\chapter{Experimental Results and Discussion} \label{chapter_results}


\section{Scanning Electron Microscopy}

A number of samples of black and non-black metal films were prepared and sent to the Centre for Microscopy Characterisation and Analysis (CMCA) at UWA for study. In this section we will present and discuss two of the images produced by CMCA. These images proved to be an invaluable aid in understanding the structural differences between metallic-black and metallic-bright films.

\begin{figure}[H]
	\centering
	\includegraphics[width=0.7\textwidth]{figures/sem/Au_semi-shiny_1_SEM.png}
	\caption{SEM Image of a Au film. Pressure of preparation $10^{-6}$ mbar. Dimensions approx. 2500 x 1900 nm} 
	\label{sem_au}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.7\textwidth]{figures/sem/Au_BLACK_200nm.png}
	\caption{SEM Image of a Black Au film. Pressure of preparation $0.18$ mbar. Dimensions approx. 2500 x 1900 nm} 
	\label{sem_blackau}
\end{figure}

\begin{comment}
\begin{figure}[H]
	\centering
	\begin{tabular}{ll}
		\includegraphics[width=0.45\textwidth]{figures/sem/Au_semi-shiny_1_SEM.png} \\
		\includegraphics[width=0.45\textwidth]{figures/sem/Au_BLACK_200nm.png}

	\end{tabular}
	\caption{SEM Images of Au and Black Au films. Pressures of preparation were $10^{-6}$mbar and $0.18$mbar respectively. Dimensions are approx. 2500 x 1900 nm}
	\label{SEM_images}
\end{figure}
\end{comment}

Figures \ref{sem_au} and \ref{sem_blackau} shows a comparison of a Black Au and a Au film imaged using a scanning electron microscope (SEM). The structural difference between the two films is striking. The surface of the Au film appears to consist of a layer of well defined metallic nanoparticles with sizes ranging from $20$ to $100$nm. In contrast, the Black Au film shows a highly irregular, patchlike pattern. Previous studies have produced similar SEM images \cite{harris1952,panjwani2011,mckenzie2006}.

Intensity distributions of the SEM images (Figure \ref{SEM_levels}) show a smooth gaussian like peak for the Au film. In contrast, the intensity distribution of the Black Au film reveals an extremely high maxima at zero intensity, indicating that most of the surface has a very low secondary electron emission coefficient. The tail of this distribution is very flat, and extends to high intensity values, consistent with the observed patch like regions of high intensity values.



\begin{figure}[H]
	\centering
	\begin{tabular}{ll}
		\includegraphics[width=0.8\textwidth]{figures/sem/au_levels.eps} \\
		\includegraphics[width=0.8\textwidth]{figures/sem/blackau_levels.eps}
	\end{tabular}
	
	\caption{Intensity distributions for the SEM images in Figures \ref{sem_au} and \ref{sem_blackau}. The total number of pixels for each intensity level (0-255) is shown. Similar analysis have been performed by Panjwani \cite{panjwani2011}.}

	\label{SEM_levels}
\end{figure}

\begin{comment}
\begin{figure}[H]
	\centering
	\includegraphics[width=0.8\textwidth]{figures/sem/au_black_magnified.png}
	\caption{Increasing magnification images of Black Au taken at CMCA}
	\label{Au_BLACK_increasing_magnifications.jpg}
\end{figure}


Several higher magnification SEM images of the Black Au film were also prepared by CMCA. These reveal structure on a range of scales from several nanometers, to several hundred nanometers. The structures seen in Figure \ref{} are only several nanometers in size. Since classical descriptions of plasmonic behaviour tend to break down below 20nm length scales, a theoretical description of plasmonic behaviour in these structures may need to consider quantum effects \cite{}

\begin{comment}
 
As it is well known that plasmonic resonances can be created in highly periodic nanostructures, there has been some interest in using Fourier Techniques for description of more complicated structures in terms of periodic plasmonic components\cite{} \cite{sersic2011}. However, Discrete Fourier Transforms (DFT) of the SEM images in Figure \ref{SEM_images} revealed little information not already clear from the original image; cross sections of the DFT showed a similar spectra to $\frac{1}{f}$ (pink) noise. We have presented these results in an Appendix. Taking the DFT has limitations with regards to resolution and introduced noise; a more effective approach may be to use Fourier Microscopy techniques for producing the Fourier Transform directly within the SEM \cite{sersic2011}.

