thesis.tex
+
A measurement point was included for the total leak current through most of the gun electrodes.
-\subsection{The Ammeters}
-An ideal ammeter has no input resistance. In reality, it is not the current that is measured, but the voltage accross a fixed input resistor. This voltage can either be amplified, or the resistance increased, for measuring a smaller current.
-
-The 602 and 610B electrometers both provide a large range of scales and amplifier settings for current measurement. Using a low scale setting increases the input impedance, which increases the potential drop accross the ammeter. However, using a large amplifier gain increases noise; hence there is a trade off. For the 602 and 610B electrometers, a significant drift (typical +5\% of scale in 10min) in the zero level was also observed at high amplifier gains, whilst low gains appeared more stable (+10\% noted after 2 days).
\section{Data Aquisition and Automation}
--- /dev/null
+\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
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+\usepackage{hyperref}
+
+ \topmargin -1.5cm % read Lamport p.163
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+
+\begin{document}
+
+\pagestyle{fancy}
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+
+\fancyhead[LO, L]{}
+\fancyfoot[CO, C]{\thepage}
+
+%\title{}
+%\author{}
+%\date{}
+%\maketitle
+
+%\tableofcontents
+
+%\pagebreak
+
+\section{Overview}
+
+The complete control circuit for the electron gun, including all power supplies, current measurement points, and part of the control and measurement circuitry from the Data Aquisition system is shown in Figure \ref{fig_electron_gun}.
+
+\section{Electron Optics}
+
+A diagram of the electron gun without attached electronics is shown in Figure \ref{fig_electron_gun_simple}, and a photograph of the gun is shown in Figure \ref{fig_electron_gun_photo}.
+
+
+
+\subsection{Focusing the Gun}
+
+The electron gun was been salvaged from an old Cathode Ray Oscilloscope (CRO). The original phosphor screen was also saved, which allowed for very rough focusing of the beam by viewing the illuminated region of the screen through a porthole in the vacuum chamber. Figure \ref{fig_electron_gun_screen_unfocused} and \ref{fig_electron_gun_screen_focused} are photographs of the illuminated spot under focusing conditions chosen to create the largest and sharpest possible spot sizes respectively.
+
+The distance between the gun and target sample was different to the distance from the gun to its original screen. In addition, the original screen consisted of a cylinder with conductive coating at the same potential as the final electrode. These differences in configuration mean that the gun must be refocused for use in TCS.
+
+The electron gun may be considered ``focussed'' if the beam is paraxial to the surface of the sample.
+
+By a process of trial and error
+
+\section{Current Measurements}
+
+\subsection{Total Current}
+Total Current Spectroscopy methods measure the slope of current through a sample with respect to the energy of electrons relative to the sample surface. Often lock-in amplifier techniques are used \cite{???}. These have the advantage of reducing system noise whilst determining the slope directly, but require more time to set up than measuring the current through the sample as a function of incident electron energy. Hence lock-in amplifier techniques were not used for this project, instead current was measured through a conventional ammeter (Keithley 610B electrometer).
+
+
+\subsection{Emission Current}
+Ideally, the electron gun should produce a constant emission current for fixed electrode potentials. In reality, the emission current changes as the filament reaches thermal equilibrium or ``ages'', and so it was desirable to measure the emission current. Applying Kirchoff's current law, it can be seen that the current flowing into the initial energy set point is equal to the total current leaving the filament. This current was measured using a Keithly 602 electrometer.
+
+\subsection{Leak Current}
+``Leak'' currents are currents flowing through the electrodes of the gun. These can be reduced by optimising the potential of the gun electrodes, but are almost impossible to eliminate entirely. The leak current is expected to be equal to a constant (and usually large) fraction of the emission current.
+
+A measurement point was included for the total leak current through most of the gun electrodes.
+
+\subsection{The Ammeters}
+
+An ideal ammeter has no input resistance. In reality, it is not the current that is measured, but the voltage accross a fixed input resistor. This voltage can either be amplified, or the resistance increased, for measuring a smaller current.
+
+The 602 and 610B electrometers both provide a large range of scales and amplifier settings for current measurement. Using a low scale setting increases the input impedance, which increases the potential drop accross the ammeter. However, using a large amplifier gain increases noise; hence there is a trade off. For the 602 and 610B electrometers, a significant drift (typical +5\% of scale in 10min) in the zero level was also observed at high amplifier gains, whilst low gains appeared more stable (+10\% noted after 2 days).
+
+\section{Data Aquisition and Automation}
+
+\subsection{ADC Measurements}
+
+\subsection{DAC Control of Initial Energy}
+
+
+\section{Vacuum Chamber and Sample Holder}
+
+\subsection{Vacuum Chamber}
+
+\subsection{Sample Holder}
+
+\section{Sources of Error}
+
+\subsection{Accuracy of ADCs}
+
+Figure \ref{fig_adc_noise} shows the ADC counts vs time measured for a controlled input voltage. The input voltages were set using a GW Instek GPS-1850D Power Supply, which has a quoted noise of
+
+Figure \ref{fig_gps_noise} shows the same output voltages of the GPS-1850D Power supply measured using an Agilent Oscilloscope.
+
+Based on these figures, an estimate of $\pm 1$ count for the error of the ADC seems reasonable. This corresponds to $3.2mV$.
+
+\subsection{Noise due to Instruments}
+
+The Keithly 602 electrometer quotes a minimum noise value of $10mV$ and maximum of , whilst the 610B electrometer quotes
+The noise was found to increase with the amplifier gain setting on each electrometer. Figure \ref{fig_610B_noise} shows the
+
+
+\subsection{Noise due to Ground Loops}
+
+By far the greatest source of noise encountered in this project was a 50Hz sinusoidal ``hum''. The amplitude of this sine noise varied with instrument from $\pm10mV$ (610B) to $\pm1V$ (602).
+
+The 50Hz nature of the noise suggests that it is related to mains power. So called ``Ground Loops'' arise when a circuit incorporates multiple paths to mains Earth. This is indeed the case with the circuit in Figure \ref{fig_electron_gun}.
+
+In an ideal situation, mains earth would never be used as a signal ground source. Unfortunately, the use of mains earth as signal ground was unavoidable in this project due to safety and practicallity reasons. The turbo-molecular pump attached to the vacuum chamber was housed within a steel casing, which was grounded to mains earth for obvious safety reasons. This in turn grounded the entire steel vacuum chamber and the table upon which it rested to mains earth. The sample holder must be kept at the same potential as the surrounding vacuum chamber and shielding, and hence it was also connected to mains earth.
+
+The DAQ box itself became grounded to mains earth both through the RS-232 connection to the laptop, and also through the input from the sample current electrometer (610B).
+
+\subsection{Reduction of Noise}
+
+The simplest way to determine the DC level of the ADC inputs was use of a large number of averages. Performing averaging on a signal is equivelant to passing the signal through a low pass filter \ref{}.
+
+Software averaging alone is not always sufficient to reduce noise. If the sinusoidal noise has a larger amplitude than the DC level, part of the signal will be negative with respect to ADC ground. ADCs are only capable of measuring positive voltages with respect to ground. A negative voltage is measured as a zero. Hence the averaged signal will be larger than the DC level of the input. This was found to be the case for measurements of the emission current.
+
+To solve this difficulty, a physical low pass filter was added at the input for the differential ADC. The cutoff of the low pass filter is:
+Although some sinusoidal noise was still observed after the addition of the filter, it was reduced to a level that made software averaging feasable.
+
+\subsection{Time variance of measured current}
+
+There are two effects:
+\begin{enumerate}
+ \item When the initial energy is changed, the sample current trends towards an assymptote. The trend is exponential with a very large time constant (~2min to ~5min).
+ \item The general shape of successive I-V curves changes noticably
+\end{enumerate}
+
+Possible causes:
+\begin{itemize}
+ \item Capacitance of Sample holder
+\end{itemize}
+
+\end{document}
+
--- /dev/null
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--- /dev/null
+\chapter*{Appendix - Data Aquisition Hardware}
+
+\section{Overview}
+
+In order to automate TCS experiments, both Digital to Analogue and Analogue to Digital Convertors were required (DAC and ADC). To provide these, a custom DAC/ADC Box was designed and constructed. The box can be controlled by any conventional computer with available RS-232 serial communication (COM) ports. Most modern computers no longer feature COM ports; a commercially available convertor can be used to interface between the box's RS-232 output and a standard Universal Serial Bus (USB) port.
+
+
+The key components of the DAC/ADC box hardware include:
+
+\begin{itemize}
+ \item Microprocessor (AVR Butterfly ATMega169)
+ \item Four Analogue to Digital Converter (ADC) inputs
+ \item Single Digital to Analogue Converter (DAC) output (Microchip MCP4922)
+ \item Analogue electronics for amplification at ADC inputs and DAC outputs
+ \item Seperate power supply circuitry for Digital and Analogue electronics
+ \item RS-232 communications for control by a conventional PC or laptop
+\end{itemize}
+
+\section{Microprocessor}
+The DAC/ADC box has been based upon Atmel's AVR Butterfly; an inexpensive and simple demonstration board for the ATMega169 16 Bit microprocessor. The features of the AVR Butterfly include easily accessible ports for Analogue to Digital Convertor (ADC) inputs and digital input/output, an onboard Universal Asynchronous Reciever/Transmitter (USART) for RS-232 serial communications, and a 6 character Liquid Crystal Display (LCD). The AVR Butterfly can be programmed using a conventional computer over the USART using a RS-232 COM port. For modern computers (which do not usually posess COM ports), a RS-232 to USB converter may be used.
+
+Figure \ref{avr_butterfly.pdf} is a labelled photograph of the AVR Butterfly showing the use of the available ports for this project.
+
+
+%Figure of Butterfly
+\begin{center}
+ \includegraphics[scale=0.70]{figures/dac_adc_box/avr_butterfly.pdf}
+ \captionof{figure}{AVR Butterfly} \label{avr_butterfly.pdf}
+\end{center}
+
+Unless otherwise stated, all voltage differences are specified relative to the power supply ground of the AVR Butterfly.
+
+\subsection*{ADC Inputs}
+
+The AVR Butterfly offers easy access to four of the ATMega169's ADCs through PORTF. Each ADC is capable of measuring voltages of $0 < V_{\text{adc}} < V_{cc}$ with 10 Bit resolution. For measuring voltages outside this range, some circuitry is required between the input voltage and the ADC input. In addition, it is desirable to provide the ADC with some form of input protection against accidental overloading. Figure \ref{adc_normal.pdf} shows the input circuit which was used for three of the four available ADCs.
+
+\begin{center}
+ \includegraphics[scale=0.50]{figures/dac_adc_box/adc_normal.pdf}
+ \captionof{figure}{ADC4,6,7 Input} \label{adc_normal.pdf}
+\end{center}
+
+
+For making voltage measurements above $V_{cc}$, a voltage divider allows reduction of the voltage at the ADC. By constructing the voltage divider using a variable resistor, the range of measurable inputs could be manually adjusted.
+
+The diodes shown in Figure \ref{adc_normal.pdf} ensure that the ADC is protected from accidental exposure to voltages outside the acceptable range. In normal operation both diodes are off. If $V_{\text{adc}}$ were to become greater than the reference point $V_{cc}$, current would flow between the ADC input and the reference point, acting to reduce $V_{\text{adc}}$ until it reached $V_{cc}$. Similarly, if $V_{\text{adc}}$ fell below ground, current would flow from ground to the ADC input, acting to increase $V_{\text{adc}}$ until it reached ground.
+
+The voltage at the ADC input can be related to the input of the voltage divider using Kirchoff's Voltage Law and Ohm's Law:
+\begin{align*}
+ V_{\text{adc}} &= \frac{R_1}{R_1 + R_2} V_{\text{in}}
+\end{align*}
+Where $V_{\text{in}}$ is the voltage at the input of the circuit, $R_1$ is a fixed resistor, and $R_2$ is variable resistor.
+
+$V_{\text{in}}$ can be therefore be determined from the registered ADC counts by:
+\begin{align*}
+ V_{\text{in}} &= \left(\frac{\text{ADC counts}}{2^{10}}\right) \times \frac{R_1 + R_2}{R_1} V_{cc}
+\end{align*}
+
+\subsubsection*{Differential ADC Input}
+
+During the testing of the TCS experimental apparatus, it became desirable to measure the emission current of the electron gun. The electrometer used for this current measurement was capable of producing an analogue output in the range of $0-1V$. However, the negative terminal of this output was not at ground potential, but rather at the same terminal as the negative input terminal. Directly connecting the electrometer output to one of the ADC inputs discussed above would create a short circuit between the initial energy power supply, and ground (refer to Figures \ref{} and \ref{}). Therefore, it was decided to add a differential stage before the input of one of the ADCs.
+
+Figure \ref{adc5.pdf} shows the modification made to the input for ADC5 on the AVR Butterfly. The original voltage divider and input protection discussed above are still present. The modifications include the addition of an instrumentation amplifier, and low pass filters.
+
+\begin{center}
+ \includegraphics[scale=0.70]{figures/dac_adc_box/adc5}
+ \captionof{figure}{Differential Input stage for ADC5}
+ \label{adc5.pdf}
+\end{center}
+
+asdfa
+The instrumentation amplifier consists of two stages of operational amplifiers (op-amps); input buffers, and a difference amplifier.
+The difference amplifier can be shown using the ideal op-amp model to produce an output voltage proportional to the difference between its inputs:
+
+\begin{align*}
+ V_{out} &= \frac{R_2}{R_1} \left(V_{2} - V_{1}\right)
+\end{align*}
+
+The two op-amps at the inputs to the differential amplifier are unity gain buffers. Although the outputs of the op amps are equal to their inputs, current is prevented from flowing from the circuit under measurement, and is instead drawn from the op amp power supply.
+
+In principle, two ADC channels could be used to record the positive and negative outputs of the electrometer seperately, with differencing done in software. However this would require modification to the output cable of the electrometer, which may prove inconvenient for future uses.It was decided that the modification of the cable and added complexity of the software required would be more time consuming than differencing the two inputs using the hardware methods described above.
+
+The low pass filters were added to the inputs of ADC5 after it was found that an unacceptable level of AC noise was being output by the electrometer. The level of noise was too high to be filtered in software, for reasons that will be discussed in Appendix D.
+
+\subsection*{Temperature Measurement}
+
+The AVR Butterfly features an onboard thermistor connected to ADC0. Reading ADC0 and applying the formula given in the AVR Butterfly User's Guide \cite{} results in a temperature measurement. This was useful in establishing a link between the changing chamber pressure and the temperature of the laboratory (see Appendix C).
+
+\subsection*{Power Supplies}
+Due to the presence of both analogue and digital electronics in the DAC/ADC box, three seperate supply voltages were required:
+\begin{enumerate}
+ \item Digital logic in the range $3 \to 4.5$V
+ \item Positive op-amp supply in the range $10 \to 15$V
+ \item Negative op-amp supply in the range $-10 \to -15$V
+\end{enumerate}
+
+Circuitry was designed which allowed two seperate single pole power supplies to be used for Digital logic and the op-amps. A dual 0-30V DC power supply has been used for both digital and analogue circuitry.
+
+\subsubsection*{Logic Power Supply}
+The AVR Butterfly runs off $3V < V_{cc} < 4.5V$ DC. Since $V_{cc}$ was also used as the reference voltage for the ADCs and DAC output, it was desirable that $V_{cc}$ be kept constant, despite the absolute level of the power supply. A $3.3V$ voltage regulator has been used for this purpose. The capacitor further smooths the output by shorting high frequency fluctuations to ground.
+
+When the DAC/ADC box was first constructed $V_{cc}$ was supplied by three $1.5V$ batteries. However, due to higher than expected power usage, and the unreliability of the voltage regulator as the input voltage fell below $4V$, inputs for an external power supply were later added.
