srtio3.tex

\section{Introduction}
As part of the ongoing research into the growth of CdTe, other oxide single crystals were examined for possible use as substrates.
One of those substrates, SrTiO\textsubscript{3}, while it did not ultimately yield particularly high quality CdTe, did provide some interesting insights into the potential for surface reconstructions to play a role in epitaxy.

The role of both substrate offcut and high temperature surface reconstructions were examined through the growth of CdTe on as-received and reconstructed SrTiO\textsubscript{3} substrates.
This work was published as:\\
\fullcite{Neretina2009a} \cite{Neretina2009a}.\\
This work was done in close collaboration with Dr. Robert Hughes and Dr. Svetlana Neretina. Dr. Hughes grew the samples of interest, Dr. Neretina measured 2DXRD and AFM and I collected and produced the models of the CdTe (211) and reconstructed SrTiO\textsubscript{3} interfaces.
\section{Experimental}
CdTe films were deposited on both the as-received and reconstructed surface of (100) SrTiO\textsubscript{3} (MTI Corporation).
Step-terrace formation relied upon the miscut originating from the inaccuracies in the crystallographic alignment carried out before cutting and polishing of the substrates (manufacturer's miscut tolerance 0.5\degree{}).
As a result, the degree of miscut could only be varied through the selection of substrates from different manufacturer batches.
Due to the high temperatures required, the surface reconstruction took place ex-situ in a quartz tube furnace.
Prior to annealing, the substrates were etched in BHF for 90~s.
Anneals were conducted in 60~SCCM of flowing oxygen at 1000\celsius{} for 10~h.
\cref{fig:srtio3_sub_afm} shows atomic force microscopy (AFM) images for the as-received and surface reconstructed substrates relevant to this work.
As expected, only the annealed substrates exhibit the step-terrace structure with unit cell step heights.
The difference in terrace width for the surfaces shown in \cref{fig:srtio3_sub_afm}b and c can be attributed to a miscut difference estimated at 0.358\degree{}.
Also present on each image are the crystallographic axes obtained through X-ray diffraction (XRD).
A nearly identical in-plane step direction exists for both reconstructed surfaces.
As this direction is close to, but not aligned with the [011] axis of SrTiO\textsubscript{3}, it is expected that the steps exhibit a sawtooth morphology, but on length scales not readily observed using atomic force microscopy.
\begin{figure}
 \centering \includegraphics[width=\textwidth]{srtio3_sub_afm}
 \caption[AFM of SrTiO\textsubscript{3} surfaces]{\label{fig:srtio3_sub_afm}AFM images for the (a) as-received (100) SrTiO\textsubscript{3} substrate, (b) a reconstructed surface with an average terrace width of approximately 200 nm and (c) a reconstructed surface with a terrace width of approximately 50~nm.
  From the step heights and terrace widths it is estimated that the miscuts for the two reconstructed surfaces are (b) 0.118\degree{} and (c) 0.468\degree{}.}
\end{figure}

