nanocdte.tex

\section{Introduction} \label{sec:cdtenanowires}
A topic of substantial interest in semiconductor physics in recent years has been the potential of confined dimensional materials such as nanowires, particularly through the vapour-liquid-solid (VLS) growth process.
As the research group had been successful at producing thin films of CdTe, experiments were attempted in the production of CdTe nanowires using a number of metal catalysts.

CdTe VLS nanowires were successfully grown using the PLD process and several insights were gained into the role of energetics at the epitaxial growth surface, and how they can affect nanowires during growth.
This work was published as:\\
\fullcite{Neretina2008b} \cite{Neretina2008b}.\\
This work was done in close collaboration with Dr. Robert Hughes and Dr. Svetlana Neretina. Dr. Hughes grew the samples of interest, Dr. Neretina performed the SEM imaging and 2DXRD measurements and I performed the statistical analysis of the nanowire SEM images and numerically modelled the growth process.
\section{Experimental}
The experimental results and procedures presented here will focus on those nanowires derived from Bi\textsubscript{2}Te\textsubscript{3} catalytic seeds deposited on pristine (0001) sapphire substrates.
The results obtained will then be compared to the CdTe nanowires, described elsewhere\cite{Neretina2007b}, obtained using bismuth catalytic seeds deposited on polyvinyl alcohol or terpineol treated (0001) sapphire substrates.

The Bi\textsubscript{2}Te\textsubscript{3} seeds were prepared using the PLD process (GSI Lumonics IPEX-848 excimer laser at 248~nm, laser energy density 2 J~cm\textsuperscript{-2}, laser spot size  1.2\(\times\)1.2 mm\textsuperscript{2}).
The target used was prepared in-house from commercially available Bi\textsubscript{2}Te\textsubscript{3} pieces (99.999\% purity).
These pieces were
melted in a cylindrical graphite mould that was machined to sizes able to yield a 1 inch target weighing approximately 10 g.
This procedure was carried out in an argon background gas.
Before the deposition, the sapphire substrate was heated to 400\celsius{} and held there for 10~min in an oxygen background pressure of 300~mTorr.The substrate was then cooled to room temperature where a 20~\AA{} thick film of Bi\textsubscript{2}Te\textsubscript{3} was deposited.
This deposition lasted 35 s at a laser repetition rate of 3~Hz.
Once deposited, the film was then heated to 370\celsius{} where, over the course of 10 min, it would dewet forming Bi\textsubscript{2}Te\textsubscript{3} seeds.
At this point, a 30~sccm helium flow was introduced into the chamber such that the pressure was maintained at 400~mTorr.
Material from a rotating CdTe target, grown using the Bridgman method, was then deposited onto the substrate for time intervals typically in the range of 30--45~min at a laser repetition rate of 8~Hz.
The nanowires were then allowed to cool to room temperature in the helium ambient.

\section{Results and Discussion}
\Cref{fig:nanocdte_bite} shows an SEM image, of the Bi\textsubscript{2}Te\textsubscript{3} catalytic seeds formed on the (0001) sapphire substrate.
The seeds show a substantial size distribution with diameters as large as 150~nm.
While these seeds show enhanced stability, they are still prone to evaporation and will disappear completely if the CdTe deposition is delayed by approximately 10~min.
As was the case for the bismuth catalysts, the Bi\textsubscript{2}Te\textsubscript{3} seeds gain stability from exposure to the cadmium/tellurium flux.
It is also likely that the seeds shown in the image are somewhat different from those available when nanowire growth commences as the time required to cool these seeds to room temperature provided ample opportunity for further evaporation and Ostwald ripening.
\begin{figure}
 \centering
 \begin{subfigure}[t]{0.47\textwidth}
  \centering \includegraphics[width=\textwidth]{nanocdte_bite}
  \caption{\label{fig:nanocdte_bite}SEM image of the Bi\textsubscript{2}Te\textsubscript{3} seeds that were used as catalysts for CdTe nanowires.}
 \end{subfigure}\quad%
 \begin{subfigure}[t]{0.47\textwidth}
  \centering \includegraphics[width=\textwidth]{nanocdte_nanowires}
  \caption{\label{fig:nanocdte_nanowires} SEM image of CdTe nanowires derived from Bi\textsubscript{2}Te\textsubscript{3} catalytic seeds presented from a 70\degree{} tilt side view.}
 \end{subfigure}
 \caption{\label{fig:nanocdte_sem}SEMs of seeds and resulting wires.}
\end{figure}