+
+\begin{center}
+ \includegraphics[scale=0.70]{figures/dac_adc_box/logic_ps}
+ \captionof{figure}{Logic Power Supply}
+ \label{logic_ps.pdf}
+\end{center}
+
+\subsubsection*{Op-amp Power Supply}
+The DAC/ADC box circuitry involves several operational amplifiers (LF356), which require dual $\pm 10-15V$ supplies. As there were no dual $\pm$ power supplies available, a single $30V$ power supply was used, with the circuit shown in figure \ref{} used to produce $\pm 15V$ relative to ground.
+
+The buffer amplifier ensures that negligable current can flow from the power supply into the logic and ADC circuits, whilst the capacitor removes high frequency fluctuations of the power supply relative to ground.
+
+\subsection*{DAC Output}
+A commercial DAC board was used to produce the DAC output. The Microchip MCP4922 ET-Mini DAC is controlled by the AVR Butterfly using Motorola's Serial Peripheral Interface (SPI) Bus. The software used to implement SPI between the MCP4922 and the AVR Butterfly is discussed in Appendix D.
+
+The ET-Mini DAC can only be powered off $3V$ to $5V$. Using $V_{cc} = 3.3V$ means that the DAC output cannot exceed $V_{cc} = 3.3V$. For TCS, energies of up to $15eV$ are required, so amplification of the DAC output was clearly necessary. A simple non-inverting amplifier with a manually adjustable gain was used to amplify the DAC output by a factor of three. This output was then used to control a laboratory power supply to produce the full range of initial energies.
+
+\subsection*{RS-232 Communications}
+
+The AVR Butterfly features an onboard USART, which can be used both for programming and communication with the ATMega169 processor. The RS-232 communications requires only three wires; Recieve (RX), Transmit (TX) and a common ground.
+
+The requirement that the AVR Butterfly share a common ground with the controlling computer lead to increased noise through ground loops. This is discussed in more detail in Appendix D.
+
+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.
+
--- /dev/null
+\chapter*{Appendix - Data Aquisition Hardware}
+
+\section{Overview}
+
+In order to automate TCS experiments, both Digital to Analogue and Analogue to Digital Convertors were required (DAC and ADC). To provide these, a custom DAC/ADC Box was designed and constructed. The box can be controlled by any conventional computer with available RS-232 serial communication (COM) ports. Most modern computers no longer feature COM ports; a commercially available convertor can be used to interface between the box's RS-232 output and a standard Universal Serial Bus (USB) port.
+
+
+The key components of the DAC/ADC box hardware include:
+
+\begin{itemize}
+ \item Microprocessor (AVR Butterfly ATMega169)
+ \item Four Analogue to Digital Converter (ADC) inputs
+ \item Single Digital to Analogue Converter (DAC) output (Microchip MCP4922)
+ \item Analogue electronics for amplification at ADC inputs and DAC outputs
+ \item Seperate power supply circuitry for Digital and Analogue electronics
+ \item RS-232 communications for control by a conventional PC or laptop
+\end{itemize}
+
+\section{Microprocessor}
+The DAC/ADC box has been based upon Atmel's AVR Butterfly; an inexpensive and simple demonstration board for the ATMega169 16 Bit microprocessor. The features of the AVR Butterfly include easily accessible ports for Analogue to Digital Convertor (ADC) inputs and digital input/output, an onboard Universal Asynchronous Reciever/Transmitter (USART) for RS-232 serial communications, and a 6 character Liquid Crystal Display (LCD). The AVR Butterfly can be programmed using a conventional computer over the USART using a RS-232 COM port. For modern computers (which do not usually posess COM ports), a RS-232 to USB converter may be used.
+
+Figure \ref{avr_butterfly.pdf} is a labelled photograph of the AVR Butterfly showing the use of the available ports for this project.
+
+
+%Figure of Butterfly
+\begin{center}
+ \includegraphics[scale=0.70]{figures/dac_adc_box/avr_butterfly.pdf}
+ \captionof{figure}{AVR Butterfly} \label{avr_butterfly.pdf}
+\end{center}
+
+Unless otherwise stated, all voltage differences are specified relative to the power supply ground of the AVR Butterfly.
+
+\subsection*{ADC Inputs}
+
+The AVR Butterfly offers easy access to four of the ATMega169's ADCs through PORTF. Each ADC is capable of measuring voltages of $0 < V_{\text{adc}} < V_{cc}$ with 10 Bit resolution. For measuring voltages outside this range, some circuitry is required between the input voltage and the ADC input. In addition, it is desirable to provide the ADC with some form of input protection against accidental overloading. Figure \ref{adc_normal.pdf} shows the input circuit which was used for three of the four available ADCs.
+
+\begin{center}
+ \includegraphics[scale=0.50]{figures/dac_adc_box/adc_normal.pdf}
+ \captionof{figure}{ADC4,6,7 Input} \label{adc_normal.pdf}
+\end{center}
+
+
+For making voltage measurements above $V_{cc}$, a voltage divider allows reduction of the voltage at the ADC. By constructing the voltage divider using a variable resistor, the range of measurable inputs could be manually adjusted.
+
+The diodes shown in Figure \ref{adc_normal.pdf} ensure that the ADC is protected from accidental exposure to voltages outside the acceptable range. In normal operation both diodes are off. If $V_{\text{adc}}$ were to become greater than the reference point $V_{cc}$, current would flow between the ADC input and the reference point, acting to reduce $V_{\text{adc}}$ until it reached $V_{cc}$. Similarly, if $V_{\text{adc}}$ fell below ground, current would flow from ground to the ADC input, acting to increase $V_{\text{adc}}$ until it reached ground.
+
+The voltage at the ADC input can be related to the input of the voltage divider using Kirchoff's Voltage Law and Ohm's Law:
+\begin{align*}
+ V_{\text{adc}} &= \frac{R_1}{R_1 + R_2} V_{\text{in}}
+\end{align*}
+Where $V_{\text{in}}$ is the voltage at the input of the circuit, $R_1$ is a fixed resistor, and $R_2$ is variable resistor.
+
+$V_{\text{in}}$ can be therefore be determined from the registered ADC counts by:
+\begin{align*}
+ V_{\text{in}} &= \left(\frac{\text{ADC counts}}{2^{10}}\right) \times \frac{R_1 + R_2}{R_1} V_{cc}
+\end{align*}
+
+\subsubsection*{Differential ADC Input}
+
+During the testing of the TCS experimental apparatus, it became desirable to measure the emission current of the electron gun. The electrometer used for this current measurement was capable of producing an analogue output in the range of $0-1V$. However, the negative terminal of this output was not at ground potential, but rather at the same terminal as the negative input terminal. Directly connecting the electrometer output to one of the ADC inputs discussed above would create a short circuit between the initial energy power supply, and ground (refer to Figures \ref{} and \ref{}). Therefore, it was decided to add a differential stage before the input of one of the ADCs.
+
+Figure \ref{adc5.pdf} shows the modification made to the input for ADC5 on the AVR Butterfly. The original voltage divider and input protection discussed above are still present. The modifications include the addition of an instrumentation amplifier, and low pass filters.
+
+\begin{center}
+ \includegraphics[scale=0.70]{figures/dac_adc_box/adc5}
+ \captionof{figure}{Differential Input stage for ADC5}
+ \label{adc5.pdf}
+\end{center}
+
+asdfa
+The instrumentation amplifier consists of two stages of operational amplifiers (op-amps); input buffers, and a difference amplifier.
+The difference amplifier can be shown using the ideal op-amp model to produce an output voltage proportional to the difference between its inputs:
+
+\begin{align*}
+ V_{out} &= \frac{R_2}{R_1} \left(V_{2} - V_{1}\right)
+\end{align*}
+
+The two op-amps at the inputs to the differential amplifier are unity gain buffers. Although the outputs of the op amps are equal to their inputs, current is prevented from flowing from the circuit under measurement, and is instead drawn from the op amp power supply.
+
+In principle, two ADC channels could be used to record the positive and negative outputs of the electrometer seperately, with differencing done in software. However this would require modification to the output cable of the electrometer, which may prove inconvenient for future uses.It was decided that the modification of the cable and added complexity of the software required would be more time consuming than differencing the two inputs using the hardware methods described above.
+
+The low pass filters were added to the inputs of ADC5 after it was found that an unacceptable level of AC noise was being output by the electrometer. The level of noise was too high to be filtered in software, for reasons that will be discussed in Appendix D.
+
+\subsection*{Temperature Measurement}
+
+The AVR Butterfly features an onboard thermistor connected to ADC0. Reading ADC0 and applying the formula given in the AVR Butterfly User's Guide \cite{} results in a temperature measurement. This was useful in establishing a link between the changing chamber pressure and the temperature of the laboratory (see Appendix C).
+
+\subsection*{Power Supplies}
+Due to the presence of both analogue and digital electronics in the DAC/ADC box, three seperate supply voltages were required:
+\begin{enumerate}
+ \item Digital logic in the range $3 \to 4.5$V
+ \item Positive op-amp supply in the range $10 \to 15$V
+ \item Negative op-amp supply in the range $-10 \to -15$V
+\end{enumerate}
+
+Circuitry was designed which allowed two seperate single pole power supplies to be used for Digital logic and the op-amps. A dual 0-30V DC power supply has been used for both digital and analogue circuitry.
+
+\subsubsection*{Logic Power Supply}
+The AVR Butterfly runs off $3V < V_{cc} < 4.5V$ DC. Since $V_{cc}$ was also used as the reference voltage for the ADCs and DAC output, it was desirable that $V_{cc}$ be kept constant, despite the absolute level of the power supply. A $3.3V$ voltage regulator has been used for this purpose. The capacitor further smooths the output by shorting high frequency fluctuations to ground.
+
+When the DAC/ADC box was first constructed $V_{cc}$ was supplied by three $1.5V$ batteries. However, due to higher than expected power usage, and the unreliability of the voltage regulator as the input voltage fell below $4V$, inputs for an external power supply were later added.
+
+\begin{center}
+ \includegraphics[scale=0.70]{figures/logic_ps}
+ \captionof{figure}{Logic Power Supply}
+ \label{logic_ps.pdf}
+\end{center}
+
+\subsubsection*{Op-amp Power Supply}
+The DAC/ADC box circuitry involves several operational amplifiers (LF356), which require dual $\pm 10-15V$ supplies. As there were no dual $\pm$ power supplies available, a single $30V$ power supply was used, with the circuit shown in figure \ref{} used to produce $\pm 15V$ relative to ground.
+
+The buffer amplifier ensures that negligable current can flow from the power supply into the logic and ADC circuits, whilst the capacitor removes high frequency fluctuations of the power supply relative to ground.
+
+\subsection*{DAC Output}
+A commercial DAC board was used to produce the DAC output. The Microchip MCP4922 ET-Mini DAC is controlled by the AVR Butterfly using Motorola's Serial Peripheral Interface (SPI) Bus. The software used to implement SPI between the MCP4922 and the AVR Butterfly is discussed in Appendix D.
+
+The ET-Mini DAC can only be powered off $3V$ to $5V$. Using $V_{cc} = 3.3V$ means that the DAC output cannot exceed $V_{cc} = 3.3V$. For TCS, energies of up to $15eV$ are required, so amplification of the DAC output was clearly necessary. A simple non-inverting amplifier with a manually adjustable gain was used to amplify the DAC output by a factor of three. This output was then used to control a laboratory power supply to produce the full range of initial energies.
+
+\subsection*{RS-232 Communications}
+
+The AVR Butterfly features an onboard USART, which can be used both for programming and communication with the ATMega169 processor. The RS-232 communications requires only three wires; Recieve (RX), Transmit (TX) and a common ground.
+
+The requirement that the AVR Butterfly share a common ground with the controlling computer lead to increased noise through ground loops. This is discussed in more detail in Appendix D.
+
+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.
+
\relax
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-\chapter*{Electron Gun Control Circuit}
+\chapter*{Appendix - Electron Gun Control Circuit}
The control circuit diagram for the electron gun is shown in Figure \ref{electron_gun.pdf}. The wiring of the circuit, including resistors and potentiometers, was incoroprated into a single box, with external connections available for the power supplies, ammeters, electron gun, and sample holder. Both the components and operation of this circuit are straightforward; we will give a brief overview here for completeness.
\end{itemize}
\begin{landscape}
\begin{center}
- \includegraphics[scale=0.80]{/home/sam/Documents/University/honours/thesis/figures/electron_gun.pdf}
+ \includegraphics[scale=0.80]{figures/egun/electron_gun.pdf}
\captionof{figure}{Circuit Diagram for Electron Gun Control}
\label{electron_gun.pdf}
\end{center}
+
+\subsection{The Ammeters}
+
+An ideal ammeter has no input resistance. In reality, it is not the current that is measured, but the voltage accross a fixed input resistor. This voltage can either be amplified, or the resistance increased, for measuring a smaller current.
+
+The 602 and 610B electrometers both provide a large range of scales and amplifier settings for current measurement. Using a low scale setting increases the input impedance, which increases the potential drop accross the ammeter. However, using a large amplifier gain increases noise; hence there is a trade off. For the 602 and 610B electrometers, a significant drift (typical +5\% of scale in 10min) in the zero level was also observed at high amplifier gains, whilst low gains appeared more stable (+10\% noted after 2 days).
\end{landscape}
-\chapter*{Electron Gun Control Circuit}
+\chapter*{Appendix - Electron Gun Control Circuit}
The control circuit diagram for the electron gun is shown in Figure \ref{electron_gun.pdf}. The wiring of the circuit, including resistors and potentiometers, was incoroprated into a single box, with external connections available for the power supplies, ammeters, electron gun, and sample holder. Both the components and operation of this circuit are straightforward; we will give a brief overview here for completeness.
\end{itemize}
\begin{landscape}
\begin{center}
- \includegraphics[scale=0.80]{figures/electron_gun.pdf}
+ \includegraphics[scale=0.80]{figures/egun/electron_gun.pdf}
\captionof{figure}{Circuit Diagram for Electron Gun Control}
\label{electron_gun.pdf}
\end{center}
\relax
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-\chapter*{Electron Optics}
+\chapter*{Appendix - 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 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}
+ \includegraphics[scale=0.45, angle=270]{figures/egun/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}
+ \includegraphics[scale=0.45, angle=270]{figures/egun/egun_simulation2.pdf}
\captionof{figure}{{\bf 2D Simulation of the electrostatic potential produced by the electron gun}}\label{egun_simulation2.pdf}
\end{center}
-\chapter*{Electron Optics}
+\appendix{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 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}
+ \includegraphics[scale=0.45, angle=270]{figures/egun/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]{figures/egun_simulation2.pdf}
+ \includegraphics[scale=0.45, angle=270]{figures/egun/egun_simulation2.pdf}
\captionof{figure}{{\bf 2D Simulation of the electrostatic potential produced by the electron gun}}\label{egun_simulation2.pdf}
\end{center}
--- /dev/null
+\relax
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--- /dev/null
+\chapter*{Appendix - Effect of Noise on the TCS Curve}
+
+Taking the derivative of discrete data is problematic. Using a centred difference finite derivative approximation:
+\begin{align*}
+ \der{f}{x} &= \frac{f(x + h) - f(x - h)}{h} + O(h^2)
+\end{align*}
+The accuraracy of this approximation increases as $h \to 0$\footnote{Ignoring any effects due to rounding of floating point numbers}.
+
+However, if $f_s(x)$ is the result of sampling $f(x)$, with $\Delta f$ the uncertainty in a measurement:
+\begin{align*}
+ f_s(x) &= f(x) \pm \Delta f \\
+ \der{f_s}{x} &\approx \der{f}{x} \\
+ &= \frac{f(x + h) - f(x - h)}{h} + O(h^2) \pm \frac{\Delta f}{h}
+\end{align*}
+The uncertainty in the sampled derivative has a pole at $h = 0$.
