\chapter{Results and Discussion}

\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}

\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.



