Thus, substitutional C enables strain engineering of Si and Si/Si$_{1-x}$Ge$_x$ heterostructures \cite{yagi02,chang05,kissinger94,osten97}, which is used to increase charge carrier mobilities in Si as well as to adjust its band structure \cite{soref91,kasper91}.
% increase of C at substitutional sites
Epitaxial layers with \unit[1.4]{at.\%} of substitutional C have been successfully synthesized in preamorphized Si$_{0.86}$Ge$_{0.14}$ layers, which were grown by CVD on Si substrates, using multiple-energy C implantation followed by solid-physe epitaxial regrowth at \unit[700]{$^{\circ}$C} \cite{strane93}.
-The tensile strain induced by the C atoms is found to compensates the compressive strain present due to the Ge atoms.
+The tensile strain induced by the C atoms is found to compensate the compressive strain present due to the Ge atoms.
Studies on the thermal stability of Si$_{1-y}$C$_y$/Si heterostructures formed in the same way and equal C concentrations showed a loss of substitutional C accompanied by strain relaxation for temperatures ranging from \unit[810-925]{$^{\circ}$C} and the formation of spherical 3C-SiC precipitates with diameters of \unit[2-4]{nm}, which are incoherent but aligned to the Si host \cite{strane94}.
During the initial stages of precipitation C-rich clusters are assumed, which maintain coherency with the Si matrix and the associated biaxial strain.
Using this technique a metastable solubility limit was achieved, which corresponds to a C concentration exceeding the solid solubility limit at the Si melting point by nearly three orders of magnitude and, furthermore, a reduction of the defect denisty near the metastable solubility limit is assumed if the regrowth temperature is increased by rapid thermal annealing \cite{strane96}.
High resolution transmission electron microscopy (HREM) investigations of C-implanted Si at room temperature followed by rapid thermal annealing (RTA) show the formation of C-Si dumbbell agglomerates, which are stable up to annealing temperatures of about \unit[700-800]{$^{\circ}$C}, and a transformation into 3C-SiC precipitates at higher temperatures \cite{werner96,werner97}.
The precipitates with diamateres between \unit[2]{nm} and \unit[5]{nm} are incorporated in the Si matrix without any remarkable strain fields, which is explained by the nearly equal atomic density of C-Si agglomerates and the SiC unit cell.
Implantations at \unit[500]{$^{\circ}$C} likewise suggest an initial formation of C-Si dumbbells on regular Si lattice sites, which agglomerate into large clusters \cite{lindner99_2}.
-The agglomerates of such dimers, which do not generate lattice strain but lead to a local increase of the lattice potential \cite{werner96}, are indicated by dark contrasts and otherwise undisturbed Si lattice fringes in HREM, as can be seen in Fig.~\ref{fig:sic:hrem:c-si}.
+The agglomerates of such dimers, which do not generate lattice strain but lead to a local increase of the lattice potential \cite{werner96,wener97}, are indicated by dark contrasts and otherwise undisturbed Si lattice fringes in HREM, as can be seen in Fig.~\ref{fig:sic:hrem:c-si}.
\begin{figure}[t]
\begin{center}
\subfigure[]{\label{fig:sic:hrem:c-si}\includegraphics[width=0.25\columnwidth]{tem_c-si-db.eps}}
% eichhorn02: high imp temp more efficient than postimp treatment
% eichhorn99: same as 02 + c-si agglomerates at low concentrations
% strane94/guedj98: my model - c redist by si int (spe) and surface diff (mbe)
+% serre95: low/high t implants -> mobile c_i / non-mobile sic precipitates
% todo
% own polytype stacking sequence image
Entropic contributions are assumed to be responsible for these structures at elevated temperatures that deviate from the ground state at 0 K.
Indeed, utilizing increased temperatures is assumed to constitute a necessary condition to simulate IBS of 3C-SiC in c-Si.
+
+% todo - sync with respective conclusion chapter
+
% conclusions 2nd part
\paragraph{Conclusions}
concerning the SiC conversion mechanism are derived from results of both, first-principles and classical potential calculations.
First of all, increased temperatures are considered a necessary condition to simulate the IBS of epitaxially aligned 3C-SiC in Si, which constitutes a process far from thermodynamic equilibrium.
The strong deviation from equilibrium by elevated temperatures enables the formation of \cs{}-\si{} structures as observed in the quantum-mechanical calculations.
In contrast, structures of \ci{} \hkl<1 0 0> DBs, which constitute the thermodynamic ground state, appear at low temperatures.