+
+{\emph Note: I now suspect that this is a major reason why Komolov has used Lock-in amplifiers}
+
+The problem may be fixed [dodged?] by increasing $h$ (in which case the resolution of the derivative is decreased dramatically), or application of smoothing averages (which also decrease the resolution, but not as much). \emph{Needs rephrasing}
+
+Smoothing of the sampled curve $f_s(x)$ (by application of a moving average) will reduce the deviation of points the smooth curve which best fits the data. As shown in Figures \ref{siI.eps} and \ref{siI_tcs.eps}, smoothing of $f_s(x)$ has a far greater effect on the derivative of $f_s$ than on $f_s$ itself.
+
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{figures/tcs/plots/siI.eps}
+ \caption{An unprocessed and smoothed I(E) curve for a Si sample.}
+ \label{siI.eps}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{figures/tcs/plots/siI_tcs.eps}
+ \caption{The effect of smoothing the original I(E) curve on its derivative.}
+ \label{siI_tcs.eps}
+\end{figure}
+
--- /dev/null
+\chapter*{Appendix - Effect of Noise on the TCS Curve}
+
+Taking the derivative of discrete data is problematic. Using a centred difference finite derivative approximation:
+\begin{align*}
+ \der{f}{x} &= \frac{f(x + h) - f(x - h)}{h} + O(h^2)
+\end{align*}
+The accuraracy of this approximation increases as $h \to 0$\footnote{Ignoring any effects due to rounding of floating point numbers}.
+
+However, if $f_s(x)$ is the result of sampling $f(x)$, with $\Delta f$ the uncertainty in a measurement:
+\begin{align*}
+ f_s(x) &= f(x) \pm \Delta f \\
+ \der{f_s}{x} &\approx \der{f}{x} \\
+ &= \frac{f(x + h) - f(x - h)}{h} + O(h^2) \pm \frac{\Delta f}{h}
+\end{align*}
+The uncertainty in the sampled derivative has a pole at $h = 0$.
+
+{\emph Note: I now suspect that this is a major reason why Komolov has used Lock-in amplifiers}
+
+The problem may be fixed [dodged?] by increasing $h$ (in which case the resolution of the derivative is decreased dramatically), or application of smoothing averages (which also decrease the resolution, but not as much). \emph{Needs rephrasing}
+
+Smoothing of the sampled curve $f_s(x)$ (by application of a moving average) will reduce the deviation of points the smooth curve which best fits the data. As shown in Figures \ref{siI.eps} and \ref{siI_tcs.eps}, smoothing of $f_s(x)$ has a far greater effect on the derivative of $f_s$ than on $f_s$ itself.
+
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{figures/tcs/plots/siI.eps}
+ \caption{An unprocessed and smoothed I(E) curve for a Si sample.}
+ \label{siI.eps}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{figures/tcs/plots/siI_tcs.eps}
+ \caption{The effect of smoothing the original I(E) curve on its derivative.}
+ \label{siI_tcs.eps}
+\end{figure}
+
--- /dev/null
+[LATEX]
+master-filename = ../thesis.tex
+
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\chapter{Conclusion}
-In conclusion, AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
+We have demonstrated the use of multiple techniques for characterisation and analysis of metallic thin films. In particular we have focused on measurable differences in the properties of metallic-black thin films in comparison with bright metallic thin films.
+\chapter{Conclusion}
+
+We have demonstrated the use of multiple techniques for characterisation and analysis of metallic thin films. In particular we have focused on measurable differences in the properties of metallic-black thin films in comparison with bright metallic thin films.
\citation{harris1948}
\citation{harris1952}
\citation{harris1953}
-\citation{mckenzie2006}
\@writefile{toc}{\contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.1}}
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\citation{sondergaard2012}
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% TODO: Broad general sweeping statements about thin films
-
+Motivation:
+\begin{itemize}
+ \item The properties of solids can be understood in terms of an infinite periodic lattice
+ \item In reality, every solid must have a finite spatial extent. The
+ \item Thin films can have extremely complicated and interesting properties.
+ \item The characterisation of thin films is important research in electronics as the surface to volume ratio increases.
+ \item Most recent research has been into completely new technologies which exploit phenomena (
+ \item Somehow link to metallic-black films (?)
+\end{itemize}
So called metallic-black films are the result of deposition of metal elements at a relatively high pressure (of the order of $10^{-2}$ mbar). The films are named due to their high absorbance at visible wavelengths; they appear black to the naked eye. There is a remarkable contrast between such films and films deposited under low pressure (less than $10^{-6}$mbar), which are typically highly reflective and brightly coloured.
% TODO: Broad general sweeping statements about thin films
+Motivation:
+\begin{itemize}
+ \item The properties of solids can be understood in terms of an infinite periodic lattice
+ \item In reality, every solid must have a finite spatial extent. The
+ \item Thin films can have extremely complicated and interesting properties.
+ \item The characterisation of thin films is important research in electronics as the surface to volume ratio increases.
+ \item Most recent research has been into completely new technologies which exploit the p
+ \item Somehow link to metallic-black films (?)
+\end{itemize}
+
So called metallic-black films are the result of deposition of metal elements at a relatively high pressure (of the order of $10^{-2}$ mbar). The films are named due to their high absorbance at visible wavelengths; they appear black to the naked eye. There is a remarkable contrast between such films and films deposited under low pressure (less than $10^{-6}$mbar), which are typically highly reflective and brightly coloured.
% First mentions and early research; Pfund
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+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 5--6
+[]
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type H <return> for immediate help.
+ ...
+
+l.8 F
+ igure \ref{SEM_images} shows a comparison of an Au-Black and Au-Bright ...
+
+You're in trouble here. Try typing <return> to proceed.
+If that doesn't work, type X <return> to quit.
+
+Missing character: There is no F in font nullfont!
+Missing character: There is no i in font nullfont!
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+Missing character: There is no u in font nullfont!
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+Missing character: There is no e in font nullfont!
+! Undefined control sequence.
+<write> ...eference `SEM_images' on page \thepage
+ \space undefined\on@line .
+l.8 Figure \ref{SEM_images}
+ shows a comparison of an Au-Black and Au-Bright ...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+LaTeX Warning: Reference `SEM_images' on page undefined on input line 8.
+
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+Missing character: There is no t in font nullfont!
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+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 8--9
+[]
+ []
+
+
+Overfull \hbox (10.86105pt too wide) in paragraph at lines 8--9
+[]
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type H <return> for immediate help.
+ ...
+
+l.10 \begin{center}
+
+You're in trouble here. Try typing <return> to proceed.
+If that doesn't work, type X <return> to quit.
+
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 10--10
+[]
+ []
+
+LaTeX Font Info: External font `cmex10' loaded for size
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+LaTeX Font Info: External font `cmex10' loaded for size
+(Font) <5> on input line 13.
+! Undefined control sequence.
+l.14 \includegraphics
+ [scale=0.20]{figures/sem/Au_BLACK_200nm.png} & %\capti...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no g in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no / in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no / in font nullfont!
+Missing character: There is no A in font nullfont!
+Missing character: There is no u in font nullfont!
+! Missing $ inserted.
+<inserted text>
+ $
+l.14 \includegraphics[scale=0.20]{figures/sem/Au_
+ BLACK_200nm.png} & %\capti...
+I've inserted a begin-math/end-math symbol since I think
+you left one out. Proceed, with fingers crossed.
+
+! Extra }, or forgotten $.
+l.14 ...cale=0.20]{figures/sem/Au_BLACK_200nm.png}
+ & %\captionof{figure}{Au-...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've put in what seems to be necessary to fix
+the current column of the current alignment.
+Try to go on, since this might almost work.
+
+! Extra }, or forgotten $.
+<inserted text> }
+
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing } inserted.
+<inserted text>
+ }
+l.14 ...le=0.20]{figures/sem/Au_BLACK_200nm.png} &
+ %\captionof{figure}{Au-Bl...
+(That makes 100 errors; please try again.)
+Here is how much of TeX's memory you used:
+ 13 strings out of 495061
+ 376 string characters out of 1182621
+ 45108 words of memory out of 3000000
+ 3288 multiletter control sequences out of 15000+50000
+ 3948 words of font info for 15 fonts, out of 3000000 for 9000
+ 28 hyphenation exceptions out of 8191
+ 20i,7n,19p,544b,130s stack positions out of 5000i,500n,10000p,200000b,50000s
+
+! ==> Fatal error occurred, no output PDF file produced!
\section{Scanning Electron Microscopy}
-% Model of structure
-Nanostructured metal films prepared at low pressure are often approximated by an isotropic layer of spherical blobs upon the substrate, or even as a uniform layer with an ``effective'' thickness \cite{}. As the right image in Figure \ref{SEM_images} shows, this is a good representation of the structure of such a film. In contrast, the metallic-black film is highly non-uniform; as a result, detailed characterisation of the properties of such a film is difficult.
+A number of samples of metallic-black and metallic-bright films were sent to the Centre for Microscopy Characterisation and Analysis (CMCA) at UWA for study. In this section we will present and discuss some of the images produced by CMCA. These images provide an invaluable aid to understanding the structural differences between metallic-black and metallic-bright films.
+
+
+Figure \ref{SEM_images} shows a comparison of an Au-Black and Au-Bright film imaged using a scanning electron microscope (SEM). The intensity of each pixel is proportional to the total current of secondary electrons scattered from the surface at that point from the metal in the film (the current due to the Si substrate has been subtracted from the image), which is in turn proportional to the density of metal at the considered point.
+
+\begin{center}
+
+\begin{tabular}{cc}
+ \includegraphics[scale=0.20]{figures/sem/Au_BLACK_200nm.png} & %\captionof{figure}{Au-Black SEM Image} \label{Au_BLACK_200nm.png} &
+ \includegraphics[scale=0.20]{figures/sem/Au_semi-shiny_1_SEM.png} %\captionof{figure}{Au SEM Image} \label{Au_semi-shiny_1_SEM.png}
+
+ \label{SEM_images}
+\end{tabular}
+
+ \captionof{figure}{{\bf 2500 x 1900nm SEM images of Au-Black (left) and Au-Bright (right) deposited on Si} \\ Preparation pressures were $2\times10^{-2}$mbar and $1\times10^{-6}$mbar respectively. \\ The films are sufficiently thick to be able to observe the colour with the naked eye.}
+
+\end{center}
+
+The structural differences between the two films are striking. The surface of the Au-bright film appears to consist of a layer of well defined metallic nanoparticles with sizes ranging from $20$ to $100$nm. In contrast, the Au-black film shows a highly irregular pattern, of interconnected strands of material. This pattern has lead some researchers to refer to metallic-black films as ``smokes'' \cite{}.
+
+
+\subsection*{Fourier Analysis of SEM Images}
+
+Fourier Analysis of the above SEM images can be used to provide more quantitative information about the structural differences between the two films.
+
+The two dimensional Discrete Fourier Transform is given by:
+\begin{align}
+ F(k_x, k_y) &= \displaystyle\sum_{x=0}^{N-1}\displaystyle\sum_{y=0}^{N-1} f(x, y) e^{\frac{-2 \pi i}{N}\left(k_x x + k_y y\right)} \label{dft}
+\end{align}
+
+Where $f(x, y)$ is a discrete data value (in this case the pixel intensity of the image) co-ordinates $(x, y)$, $N \times N$ are the dimensions of the image, and $F(k_x, k_y)$ gives the Fourier Coefficient. If the image represents a region with dimensions of $L \times L$, then the largest frequency components that can be contained in $F$ are $\frac{N}{L}$ \cite{}.
+
+Figures \ref{} and \ref{} show the amplitude plots of the DFT for each of the SEM images in figure \ref{SEM_images}. Since the phase plots give little additional information, they will not be presented or discussed here.
+
+There are two notable differences between the SEM images. Firstly, the central peak in low frequency components appears isotropic for the Au-Black sample, but is elliptically shaped for the Au-Bright image, indicating a. Secondly the
+
+Equation \eqref{dft} actually gives the Fourier coefficients of the infinite periodic extension of $f(x, y)$. If $f(x, y)$ is not periodic, then applying \eqref{dft} introduces extra high frequency components due to sharp discontinuities at the boundaries. The central
+
+\pagebreak
+\begin{center}
+ \includegraphics[scale=0.35]{figures/sem/Au_BLACK_82pix_200nm_fft_abs.png}
+ \captionof{figure}{Amplitude density plot of DFT for Au-Black SEM image}
+ %\captionof[figure]{Amplitude density plot of DFT for Au-Black}
+\end{center}
+\begin{center}
+ \includegraphics[scale=0.35]{figures/sem/Au_BRIGHT_42pix_100nm_fft_abs.png}
+ \captionof{figure}{Amplitude density plot of DFT for Au-Bright SEM image}
+\end{center}
+
+
+%\begin{center}
+% \includegraphics[scale=0.35]{fourier/Au_BLACK_82pix_200nm_fft_phase.png}
+% \captionof{figure}{Phase density plot of DFT for Au-Black}
+%\end{center}
+%\begin{center}
+% \includegraphics[scale=0.35]{fourier/Au_BRIGHT_42pix_100nm_fft_phase.png}
+% \captionof{figure}{Phase density plot of DFT for Au-Bright}
+%\end{center}
+%\pagebreak
+
+\subsection{Higher Magnification Images of Au-Black}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth]{figures/sem/Au_BLACK_increasing_magnifications.jpg}
+ \caption{Increasing magnification images of Au-Black}
+ \label{Au_BLACK_increasing_magnifications.jpg}
+\end{figure}
+
+\section{Atomic Force Microscopy of Au}
+
+One of the Au-Bright samples sent to CMCA was imaged using Atomic Force Microscopy.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth]{figures/afm/Au_BRIGHT_amplitude.png}
+ \caption{AFM amplitude image of Au-Bright}
+ \label{afm/Au_BRIGHT_AFM.tif}
+\end{figure}
+
+\pagebreak
\section{Total Current Spectropy}
+
+
+\subsection{Effect of Focusing of the Electron Gun on the TCS}
+
+{\bf Note: Maybe this should be put into the appendix ``Electron Optics''}
+
+The goal of electron optics applied to TCS is to minimise the effective energy distribution $f(E - E_1)$ of primary electrons at the surface. $f(E - E_1)$ is limited by the emission properties of the cathode, but significantly affected by the focus of the electron gun.
+
+The angular distribution of electrons incident on the sample can be related to $f(E - E_1)$ by treating each electron arriving at angle $\theta$ to the surface as having an effective energy $E_{eff} = E \cos^2 (\theta)$. The width of this angular distribution determines the width of $f(E - E_1)$, whilst the centre determines the value of $U$ for which the measured TCS elastic peak occurs.
+
+It is also important to ensure that the primary electron beam only strikes the sample of interest (and not the sample holder).
+
+\emph{TODO: Choose which plots to include; Can get a range of similar effects from adjustment of each electrode potential; I have reproduced all the plots here for now}.
+
+Figure \ref{focus_accel_tcs.eps} - Adjusting the accelerating potential
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/focus_accel_tcs.eps}
+ \caption{Comparison of TCS curves due to different sets of electron gun potentials; same sample (Au on Si).}
+ \label{focus_accel_tcs.eps}
+\end{figure}
+
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/focus_central_tcs.eps}
+ \caption{Comparison of TCS curves due to different sets of electron gun potentials; same sample (Au on Si).}
+ \label{focus_central_tcs.eps}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/focus_deflection_tcs.eps}
+ \caption{Comparison of TCS curves due to different sets of electron gun potentials; same sample (Au on Si).}
+ \label{focus_deflection_tcs.eps}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/focus_wenhault_tcs.eps}
+ \caption{Comparison of TCS curves due to different sets of electron gun potentials; same sample (Au on Si).}
+ \label{focus_wenhault_tcs.eps}
+\end{figure}
+
+
+
+
+\subsection{Effect of Evaporation of Ag onto an Si substrate}
+
+\emph{Note to Sergey: I know you said not to do any more experiments, but I did these on Tuesday night because I wanted to compare curves taken under as similar conditions as possible (most previous results were obtained over several days at the least). I used Ag because I was running low on Au.}
+
+Figures \ref{agsiI_tcs.eps} and \ref{agsiII_tcs.eps} show the processed TCS curves for layers of Ag, followed by Ag-Black, evaporated on Si substrates. For comparison, the sample holder (stainless steel) TCS is also shown.