\Cref{fig:nanocdte_nanowires} shows an SEM image of the CdTe nanowires derived from Bi\textsubscript{2}Te\textsubscript{3} seeds.
In many respects, these nanowires are indistinguishable from those grown using bismuth seeds in conjunction with an alcohol-altered surface\cite{Neretina2007b}.
The two methods both yield vertically aligned nanowires that are highly faceted, share an epitaxial relationship with the substrate and grow without a two-dimensional planar layer.
The nanowires are identical from a structural standpoint as well, exhibiting the wurtzite crystal structure instead of the bulk zincblende phase.
\Cref{fig:nanocdte_polefigure} shows a pole figure that includes contributions from both the (111) zincblende and (0002) wurtzite planes.
Both phases give rise to a peak in the centre of the pole, but a zincblende phase must also give rise to a ring of three peaks at the outer extent of the pole.
For the pole figure shown no such peaks are observed, but in general a small zincblende signature was visible.
The three small peaks that do appear in the pole figure are associated with the sapphire substrate.
\begin{figure}
 \centering \includegraphics[width=0.6\textwidth]{nanocdte_polefigure}
 \caption[Pole figure of CdTe nanowires]{\label{fig:nanocdte_polefigure}CdTe pole figure results for 2\straighttheta{}values that include contributions from both the (111) zincblende and (0002) wurtzite phases.
  The pole figure shows no evidence of a zincblende phase.
  The three small peaks originate from the (0001) sapphire substrate.}
\end{figure}