\end{comment}

\section{Total Current Spectropy}

\subsection{Tuning the Electron Gun}

In \ref{tcs}, it was assumed that all primary electrons were incident normal to the surface, with an energy distribution $f(E - E_1)$ determined by the cathode. In reality, the primary beam has both angular and energy distributions. One can think of the cathode as producing initial angular and energy distributions, which are altered by the focusing properties of the electron gun to produce the distributions at the sample.

\begin{comment}

The angular and energy distributions may be crudely combined into an effective energy distribution by considering each electron arriving at angle $\theta$ to the surface as having effective energy $E' = E \cos^2 \theta$, where the $\cos^2 \theta$ arises from considering only the component of momentum normal to the surface.

\end{comment}
%\footnote{An expression for the effective energy distribution is: $f'(E' - E_1') = \int \int f(E - E_1) n(\theta - \theta_1) \delta(E' - E \cos^2 \theta) d\theta dE$}

\begin{comment}
An expression for the effective energy distribution in terms of $f(E - E_1)$ and the angular distribution $n(\theta - \theta_1)$ is:

\begin{align*}
	f'(E' - E_1') &= \int_{-\infty}^{\infty} \int_{-\frac{\pi}{2}}{\frac{\pi}{2}} f(E - E_1) n(\theta - \theta_1) \delta(E' - E \cos^2 \theta) d\theta dE
\end{align*}
\end{comment}


As discussed in \ref{tcs}, the effective energy distribution of primary electrons appears at the contact potential as the first peak in $S(U)$. Any peaks due to inelastic processes are convolved with the effective energy distribution. If the angular distribution is not centred about $\theta_1 = 0$ (due to misalignment of the sample holder) the observed contact potential is increased. Therefore it is desirable to adjust the electron gun so as to produce the narrowest possible distribution, at the lowest possible contact potential. In Figure \ref{focus_central_tcs.eps} we show the adjustment of the central electrodes to minimise the width of the elastic scattering peak.

\begin{figure}[H]
	\centering
	\includegraphics[width=0.5\textwidth, angle=270]{figures/tcs/plots/focus_central_tcs.eps}
	\caption{Adjusting the central electrodes to optimise the effective energy distribution}
	\label{focus_central_tcs.eps}
\end{figure}

\subsection{Electron gun simulation}

Figures \ref{egun_simulation1.pdf} and \ref{egun_simulation2.pdf} show the results of an electron gun simulation written for this project. The results of this simulation were not used to focus the actual electron gun; however Figure \ref{egun_simulation1.pdf} was useful, as it shows the possibility for electrons to strike the insulating posts holding the gun together. An insulating material in the path of the electron beam would become charged over time, and affect the focusing properties of the gun. When these posts were covered with tantalum strips connected to the final electrode, the stability of the measured current at fixed $U$ was improved.

\begin{figure}[H]
	\centering
	\includegraphics[scale=0.4, angle=270]{figures/egun/egun_simulation1.pdf} 
	\caption{Simulated electron trajectories}
	\label{egun_simulation1.pdf}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[scale=0.4, angle=270]{figures/egun/egun_simulation2.pdf} 
	\captionof{figure}{2D Simulation of the electrostatic potential produced by the electron gun}\label{egun_simulation2.pdf}
\end{figure}

\subsection{Deposition of Ag films onto a Si substrate}

We have measured the total current spectra for Ag films deposited onto an Si substrate. An optically thick layer of Ag, followed by a thin layer of Black Ag \footnote{pressures approx $10^{-7}$ and $0.18\text{mbar}$ respectively} were deposited, with measurements performed before and after each deposition.

\begin{figure}[H]
	\centering
	\includegraphics[width=0.80\textwidth, angle=0]{figures/tcs/plots/ag_si.eps}
	\caption{Comparison of Si and Ag on Si TCS}
	\label{agsiI_tcs}
\end{figure}

In Figure \ref{agsiI_tcs}, the total current spectrum of the sample changes dramatically with the Ag deposition. The contact potential of the surface decreases by about $1.7$V. Typical literature values for Si and Ag work functions would predict a shift of at most $4.9 - 4.2 = 0.7$V. In interpreting this shift it is important to note that our surfaces are not atomically clean.