+
+
+The electron gun was focused on the sample shown in \ref{agsiI_tcs.eps}. The sample shown in \ref{agsiII_tcs.eps} was placed in a second sample holder on the opposite side of a rotation manipulator; the gun was not refocused on this sample.
+
+
+\emph{TODO: Explain curves!}
+\begin{enumerate}
+ \item Contact potential decreases in going from Si to Ag on Si
+ \item BlackAg appears to have a higher elastic peak
+ \item The gun electrodes are the same, but the two sets of curves are clearly different; due to dodgy sample holder; best not mention
+ (Only present one of these graphs?)
+ \item Can see that beam is not hitting the sample holder (best seen in the second plot), because the elastic peak of the sample holder is clearly not visible in the TCS of the Si substrate.
+ \item Positive TCS - Indicates more inelastic interaction mechanisms are possible (threshold energy reached)
+ \item Negative TCS - Indicates fewer inelastic interaction mechanisms. ???
+ \item Why does TCS change very smoothly? Is the convolution of primary and secondary maxima sufficient to explain this?
+ \begin{itemize}
+ \item I can fit for the location and size of gaussian peaks if required.
+ \end{itemize}
+ \item TCS of BlackAg appears very similar, but shifted, for the two trials
+\end{enumerate}
+
+\emph{Note: I also have plots of I(E) curves}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/blackagI_agsiI_siI_holderI_tcs.eps}
+ \caption{Successive TCS curves for a BlackAg evaporated on Ag on a Si substrate.}
+ \label{agsiI_tcs.eps}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/blackagII_agsiII_siII_holderII_tcs.eps}
+ \caption{The above TCS comparison repeated for a second sample \\(NB: Ag evaporation time is half that of the first sample; layer is still visible by eye)}
+ \label{agsiII_tcs.eps}
+\end{figure}
+
+\subsection{Effect of Evaporation of Au on Si}
+
+Figure \ref{increased_au_thickness_tcs.eps} shows the comparison between TCS obtained from a thin layer of Au on Si and a thicker layer of Au.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/increased_au_thickness_tcs.eps}
+ \label{increased_au_thickness_tcs.eps}
+\end{figure}
+
+Figure \ref{blackau_on_au_on_si_tcs.eps} shows the effect of evaporating Black-Au on a thick layer of Au on Si.
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/blackau_on_au_on_si_tcs.eps}
+ \label{blackau_on_au_on_si_tcs.eps}
+\end{figure}
+Disagrees with the BlackAg on Ag on Si... I am really confused.
+
+\pagebreak
+
\section{Variable Angle Spectroscopy Ellipsometry}
-\section{Optical Transmission Spectroscopy}
+\subsection{Ag-Bright on Si substrate}
+
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/ag_on_si/psi_final_model.png}
+ \label{psi_final_model.png}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/ag_on_si/delta_final_model.png}
+ \label{delta_final_model.png}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/ag_on_si/ag_fit_vs_bulk_opticalconstants.png}
+ \label{ag_fit_vs_bulk_opticalconstants.png}
+\end{figure}
+
+The plots show the measured and fitted ellipsometric parameters for a thin film of Ag on a Si substrate. The model was constructed to include an $\text{SiO}^2$ oxide layer on the Si, and a surface roughness Effective Medium Approximation (EMA) (Bruggeman). A fit was first performed for the thickness of the Ag film assuming bulk optical constants; this fit was then improved by allowing the software to adjust the Ag film's optical constants. Final model:
+
+\begin{center}
+ \begin{tabular}{lll}
+ {\bf Layer} & {\bf Thickness} \\
+ Ag (fit for $n$ and $k$) & $16.092 \pm 2.7$ nm \\
+ Intermix (Ag/$\text{SiO}^2$) & $0.267 \pm 0.03$ nm \\
+ $\text{SiO}^2$ & $4.02 \pm 0.57$ nm \\
+ Si & (substrate)
+ \end{tabular}
+ \captionof{table}{Model for thin Ag on Si}
+\end{center}
+
+\subsection{Black Ag on Si}
+
+
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/blackag_on_si/psi.png}
+ \label{psi_final_model.png}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/blackag_on_si/delta.png}
+ \label{delta_final_model.png}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/blackag_on_si/blackag_opticalconstants_comparison.png}
+ \label{ag_fit_vs_bulk_opticalconstants.png}
+\end{figure}
+
+\begin{center}
+ \begin{tabular}{lll}
+ {\bf Layer} & {\bf Thickness} \\
+ Surface roughness EMA (75.8\% void) & 2.708 nm \\
+ Black Ag (fit for $n$ and $k$) & 3.726 nm \\
+ $\text{SiO}^2$ & 8.00 nm \\
+ Si & (substrate)
+ \end{tabular}
+ \captionof{table}{Model for thin Ag on Si}
+\end{center}
+
+\pagebreak
+
+\section{Optical Transmission and Reflection Measurements using the VASE}
+
+\pagebreak
+
+\section{Optical Transmission Spectroscopy using OceanOptics Spectrometer}
+
+\subsection{Dark Spectrum}
+
+{\bf NOTE: Probably won't include in the final thesis}
+
+Figure \ref{dark_comparison.eps} shows the spectrum of the background (taken at different times on the same day), without the light source.
+The room lights were off, the experiment was covered with a cardboard box and layers of black plastic sheeting; but the spectra still changed for different times of the day.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/dark_comparison.eps}
+ \caption{Dark spectra}
+ \label{dark_comparison.eps}
+\end{figure}
+
+In all subsequent experiments, the dark intensity has been subtracted from measured intensity counts:
+\begin{align*}
+ I(\lambda) = I_{\text{measured}}(\lambda) - I_{\text{dark}}(\lambda)
+\end{align*}
+
+\pagebreak
+\subsection{Reference Spectrum}
+
+{\bf Note: Also don't include in final thesis? Or at least, remove the time dependence; just show one curve.}
+
+The Ellipsometer's Xe Arc Lamp was used as a light source. It's spectrum $I_0(\lambda)$ is shown in Figure \ref{reference.eps}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/reference.eps}
+ \caption{Xe Lamp reference spectra}
+ \label{reference.eps}
+\end{figure}
+
+Because the dark spectra changed over time scales comparable to the length of measurement, some features in the processed spectra are due to the reference spectra of the Xe lamp.
+
+\pagebreak
+\subsection{Testing the Spectrometer}
+
+{\bf Note: Also don't include?}
+
+The spectrometer was tested using a 653nm filter. \ref{653nm_filter.eps}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/653nm_filter.eps}
+ \caption{Tested Spectrometer with 653nm Filter}
+ \label{653nm_filter.eps}
+\end{figure}
+
+The transmission was calculated as:
+\begin{align}
+ t(\lambda) &= \frac{I(\lambda)}{I_0{\lambda}} \label{transmission1}
+\end{align}
+Where $I_0(\lambda)$ was the intensity (arbitrary units) of the Xe Arc Lamp at wavelength $\lambda$, and $I(\lambda)$ was the measured intensity.
+
+\subsection{Transmission Spectra of Glass}
+
+{\bf Note: Should probably include this, as the substrate is important to the final transmission}
+
+All films were prepared on microscope glass; the transmission of the glass must be known to determine the transmission of the films.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/glass_transmission.eps}
+ \caption{Glass reference transmission spectrum}
+ \label{glass_transmission.eps}
+\end{figure}
+
+{\bf NOTE:} The reason that the glass has transmission $> 1$ is (probably) because the background level has increased between the reference measurement and the measurement of glass. I should probably normalise the glass transmission spectrum to its maximum value.
+
+Transmission was calculated using \eqref{transmission1}.
+
+\subsection{Transmission Spectra of Au and Au-Black on Glass}
+
+Figure \ref{blackau_vs_au.eps} shows all measured transmission spectra for Au vs Au-Black (pressure 1e-6 is for the Au-bright films, all others are Au-Black) {\bf NOTE: Need to relabel plot}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/blackau_vs_au.eps}
+ \caption{Transmission Spectra for various Au films}
+ \label{blackau_vs_au.eps}
+\end{figure}
+
+Transmission is calculated as:
+\begin{align*}
+ t &= \frac{I(\lambda)}{I_0(\lambda)} \times \frac{I_\text{glass}(\lambda)}{I_0(\lambda)}
+\end{align*}
+Where $t_{\text{glass}} = \frac{I_\text{glass}}{I_0}$ is the transmission spectrum of the microscope slide glass.
+
+{\bf Note: I should select just 2 or 3 of these spectra to use in the final report}
+
+The general trends:
+\begin{enumerate}
+ \item Thin films (low current or short evaporation time) show similar shape regardless of pressure (1e-6 or 1e-2 mbar)
+ \item Thicker layers all show peak near 500nm, followed by minima at 600-700nm
+ \item All curves show fine structure at same wavelengths above 800nm. This may be due to the Xe lamp spectrum; if the background level has increased, then Xe lamp spectral features will show up in the final spectrum.
+ \item Thick layers of Au-Black show much lower transmission to 700nm, but a much faster increase at longer $\lambda$
+ \item At least one of the Au-Black samples shows a similar spectrum to a (thick) Au-Bright sample.
+\end{enumerate}
+
+\subsubsection{Effect of Atmosphere on Transmission Spectra of Au-Black}
+
+A paper \cite{} has found differences between Au-Black prepared in Air or an inert gas. The Au-Black prepared in Air contains traces of Tungsten Oxides; the Au-Black prepared in an inert gas does not. This was the motivation for making a comparison between samples prepared in Air and He.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/he_blackau_vs_air_blackau.eps}
+ \caption{Transmission Spectra for Black Au films prepared in different atmospheres}
+ \label{he_blackau_vs_air_blackau.eps}
+\end{figure}
+
+\subsection{Transmission Spectra of Ag}
+
+A pre-existing Ag sample (unknown preparation conditions), on glass.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/silver_transmission.eps}
+ \caption{Transmission Spectra for a Silver film on glass}
+ \label{silver_transmission.eps}
+\end{figure}
+
+
+\subsection{Transmission Spectra of Ag and Ag-Black on Glass}
+
+The Ag sample compared with Ag-Black.
+Notice fine structure not in original Ag sample. Probably due to dark spectrum changing.
+
+A pre-existing Ag sample (unknown preparation conditions), on glass.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/blackag_vs_ag.eps}
+ \caption{Transmission Spectra for a Silver film on glass}
+ \label{blackag_vs_ag.eps}
+\end{figure}
+
+{\bf Note:} The Ag-Black is much thinner than the Ag-Bright sample; by eye it appears to be a thin grey layer. Also, the Ag-Bright sample was not uniformly thick; part of the film had been scratched or wiped off.
+
\section{Scanning Electron Microscopy}
+A number of samples of metallic-black and metallic-bright films were sent to the Centre for Microscopy Characterisation and Analysis (CMCA) at UWA for study. In this section we will present and discuss some of the images produced by CMCA. These images provide an invaluable aid to understanding the structural differences between metallic-black and metallic-bright films.
+
+
+Figure \ref{SEM_images} shows a comparison of an Au-Black and Au-Bright film imaged using a scanning electron microscope (SEM). The intensity of each pixel is proportional to the total current of secondary electrons scattered from the surface at that point from the metal in the film (the current due to the Si substrate has been subtracted from the image), which is in turn proportional to the density of metal at the considered point.
+
+\begin{center}
+
+
+\begin{tabular}{cc}
+ \includegraphics[scale=0.20]{figures/sem/Au_BLACK_200nm.png} & %\captionof{figure}{Au-Black SEM Image} \label{Au_BLACK_200nm.png} &
+ \includegraphics[scale=0.20]{figures/sem/Au_semi-shiny_1_SEM.png} %\captionof{figure}{Au SEM Image} \label{Au_semi-shiny_1_SEM.png}
+
+ \label{SEM_images}
+\end{tabular}
+
+ \captionof{figure}{{\bf 2500 x 1900nm SEM images of Au-Black (left) and Au-Bright (right) deposited on Si} \\ Preparation pressures were $2\times10^{-2}$mbar and $1\times10^{-6}$mbar respectively. \\ The films are sufficiently thick to be able to observe the colour with the naked eye.}
+
+\end{center}
+
+The structural differences between the two films are striking. The surface of the Au-bright film appears to consist of a layer of well defined metallic nanoparticles with sizes ranging from $20$ to $100$nm. In contrast, the Au-black film shows a highly irregular pattern, of interconnected strands of material. This pattern has lead some researchers to refer to metallic-black films as ``smokes'' \cite{}.
+
+
+\subsection*{Fourier Analysis of SEM Images}
+
+Fourier Analysis of the above SEM images can be used to provide more quantitative information about the structural differences between the two films.
+
+The two dimensional Discrete Fourier Transform is given by:
+\begin{align}
+ F(k_x, k_y) &= \displaystyle\sum_{x=0}^{N-1}\displaystyle\sum_{y=0}^{N-1} f(x, y) e^{\frac{-2 \pi i}{N}\left(k_x x + k_y y\right)} \label{dft}
+\end{align}
+
+Where $f(x, y)$ is a discrete data value (in this case the pixel intensity of the image) co-ordinates $(x, y)$, $N \times N$ are the dimensions of the image, and $F(k_x, k_y)$ gives the Fourier Coefficient. If the image represents a region with dimensions of $L \times L$, then the largest frequency components that can be contained in $F$ are $\frac{N}{L}$ \cite{}.
+
+Figures \ref{} and \ref{} show the amplitude plots of the DFT for each of the SEM images in figure \ref{SEM_images}. Since the phase plots give little additional information, they will not be presented or discussed here.
+
+There are two notable differences between the SEM images. Firstly, the central peak in low frequency components appears isotropic for the Au-Black sample, but is elliptically shaped for the Au-Bright image, indicating a. Secondly the
+
+Equation \eqref{dft} actually gives the Fourier coefficients of the infinite periodic extension of $f(x, y)$. If $f(x, y)$ is not periodic, then applying \eqref{dft} introduces extra high frequency components due to sharp discontinuities at the boundaries. The central
+
+\pagebreak
+\begin{center}
+ \includegraphics[scale=0.35]{figures/sem/Au_BLACK_82pix_200nm_fft_abs.png}
+ \captionof{figure}{Amplitude density plot of DFT for Au-Black SEM image}
+ %\captionof[figure]{Amplitude density plot of DFT for Au-Black}
+\end{center}
+\begin{center}
+ \includegraphics[scale=0.35]{figures/sem/Au_BRIGHT_42pix_100nm_fft_abs.png}
+ \captionof{figure}{Amplitude density plot of DFT for Au-Bright SEM image}
+\end{center}
+
+
+%\begin{center}
+% \includegraphics[scale=0.35]{fourier/Au_BLACK_82pix_200nm_fft_phase.png}
+% \captionof{figure}{Phase density plot of DFT for Au-Black}
+%\end{center}
+%\begin{center}
+% \includegraphics[scale=0.35]{fourier/Au_BRIGHT_42pix_100nm_fft_phase.png}
+% \captionof{figure}{Phase density plot of DFT for Au-Bright}
+%\end{center}
+%\pagebreak
+
+\subsection{Higher Magnification Images of Au-Black}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth]{figures/sem/Au_BLACK_increasing_magnifications.jpg}
+ \caption{Increasing magnification images of Au-Black}
+ \label{Au_BLACK_increasing_magnifications.jpg}
+\end{figure}
+
+\section{Atomic Force Microscopy of Au}
+
+One of the Au-Bright samples sent to CMCA was imaged using Atomic Force Microscopy.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth]{figures/afm/Au_BRIGHT_amplitude.png}
+ \caption{AFM amplitude image of Au-Bright}
+ \label{afm/Au_BRIGHT_AFM.tif}
+\end{figure}
+
+\pagebreak
+
\section{Total Current Spectropy}
+
+
+\subsection{Effect of Focusing of the Electron Gun on the TCS}
+
+{\bf Note: Maybe this should be put into the appendix ``Electron Optics''}
+
+The goal of electron optics applied to TCS is to minimise the effective energy distribution $f(E - E_1)$ of primary electrons at the surface. $f(E - E_1)$ is limited by the emission properties of the cathode, but significantly affected by the focus of the electron gun.