Even though these Bi\textsubscript{2}Te\textsubscript{3} catalysed nanowires share many similarities with those derived from the bismuth seeds deposited on an alcohol-altered surface, there do exist substantial differences.
One of the most striking differences is the nanowire size distribution observed in the SEM images of \cref{fig:nanocdte_SEM2}.
This size distribution is quantified by the colour map presented in \cref{fig:nanocdte_stats}a.
It shows a nanowire height versus diameter distribution for the Bi\textsubscript{2}Te\textsubscript{3} seeded nanowires.
It is quite clear from the map that larger diameter nanowires exhibit higher axial growth rates than those with smaller diameters.
\Cref{fig:nanocdte_stats}b shows the same distribution for nanowires derived from bismuth seeds deposited on an alcohol-altered surface.
A comparison of the two colour maps shows that the alcohol-altered surface gives rise to a narrower size distribution.
It is also apparent from the distributions that the Bi\textsubscript{2}Te\textsubscript{3} seeded nanowires are of larger diameter with values typically in the range of 80--200~nm.
Also different is the fact that the Bi\textsubscript{2}Te\textsubscript{3} nanowire height is not limited to 300~nm.
Instead the nanowires grow longer while exhibiting substantial growth in the lateral direction (\cref{fig:nanocdte_lateral}).
Moving away from the optimum growth conditions gives rise to other differences between the two nanowire growth procedures.
First, nanowires formed at the substrate's edge have slanted tops where the direction of the slant at the left and right edges of the substrate point in opposite directions (\cref{fig:nanocdte_slanted}).
Also of note is the fact that the nanowire's cross-section is no longer hexagonal, but instead elongates along the direction of the slant.
Second, at high growth rates Bi\textsubscript{2}Te\textsubscript{3} seeded nanowires show distinct tapering (\cref{fig:nanocdte_tapered}).
\begin{figure}
 \centering \includegraphics[width=\textwidth]{nanocdte_SEM2}
 \caption[SEM image of CdTe nanowires]{\label{fig:nanocdte_SEM2}SEM images of CdTe nanowires from a (a) top and (b) side view (70\degree{} tilt).
  Highly faceted wires exhibit a substantial variation in both heights and diameters.}
\end{figure}
\begin{figure}
 \centering \includegraphics[width=\textwidth]{nanocdte_stats}
 \caption[CdTe nanowire dimension colourmap]{\label{fig:nanocdte_stats}Colour map showing the nanowire height versus diameter size distribution for nanowires derived from (a) Bi\textsubscript{2}Te\textsubscript{3} catalytic seeds and (b) bismuth seeds deposited on an alcohol-altered surface.
  The maps were generated from the measured dimensions of (a) 1344 and (b) 966 nanowires.
  The colour bar below each figure denotes the number of times a nanowire of a given dimension is observed.
  The Bi\textsubscript{2}Te\textsubscript{3} seeded nanowires exhibit a broader size distribution and sizes that are, in general, larger than the bismuth seeded wires.}
\end{figure}
\begin{figure}
 \centering \includegraphics[width=0.6\textwidth]{nanocdte_lateral}
 \caption[CdTe nanowire lateral growth]{\label{fig:nanocdte_lateral}SEM images of CdTe nanowires deposited using extended growth times where increases to the height are met with substantial lateral growth.}
\end{figure}
\begin{figure}
 \centering \includegraphics[width=\textwidth]{nanocdte_slanted}
 \caption[CdTe nanowires with slanted tops]{\label{fig:nanocdte_slanted}SEM images of CdTe nanowires with slanted tops that have formed at the (a) left and (b) right edge of the substrate.
  The tilt is in opposite directions.
  The top views of these nanostructures, shown in the inset to (a), indicate that the hexagonal cross-sections are elongated in the horizontal direction.}
\end{figure}
\begin{figure}
 \centering \includegraphics[width=0.6\textwidth]{nanocdte_tapered}
 \caption{\label{fig:nanocdte_tapered}SEM image showing tapered CdTe nanowires.}
\end{figure}
This work combined with our previous results has demonstrated that CdTe nanowire structures can originate from catalytic seeds derived from two separate processes, with each of these processes having advantages and disadvantages.
Bismuth seeds, in combination with an alcohol-altered surface, give rise to superior nanowire uniformity, but there exist nanowire height limitations and fabrication can only proceed using volatile catalytic seeds maintained in a narrow window of processing parameters.
The Bi\textsubscript{2}Te\textsubscript{3} seeds are much more stable at the temperatures needed to initiate CdTe nanowire growth.
This makes nanowire production possible without the cumbersome alcohol pre-treatment of the substrate's surface.
The main disadvantage is that the nanowire size and shape distributions are severely compromised.

Over one hundred samples have been characterized for each of the two nanowire deposition methods.
As a result, nanowire fabrication has been attempted over a broad range of growth conditions.
Thus, the features presented here as unique to the Bi\textsubscript{2}Te\textsubscript{3} initiated nanowires have been shown to decisively differentiate themselves from those observed using bismuth seeds deposited on an alcohol-altered surface.
If, as expected, both the bismuth and Bi\textsubscript{2}Te\textsubscript{3} catalytic seeds assume the same composition once exposed to a flux of cadmium and tellurium then the differences observed between the two methods must be attributed to the presence or absence of an alcohol-altered substrate surface.
It is our conjecture that this can be done within the confines of the existing nanowire growth modes.