Ellipsometric measurements had found that the Si substrates used in this study had $\text{SiO}_2$ surface layers with thicknesses of several nanometers. Comparing literature values for Ag and $\text{SiO}_2$ work functions shows that the expected difference in contact potentials for an Ag and $\text{SiO}_2$ is between $0.8$V and $1.8$V\footnote{The exact values of the work functions depend upon the orientation of the crystal lattice at the surface layer and shape of the Fermi-surface of the material}.

In addition to the change in contact potential of the surface, an inflection point is visible in the Ag spectrum at the location of the contact potential for $\text{SiO}_2$. Even though the Ag sample was optically thick, it seems that the surface potential of the underlying $\text{SiO}_2$ layer may still be contributing to $S(U)$.


\begin{figure}[H]
	\centering
	\includegraphics[width=0.80\textwidth]{figures/tcs/plots/blackag_ag.eps}
	\caption{Comparison of Ag/Si and Black Ag on Ag/Si spectra}
	\label{blackagsiI_tcs}
\end{figure}

Figure \ref{blackagsiI_tcs} shows the change in TCS after a layer of Black Ag is deposited on the existing Ag layer. The contact potential of the surface changes only slightly. This is unsurprising, as the new surface layer consists mostly of the same material. However, the surface peak has narrowed, despite no change in the focusing of the electron gun. This change in surface peak may be attributed to a change in the surface potential of the sample after the Black Ag layer was deposited. In particular the surface peak has narrowed, which is indicative of either a sharper potential barrier at the surface, or a more uniform potential accross the irradiated surface area.

Our experimental setup has been limited to applied potentials of $0$ to $16$V. The contact potentials of the surfaces have limited the range of primary electron energies to just over $10$ eV. Referring to Figure \ref{komolov1979} (which is idealised), it is recommended that this range be extended if the experiment were to be used for study of inelastic scattering processes.

\begin{comment}
Each stage in this experiment was repeated for another Si sample in the second sample holder. Although the exact shape of the total current spectra differed\footnote{The contact potentials were roughly 5V higher. This is most likely because the optimum focusing potentials for the first sample holder were suboptimal for the second, due to differences in height and distance from the electron gun}, we observed similar changes in the contact potential difference with the deposition of Ag and Black-Ag films.
\end{comment}

%\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}

%\begin{comment}


\section{Optical Transmission Spectroscopy}

In the transmission spectroscopy experiments, white light has been shone through a thin metallic film mounted on a glass slide. A commercial visible range optical spectrometer\footnote{OceanOptics QE65000} was used to measure the spectrum of the transmitted light in comparison. The transmission of a sample can be determined after first measuring the spectrum of the white light source. For thin films on a glass substrate, the transmission spectrum may be estimated after first determining the transmission spectrum of the glass.

\begin{figure}[H]
	\centering
	\includegraphics[width=0.6\textwidth]{figures/transmission_spectroscopy/transmission_spectroscopy.pdf}
	\caption{Setup for a transmission spectroscopy experiment}
\end{figure}

A 653nm filter was used to test the response of the spectrometer. The measured wavelength for peak transmission was $650.8$nm. The stated uncertainty in the filter's peak transmission wavelength was $\pm 2\%$ (approx. 13nm).



\subsection{Reference Spectrum}

The Ellipsometer's Xe Arc Lamp was used as a light source. Its spectrum $I_0(\lambda)$ is shown in Figure \ref{reference.eps}.  This measurement established that the Xe Arc lamp was indistinguishable from background light levels below $\lambda \approx 320$nm. %The Xe arc lamp has several strong emission lines in the near infra-red (above 800nm). %The subsequent results have all been normalised to this reference spectrum.

\begin{figure}[H]
	\centering
	\includegraphics[width=0.7\textwidth]{figures/transmission_spectroscopy/reference.eps}
	\caption{Xe Lamp reference spectrum}
	\label{reference.eps}
\end{figure}

\begin{comment}
\subsection{Testing the Spectrometer}

A 653nm filter was used to test the response of the spectrometer. Figure \ref{653nm_filter.eps} shows a spectrum for the Xe lamp shone through this filter; according to the spectrometer, the location of the peak is at 650.8nm. The stated uncertainty in the filter's peak transmission wavelength is $\pm 2$.