+Thus, the mechanism based on the agglomeration of \cs{} is reinforced.
%
Secondly, in configurations of stretched SiC composed by \cs, the accompanied \si{} defect may be assigned further functionality.
Next to that as a vehicle that is able to rearrange \cs{} and a building block for the surrounding Si host or further SiC, the analyzed configurations suggest \si{} to be required for stress compensation.
As evidently observed in these structures, \si{} reduces tensile strain by capturing a position near one of the C atoms within a configuration of two C atoms that basically reside on Si lattice sites.
-Furthermore, \si{} might compensate strain in the interface region of an incoherent, nucleated SiC precipitate and the c-Si matrix.
-This could be achieved by \ci{} \hkl<1 0 0> DBs in the Si region slightly contracting the Si atoms next to the C atom to better match the spacing of Si atoms present in 3C-SiC.
-Indeed, combinations of \cs{} and \ci{} \hkl<1 0 0> DBs are observed.
+Furthermore, \si{} might similarly compensate strain in the interface region of an incoherent, nucleated SiC precipitate and the c-Si matrix.
+%This could be achieved by the formation of \ci{} \hkl<1 0 0> DBs in the Si region slightly contracting the Si atoms next to the C atom to better match the spacing of Si atoms present in 3C-SiC.
+%Indeed, combinations of \cs{} and \ci{} \hkl<1 0 0> DBs are observed.
%
-Further conclusions are derived from results of the high C concentration simulations, in which a large amount of C atoms is incorporated into a small volume within a short period of time, which results in essentially no time for the system to rearrange.
-Due to this, the formation of strong C-C bonds and the production of a vast amount of damage is observed, which finally results in the formation of an amorphous phase.
+Further conclusions are derived from results of the high C concentration simulations, in which a large amount of C atoms to obtain stoichiometry is incorporated into a small volume within a short period of time, which results in essentially no time for the system to rearrange.
+Due to this, the occurence of strong C-C bonds and the production of a vast amount of damage is observed, which finally results in the formation of an amorphous phase.
The strong bonds and damage obviously decelerate structural evolution.
-The short time, which is not sufficient for structural evolution, can be mapped to a system of low temperature, which lacks the kinetic energy required for the restructuring process.
-
-
-HIER WEITER ...
-
+The short time, which is not sufficient for structural evolution of the strongly damaged region, can be mapped to a system of low temperature, which lacks the kinetic energy required for the restructuring process.
+
+% experimental findings
+These findings as well as the derived conclusion on the precipitation mechanism involving an increased participation of \cs{} agree well with experimental results.
+% low t high mobility
+% high t stable config, no redistr
+C implanted at room temperature was found to be able to migrate towards the surface in contrast to implantations at \degc{500}, which do not show redistribution of the C atoms \cite{serre95}.
+This excellently conforms to the results of the MD simulations at different temperatures, which show the formation of highly mobile \ci{} \hkl<1 0 0> DBs for low and much more stable \cs{} defects for high temperatures.
+% high imp temps more effective to achieve ?!? ...
+Furthermore, increased implantation temperatures were found to be more efficient than high temperatures in the postannealing step concerning the formation of topotactically aligned 3C-SiC precipitates \cite{kimura82,eichhorn02}.
+Strong C-C bonds, which are hard to break by thermal annealing, were found to effectively aggravate the restructuring process of such configurations \cite{deguchi92}.
+These bonds preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements in regions exhibiting a large amount of C atoms.
+This is assumed to be related to the problem of slow structural evolution encountered in the high C concentration simulations.
+%
+% WTF!
+% hier lieber guedj98 und strane94 ... ?
+Indeed, considering the efficiency of high implantation temperatures, an experimental argument exists, which points to the precipitation mechanism based on agglomeration of \cs.
+Implantations of an understoichiometric dose at room temperature followed by thermal annealing result in small spherical sized C$_{\text{i}}$ agglomerates below \unit[700]{$^{\circ}$C} and SiC precipitates of the same size above \unit[700]{$^{\circ}$C}\cite{werner96} annealing temperature.
+Since, however, the implantation temperature is considered more efficient than the postannealing temperature, SiC precipitates are expected -- and indeed are observed for as-implanted samples \cite{lindner99,lindner01} -- in implantations performed at \unit[450]{$^{\circ}$C}.
+Implanted C is therefore expected to occupy substitutionally usual Si lattice sites right from the start.
+%
+% low t - randomly ...
+% high t - epitaxial relation ...
+Moreover, implantations below the optimum temperature for the IBS of SiC show regions of randomly oriented SiC crystallites whereas epitaxial crystallites are found for increased temperatures \cite{lindner99}.