For both nanowire deposition methods the catalytic seeds are derived from a thin film that dewets at elevated temperatures.
Once formed, these seeds are subject to Ostwald ripening, where there is an exchange of atoms along the substrate's surface with larger seeds growing at the expense of smaller ones\cite{Raab2000a,Li2003b}.
The effectiveness of this process is governed by the adatom's surface diffusion length given by the square root of the product of its diffusion coefficient and lifetime.
If this length is larger than the separation between seeds then Ostwald ripening proceeds in the usual manner where, as time progresses, there is an increasing variation in seed size.
On the other hand, if this length is reduced to where atoms liberated from one seed evaporate before encountering a second one, then a narrow size distribution will be maintained, but accompanied by a continuous reduction in the seed's diameter.

It is clear from our results that the pristine substrate used for the Bi\textsubscript{2}Te\textsubscript{3} seeds leads to sufficient surface mobility for Ostwald ripening to broaden the distribution of seed diameters.
Due to the higher volatility of tellurium we expect that this ripening process will result in bismuth-rich seeds.
Indeed, the binary phase diagram indicates that the growth temperature is too low for the seeds to melt unless there is first a substantial loss of tellurium\cite{MassalskiTBMurrayJL1986}.
The combination of Ostwald ripening in conjunction with evaporation leads to bismuth-rich catalytic seeds of different sizes which in turn cause nanowires of varying diameters.
Corrupting the surface with alcohol alters this process by dramatically reducing the surface mobility; this increases the lifetime of the seed on the surface and frustrates the Ostwald ripening process, i.e., any bismuth atoms liberated from an individual seed are backscattered to the original seed or evaporate from the surface before reaching a second seed.
With the ripening process halted, the distribution of seed diameters remains narrow, ultimately giving rise to a narrow distribution of nanowires.

With the catalytic seeds in place and exposed to a flux of cadmium and tellurium atoms it is expected that both the bismuth and Bi\textsubscript{2}Te\textsubscript{3} seeds will evolve to the same ternary composition.
While the ternary phase diagram for the cadmium/tellurium/bismuth system is unknown, it is well established that individually both tellurium and cadmium are soluble in bismuth\cite{MassalskiTBMurrayJL1986}.
The catalytic seed's ability to stabilize both elements on the timescales necessary for CdTe formation is crucial.
This is made evident by the fact that the CdTe nanowires grow without a two-dimensional planar layer.
This is attributable to the fact that both cadmium and tellurium have negligible sticking coefficients at the substrate temperature used.
It is only through the formation of CdTe that these species have significant lifetimes on the substrate's surface.
For the growth conditions used, however, the adatom lifetimes are too small to enable CdTe formation directly on the sapphire negating a planar growth mode.
As a result, CdTe growth can only proceed through the catalytically driven process.
Consistent with this analysis is a nanowire height distribution with the tallest nanowires having the largest diameters.
This is in contrast to substrate-based nanowire growth modes where the tallest nanowires are those with the smallest diameters.
For these systems, the nanowire height distribution is driven by adatoms arriving at the substrate's surface and making their way to the growth front via a random walk that takes them up the nanowire's sidewalls.
For the CdTe case, the small adatom lifetime negates this process resulting in a nanowire growth mode that is dependent upon the direct impingement of atoms onto the catalytic seeds.
Such a growth mode is not commonly observed in semiconductor nanowire systems.
\begin{figure}
 \centering
 \begin{subfigure}[t]{0.49\textwidth}
  \centering \includegraphics[width=\textwidth]{nanocdte_model_thickness}
  \caption{\label{fig:nanocdte_model_thickness}}
 \end{subfigure}%
 \begin{subfigure}[t]{0.49\textwidth}
  \centering \includegraphics[width=\textwidth]{nanocdte_model_time}
  \caption{\label{fig:nanocdte_model_time}}
 \end{subfigure}
 \caption[Simulated CdTe nanowire dimension distributions]{\label{fig:nanocdte_model}Simulation results showing (a) the time evolution of the nanowire height for the five labelled diameters and (b) time snapshots of the height versus diameter dependence for the times labelled.
  The dashed line shows the linear dependence expected when all nanowires reach an equilibrium condition.
  Superimposed over the simulation is the experimental data (black dots) of \protect{\cref{fig:nanocdte_stats}}.
  The values used in this simulation have been scaled so to fit this experimental distribution.}
\end{figure}