CdTe films were deposited on the three SrTiO\textsubscript{3} surfaces shown in \cref{fig:srtio3_sub_afm} using pulsed laser deposition.
A deposition rate of 20 nm/min was achieved by operating the laser at a repetition rate of 10~Hz with a substrate to target distance of 3.5~cm.
Films were grown to a thickness of 300~nm as determined using a spectroscopic variable angle ellipsometer (Horiba Jobin Yvon, France).
Morphological and structural characterization was then conducted on the films using AFM and 2DXRD\@.
\section{Results and Discussion}
\cref{fig:srtio3_pole} shows the (111) CdTe pole figures for the three substrates shown in \cref{fig:srtio3_sub_afm}.
The dramatic differences observed between films deposited on the as-received and annealed substrates indicate that the surface reconstruction gives rise to a complete re-alignment of the CdTe grains.
The pole figure for the as-received surface is consistent with a [111] oriented film.
Twelve peaks are present in the outer ring, instead of the three expected for a single crystal, indicates that there are four in-plane grain orientations.
The pole figures for the films deposited on the surface reconstructed substrates show that both films are predominantly [211] oriented.
The twelve peaks in the central ring and 24 peaks in the outer ring denote twelve in-plane grain orientations.
Each peak in the central ring comes from a different grain, the intensity differences indicate that some grains form preferentially over others.
Of the twelve peaks both the strongest and weakest is in-line with the miscut direction for both of the reconstructed surfaces and that the degree of this preferential orientation is stronger for the reconstructed surface having the narrow terrace width.
An examination of the low intensity pole figure peaks (not visible in the figures), indicates that some [111] CdTe grains exist in these nominally [211] films, but at the 10\% level.
While these [111] grains contribute to
the intensity at the centre of the pole, the response there is due to the (100) SrTiO\textsubscript{3} substrate.
The simulated pole figures for single crystal [111] and [211] CdTe and [001] SrTiO\textsubscript{3} are shown in \cref{fig:srtio3_sim_pole}.
\begin{figure}
 \centering \includegraphics[width=\textwidth]{srtio3_pole}
 \caption[Pole figures of CdTe grown on SrTiO\textsubscript{3}]{\label{fig:srtio3_pole}(111) CdTe pole figures for films deposited on (a) the as-received (100) SrTiO\textsubscript{3} substrate (b) the reconstructed surface with wide terraces and (c) the reconstructed surface with narrow terraces.
  Indicated on each image are the substrate's in-plane crystallographic axes obtained from XRD measurements.}
\end{figure}
\begin{figure}
 \centering \includegraphics[width=\textwidth]{srtio3_sim_pole}
 \caption[Simulated pole figures of CdTe on SrTiO\(_3\) surfaces]{\label{fig:srtio3_sim_pole}Schematics showing the (111) pole figure expected for a single crystal CdTe film with a) [111] and b) [211] orientation.
  c) Schematic showing the (100) pole figure expected for a [100] oriented SrTiO\textsubscript{3} substrate.
  The surface normal and in-plane Miller indicies are also shown for each case.}
\end{figure}

Grain formation for a given film/substrate combination is determined by the interface energy.
For the case of the as-received (100) SrTiO\textsubscript{3} substrate the interface energy is minimized through the formation of [111] CdTe grains.
This interfacial relationship is not surprising as CdTe has demonstrated a high propensity for forming it regardless of the substrate surface offered\cite{Neretina2006}.
The resulting interface, however, must overcome the seemingly incompatible situation brought about when the four-fold symmetric substrate surface mates with the six-fold symmetric (111) plane of CdTe.
In this scenario it is reasonable to expect that the resulting in-plane grain structure reflects both a suitable fit to the substrate's atomic arrangement as well as its underlying symmetry.
The (111) pole figure results indicate that this is indeed the case as there is a four-fold symmetric grain structure which is commensurate with the substrate's cubic crystal structure.
The XRD data indicates that these grains are oriented as shown schematically in \cref{fig:srtio3_tri_on_100}a.
The triangles symbolize the orientation of the (111) planes on the surface of SrTiO\textsubscript{3} represented by the dotted pattern.
The arrows on the triangles denote the three equivalent (111) CdTe planes that project out of its surface.
Each of these four triangles match poorly to the substrate's lattice constant in all but one direction.
In this direction, it is nearly equal to two of the substrate's unit cells (mismatch = 1.6\%).
This
one-dimensional match is preferred to such extents that only grains that comply with it exist within the film.
To appreciate the uniqueness of the four grains, for the arrows denoting the (111) equivalent planes, no two arrows point in the same direction.
It is these directions that give rise to the twelve peaks in the outer ring of the (111) pole figure as is evident from \cref{fig:srtio3_tri_on_100}b.
\begin{figure}
 \centering \includegraphics{srtio3_tri_on_100}
 \caption[CdTe grains on (100) SrTiO\textsubscript{3}]{\label{fig:srtio3_tri_on_100}a) Schematic illustrating the four possible [111] CdTe grain orientations (triangles) for films deposited on the SrTiO\textsubscript{3}
  substrate (dotted background).
  The arrows on each triangle denote the direction of the three equivalent (111) planes that emerge from the surface.
  For each grain orientation there is a one-dimensional geometrical fit (mismatch = 1.6\%) to the substrate in either the vertical or horizontal directions.
  b) Schematic showing the
  resulting (111) pole figure obtained from the four grains where the colour of the dot on the pole figure corresponds to the grain from which it was derived.}
\end{figure}
\begin{figure}
 \centering \includegraphics{srtio3_211_sim_polefigure}
 \caption[Simulated pole figure of CdTe on reconstructed SrTiO\textsubscript{3}]{\label{fig:srtio3_211_sim_polefigure}a) Schematic detailing the twelve-fold symmetric [211] CdTe grain structure observed for films deposited on the surface reconstructed substrates.
  The contribution from each grain is denoted by a different colour.
  The pattern corresponding to a single crystal [211] CdTe film (\cref{fig:srtio3_sim_pole}b) is repeated twelve times.
  b) Schematic showing the in-plane [\(\overline{1}\)11] direction for each of the [211] grains.}
\end{figure}