+
+The angular distribution of electrons incident on the sample can be related to $f(E - E_1)$ by treating each electron arriving at angle $\theta$ to the surface as having an effective energy $E_{eff} = E \cos^2 (\theta)$. The width of this angular distribution determines the width of $f(E - E_1)$, whilst the centre determines the value of $U$ for which the measured TCS elastic peak occurs.
+
+It is also important to ensure that the primary electron beam only strikes the sample of interest (and not the sample holder).
+
+\emph{TODO: Choose which plots to include; Can get a range of similar effects from adjustment of each electrode potential; I have reproduced all the plots here for now}.
+
+Figure \ref{focus_accel_tcs.eps} - Adjusting the accelerating potential
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/focus_accel_tcs.eps}
+ \caption{Comparison of TCS curves due to different sets of electron gun potentials; same sample (Au on Si).}
+ \label{focus_accel_tcs.eps}
+\end{figure}
+
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/focus_central_tcs.eps}
+ \caption{Comparison of TCS curves due to different sets of electron gun potentials; same sample (Au on Si).}
+ \label{focus_central_tcs.eps}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/focus_deflection_tcs.eps}
+ \caption{Comparison of TCS curves due to different sets of electron gun potentials; same sample (Au on Si).}
+ \label{focus_deflection_tcs.eps}
+\end{figure}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/focus_wenhault_tcs.eps}
+ \caption{Comparison of TCS curves due to different sets of electron gun potentials; same sample (Au on Si).}
+ \label{focus_wenhault_tcs.eps}
+\end{figure}
+
+
+
+
+\subsection{Effect of Evaporation of Ag onto an Si substrate}
+
+\emph{Note to Sergey: I know you said not to do any more experiments, but I did these on Tuesday night because I wanted to compare curves taken under as similar conditions as possible (most previous results were obtained over several days at the least). I used Ag because I was running low on Au.}
+
+Figures \ref{agsiI_tcs.eps} and \ref{agsiII_tcs.eps} show the processed TCS curves for layers of Ag, followed by Ag-Black, evaporated on Si substrates. For comparison, the sample holder (stainless steel) TCS is also shown.
+
+
+The electron gun was focused on the sample shown in \ref{agsiI_tcs.eps}. The sample shown in \ref{agsiII_tcs.eps} was placed in a second sample holder on the opposite side of a rotation manipulator; the gun was not refocused on this sample.
+
+
+\emph{TODO: Explain curves!}
+\begin{enumerate}
+ \item Contact potential decreases in going from Si to Ag on Si
+ \item BlackAg appears to have a higher elastic peak
+ \item The gun electrodes are the same, but the two sets of curves are clearly different; due to dodgy sample holder; best not mention
+ (Only present one of these graphs?)
+ \item Can see that beam is not hitting the sample holder (best seen in the second plot), because the elastic peak of the sample holder is clearly not visible in the TCS of the Si substrate.
+ \item Positive TCS - Indicates more inelastic interaction mechanisms are possible (threshold energy reached)
+ \item Negative TCS - Indicates fewer inelastic interaction mechanisms. ???
+ \item Why does TCS change very smoothly? Is the convolution of primary and secondary maxima sufficient to explain this?
+ \begin{itemize}
+ \item I can fit for the location and size of gaussian peaks if required.
+ \end{itemize}
+ \item TCS of BlackAg appears very similar, but shifted, for the two trials
+\end{enumerate}
+
+\emph{Note: I also have plots of I(E) curves}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/blackagI_agsiI_siI_holderI_tcs.eps}
+ \caption{Successive TCS curves for a BlackAg evaporated on Ag on a Si substrate.}
+ \label{agsiI_tcs.eps}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/blackagII_agsiII_siII_holderII_tcs.eps}
+ \caption{The above TCS comparison repeated for a second sample \\(NB: Ag evaporation time is half that of the first sample; layer is still visible by eye)}
+ \label{agsiII_tcs.eps}
+\end{figure}
+
+\subsection{Effect of Evaporation of Au on Si}
+
+Figure \ref{increased_au_thickness_tcs.eps} shows the comparison between TCS obtained from a thin layer of Au on Si and a thicker layer of Au.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/increased_au_thickness_tcs.eps}
+ \label{increased_au_thickness_tcs.eps}
+\end{figure}
+
+Figure \ref{blackau_on_au_on_si_tcs.eps} shows the effect of evaporating Black-Au on a thick layer of Au on Si.
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.6\textwidth, angle=270]{figures/tcs/plots/blackau_on_au_on_si_tcs.eps}
+ \label{blackau_on_au_on_si_tcs.eps}
+\end{figure}
+Disagrees with the BlackAg on Ag on Si... I am really confused.
+
+\pagebreak
+
\section{Variable Angle Spectroscopy Ellipsometry}
-\section{Optical Transmission Spectroscopy}
+\subsection{Ag-Bright on Si substrate}
+
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/ag_on_si/psi_final_model.png}
+ \label{psi_final_model.png}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/ag_on_si/delta_final_model.png}
+ \label{delta_final_model.png}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/ag_on_si/ag_fit_vs_bulk_opticalconstants.png}
+ \label{ag_fit_vs_bulk_opticalconstants.png}
+\end{figure}
+
+The plots show the measured and fitted ellipsometric parameters for a thin film of Ag on a Si substrate. The model was constructed to include an $\text{SiO}^2$ oxide layer on the Si, and a surface roughness Effective Medium Approximation (EMA) (Bruggeman). A fit was first performed for the thickness of the Ag film assuming bulk optical constants; this fit was then improved by allowing the software to adjust the Ag film's optical constants. Final model:
+
+\begin{center}
+ \begin{tabular}{lll}
+ {\bf Layer} & {\bf Thickness} \\
+ Ag (fit for $n$ and $k$) & $16.092 \pm 2.7$ nm \\
+ Intermix (Ag/$\text{SiO}^2$) & $0.267 \pm 0.03$ nm \\
+ $\text{SiO}^2$ & $4.02 \pm 0.57$ nm \\
+ Si & (substrate)
+ \end{tabular}
+ \captionof{table}{Model for thin Ag on Si}
+\end{center}
+
+\subsection{Black Ag on Si}
+
+
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/blackag_on_si/psi.png}
+ \label{psi_final_model.png}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/blackag_on_si/delta.png}
+ \label{delta_final_model.png}
+\end{figure}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth, angle=0]{figures/ellipsometer/blackag_on_si/blackag_opticalconstants_comparison.png}
+ \label{ag_fit_vs_bulk_opticalconstants.png}
+\end{figure}
+
+\begin{center}
+ \begin{tabular}{lll}
+ {\bf Layer} & {\bf Thickness} \\
+ Surface roughness EMA (75.8\% void) & 2.708 nm \\
+ Black Ag (fit for $n$ and $k$) & 3.726 nm \\
+ $\text{SiO}^2$ & 8.00 nm \\
+ Si & (substrate)
+ \end{tabular}
+ \captionof{table}{Model for thin Ag on Si}
+\end{center}
+
+\pagebreak
+
+\section{Optical Transmission and Reflection Measurements using the VASE}
+
+\pagebreak
+
+\section{Optical Transmission Spectroscopy using OceanOptics Spectrometer}
+
+\subsection{Dark Spectrum}
+
+{\bf NOTE: Probably won't include in the final thesis}
+
+Figure \ref{dark_comparison.eps} shows the spectrum of the background (taken at different times on the same day), without the light source.
+The room lights were off, the experiment was covered with a cardboard box and layers of black plastic sheeting; but the spectra still changed for different times of the day.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/dark_comparison.eps}
+ \caption{Dark spectra}
+ \label{dark_comparison.eps}
+\end{figure}
+
+In all subsequent experiments, the dark intensity has been subtracted from measured intensity counts:
+\begin{align*}
+ I(\lambda) = I_{\text{measured}}(\lambda) - I_{\text{dark}}(\lambda)
+\end{align*}
+
+\pagebreak
+\subsection{Reference Spectrum}
+
+{\bf Note: Also don't include in final thesis? Or at least, remove the time dependence; just show one curve.}
+
+The Ellipsometer's Xe Arc Lamp was used as a light source. It's spectrum $I_0(\lambda)$ is shown in Figure \ref{reference.eps}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/reference.eps}
+ \caption{Xe Lamp reference spectra}
+ \label{reference.eps}
+\end{figure}
+
+Because the dark spectra changed over time scales comparable to the length of measurement, some features in the processed spectra are due to the reference spectra of the Xe lamp.
+
+\pagebreak
+\subsection{Testing the Spectrometer}
+
+{\bf Note: Also don't include?}
+
+The spectrometer was tested using a 653nm filter. \ref{653nm_filter.eps}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/653nm_filter.eps}
+ \caption{Tested Spectrometer with 653nm Filter}
+ \label{653nm_filter.eps}
+\end{figure}
+
+The transmission was calculated as:
+\begin{align}
+ t(\lambda) &= \frac{I(\lambda)}{I_0{\lambda}} \label{transmission1}
+\end{align}
+Where $I_0(\lambda)$ was the intensity (arbitrary units) of the Xe Arc Lamp at wavelength $\lambda$, and $I(\lambda)$ was the measured intensity.
+
+\subsection{Transmission Spectra of Glass}
+
+{\bf Note: Should probably include this, as the substrate is important to the final transmission}
+
+All films were prepared on microscope glass; the transmission of the glass must be known to determine the transmission of the films.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.5\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/glass_transmission.eps}
+ \caption{Glass reference transmission spectrum}
+ \label{glass_transmission.eps}
+\end{figure}
+
+{\bf NOTE:} The reason that the glass has transmission $> 1$ is (probably) because the background level has increased between the reference measurement and the measurement of glass. I should probably normalise the glass transmission spectrum to its maximum value.
+
+Transmission was calculated using \eqref{transmission1}.
+
+\subsection{Transmission Spectra of Au and Au-Black on Glass}
+
+Figure \ref{blackau_vs_au.eps} shows all measured transmission spectra for Au vs Au-Black (pressure 1e-6 is for the Au-bright films, all others are Au-Black) {\bf NOTE: Need to relabel plot}
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/blackau_vs_au.eps}
+ \caption{Transmission Spectra for various Au films}
+ \label{blackau_vs_au.eps}
+\end{figure}
+
+Transmission is calculated as:
+\begin{align*}
+ t &= \frac{I(\lambda)}{I_0(\lambda)} \times \frac{I_\text{glass}(\lambda)}{I_0(\lambda)}
+\end{align*}
+Where $t_{\text{glass}} = \frac{I_\text{glass}}{I_0}$ is the transmission spectrum of the microscope slide glass.
+
+{\bf Note: I should select just 2 or 3 of these spectra to use in the final report}
+
+The general trends:
+\begin{enumerate}
+ \item Thin films (low current or short evaporation time) show similar shape regardless of pressure (1e-6 or 1e-2 mbar)
+ \item Thicker layers all show peak near 500nm, followed by minima at 600-700nm
+ \item All curves show fine structure at same wavelengths above 800nm. This may be due to the Xe lamp spectrum; if the background level has increased, then Xe lamp spectral features will show up in the final spectrum.
+ \item Thick layers of Au-Black show much lower transmission to 700nm, but a much faster increase at longer $\lambda$
+ \item At least one of the Au-Black samples shows a similar spectrum to a (thick) Au-Bright sample.
+\end{enumerate}
+
+\subsubsection{Effect of Atmosphere on Transmission Spectra of Au-Black}
+
+A paper \cite{} has found differences between Au-Black prepared in Air or an inert gas. The Au-Black prepared in Air contains traces of Tungsten Oxides; the Au-Black prepared in an inert gas does not. This was the motivation for making a comparison between samples prepared in Air and He.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/he_blackau_vs_air_blackau.eps}
+ \caption{Transmission Spectra for Black Au films prepared in different atmospheres}
+ \label{he_blackau_vs_air_blackau.eps}
+\end{figure}
+
+\subsection{Transmission Spectra of Ag}
+
+A pre-existing Ag sample (unknown preparation conditions), on glass.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/silver_transmission.eps}
+ \caption{Transmission Spectra for a Silver film on glass}
+ \label{silver_transmission.eps}
+\end{figure}
+
+
+\subsection{Transmission Spectra of Ag and Ag-Black on Glass}
+
+The Ag sample compared with Ag-Black.
+Notice fine structure not in original Ag sample. Probably due to dark spectrum changing.
+
+A pre-existing Ag sample (unknown preparation conditions), on glass.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.7\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/blackag_vs_ag.eps}
+ \caption{Transmission Spectra for a Silver film on glass}
+ \label{blackag_vs_ag.eps}
+\end{figure}
+
+{\bf Note:} The Ag-Black is much thinner than the Ag-Bright sample; by eye it appears to be a thin grey layer. Also, the Ag-Bright sample was not uniformly thick; part of the film had been scratched or wiped off.
+
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+\citation{woolam1999}
+\citation{woolam1999}
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+\@writefile{toc}{\contentsline {subsection}{\numberline {3.2.1}Overview}{7}{subsection.3.2.1}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3.2}{\ignorespaces Diagram of an Ellipsometric Measurement \cite {woolam1999}\relax }}{7}{figure.caption.3}}
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+\newlabel{ellipsometer_measurement}{{3.2}{7}{Diagram of an Ellipsometric Measurement \cite {woolam1999}\relax \relax }{figure.caption.3}{}}
+\newlabel{ellipso}{{3.1}{7}{Overview\relax }{equation.3.2.1}{}}
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+\@writefile{lof}{\contentsline {figure}{\numberline {3.3}{\ignorespaces From left to right, circular, elliptical and linearly polaristed light, viewed down the axis of beam propagation\relax }}{8}{table.caption.4}}
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+\newlabel{ellipsometer.png}{{3.4}{9}{Block diagram of the VASE \\(taken from \emph {Overview of Variable Angle Spectroscopic Ellipsometry (VASE), Part I: Basic Theory and Typical Applications} \cite {woolam1999})\relax \relax }{figure.caption.5}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.2.3}Relation of $\psi $ and $\Delta $ to properties of the sample}{9}{subsection.3.2.3}}
+\@writefile{toc}{\contentsline {subsubsection}{Bulk Substrates}{9}{section*.6}}
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+\@writefile{toc}{\contentsline {subsubsection}{Multi-layered Thin Films}{9}{section*.8}}
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\begin{center}
- \includegraphics[scale=0.60]{figures/tcs_simple}
+ \includegraphics[scale=0.60]{figures/tcs/tcs_simple}
\captionof{figure}{ A simplified schematic of Total Current Spectroscopy Experiments }
\label{tcs_simple.pdf}
\end{center}
The experimental goal of Total Current Spectroscopy is the measurement of $S(E_1) \propto \der{I_2}{E_1}$. More information on the experimental setup and techniques are presented in Appendix \ref{}. The remainder of this section will give an overview of concepts needed for relating $S(E_1)$ to properties of a sample.
-\subsubsection{Theory of Signal Formation in Total Current Spectroscopy Experiments} \label{tcs_theory1}
+\subsubsection{Relationship between $S(E_1)$ and electron-surface interactions} \label{tcs_theory1}
Here we will summarise the approach of Komolov \cite{komolov} in constructing a theory relating $S(E_1)$ to scattering events within the target surface.
S(E_1) &= \der{I}{E_1} = e A \frac{d}{dE_1} \left( 1 - \sigma(E_1) \right) = e A \der{\sigma(E_1)}{E_1}
\end{align*}
+{\bf NOTE: Komolov goes on to find expressions for $\sigma(E_1)$ in terms of specific inelastic processes...}
+
\pagebreak
\section{Ellipsometry}
-Ellipsometry is an optical technique which measures the change in polarisation of light reflected from a surface. This change in polarisation can be related to properties of the surface; a common application of ellipsometry is determining the thickness of multilayered thin films.