A growth mode driven by direct impingement, where all the adatoms arrive normal to and are incorporated into the nanostructure, will result in a nanowire height distribution that is independent of diameter.
There are, however, other factors that can come into play.
It has been demonstrated both experimentally\cite{Schubert2004a,Wu2002} and theoretically\cite{Kashchiev2006,Chen2006} that the Gibbs-Thomson effect can give rise to a height distribution directly proportional to the nanowire diameter.
The effect stipulates that the higher curvature associated with smaller diameter seeds yields a higher effective vapour pressure, reducing the uptake of atoms from the impinging vapour.
While this effect qualitatively gives rise to the observed CdTe nanowire height distribution, it is unable to account for the observed height limitation for the bismuth seeded nanowires as it provides no means of halting the growth.

The self-limiting growth mode displayed by the bismuth seeded nanowires deposited on an alcohol-altered surface likely originates from an equilibrium that develops between the addition of adatoms through direct impingement on the catalyst and the loss of atoms from the sidewalls through sublimation.
The sublimation process is significant for the CdTe nanowires as they will disappear completely in approximately 30~min if left at the growth temperature without an incoming flux of cadmium and tellurium atoms.
A similar situation must exist for the Bi\textsubscript{2}Te\textsubscript{3} seeded nanowires, but in this case the results are complicated by the distribution of the nanowires' diameters and the lateral growth that becomes apparent for long growth times.
A stochastic simulation was conducted to show the time evolution of the nanowires subject to a sublimation process.
Arrays of nanowires with random diameters were exposed to a simulated random flux of incoming atoms, atoms which caused them to grow larger while surface area caused them to sublimate.
With the uptake of material being proportional to the area of the catalytic seed and the loss of material being proportional to the area of the sidewalls, the simulation yields nanowire heights showing the time evolution presented in \cref{fig:nanocdte_model_thickness}.
Snapshots in time of the nanowire height versus diameter distribution are shown in \cref{fig:nanocdte_model_time} with the experimentally observed distribution of \cref{fig:nanocdte_stats}a superimposed.
The intent of this simulation was not to rigorously model the nanowire growth as it ignores such factors as the Gibbs-Thomson effect.
It does, however, show that sidewall sublimation limits nanowire height and results in a size distribution qualitatively similar to that observed experimentally.

Essential to this work is the observation that Bi\textsubscript{2}Te\textsubscript{3} seeded nanowires show a marked tendency towards lateral growth, while the bismuth seeded nanowires deposited on an alcohol-altered substrate do not.
This tendency is displayed not only at long growth times, but also in the tapering shown at high growth rates and in the elongation of the slanted-top nanowires formed at the edge of the substrates.
These three observations are consistent with the preferential nucleation of adatoms at the base of the nanowire where a weak nucleation site forms due to atomic bonding from both the sidewall facet and the substrate.
Such a nucleation site would be analogous to the ones formed on a vicinal substrate\cite{Ratsch2005a}.
The atoms forming at the base would then have to promote the propagation of a layer up the nanowire's sidewall.
The existence of a lateral growth mode accounts for the formation of tall, large diameter nanowires for extended growth times (\cref{fig:nanocdte_lateral}).
In the initial stages of growth the axial growth rate exceeds the lateral growth rate by a wide margin, but as the nanowire approaches its height limit the axial growth slows dramatically as shown in \cref{fig:nanocdte_model_thickness}.
The model presented, however, does not account for the situation where a slow lateral growth mode accompanies the axial growth.
In this scenario, lateral growth results in larger diameter nanowires which, in turn, allow for increased axial growth.
As a result, both dimensions will grow slowly in tandem provided that the catalytic material remains active as it spreads out over the expanding top surface of the nanowire.