\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}
\end{comment}


\begin{comment}
\subsection{Transmission Spectra of Glass}

Past studies of the transmissive properties of Black Metal films have generally used nitrocellulose backings for the film \cite{pfund1933} \cite{harris1948}. For our purpose more qualitative measurements were sufficient, and so microscope slide glass available at CAMSP have been used instead. Figure \ref{glass.eps} shows the calculated transmission spectrum for a piece of microscope slide glass. The formula used in calculating the spectrum is:

\begin{align}
	t(\lambda) &= \frac{I_{\text{measured}}(\lambda)}{I_0(\lambda)} \label{transmission_formula}
\end{align}
Where $I_\text{measured}$ is the measured intensity and $I_0$ is the intensity of the reference spectrum.



\begin{figure}[H]
	\centering
	\includegraphics[width=0.5\textwidth, angle=270]{/home/sam/Documents/University/honours/thesis/figures/transmission_spectroscopy/glass.eps}
	\caption{Glass reference transmission spectrum}
	\label{glass.eps}
\end{figure}
\end{comment}

\subsection{Transmission Spectra of Au and Black Au on Glass}

Transmission spectra for similar thickness Au and Black Au films were measured, accounting for the transmission of the glass and the reference spectrum.
\begin{comment}
Equation \ref{shitty_assumption} does not take into account possible backside reflections at the interfaces between the air and glass, and the glass and the film. Such reflections would lead to interference effects, dependent upon the optical properties of both the films and glass, as well as the film thickness. Because the transmission of the glass was measured to be relatively high, \eqref{shitty_assumption} may be used to obtain a reasonable first approximation of the metal films' transmission spectra. Ellipsometric measurement would better characterise the sample.
\end{comment}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.8\textwidth]{figures/transmission_spectroscopy/blackau.eps}
	\caption{Transmission Spectra of Au and Black Au films}
\end{figure}
\begin{figure}[H]
	\centering
	\begin{tabular}{ll}
		\includegraphics[width=0.5\textwidth]{figures/transmission_spectroscopy/au_zoom.eps} &
		\includegraphics[width=0.5\textwidth]{figures/transmission_spectroscopy/blackau_zoom.eps}
	\end{tabular}
	\caption{Transmission Spectra for $\lambda \leq 620$nm}
	\label{zoom_transmission}
\end{figure}

The results show that Black Au is far less transmissive than Au in the visible part of the spectrum. Both spectra reveal a similar double peak shape. As found by Pfund and other researchers, the transmission of the Black Au film increases into the infra-red part of the spectrum. There are particularly interesting differences near $350$nm. The Black Au film shows a dip in transmission which is notably absent in the Au film.



\begin{comment}
It is difficult to arrive at a possible explanation for this dip based upon the transmission data alone. Plasmonic behaviour is often sensitive to the polarisation of incident light. Ellipsometry, which measures polarisation, was found to be more useful for characterising samples\footnote{The Ellipsometer was unavailable at the time of the Optical Transmission Spectroscopy measurements}.

\subsection{Effect of Atmosphere on Transmission Spectra of Black Au}

Harris et al \cite{harris1952} and other studies \cite{mckenzie2006} have examined the differences between Black Au deposited in an atmosphere with or without oxygen present. The Black Au prepared in air may contain traces of tungsten oxides formed at the tungsten filament, whilst Black Au prepared in inert gases was shown to consist entirely of Au. This was the motivation for making a comparison between samples prepared in air and He atmospheres.

\begin{figure}[H]
	\centering
	\includegraphics[width=0.6\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}

\end{comment}

\pagebreak

\section{Variable Angle Spectroscopy Ellipsometry}



\subsection{Model for Ag and Black Ag on a Si substrate}

Testing showed that it is difficult to use Ellipsometry to characterise black metal films of considerable thickness (estimated $>30nm$), due to the extremely low reflectivity of such films. However, using the WVASE32 software, it was possible to fit for the optical constants of an extremely thin layer of Black Ag prepared on Si using ellipsometric measurements. Figures \ref{n_compare.pdf} and \ref{k_compare.pdf} show the fitted optical constants for the Ag layer in a multilayered model for both a Black Ag thin film, and Ag thin film. Bulk Ag optical constants from Palik's Handbook \cite{palik} were specified for the initial values.