The formation of a [211] CdTe film on a surface reconstructed (100) SrTiO\textsubscript{3} substrate was unexpected.
CdTe films with this orientation have been deposited, but only when the interface energy is minimized through the use of [211] oriented substrates \cite{Lange1991b,Million1996,Rujirawat1997a,Zanatta1998}.
While [211] substrates provide an appropriate template for [211] growth, there exist no obvious symmetry arguments that would allow for twelve symmetrically distributed grains to be accommodated on the bulk surface of (100) SrTiO\textsubscript{3}.
Instead, it is expected that the origin of the [211] CdTe grains lies with the epitaxial relationship formed between the (211) planes and the surface reconstruction.
In this case, it is expected that the twelve-fold symmetric grain structure is commensurate with the underlying symmetry of the substrate's surface reconstruction.
Thus, insight into the nature of the reconstruction is obtained from the observed grain structure.
\Cref{fig:srtio3_211_sim_polefigure} shows a schematic representation of the (111) CdTe pole figure where the contributions from each grain are shown.
The pole figure's inner ring demonstrates a twelve-fold symmetry in the grain structure as it is composed of twelve nearly equally spaced peaks where each peak originates from a different grain orientation.
The wide terrace widths shown in \cref{fig:srtio3_sub_afm}b give rise to [211] CdTe grains even though the film grain size is often smaller than the width of the terrace.
Thus, it appears that [211] grain formation does not rely on nucleation at the substrate steps.
The insensitivity to step edges indicates that the atomic scale surface reconstruction is the dominant factor in the promotion of the [211] grains.