-
-
-\begin{center}
- \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/thesis/figures/ellipsometry_measurement}
- \captionof{figure}{Diagram of Ellipsometry Measurements}
- \label{ellipsometer_measurement.png}
-\end{center}
+\subsection{Overview}
-As shown in figure \ref{}, linearly polarised light incident upon a surface is in general reflected as elliptically polarised light. Ellipsometers are designed to produce a known linear polarisation of light incident on a sample, and to record the polarisation of reflected light.
+Ellipsometry is an optical technique which measures the change in polarisation of light reflected from a surface. This change in polarisation can be related to the optical properties of the surface, including optical constants or the thickness of thin film surface layers.
In the Jone's formalism, polarisation states may be represented by orthogonal electric field components $E_p$ and $E_s$, which are polarised parallel and perpendicular to the plane of incidence respectively. The reflection of a light ray from the surface is described by the matrix equation:
\begin{align*}
\left[\begin{array}{c} E_{rp} \\ E_{rs} \end{array}\right] &= \left[ \begin{array}{cc} r_{pp} & r_{ps} \\ r_{sp} & r_{ss} \end{array} \right] \left[\begin{array}{c} E_{ip} \\ E_{is} \end{array}\right]
\end{align*}
-Where $\vect{E}_i$ and $\vect{E}_r$ are the incident and reflected rays. Each element of the $2\times 2$ matrix $r_{ij}$ is the reflection coefficient for $i$ polarised light due to incident $j$ polarised light; these values are generally complex to include the phase change.
+Where $\vect{E}_i$ and $\vect{E}_r$ are the incident and reflected rays. Each element of the $2\times 2$ matrix $r_{ij}$ is the reflection coefficient for $i$ polarised light due to incident $j$ polarised light; these values are generally complex to include the phase change.
-Generalised Ellipsometry measures three ratios of $r_{ij}$ values:
-\begin{align*}
- \rho_{pp} &= \frac{r_{pp}}{r_{ss}} = \tan \psi_{pp} e^{-i \Delta_{pp}} \\
- \rho_{ps} &= \frac{r_{ps}}{r_{ss}} = \tan \psi_{ps} e^{-i \Delta_{ps}} \\
- \rho_{sp} &= \frac{r_{sp}}{r_{ss}} = \tan \psi_{sp} e^{-i \Delta_{sp}}
-\end{align*}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.80\textwidth]{figures/ellipsometer/ellipsometer_measurement.png}
+ \caption{Diagram of an Ellipsometric Measurement \cite{woolam1999}}
+ \label{ellipsometer_measurement}
+\end{figure}
-If the sample is isotropic, then $r_{ps} = r_{sp} = 0$. In this case, only the ratio $\frac{r_p}{r_s} = \frac{r_{pp}}{r_{ss}}$ must be measured:
+As shown in figure \ref{ellipsometer_measurement}, linearly polarised light incident upon a surface is in general reflected as elliptically polarised light. For an isotropic sample, $r_{ps} = r_{sp} = 0$, and we can write $r_{pp} \equiv r_{p}$ and $r_{ss} \equiv r_{s}$. A standard ellipsometric measurement expresses the ratio of the $p$ and $s$ reflection coefficients in terms of the two parameters $\psi$ and $\Delta$
\begin{align}
\tan(\psi) e^{i \Delta} &= \rho = \frac{r_p}{r_s} \label{ellipso}
\end{align}
-The parameter $\psi$ gives the angle by which ...., whilst $\Delta$ gives the phase difference between $E_p$ and $E_s$ components.
-The Jone's formalism is not sufficient to describe the response of samples which de-polarise the incident beam; the more general Stoke's formalism must be used for such cases \cite{woolam2000} \cite{oates2011}.
+The value of $\tan(\psi)$ gives the ratio of amplitudes between the $p$ and $s$ components of the reflected electric field, whilst $\Delta$ gives the phase difference.
+
+In the case where the sample is anisotropic, $\psi$ and $\Delta$ alone are not sufficient to characterise the sample; three seperate ratios of fresnel reflection coefficients are required \cite{woolam2000}:
+
+Light may consist of two or more components of well defined polarisation states; as a result, the total beam cannot be described with a single well defined Jones vector. Ellipsometers are designed to establish a well defined polarisation state of light incident on the sample; however non-uniform films or backside reflection from a substrate may cause the reflected beam to be partially polarised. As a result, the Jone's formalism is not sufficient for characterisation of these samples, and the more general Stokes formalise (with 4 component vectors) must be employed \cite{woolam2000} \cite{oates2011}.
+
+\begin{table}[H]
+ \centering
+ \begin{tabular}{lll}
+ \includegraphics[scale=0.75]{figures/ellipsometer/circular_polarisation} &
+ \includegraphics[scale=0.75]{figures/ellipsometer/elliptical_polarisation} &
+ \includegraphics[scale=0.75]{figures/ellipsometer/linear_polarisation} \\
+ \end{tabular}
+
+ \captionof{figure}{From left to right, circular, elliptical and linearly polaristed light, viewed down the axis of beam propagation}
+\end{table}
\subsection{Variable Angle Spectroscopic Ellipsometry}
-Traditional ellipsometers were restricted to single angle and often single wavelength measurements \cite{}. With advances in computing technology in the 1970s,
+Although Ellipsometers have been in use for thin film analysis since the ??? \cite{}, traditional instruments were usually limited to single angle and single wavelength measurements, due to the painstaking manual process of repeated measurements. With advances both in software and hardware during the last half of the 20th century, Ellipsometric measurements have become largely automated, allowing for a wide range of optical information to be obtained from a sample. Spectroscopic Ellipsometry obtains measurements for a range of wavelengths, whilst Variable Angle Spectroscopic Ellipsometry repeats these measurements over a range of angles of incidence.
-\begin{center}
- \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/thesis/figures/ellipsometer.png}
- \captionof{figure}{Block diagram of the VASE \\(taken from \emph{Overview of Variable Angle Spectroscopic
+The ease with which large amounts of data can be taken from an ellipsometer means that the method is well suited to numerical analysis and fitting procedures. At CAMSP a Variable Angle Spectroscopic Ellipsometer (VASE)\footnote{J. A. Woolam and Co} and the associated software\footnote{WVASE32} have been employed in the analysis of thin film samples.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth]{figures/ellipsometer/ellipsometer.png}
+ \caption{Block diagram of the VASE \\(taken from \emph{Overview of Variable Angle Spectroscopic
Ellipsometry (VASE), Part I:
Basic Theory and Typical Applications}
\cite{woolam1999})}
\label{ellipsometer.png}
-\end{center}
+\end{figure}
+
+\subsection{Relation of $\psi$ and $\Delta$ to properties of the sample}
+
+\subsubsection{Bulk Substrates}
+
+The simplest sample is a bulk substrate. In this case,
+
+\subsubsection{Single Layered Thin Films}
+
+
+
+\subsubsection{Multi-layered Thin Films}
+
+Magical analysis
+
+\section{Optical Transmission and Reflection Spectroscopy}
-\section{Transmission Spectroscopy}
+Can be done with the VASE or with OceanOptics spectrometer.
\section{Scanning Electron Microscopy}
+Done by CMCA, not me.
\begin{center}
- \includegraphics[scale=0.60]{figures/tcs_simple}
+ \includegraphics[scale=0.60]{figures/tcs/tcs_simple}
\captionof{figure}{ A simplified schematic of Total Current Spectroscopy Experiments }
\label{tcs_simple.pdf}
\end{center}
The experimental goal of Total Current Spectroscopy is the measurement of $S(E_1) \propto \der{I_2}{E_1}$. More information on the experimental setup and techniques are presented in Appendix \ref{}. The remainder of this section will give an overview of concepts needed for relating $S(E_1)$ to properties of a sample.
-\subsubsection{Theory of Signal Formation in Total Current Spectroscopy Experiments} \label{tcs_theory1}
+\subsubsection{Relationship between $S(E_1)$ and electron-surface interactions} \label{tcs_theory1}
Here we will summarise the approach of Komolov \cite{komolov} in constructing a theory relating $S(E_1)$ to scattering events within the target surface.
S(E_1) &= \der{I}{E_1} = e A \frac{d}{dE_1} \left( 1 - \sigma(E_1) \right) = e A \der{\sigma(E_1)}{E_1}
\end{align*}
+{\bf NOTE: Komolov goes on to find expressions for $\sigma(E_1)$ in terms of specific inelastic processes...}
+
\pagebreak
\section{Ellipsometry}
-Ellipsometry is an optical technique which measures the change in polarisation of light reflected from a surface. This change in polarisation can be related to properties of the surface; a common application of ellipsometry is determining the thickness of multilayered thin films.
-
-
-\begin{center}
- \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/thesis/figures/ellipsometry_measurement}
- \captionof{figure}{Diagram of Ellipsometry Measurements}
- \label{ellipsometer_measurement.png}
-\end{center}
+\subsection{Overview}
-As shown in figure \ref{}, linearly polarised light incident upon a surface is in general reflected as elliptically polarised light. Ellipsometers are designed to produce a known linear polarisation of light incident on a sample, and to record the polarisation of reflected light.
+Ellipsometry is an optical technique which measures the change in polarisation of light reflected from a surface. This change in polarisation can be related to the optical properties of the surface, including optical constants or the thickness of thin film surface layers.
In the Jone's formalism, polarisation states may be represented by orthogonal electric field components $E_p$ and $E_s$, which are polarised parallel and perpendicular to the plane of incidence respectively. The reflection of a light ray from the surface is described by the matrix equation:
\begin{align*}
\left[\begin{array}{c} E_{rp} \\ E_{rs} \end{array}\right] &= \left[ \begin{array}{cc} r_{pp} & r_{ps} \\ r_{sp} & r_{ss} \end{array} \right] \left[\begin{array}{c} E_{ip} \\ E_{is} \end{array}\right]
\end{align*}
-Where $\vect{E}_i$ and $\vect{E}_r$ are the incident and reflected rays. Each element of the $2\times 2$ matrix $r_{ij}$ is the reflection coefficient for $i$ polarised light due to incident $j$ polarised light; these values are generally complex to include the phase change.
+Where $\vect{E}_i$ and $\vect{E}_r$ are the incident and reflected rays. Each element of the $2\times 2$ matrix $r_{ij}$ is the reflection coefficient for $i$ polarised light due to incident $j$ polarised light; these values are generally complex to include the phase change.
-Generalised Ellipsometry measures three ratios of $r_{ij}$ values:
-\begin{align*}
- \rho_{pp} &= \frac{r_{pp}}{r_{ss}} = \tan \psi_{pp} e^{-i \Delta_{pp}} \\
- \rho_{ps} &= \frac{r_{ps}}{r_{ss}} = \tan \psi_{ps} e^{-i \Delta_{ps}} \\
- \rho_{sp} &= \frac{r_{sp}}{r_{ss}} = \tan \psi_{sp} e^{-i \Delta_{sp}}
-\end{align*}
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.80\textwidth]{figures/ellipsometer/ellipsometer_measurement.png}
+ \caption{Diagram of an Ellipsometric Measurement \cite{woolam1999}}
+ \label{ellipsometer_measurement}
+\end{figure}
-If the sample is isotropic, then $r_{ps} = r_{sp} = 0$. In this case, only the ratio $\frac{r_p}{r_s} = \frac{r_{pp}}{r_{ss}}$ must be measured:
+As shown in figure \ref{ellipsometer_measurement}, linearly polarised light incident upon a surface is in general reflected as elliptically polarised light. For an isotropic sample, $r_{ps} = r_{sp} = 0$, and we can write $r_{pp} \equiv r_{p}$ and $r_{ss} \equiv r_{s}$. A standard ellipsometric measurement expresses the ratio of the $p$ and $s$ reflection coefficients in terms of the two parameters $\psi$ and $\Delta$
\begin{align}
\tan(\psi) e^{i \Delta} &= \rho = \frac{r_p}{r_s} \label{ellipso}
\end{align}
-The parameter $\psi$ gives the angle by which ...., whilst $\Delta$ gives the phase difference between $E_p$ and $E_s$ components.
-The Jone's formalism is not sufficient to describe the response of samples which de-polarise the incident beam; the more general Stoke's formalism must be used for such cases \cite{woolam2000} \cite{oates2011}.
+The value of $\tan(\psi)$ gives the ratio of amplitudes between the $p$ and $s$ components of the reflected electric field, whilst $\Delta$ gives the phase difference.
+
+In the case where the sample is anisotropic, $\psi$ and $\Delta$ alone are not sufficient to characterise the sample; three seperate ratios of fresnel reflection coefficients are required \cite{woolam2000}:
+
+Light may consist of two or more components of well defined polarisation states; as a result, the total beam cannot be described with a single well defined Jones vector. Ellipsometers are designed to establish a well defined polarisation state of light incident on the sample; however non-uniform films or backside reflection from a substrate may cause the reflected beam to be partially polarised. As a result, the Jone's formalism is not sufficient for characterisation of these samples, and the more general Stokes formalise (with 4 component vectors) must be employed \cite{woolam2000} \cite{oates2011}.
+
+\begin{table}[H]
+ \centering
+ \begin{tabular}{lll}
+ \includegraphics[scale=0.75]{figures/ellipsometer/circular_polarisation} &
+ \includegraphics[scale=0.75]{figures/ellipsometer/elliptical_polarisation} &
+ \includegraphics[scale=0.75]{figures/ellipsometer/linear_polarisation} \\
+ \end{tabular}
+
+ \captionof{figure}{From left to right, circular, elliptical and linearly polaristed light, viewed down the axis of beam propagation}
+\end{table}
\subsection{Variable Angle Spectroscopic Ellipsometry}
-Traditional ellipsometers were restricted to single angle and often single wavelength measurements \cite{}. Although the measurement of With advantages in computing technology in the 1970s,
+Although Ellipsometers have been in use for thin film analysis since the ??? \cite{}, traditional instruments were usually limited to single angle and single wavelength measurements, due to the painstaking manual process of repeated measurements. With advances both in software and hardware during the last half of the 20th century, Ellipsometric measurements have become largely automated, allowing for a wide range of optical information to be obtained from a sample. Spectroscopic Ellipsometry obtains measurements for a range of wavelengths, whilst Variable Angle Spectroscopic Ellipsometry repeats these measurements over a range of angles of incidence.
-\begin{center}
- \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/thesis/figures/ellipsometer.png}
- \captionof{figure}{Block diagram of the VASE \\(taken from \emph{Overview of Variable Angle Spectroscopic
+The ease with which large amounts of data can be taken from an ellipsometer means that the method is well suited to numerical analysis and fitting procedures. At CAMSP a Variable Angle Spectroscopic Ellipsometer (VASE)\footnote{J. A. Woolam and Co} and the associated software\footnote{WVASE32} have been employed in the analysis of thin film samples.
+
+\begin{figure}[H]
+ \centering
+ \includegraphics[width=0.8\textwidth]{figures/ellipsometer/ellipsometer.png}
+ \caption{Block diagram of the VASE \\(taken from \emph{Overview of Variable Angle Spectroscopic
Ellipsometry (VASE), Part I:
Basic Theory and Typical Applications}
\cite{woolam1999})}
\label{ellipsometer.png}
-\end{center}
+\end{figure}
+
+\subsection{Relation of $\psi$ and $\Delta$ to properties of the sample}
+
+\subsubsection{Bulk Substrates}
+
+The simplest sample is a bulk substrate. In this case,
+
+\subsubsection{Single Layered Thin Films}
+
+
+
+\subsubsection{Multi-layered Thin Films}
+
+Magical analysis
+
+\section{Optical Transmission and Reflection Spectroscopy}
-\section{Transmission Spectroscopy}
+Can be done with the VASE or with OceanOptics spectrometer.