The models include an $\text{SiO}_2$ surface layer, with the thickness fit. The EMA layer models the effect of surface roughness in the film. This layer uses the Bruggeman model to describe the surface as a set of spherical inclusions of the Black Ag material in a void. The Bruggeman EMA formula is \cite{bruggeman1935, oates2011}:
\begin{align*}
	F \frac{\epsilon_b - \epsilon_{eff}}{\epsilon_b + 2 \epsilon_{eff}} + (1 - F) \frac{\epsilon_c - \epsilon_{eff}}{\epsilon_c + 2\epsilon_{eff}} &= 0
\end{align*}
where $\epsilon_b$ and $\epsilon_c$ are the dielectric functions of the two materials (in our case, material $b$ is air; $\epsilon_b = 1$), and $F$ is the volume fraction of material $b$. This model is incorporated into the WVASE32 software.


Although from SEM images it is clear that the structure of Black films is far more complicated than this approximation, fitting for the fraction of Black Ag in the surface layer shows a majority of the surface is empty. This is consistent with the porous nature of Black metal films seen in SEM images. The thickness of this layer was also a free parameter in the model.

Both the refractive index and extinction coefficient of the Black Ag film show a strong peak around $370$ nm. From the refractive index, the Black Ag film has a much stronger dispersion relation than the Ag film. The extinction coefficient peak indicates a preferential scattering or absorbsion of light at $370$ nm. This may be indicative of surface plasmon resonance effects \cite{oates2011, sonnichsen2001, zheng2008}, particularly since it occurs near to the bulk plasmon frequency for Ag. It is interesting to note that the peak in extinction for the thin Ag film occurs within $30$ nm of the dip in transmission measured for an Au film (Figure \ref{zoom_transmission}).



\begin{figure}[H]
	\centering
	\includegraphics[width=0.80\textwidth]{figures/ellipsometer/ag_vs_blackag/n_compare.pdf}
	\caption{Fitted refractive index for the Ag layer in multilayered models for Ag and Black Ag (step size 50 nm)}
	\label{n_compare.pdf}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.80\textwidth]{figures/ellipsometer/ag_vs_blackag/k_compare.pdf}
	\caption{Fitted extinction coefficient for the Ag layer in multilayered models for Ag and Black Ag (step size 50 nm)}
	\label{k_compare.pdf}
\end{figure}


\subsection{Surface and Bulk Plasmons in the Ag and Black Ag films}

The bulk loss function as introduced in Section \ref{tcs_e} is:
\begin{align*}
	L_b = -\text{Im}\frac{1}{\phasor{\epsilon}}
\end{align*}

The occurance of maxima in $L_b$ can be used as a condition for determining bulk plasmon excitation frequencies \cite{komolov}. 

For surface plasmon excitations, the surface loss function is \cite{ibach2010}: 
\begin{align*}
	L_s &= -\omega \text{Im}\left(\frac{1}{1 + \phasor{\epsilon}}\right)
\end{align*}

When applied to the thin Ag film (Figure \ref{ag_loss}) the bulk loss function shows a strong peak at $320$nm, and is otherwise rather flat. This peak corresponds to the bulk plasmon frequency for Ag ($\hbar \omega_p \approx 3.8\text{eV}$. It should be noted that the stated uncertainty of Ellipsometric measurements is above 20\% for wavelengths below $320$nm. In addition we initially specified the film to have bulk optical constants, for which this result is to be expected.

When the bulk and surface loss functions are applied to the Black Ag film (Figure \ref{blackag_loss}), there is in fact a shallow minima at $370$nm. In contrast to the Ag film, the loss functions appear to increase monatomically for longer wavelengths.


Based upon these results, we cannot conclude that this particular Black Ag film will support surface or bulk plasmon oscillations. However, we cannot rule out that localised plasmonic resonance effects contribute to a scattering of light causing the peak in $k$ around $3800$. Due to the complicated structure of the surface it would be difficult to theoretically describe the nature of such effects. A starting point for future theoretical work may be Harris' models of black metal films as a series of interwoven conducting strands \cite{harris1952}.


\begin{figure}[H]
	\centering
	\includegraphics[width=0.9\textwidth]{figures/ellipsometer/ag_loss.eps}
	\caption{Pseudo-loss functions for the Ag thin film}
	\label{ag_loss}
\end{figure}


\begin{figure}[H]
	\centering
	\includegraphics[width=0.9\textwidth]{figures/ellipsometer/blackag_loss.eps}
	\caption{Pseudo-loss functions for the Black Ag thin film}
	\label{blackag_loss}
\end{figure}

\pagebreak