+The results of the MD simulations can be interpreted in terms of these experimental findings.
+The successive occupation of regular Si lattice sites by \cs{} atoms, as observed in the high temperature MD simulations and assumed from results of the quantum-mechanical investigations, perfectly statisfies the epitaxial relation of substrate and precipitate.
+In contrast, there is no obvious reason for a topotactic transition of \ci{} \hkl<1 0 0> DB agglomerates, as observed in the low temperature MD simulations, into epitaxially aligned precipitates.
+The latter transition would necessarily involve a much more profound change in structure.
+% amorphous region for low temperatures
+Experimentally, randomly oriented precipitates might also be due to SiC nucleation within the arising amorphous matrix \cite{lindner99}.
+In simulation, an amorphous SiC phase is formed for high C concentrations.
+This is due to high amounts of introduced damage within a short period of time resulting in essentially no time for structural evolution, which is comparable to the low temperature experiments, which lack the kinetic energy necessary for recrystallization of the highly damaged region.
+Indeed, the complex transformation of agglomerated \ci{} DBs, as suggested by results of the low C concentration simulations, could involve an intermediate amorphous phase probably accompanied by the loss of alignment with respect to the Si host matrix.
+%
+% perfectly explainable by Cs obvious hkl match but not for DBs
+In any case, the precipitation mechanism by accumulation of \cs{} obviously statisfies the experimental finding of identical \hkl(h k l) planes of substrate and precipitate.
+%
+% no contradictions, something in interstitial lattice, projected potential ...
+Finally, it is worth to point out that the precipitation mechanism based on \cs{} does not necessarily contradict to results of the HREM studies \cite{werner96,werner97,lindner99_2}, which propose precipitation by agglomeration of \ci.
+In these studies, regions of dark contrasts are attributed to C atoms that reside in the interstitial lattice in an otherwise undisturbed Si lattice.
+The \ci{} atoms lead to a local increase of the crystal potential, which is responsible for the dark contrast.
+However, there is no particular reason for the C species to reside in the interstitial lattice.
+Contrasts are also assumed for Si$_{\text{i}}$.
+Once precipitation occurs, regions of dark contrasts disappear in favor of Moir\'e patterns indicating 3C-SiC in c-Si due to the mismatch in the lattice constant.
+Until then, however, these may likewise be composed of stretched SiC structures coherently aligned to the Si host together with \si{} in the surrounding or of already contracted incoherent SiC surrounded by Si on regular lattice sites as well as in the interstitial lattice, where the latter is too small to be detected in HREM.
+%In both cases Si$_{\text{i}}$ might be attributed a third role, which is the partial compensation of tensile strain that is present either in the stretched SiC or at the interface of the contracted SiC and the Si host.
To conclude, results of the present study indicate a precipitation of SiC in Si by successive agglomeration of \cs.
\si{}, which is likewise existent, serves several needs:
... Incoherent but epitaxially aligned SiC precipitates are ...
-Experimental studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates \cite{kimura82,eichhorn02}.
-In particular, restructuring of strong C-C bonds is affected \cite{deguchi92}, which preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements.
-This is assumed to be related to the problem of slow structural evolution encountered in the high C concentration simulations due to the insertion of high amounts of C into a small volume within a short period of time resulting in essentially no time for the system to rearrange.
-% rt implantation + annealing
-Implantations of an understoichiometric dose at room temperature followed by thermal annealing results in small spherical sized C$_{\text{i}}$ agglomerates at temperatures below \unit[700]{$^{\circ}$C} and SiC precipitates of the same size at temperatures above \unit[700]{$^{\circ}$C} \cite{werner96}.
-Since, however, the implantation temperature is considered more efficient than the postannealing temperature, SiC precipitates are expected -- and indeed are observed for as-implanted samples \cite{lindner99,lindner01} -- in implantations performed at \unit[450]{$^{\circ}$C}.
-Implanted C is therefore expected to occupy substitutionally usual Si lattice sites right from the start.
-
Thus, we propose an increased participation of C$_{\text{s}}$ already in the initial stages of the implantation process at temperatures above \unit[450]{$^{\circ}$C}, the temperature most applicable for the formation of SiC layers of high crystalline quality and topotactical alignment\cite{lindner99}.
Thermally activated, C$_{\text{i}}$ is enabled to turn into C$_{\text{s}}$ accompanied by Si$_{\text{i}}$.
The associated emission of Si$_{\text{i}}$ is needed for several reasons.
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