Of the three surface reconstructions known to form in an oxygen ambient, only the c(\(4\times2\)) and c(\(6\times2\)) reconstructions present a surface structure where there exist reasonable symmetry arguments able to account for the formation of a [211] CdTe film having a twelve-fold symmetric grain structure.
Such a grain structure must arise from the symmetries of the underlying substrate as it provides the only means for the isolated grains to establish a symmetrical arrangement when first formed in an island growth mode.
The (211) plane of CdTe, shown in \cref{fig:srtio3_cdte211}, is lack of symmetric and consists of a series of rows comprised of alternating cadmium and tellurium atoms separated by distances of 8.49 or 2.83 \AA\@. \Cref{fig:srtio3_c4x2} shows a schematic of the c(\(4\times2\)) TiO\textsubscript{2} surface reconstruction proposed by Castell\cite{Castell2002}.
It consists of a series of alternating rows of titanium and oxygen atoms.
The top layer has a TiO\textsubscript{2} stoichiometry, but it is sparsely populated with only one quarter the number of atoms present in the TiO\textsubscript{2} layers found in the bulk\cite{Castell2002}.
With every second row of titanium atoms offset relative to each other they align in a pseudo-six-fold symmetric pattern.
Possible geometric fits of the (211) CdTe plane to this surface reconstruction are shown in \cref{fig:srtio3_c4x2}b.
Each of the three possible geometric fits shown would give rise to two unique grain types due to the one-fold symmetry of the (211) plane.
Six other domain structures would also form by virtue of the fact that the c(\(4\times2\)) surface reconstruction has two possible domains rotated 90\degree{} relative to each other\cite{Castell2002}.
The domain structure that develops on the reconstructed surface arises from the fact that the rows of titanium atoms have an equal probability of forming along the [010] or [001] directions.
The net result would be a twelve-fold symmetric [211] CdTe grain structure.
The c(\(6\times2\)) surface reconstruction, proposed by Jiang and Zegenhagen\cite{Jiang1996}, is shown schematically in \cref{fig:srtio3_cdte211}.
It too is a sparsely populated surface that has the potential to accommodate the (211) CdTe planes in select directions (\cref{fig:srtio3_cdte211}b).
Here, the four geometrical fits shown give rise to eight unique grain types.
In a manner analogous to the c(\(4\times2\)) reconstruction, the c(\(6\times2\)) reconstruction also has a domain structure that gives rise to an additional set of eight grains rotated 90\degree{} to the ones shown in the figure.
An examination of these additional grains, however, reveals that only four of them provide unique solutions as the other four rotate into solutions offered by the first domain.
Thus, a twelve-fold (\(8 + 8 \times 4 = 12\)) symmetric (211) CdTe grain structure is expected for this surface.
\begin{figure}
 \centering \includegraphics[width=0.8\textwidth]{srtio3_cdte211}
 \caption[Projection of (211) CdTe unit cell on SrTiO\textsubscript{3} surface]{\label{fig:srtio3_cdte211}Schematic of the (211) plane of CdTe with the interplanar dimensions labelled in units of angstroms.
  The area outlined by the dashed lines is used in subsequent figures to demonstrate how this structure fits to (100) SrTiO\textsubscript{3} surface reconstructions.
  The Miller indices shown correspond to the crystallographic orientation of the (211) CdTe plane.}
\end{figure}
\begin{figure}
 \centering \includegraphics[width=\textwidth]{srtio3_c4x2}
 \caption[CdTe on c(4\(\times\)2) SrTiO\textsubscript{3} surface]{\label{fig:srtio3_c4x2}(a) Schematic showing the surface of the (100) SrTiO\textsubscript{3} with a c(\(4\times2\)) surface reconstruction.
  (b) Schematic showing the uppermost layer of the reconstruction with the dashed lines being used to illustrate the closest geometrical fits of the (211) CdTe plane to this surface.
  The three orientations shown give rise to six grain orientations as a 180\degree{} rotation of the (211) plane yields a different grain structure.
  This is a consequence of the fact that the single crystal (111) CdTe pole figure for a [211] film is one-fold symmetric (see \cref{fig:srtio3_sim_pole}b).
  Six other grain structures arise from a domain structure in the substrate surface reconstruction that would be schematically represented by a 90\degree{} rotation of \cref{fig:srtio3_c4x2}b.
  The Miller indices shown in the top right corner of the figure correspond to the crystallographic orientation of the underlying bulk (100) SrTiO\textsubscript{3} substrate.}
\end{figure}

Assuming that the orientation relationships between CdTe and the surface reconstructions shown in \cref{fig:srtio3_c4x2,fig:srtio3_c6x2} are adhered to then it becomes possible to experimentally predict the surface reconstruction undergone by the substrates presented in this work.
It should be noted from \cref{fig:srtio3_c4x2}b that the c(\(4\times2\)) reconstruction is characterized by (211) CdTe grain alignment along the substrate's [010] and [001] directions.
\Cref{fig:srtio3_pole}b shows that this is not the case, ruling out this reconstruction for the work presented here.
It does not, however, rule out the possibility of [211] CdTe grain growth if a film were deposited on such a reconstruction.
The c(\(6\times2\)) reconstruction, on the other hand, requires grain growth along the substrate's [011] and [0\(\overline{1}\)1] directions, consistent with the X-ray data.
While we have no direct evidence that the c(\(6\times2\)) surface reconstruction formed, the anneal conditions used elsewhere\cite{Jiang1996} to obtain this reconstruction are similar to those used here.
While it should be understood that predicting a film-substrate orientation relationship solely on the basis of a geometrical fit is somewhat na\"{\i}ve, it is well established that this scenario occurs in the substantial balance of cases.
\begin{figure}
 \centering \includegraphics[width=\textwidth]{srtio3_c6x2}
 \caption[CdTe on c(6\(\times\)2) SrTiO\textsubscript{3} surface]{\label{fig:srtio3_c6x2}(a) Schematic showing the surface of the (100) SrTiO\textsubscript{3} with a c(\(6\times2\)) surface reconstruction.
  (b) Schematic showing the uppermost layer of the reconstruction with the dashed lines being used to illustrate the closest geometrical fits of the (211) CdTe plane to this surface.
  The four orientations shown give rise to eight grain orientations as a 180\degree{} rotation of the (211) plane yields a different grain structure.
  Eight other grain structures arise from a domain structure in the substrate surface reconstruction that would be schematically represented by a 90\degree{} rotation of \cref{fig:srtio3_c4x2}b.
  Of these eight grains only four represent unique solutions as the grains forming along the [011] and [01\(\overline{1}\)] directions rotate into each other.
  The Miller indices shown in the top right corner of the figure correspond to the crystallographic orientation of the underlying bulk (100) SrTiO\textsubscript{3} substrate.}
\end{figure}