Lateral growth is most evident for the slanted-top nanowires (\cref{fig:nanocdte_lateral}) as it proceeds in an anisotropic manner.
In the PLD process cadmium and tellurium atoms exit the target from an area a few square millimetres in diameter.
Thus, while the ablated material arrives normal to the centre of the substrate, it arrives at an angle to the edges.
As a result, nanowires growing at the edges will have cadmium and tellurium atoms preferentially landing on the sidewall facet nearest to the centre of the substrate.
Thus, the adatoms have an increased likelihood of becoming a part of both the growth front nearest to that sidewall facet as well as any layer propagating up that sidewall.
It is this asymmetry that leads to the anisotropic growth mode that is mirrored on opposite sides of the substrate.

The extent of the lateral growth at the base of the nanowire must be dependent upon the availability of adatoms on the surface of the substrate.
At slow growth rates the nucleation of adatoms will be far more difficult as singly bonded atoms and small clusters of atoms will easily dissociate, making them prone to evaporation from the surface.
At higher growth rates the availability of adatoms increases allowing for larger clusters to stabilize.
Under these conditions the nanowires will have a small, but significant, collection area.
The effect of this collection area, however, will diminish as one moves away from the surface of the substrate, a situation that should give rise to a tapered structure as shown in \cref{fig:nanocdte_tapered}.

As previously mentioned, these lateral growth modes are absent for the bismuth seeded nanowires deposited on an alcohol-altered substrate.
It is our conjecture that during the dewetting process, the bismuth seeds are able to penetrate through this surface-altered layer in a manner that effectively cleans the surface and exposes the (0001) face of sapphire; a face essential to the epitaxial alignment of the nanowires.
This statement is supported by the fact that a bismuth absorption/desorption treatment has been used to remove carbon-containing impurities from the surface of SrTiO\textsubscript{3} and LaAlO\textsubscript{3}\cite{Watanabe1991a}.
Around the periphery of each seed it is expected that the substrate's alcohol surface alteration persists.
As a result, the nucleation site at the base of the nanowire is of poor quality as the substrate's epitaxial relationship no longer exists due to the corrupted surface.
It is this deterioration in the nucleation site that inhibits the nanowire's ability to grow laterally.
In general, poor adhesion of adatoms to the substrate should be detrimental to a lateral growth mode as adatoms must already have a low probability of attaching to the sidewall facet; if this were not the case a one-dimensional nanowire growth mode would be unattainable.
The described process results in lateral overgrowth suppression in a manner analogous to that used for nanowire production through the use of selective area epitaxy.
It is well established that CdTe is prone to such a process as there is a substantive body of work detailing procedures for obtaining selective epitaxy in the CdTe system\cite{Sporken2000,Zhang2001a,Bhat2006a}.
Also supportive of this explanation are reports detailing the fabrication of vertically aligned nanowires, where non-vertically aligned growth is eliminated through the use of organic layers\cite{Krishnamachari2004,Mikkelsen2005,Martensson2007}.

\section{Implications for Symmetry and Energy at Epitaxial Surfaces}
The bond energy landscape of CdTe on oxide substrates like Al\(_2\)O\(_3\) is already not particularly strong, as demonstrated by the CdTe thin film liftoff phenomenon.
The additional chemical fouling of the sapphire substrate with alcohol has had the effect of both reducing the rate of nucleation on the substrate, and the diffusion rate of adatoms on the substrate surface.
The carbon film on the surface is more chemically reactive with the Cd and Te adatoms than they are with the substrate.
Only where the metal seeds are present can the adatoms reach the substrate and begin to assemble into the nanowire.
Such chemical fouling resembles the process of surfactant layers deposited before epitaxial growth to enhance the diffusion of adatoms\cite{PhysRevLett.63.632}.
Here, the layer instead prevents the diffusion of adatoms.

This surface energy modification is a possible route to reducing or eliminating the parasitic thin film present during the growth of semiconductor nanowires.
If the balance of growth temperature and chemical fouling can be optimized, higher quality nanowire devices may be possible.