\section{Scanning Electron Microscopy}
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--- /dev/null
+../../../../research/TCS/process.py
\ No newline at end of file
--- /dev/null
+#!/usr/bin/python -u
+
+#
+# @file process.py
+# @purpose Process TCS data
+# Takes S(E) = dI/dE
+# @author Sam Moore
+# @date August 2012
+#
+
+import sys
+import os
+import re # Regular expressions - for removing comments
+import odict #ordered dictionary
+import copy
+
+import Gnuplot, Gnuplot.funcutils
+import string
+import time
+import math
+import cmath
+import random
+import numpy
+
+gnuplot = Gnuplot.Gnuplot()
+
+def Reset():
+ gnuplot = Gnuplot.Gnuplot()
+
+def FindDataFiles(directory=".", depth=1, result=None):
+ if result == None:
+ result = []
+
+ for f in os.listdir(directory):
+ if os.path.isdir(directory+"/"+str(f)):
+ if depth > 1:
+ result += FindDataFiles(directory+"/"+str(f), depth-1, result)
+ continue
+ s = f.split(".")
+ if (len(s) == 2 and s[1] == "dat"):
+ result.append(directory+"/"+str(f))
+
+ return result
+
+def BaseName(f):
+ a = f.split("/")
+ return a[len(a)-1]
+
+
+def DirectoryName(f, start=0,back=1):
+ a = f.split("/")
+ return string.join(a[start:(len(a)-back)], "/")
+
+def GetData(filename, key=1):
+
+ if type(filename) != type(""):
+ if type(filename) == type([]):
+ return filename
+ else:
+ return [[0,0,0,0]]
+
+
+ if os.path.isdir(filename):
+ if os.path.exists(filename.strip("/")+"/average.dat"):
+ os.remove(filename.strip("/")+"/average.dat")
+ AverageAllData(filename)
+ return GetData(filename.strip("/")+"/average.dat")
+
+ input_file = open(filename, "r")
+ data = {}
+ for line in input_file:
+ line = re.sub("#.*", "", line).strip("\r\n ")
+ if len(line) == 0:
+ continue
+
+ line = map(lambda e : float(e), line.split("\t"))
+
+ if line[key] in data:
+ for i in range(len(line)):
+ data[line[key]][0][i] += line[i]
+ data[line[key]][1] += 1
+ else:
+ data.update({line[key] : [line, 1]})
+
+ d = map(lambda e : map(lambda f : float(f) / float(e[1][1]), e[1][0]), data.items())
+ d.sort(key = lambda e : e[key])
+ #for l in d:
+ # print str(l)
+ return d
+
+def DoNothing(data):
+ return data
+
+
+def GetDataSets(directory="."):
+ data_sets = []
+ for f in os.listdir(directory):
+ if os.path.isdir(directory+"/"+str(f)) == False:
+ if (len(f.split(".")) > 1 and f.split(".")[1] == "dat"):
+ d = GetData(directory+"/"+str(f))
+ if len(d) > 0:
+ data_sets.append(d)
+ return data_sets
+
+
+
+def Derivative(data, a=1, b=2, sigma=None,step=1):
+ result = [[]]
+ n = 0
+ dI = [0,0]
+ dE = [0,0]
+
+ for i in range(0, len(data),step):
+ result[len(result)-1] = [d for d in data[i]]
+ if (i >= step):
+ dE[0] = data[i][a] - data[i-step][a]
+ dI[0] = data[i][b] - data[i-step][b]
+ else:
+ dI[0] = None
+
+ if (i < len(data)-step):
+ dE[1] = data[i+step][a] - data[i][a]
+ dI[1] = data[i+step][b] - data[i][b]
+ else:
+ dI[1] = None
+
+ if sigma != None:
+ #print str(data[i]) + " ["+str(sigma)+"] = " + str(data[i][int(abs(sigma))])
+ if sigma < 0:
+ if dI[0] != None: dI[0] -= 0.5*data[i][int(abs(sigma))]
+ if dI[1] != None: dI[1] -= 0.5*data[i][int(abs(sigma))]
+ else:
+ if dI[0] != None: dI[0] += 0.5*data[i][int(abs(sigma))]
+ if dI[1] != None: dI[1] += 0.5*data[i][int(abs(sigma))]
+
+ deltaE = 0.0
+ deltaI = 0.0
+ count = 0
+ if dI[0] != None:
+ deltaE += dE[0]
+ deltaI += dI[0]
+ count += 1
+ if dI[1] != None:
+ deltaE += dE[1]
+ deltaI += dI[1]
+ count += 1
+
+ if (count > 0):
+ deltaI /= float(count)
+ deltaE /= float(count)
+
+
+ if (deltaE != 0):
+ result[len(result)-1][b] = (deltaI / deltaE)
+ else:
+ result[len(result)-1][b] = 0.0
+ else:
+ result[len(result)-1][b] = 0.0
+ result.append([])
+
+ return result[0:len(result)-1]
+
+def MaxNormalise(data, u=2):
+ result = copy.deepcopy(data)
+ if (len(data) <= 0):
+ return result
+ maxval = max(data, key = lambda e : e[u])[u]
+
+ if maxval == 0:
+ return result
+
+ for d in result:
+ d[u] = d[u] / maxval
+
+ return result
+
+def Average(data_sets, u=1):
+ avg = odict.odict()
+ for t in data_sets:
+ for p in t:
+ if p[u] in avg:
+ #print "Already have " + str(p[u])
+ avg[p[u]][1] += 1
+ for i in range(0, len(p)):
+ avg[p[u]][0][i] += p[i]
+ else:
+ #print "Create key for " + str(p[u])
+ avg.update({p[u] : [p, 1]})
+
+ for a in avg.keys():
+ for i in range(0, len(avg[a][0])):
+ avg[a][0][i] /= float(avg[a][1])
+ return map(lambda e : e[1][0], sorted(avg.items(), key = lambda e : e[0]))
+
+def FullWidthAtHalfMax(data, u=1):
+ maxval = max(data, key = lambda e : e[u])
+ peak = data.index(maxval)
+ maxval = maxval[0]
+ lhs = None
+ rhs = None
+ for i in range(1, len(data)/2):
+ if lhs == None:
+ if (peak-i > 0 and data[peak-i] < 0.50*maxval):
+ lhs = data[peak-i][u]
+ if rhs == None:
+ if (peak+i < len(data) and data[peak+i] < 0.50*maxval):
+ rhs = peak+i
+ if lhs != None and rhs != None:
+ break
+ if rhs == None or lhs == None:
+ return abs(data[len(data)-1][0] - data[0][0])
+ else:
+ return abs(rhs - lhs)
+
+def SaveData(filename, data):
+ out = open(filename, "w", 0)
+ for a in data:
+ for i in range(0, len(a)):
+ out.write(str(a[i]))
+ if (i < len(a) - 1):
+ out.write("\t")
+ out.write("\n")
+
+def AverageAllData(directory, save=None, normalise=True):
+ data_sets = []
+ if save == None: save = directory+"/average.dat"
+ for f in FindDataFiles(directory):
+ d = GetData(f)
+ if normalise:
+ d = MaxNormalise(d)
+ data_sets.append(d)
+
+ a = Average(data_sets)
+ SaveData(save, a)
+ return a
+
+def CalibrateData(original, ammeter_scale=1e-6):
+ data = copy.deepcopy(original)
+ for i in range(0, len(data)):
+ data[i][1] = 16.8 * float(data[i][1]) / 4000.0
+ data[i][2] = ammeter_scale * 0.170 * float(data[i][2]) / 268.0
+ data[i][3] = ammeter_scale * 0.170 * float(data[i][3]) / 268.0
+ return data
+
+def ShowTCS(filename, raw=True,calibrate=True, normalise=False, show_error=False, plot=gnuplot.plot,with_="lp", step=1, output=None, title="", master_title="", smooth=0, show_peak=False, inflection=1):
+
+ if raw == False:
+ calibrate = False
+ normalise = False
+
+ if type(filename) == type(""):
+ data = GetData(filename)
+ else:
+ data = filename
+ filename = "tcs data"
+
+ if (title == ""):
+ title = BaseName(filename)
+
+ if (len(data) <= 0):
+ return data
+
+ if (smooth > 0):
+ if type(smooth) == type([]):
+ for i in range(smooth[0]):
+ data = Smooth(data, m=smooth[1])
+ else:
+ data = Smooth(data, m=smooth)
+
+
+ if calibrate:
+ data = CalibrateData(data)
+ units = ["V", "uA / V"]
+ else:
+ units = ["DAC counts", "ADC counts / DAC counts"]
+
+ if not normalise:
+ gnuplot("set ylabel \"dI(E)/dE ("+str(units[1])+")\"")
+ else:
+ data = MaxNormalise(data)
+ gnuplot("set ylabel \"dI(E)/dE (normalised)\"")
+
+ if (output != None and type(output) == type("")):
+ gnuplot("set term png size 640,480")
+ gnuplot("set output \""+str(output)+"\"")
+
+ if master_title == "":
+ master_title = "Total Current Spectrum S(E)"
+ if type(filename) == type("") and plot == gnuplot.plot:
+ if filename != "tcs data":
+ p = ReadParameters(filename)
+ if "Sample" in p:
+ master_title += "\\nSample: "+p["Sample"]
+
+ gnuplot("set title \""+str(master_title)+"\"")
+ gnuplot("set xlabel \"U ("+str(units[0])+")\"")
+
+
+ if raw:
+ d = Derivative(data, 1, 2, step=step)
+ else:
+ d = data
+
+ ymax = 0.01 + 1.2 * max(d, key=lambda e : e[2])[2]
+ ymin = -0.01 + 1.2 * min(d, key=lambda e : e[2])[2]
+ gnuplot("set yrange ["+str(ymin)+":"+str(ymax)+"]")
+
+ plotList = []
+ plotList.append(Gnuplot.Data(d, using="2:3", with_=with_,title=title))
+
+ if (show_error):
+ error1 = Derivative(data, 1, 2, -3,step=step)
+ error2 = Derivative(data, 1, 2, +3,step=step)
+ plotList.append(Gnuplot.Data(error1, using="2:3", with_=w,title="-sigma/2"))
+ plotList.append(Gnuplot.Data(error2, using="2:3", with_=w, title="+sigma/2"))
+
+ if (show_peak):
+ peak = SmoothPeakFind(d, ap=DoNothing, stop=1, inflection=inflection)
+ plotList += PlotPeaks(peak,with_="l lt -1", plot=None)
+
+
+
+ if (plot != None):
+ plot(*plotList)
+ time.sleep(0.2)
+
+ if (output != None and type(output) == type("")):
+ gnuplot("set term wxt")
+
+ if (plot == None):
+ return plotList
+ return data
+
+def ShowData(filename,calibrate=True, normalise=False, show_error=False, plot=gnuplot.plot,with_="lp", step=1, output=None, title="", master_title="Sample Current I(E)", smooth=0):
+ if type(filename) == type(""):
+ data = GetData(filename)
+ else:
+ data = filename
+ filename = "raw data"
+
+ if (title == ""):
+ title = BaseName(filename)
+
+
+ if len(data) <= 0:
+ return data
+
+
+ if (smooth > 0):
+ if type(data) == type([]):
+ for i in range(0, smooth[0]):
+ data = Smooth(data, m=smooth[1])
+ else:
+ data = Smooth(data, m = smooth)
+
+ if calibrate:
+ data = CalibrateData(data)
+ units = ["V", "uA"]
+ else:
+ units = ["DAC counts", "ADC counts"]
+
+ if not normalise:
+ gnuplot("set ylabel \"I(E) ("+str(units[1])+")\"")
+ else:
+ data = MaxNormalise(data)
+ gnuplot("set ylabel \"I(E) (normalised)\"")
+
+ if (output != None and type(output) == type("")):
+ gnuplot("set term png size 640,480")
+ gnuplot("set output \""+str(output)+"\"")
+
+ gnuplot("set title \""+str(master_title)+"\"")
+ gnuplot("set xlabel \"U ("+str(units[0])+")\"")
+
+
+ ymax = 0.005 + 1.2 * max(d, key=lambda e : e[2])[2]
+ ymin = -0.005 + 1.2 * min(d, key=lambda e : e[2])[2]
+ gnuplot("set yrange ["+str(ymin)+":"+str(ymax)+"]")
+
+ #d = Derivative(data, 1, 2, step=step)
+
+ plotList = []
+
+ plotList.append(Gnuplot.Data(data, using="2:3", with_=with_,title=title))
+ time.sleep(0.1)
+ if (show_error):
+ error1 = copy.deepcopy(data)
+ error2 = copy.deepcopy(data)
+ for i in range(len(data)):
+ #print str(data[i])
+ error1[i][2] -= 0.50*float(data[i][3])
+ error2[i][2] += 0.50*float(data[i][3])
+ plotList.append(Gnuplot.Data(error1, using="2:3", with_=w,title="Error : Low bound"))
+ plotList.append(Gnuplot.Data(error2, using="2:3", with_=w, title="Error : Upper bound"))
+
+ if plot != None:
+
+ plot(*plotList)
+ if (output != None and type(output) == type("")):
+ gnuplot("set term wxt")
+ return data
+ else:
+ return plotList
+
+def ReadParameters(filename):
+ parameters = odict.odict()
+ input_file = open(filename, "r")
+ for line in input_file:
+ k = line.split("=")
+ item = None
+ #print str(k)
+ if (len(k) >= 2):
+ item = k[0].strip("# \r\n")
+ value = k[1].strip("# \r\n")
+ if (item in parameters):
+ parameters[item] = value
+ else:
+ parameters.update({str(item) : value})
+ input_file.close()
+ return parameters
+
+def PlotParameters(filename):
+ ReadParameters(filename)
+
+def Smooth(data, m, k=2):
+ smooth = copy.deepcopy(data)
+ for i in range(len(smooth)):
+ count = 0
+ smooth[i][k] = 0.0
+ for j in range(i-m,i+m):
+ if j >= 0 and j < len(smooth):
+ count += 1
+ smooth[i][k] += data[j][k]
+ if count > 0:
+ smooth[i][k] = smooth[i][k] / float(count)
+ else:
+ smooth[i][k] = data[i][k]
+
+ return smooth
+
+def PeakFind(data, k=2,threshold=0.00, inflection=0):
+ results = []
+ for i in range(len(data)):
+ if i == 0 or i == len(data)-1:
+ continue
+ #if abs(data[i][k]) < threshold * abs(max(data, key = lambda e : abs(e[k]))[k]):
+ # continue
+
+ left = data[i-1][k] - data[i][k]
+ right = data[i+1][k] - data[i][k]
+ if abs(left) < threshold*abs(data[i][k]):
+ continue
+ if abs(right) < threshold*abs(data[i][k]):
+ continue
+ if left*right > 0:
+ results.append(data[i] + [inflection])
+
+ if inflection > 0:
+ results += PeakFind(Derivative(data), k=k, threshold=threshold, inflection=inflection-1)
+
+ return results
+
+def SmoothPeakFind(data, a=1, k=2, ap=DoNothing, stop=10,smooth=5, inflection=0):
+ s = data
+ #results = []
+
+ peakList = []
+
+ m = 0
+ while m < stop:
+ #results.append([])
+ peaks = PeakFind(ap(s),k=k, inflection=inflection)
+ #print "m = " +str(m)
+ for p in peaks:
+ add = [m]
+ [add.append(f) for f in p]
+
+ if m == 0:
+ #print "*New peak at " + str(p)
+ peakList.append([add])
+ else:
+ score = []
+ for i in range(len(peakList)):
+ p2 = peakList[i][len(peakList[i])-1]
+ if m - p2[0] > 1:
+ continue
+ score.append([i, abs(p[a] - p2[1+a])])
+
+ score.sort(key = lambda e : e[1])
+ if len(score) == 0 or score[0][1] > 100:
+ #print "New peak at " + str(p)
+ peakList.append([add])
+ else:
+ #print "Peak exists near " + str(p) + " ("+str(score[0][1])+") " + str(peakList[score[0][0]][len(peakList[score[0][0]])-1])
+ peakList[score[0][0]].append(add)
+
+
+
+ #results.append([m, []])
+ #[results[len(results)-1].append(f) for f in p]
+ m += 1
+ s = Smooth(s, m=smooth,k=k)
+
+ #results.sort(key = lambda e : e[2])
+
+ #peaks = []
+ return peakList
+
+
+
+def PlotPeaks(peaks, calibrate=True, with_="lp", plot=gnuplot.replot):
+
+ plotList = []
+ for p in peaks:
+ p.append(copy.deepcopy(p[len(p)-1]))
+
+ p[len(p)-1][0] += 1
+
+
+ #print "Adding " + str(p) + " to list"
+ if len(p) >= 0:
+ l = p[len(p)-1]
+ if l[len(l)-1] < 1:
+ with_ = with_.split(" lt")[0] + " lt 9"
+ plotList.append(Gnuplot.Data(p, using="3:1", with_=with_))
+
+
+
+ if len(plotList) > 0 and plot != None:
+ plot(*plotList)
+ time.sleep(0.2)
+
+ #print str(plotList)
+ #for p in peaks:
+ # p = p[0:len(p)-1]
+ return plotList
+
+def main():
+
+ if (len(sys.argv) < 2):
+ sys.stderr.write(sys.argv[0] + " - Require arguments (filename)\n")
+ return 1
+
+ i = 1
+ plotFunc = ShowTCS
+ normalise = False
+ title = ""
+ master_title = ""
+ smooth=0
+ with_="lp"
+ while i < len(sys.argv):
+ if sys.argv[i] == "--raw":
+ plotFunc = ShowData
+ elif sys.argv[i] == "--tcs":
+ plotFunc = ShowTCS #lambda e : ShowTCS(e, show_peak=False)
+ elif sys.argv[i] == "--output":
+ if i+1 >= len(sys.argv):
+ sys.stderr.write("Need argument for "+sys.argv[i]+" switch\n")
+ sys.exit(1)
+ gnuplot("set term postscript colour")
+ gnuplot("set output \""+sys.argv[i+1]+"\"")
+ i += 1
+ elif sys.argv[i] == "--wxt":
+ gnuplot("set term wxt")
+ elif sys.argv[i] == "--normalise":
+ normalise = True
+ elif sys.argv[i] == "--unnormalise":
+ normalise = False
+ elif sys.argv[i] == "--title":
+ if i+1 >= len(sys.argv):
+ sys.stderr.write("Need argument for "+sys.argv[i]+" switch\n")
+ sys.exit(1)
+ title = sys.argv[i+1]
+ i += 1
+ elif sys.argv[i] == "--master_title":
+ if i+1 >= len(sys.argv):
+ sys.stderr.write("Need argument for "+sys.argv[i]+" switch\n")
+ sys.exit(1)
+ master_title = sys.argv[i+1]
+ i += 1
+ elif sys.argv[i] == "--smooth":
+ if i+1 >= len(sys.argv):
+ sys.stderr.write("Need argument for "+sys.argv[i]+" switch\n")
+ sys.exit(1)
+ smooth = sys.argv[i+1]
+ smooth = map(int, smooth.split("x"))
+ if len(smooth) <= 1:
+ smooth = smooth[0]
+ i += 1
+ elif sys.argv[i] == "--with":
+ if i+1 >= len(sys.argv):
+ sys.stderr.write("Need argument for "+sys.argv[i]+" switch\n")
+ sys.exit(1)
+ with_ = sys.argv[i+1]
+ i += 1
+ elif sys.argv[i] == "--output":
+ if i+1 >= len(sys.argv):
+ sys.stderr.write("Need argument for "+sys.argv[i]+" switch\n")
+ sys.exit(1)
+ gnuplot("set term postscript colour")
+ gnuplot("set output \""+str(argv[i+1])+"\"")
+ else:
+ plotFunc(sys.argv[i], plot=gnuplot.replot, normalise=normalise, title=title, master_title=master_title, smooth=smooth, with_=with_)
+
+ i += 1
+
+ print "Done. Press enter to exit, or type name of file to save as."