Even though both the [211] oriented films show pole figure peaks in similar positions, the relative intensities of the peaks are different.
This is most easily seen by examining the innermost ring of the pole figure where each of the twelve peaks corresponds to a unique grain orientation.
For both samples the peaks on one side of the ring show greater intensities than on the other.
This effect, however, is much more pronounced for the pole figure shown in \cref{fig:srtio3_pole}c.
Here, the ratio of the integrated intensities between the largest and smallest peak in the ring is 22 compared to 4 for the pole figure shown in \cref{fig:srtio3_pole}b.
The fact that the terrace width is approximately four times smaller for the film that shows the most pole figure anisotropy suggests that the step edges promote this preferential grain alignment.
Consistent with this explanation is the fact that the highest intensity peaks correspond to the CdTe grain orientation having its [111] in-plane direction normal to the step.
The larger grain sizes exhibited by the surface with smaller terraces are also expected within this scenario.
This is a simple consequence of the fact that, in the early stages of film growth, there are more similarly oriented grains that are able to merge into a single larger grain as is expected for an island growth mechanism.
With a sizeable effect being observed between the two reconstructed surfaces having a miscut difference of only 0.358\degree{}, the potential exists to amplify this effect using a substrate with a larger miscut.

The results presented here show that the reconstructed surface of (100) SrTiO\textsubscript{3} profoundly alters the grain structure of CdTe films.
While it is not unusual for the grain structure to be transformed by the presence of a step-terrace morphology, it is unprecedented for SrTiO\textsubscript{3}'s atomic-scale reconstructions to promote a film with an alternative heteroepitaxial relationship.
For the case of (100) SrTiO\textsubscript{3}, there seems to be a disconnect between the research advocating a step-flow growth mode and the wide array of atomic-scale surface reconstructions allowed, with the latter not considered as a determining factor in the film quality achieved.
This may be due to the high growth temperatures used in the fabrication of oxide thin films.
In this case, the thermal energy available likely facilitates a local rearrangement of surface atoms in response to the addition of adatoms.
This is the case for the homoepitaxial growth of silicon where the surface reconstruction gives way to bulk crystalline ordering for temperatures in excess of 300\celsius{}\cite{Gossmann1985}.
For the low growth temperatures used in the fabrication of these CdTe films the surface reconstruction is likely locked in place, forcing CdTe to accommodate itself on the reconstructed surface.
The sparsely populated nature of such a surface should make it prone to alternative epitaxial relationships as the interface would not consist of an abrupt boundary, but instead, of an amalgamation of two interpenetrating layers.
Consistent with this explanation is the fact that different (100) SrTiO\textsubscript{3} surface reconstructions give rise to palladium nanodots having variable orientations and faceting\cite{Silly2005b}.
\section{Implications for Symmetry and Energy at Epitaxial Surfaces}
While the results presented here do not explicitly improve the growth of the CdTe thin films, they do add to the understanding of the role of the interface in epitaxy.
In all the cases presented here, the substrate used for epitaxial growth has a nominal orientation of (100), with small miscut of less than 1\degree{}.
Despite a fixed orientation for the substrate, the thin surface net presented to the epitaxial thin film dominates the nucleation and growth orientation.
These results show that it is possible to leverage high temperature surface reconstructions in order to completely transform a given substrate for later growth at lower temperatures.
If a reconstruction can be created at high temperature and then locked-in at the growth temperature, substrates that do not immediately appear to be an epitaxial match can end up presenting an ideal template for growth.
The additional symmetry breaking that is available for offcut substrates can widen the range of acceptable substrates, by triggering a step-flow growth mode suppressing unwanted orientations.

For this type of surface net epitaxy to yield the most benefit, surface science research must investigate the zoo of surface reconstructions possible on the commercially available complex oxides.
The higher element complex oxides (YAG, YSZ, GGG etc.) have little to no literature examining their surface reconstructions or their behaviour when miscut.
Phase diagrams of such surfaces would be highly beneficial in predicting good matches for epitaxy.