+ out = sys.stdin.readline().strip("\t\r\n #")
+ if out != "":
+ gnuplot("set term postscript colour")
+ gnuplot("set output \""+out+"\"")
+ gnuplot.replot()
+
+
+def ModelTCS(f, sigma, Emin, Emax, dE):
+ data = []
+ E = Emin
+ while E < Emax:
+ S = (1 - sigma(0))*f(-E) + FuncIntegrate(lambda e : f(e - E) * FuncDerivative(sigma, E, dE), Emin, Emax, dE)
+ data.append([0.00, E, S,0.00])
+ E += dE
+ return data
+
+def IntegrateTCS(data, imin, imax=0, di=1):
+ i = imin
+ if imax == 0:
+ imax = len(data)-1
+ total = 0.0
+
+ while i < imax:
+ total += data[i][2] * (data[i+1][1] - data[i][1])
+ i += di
+ return total
+
+def FuncIntegrate(f, xmin, xmax, dx):
+ x = xmin
+ total = 0.0
+ while x <= xmax:
+ total += f(x) * dx
+ x += dx
+ return total
+
+def FuncDerivative(f, x, dx):
+ return 0.50*(f(x+dx) - f(x-dx))/dx
+
+def FitTCS(data, min_mse=1e-4, max_fail=100, max_adjust=4,divide=10, plot=gnuplot.plot,smooth=0):
+ if type(data) == type(""):
+ d = GetData(data)
+ d = CalibrateData(d)
+ d = MaxNormalise(d)
+ d = Derivative(d)
+ else:
+ d = data
+
+ if smooth != 0:
+ if type(smooth) == type([]):
+ for _ in range(smooth[0]):
+ d = Smooth(d, m=smooth[1])
+ else:
+ d = Smooth(d, m=smooth)
+
+
+
+ plotItems = ShowTCS(d, raw=False,smooth=smooth,plot=None)
+ plotItems.append(None)
+
+ peaks = SmoothPeakFind(d, smooth=5, stop=1, inflection=0)
+ peaks.sort(key = lambda e : e[len(e)-1][1])
+
+ fits = []
+
+ for i in range(0,len(peaks)):
+
+ p = peaks[i]
+ l = p[len(p)-1]
+ if l[len(l)-1] == 0:
+ fits.append([l[3], l[2], 1.0])
+ else:
+ if i-2 >= 0:
+ l = peaks[i-2][len(peaks[i-2])]
+ if l[len(l)-1] == 0:
+ fits.append([l[3], l[2], 1.0])
+ if i+2 <= len(peaks)-1:
+ l = peaks[i+2][len(peaks[i+2])]
+ if l[len(l)-1] == 0:
+ fits.append([l[3], l[2], 1.0])
+
+ for i in range(len(fits)):
+ left = 2.0
+ right = 2.0
+ if i > 0:
+ left = fits[i-1][1] - fits[i][1]
+ if i < len(fits)-1:
+ right = fits[i+1][1] - fits[i][1]
+
+ fits[i][2] = min([abs(0.5*left), abs(0.5*right)])
+
+
+ #print "Fits are " + str(fits)
+ #stdin.readline()
+
+
+
+ def tcs(E):
+ total = 0.0
+ for f in fits:
+ dt = f[0] * gaussian(E - f[1], f[2])
+ #print " Increase total by " + str(dt)
+ total += dt
+ #print "tcs returns " + str(total)
+ return total
+
+ mse = 1
+ old_mse = 1
+ cycle = 0
+ failcount = 0
+
+
+ adjust = 1.0
+
+ iterations = 0
+
+ while failcount < max_fail and mse > min_mse:
+ i = random.randint(0, len(fits)-1)
+ j = random.randint(0, len(fits[i])-1)
+ #while j == 1:
+ # j = random.randint(0, len(fits[i])-1)
+
+ #print "Adjust " + str(i) + ","+str(j) + ": Iteration " + str(iterations) + " mse: " + str(mse)
+
+ old = fits[i][j]
+ old_mse = mse
+
+ fits[i][j] += adjust * (random.random() - 0.50)
+ if i == 2:
+ while fits[i][j] <= 0.0005:
+ fits[i][j] = adjust * (random.random() - 0.50)
+
+
+ model = table(lambda e : [0.00, e, tcs(e), 0.00], 0, 16.8, divide*d[len(d)-1][1]/(len(d)))
+ mse = MeanSquareError(model, d[0::divide])
+ if mse >= old_mse:
+ fits[i][j] = old
+ failcount += 1
+ if failcount > max_fail / 2:
+ if adjust > 1.0/(2.0**max_adjust):
+ adjust /= 2
+ mse = old_mse
+ else:
+ #adjust /= 2.0
+ failcount = 0
+
+
+ iterations += 1
+
+
+ #model = table(lambda e : [0.00, e, tcs(e), 0.00], 0, 16.8, 16.8/len(d))
+ plotItems[len(plotItems)-1] = Gnuplot.Data(model, using="2:3", with_="l lt 3", title="model")
+ time.sleep(0.1)
+
+ fits.sort(key = lambda e : e[0] * gaussian(0, e[2]), reverse=True)
+
+ if plot != None:
+ gnuplot("set title \"MSE = "+str(mse)+"\\nfailcount = "+str(failcount)+"\\nadjust = "+str(adjust)+"\"")
+ gnuplot.plot(*plotItems)
+
+ return [fits, model]
+ else:
+ return [fits, model,plotItems]
+
+
+ #return model
+
+def SaveFit(filename, fit):
+ out = open(filename, "w", 0)
+ out.write("# TCS Fit\n")
+
+ for f in fit:
+ out.write(str(f[0]) + "\t" + str(f[1]) + "\t" + str(f[2]) + "\n")
+
+ out.close()
+
+
+def LoadFit(filename):
+ infile = open(filename, "r")
+ if (infile.readline() != "# TCS Fit\n"):
+ sys.stderr.write("Error loading fit from file " + str(filename) + "\n")
+ sys.exit(0)
+
+ fit = []
+ while True:
+ f = infile.readline().strip("# \r\n\t").split("\t")
+ if len(f) != 3:
+ break
+ fit.append(map(float, f))
+
+ infile.close()
+ fit.sort(key = lambda e : e[0] * gaussian(0, e[2]), reverse=True)
+ #def model(e):
+ # total = 0.0
+ # for f in fit:
+ # total += f[0] * gaussian(e - f[1], f[2])
+ # return total
+
+ #return table(lambda e : [0.0, e, model(e), 0.0], 0.0, 16.8, 16.8/400)
+ return fit
+
+def MeanSquareError(model, real, k = 2):
+ mse = 0.0
+ for i in range(len(real)):
+
+ mse += (model[i][k] - real[i][k])**2
+
+ mse /= len(model)
+ return mse
+
+def delta(x):
+ if (x == 0):
+ return 1.0
+ else:
+ return 0.0
+
+def table(f, xmin, xmax, dx):
+ result = []
+ x = xmin
+ while (x <= xmax):
+ result.append(f(x))
+ x += dx
+ return result
+
+def gaussian(x, sigma):
+ if (sigma == 0.0):
+ return 0.0
+ return math.exp(- (x**2.0)/(2.0 * sigma**2.0)) / (sigma * (2.0 * math.pi)**0.50)
+
+def step(x, sigma, T):
+ if T == 0:
+ return 1.0
+ return 1.0 / (math.exp((x - sigma)/T) + 1.0)
+
+if __name__ == "__main__":
+ sys.exit(main())
--- /dev/null
+%!PS-Adobe-2.0
+%%Title: siI.eps
+%%Creator: gnuplot 4.4 patchlevel 3
+%%CreationDate: Wed Oct 17 18:08:30 2012
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+ /Title (siI.eps)
+ /Subject (gnuplot plot)
+ /Creator (gnuplot 4.4 patchlevel 3)
+ /Author (sam)
+% /Producer (gnuplot)
+% /Keywords ()
+ /CreationDate (Wed Oct 17 18:08:30 2012)
+ /DOCINFO pdfmark
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\bibdata{references/refs}
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+\bibcite{pfund1933}{2}
+\bibcite{harris1948}{3}
+\bibcite{harris1952}{4}
+\bibcite{harris1953}{5}
+\bibcite{mckenzie2006}{6}
+\bibcite{sondergaard2012}{7}
+\bibcite{komolov}{8}
+\bibcite{woolam1999}{9}
+\bibcite{woolam2000}{10}
+\bibcite{oates2011}{11}
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\BOOKMARK [0][-]{chapter.3}{Experimental Techniques}{}
\BOOKMARK [1][-]{section.3.1}{Total Current Spectroscopy}{chapter.3}
\BOOKMARK [1][-]{section.3.2}{Ellipsometry}{chapter.3}
-\BOOKMARK [2][-]{subsection.3.2.1}{Variable Angle Spectroscopic Ellipsometry}{section.3.2}
-\BOOKMARK [1][-]{section.3.3}{Transmission Spectroscopy}{chapter.3}
+\BOOKMARK [2][-]{subsection.3.2.1}{Overview}{section.3.2}
+\BOOKMARK [2][-]{subsection.3.2.2}{Variable Angle Spectroscopic Ellipsometry}{section.3.2}
+\BOOKMARK [2][-]{subsection.3.2.3}{Relation of \040and \040to properties of the sample}{section.3.2}
+\BOOKMARK [1][-]{section.3.3}{Optical Transmission and Reflection Spectroscopy}{chapter.3}
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+\BOOKMARK [2][-]{subsection.4.1.1}{Higher Magnification Images of Au-Black}{section.4.1}
+\BOOKMARK [1][-]{section.4.2}{Atomic Force Microscopy of Au}{chapter.4}
+\BOOKMARK [1][-]{section.4.3}{Total Current Spectropy}{chapter.4}
+\BOOKMARK [2][-]{subsection.4.3.1}{Effect of Focusing of the Electron Gun on the TCS}{section.4.3}
+\BOOKMARK [2][-]{subsection.4.3.2}{Effect of Evaporation of Ag onto an Si substrate}{section.4.3}
+\BOOKMARK [2][-]{subsection.4.3.3}{Effect of Evaporation of Au on Si}{section.4.3}
+\BOOKMARK [1][-]{section.4.4}{Variable Angle Spectroscopy Ellipsometry}{chapter.4}
+\BOOKMARK [2][-]{subsection.4.4.1}{Ag-Bright on Si substrate}{section.4.4}
+\BOOKMARK [2][-]{subsection.4.4.2}{Black Ag on Si}{section.4.4}
+\BOOKMARK [1][-]{section.4.5}{Optical Transmission and Reflection Measurements using the VASE}{chapter.4}
+\BOOKMARK [1][-]{section.4.6}{Optical Transmission Spectroscopy using OceanOptics Spectrometer}{chapter.4}
+\BOOKMARK [2][-]{subsection.4.6.1}{Dark Spectrum}{section.4.6}
+\BOOKMARK [2][-]{subsection.4.6.2}{Reference Spectrum}{section.4.6}
+\BOOKMARK [2][-]{subsection.4.6.3}{Testing the Spectrometer}{section.4.6}
+\BOOKMARK [2][-]{subsection.4.6.4}{Transmission Spectra of Glass}{section.4.6}
+\BOOKMARK [2][-]{subsection.4.6.5}{Transmission Spectra of Au and Au-Black on Glass}{section.4.6}
+\BOOKMARK [2][-]{subsection.4.6.6}{Transmission Spectra of Ag}{section.4.6}
+\BOOKMARK [2][-]{subsection.4.6.7}{Transmission Spectra of Ag and Ag-Black on Glass}{section.4.6}
\BOOKMARK [0][-]{chapter.5}{Conclusion}{}
-\BOOKMARK [-1][-]{chapter.5}{References}{}
-\BOOKMARK [0][-]{section..1}{A two dimensional electron gun simulation}{chapter.5}
+\BOOKMARK [-1][-]{chapter*.35}{References}{}
+\BOOKMARK [0][-]{section..1}{A two dimensional electron gun simulation}{chapter*.35}
+\BOOKMARK [1][-]{subsection..1.1}{The Ammeters}{section..1}
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git.ucc.asn.au / matches / honours.git / commitdiff
UCC git Repository :: git.ucc.asn.au
