For structural relaxation of defect structures the same algorith is used with the temperature set to 0 K.
The formation energy $E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\text{C}}$ of a defect configuration is defined by chosing SiC as a particle reservoir for the C impurity, i.e. the chemical potentials are determined by the cohesive energies of a perfect Si and SiC supercell after ionic relaxation.
-Migration and recombination pathways have been investigated utilizing the constraint conjugate gradient relaxation technique (CRT)\cite{kaukonen98}.
-The binding energy of a defect pair is given by the difference of the formation energy of the complex and the sum of the two separated defect configurations.
-Accordingly, energetically favorable configurations show binding energies below zero while non-interacting isolated defects result in a binding energy of zero.
+Migration and recombination pathways have been investigated utilizing the constraint conjugate gradient relaxation technique\cite{kaukonen98}.
\section{Results}
However, huge amount of damage hampers identification.
The alignment of the investigated structures to the c-Si host is lost in many cases, which suggests the necissity of much more time for structural evolution to maintain the topotaptic orientation of the precipitate.
-\section{Discussion}
+\section{Summary and discussion}
Investigations are targeted on the initially stated controversy of SiC precipitation, i.e. whether precipitation occurs abrubtly after ehough C$_{\text{i}}$ agglomerated or a successive agglomeration of C$_{\text{s}}$ on usual Si lattice sites (and Si$_{\text{i}}$) followed by a contraction into incoherent SiC.
Results of a previous ab initio study on defects and defect combinations in C implanted Si\cite{zirkelbach10b} sugeest C$_{\text{s}}$ to play a decisive role in the precipitation of SiC in Si.
MD simulations at temperatures used in IBS resulted in structures that were dominated by the C$_{\text{i}}$ \hkl<1 0 0> DB and its combinations if C is inserted into the total volume.
Incoorporation into volmes $V_2$ and $V_3$ led to an amorphous SiC-like structure within the respective volume.
-To ensure correct diffusion behavior simulations at elevated temperatures have been performed.
-Although ...
-
-entropic contribution.
-as in \cite{zirkelbach10b}, next neighbored Cs and Sii did not recombine, but departed from each other.
-
-Sii stress compensation ...
-Thus, we prpopose (support) the follwing model ...
-
-Concluded that C sub is very probable ...
-Alignment lost, successive substitution more probable to end up with topotactic 3C-SiC.
-
-Both, low and high, acceleration not enough to either observe C agglomeration or amorphous to crystalline transition ...
-
-
-\section{Summary}
-
-To conclude, we have shown that ab initio calculations on interstitial carbon in silicon are very close to the results expected from experimental data.
-The calculations presented in this work agree well with other theoretical results.
-So far, the best quantitative agreement with experimental findings has been achieved concerning the interstitial carbon mobility.
-For the first time, we have shown that the bond-centered configuration indeed constitutes a real local minimum configuration resulting in a net magnetization if spin polarized calculations are performed.
-Classical potentials, however, fail to describe the selected processes.
-This has been shown to have two reasons, i.e. the overestimated barrier of migration due to the artificial interaction cut-off on the one hand, and on the other hand the lack of quantum-mechanical effects which are crucial in the problem under study.
-% ref mod: language - being investigated
-%In order to get more insight on the SiC precipitation mechanism, further ab initio calculations are currently investigated.
-In order to get more insight on the SiC precipitation mechanism, further ab initio calculations are currently being performed.
+To compensate overestimated diffusion barriers we performed simulations at accordingly increased temperatures.
+No significant change was observed for high C concentrations.
+The amorphous phase is maintained.
+Due to the incoorparation of a huge amount of C into a small volume within a short period of time damage is produced, which obviously decelerates strcutural evolution.
+For the low C concentrations, time scales are still too low to observe C agglomeration sufficient for SiC precipitation, which is attributed to the slow phase space propagation inherent to MD in general.
+However, we observed a phase tranisiton of the C$_{\text{i}}$-dominated into a clearly C$_{\text{s}}$-dominated structure.
+The amount of substitutionally occupied C atoms increases with increasing temperature.
+Entropic contributions are assumed to be responsible for these structures at eleveated temperatures that deviate from the ground state at 0 K.
+Indeed, in a previous ab initio MD simulation\cite{zirkelbach10b} performed at \unit[900]{$^{\circ}$C} we observed the departing of a Si$_{\text{i}}$ \hkl<1 1 0> DB located next to a C$_{\text{s}}$ atom instead of a recombination into the ground state configuration, i.e. a C$_{\text{i}}$ \hkl<1 0 0> DB.
+
+% postannealing less efficient than hot implantation
+Experimental studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates\cite{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.
+We assume this 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 therefor 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 aplicable 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.
+For the agglomeration and rearrangement of C Si$_{\text{i}}$ is needed to turn C$_{\text{s}}$ into highly mobile C$_{\text{i}}$ again.
+Since the conversion of a coherent SiC structure, i.e. C$_{\text{s}}$ occupying the Si lattice sites of one of the two fcc lattices that build up the c-Si diamond lattice, into incoherent SiC is accompanied by a reduction in volume, large amount of strain is assumed to reside in the coherent as well as incoherent structure.
+Si$_{\text{i}}$ serves either as supply of Si atoms needed in the surrounding of the contracted precipitates or as interstitial defect minimizing the emerging strain energy of a coherent precipitate.
+The latter has been directly identified in the present simulation study, i.e. structures of two C$_{\text{s}}$ atoms with one being slightly displaced by a next neighbored Si$_{\text{i}}$ atom.
+
+It is, thus, concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.\cite{nejim95}.
+This agrees well with a previous ab inito study on defects in C implanted Si\cite{zirkelbach10b}, which showed C$_{\text{s}}$ to occur in all probability.
+However, agglomeration and rearrangement is enabled by mobile C$_{\text{i}}$, which has to be present at the same time and is formed by recombination of C$_{\text{s}}$ and Si$_{\text{i}}$.
+In contrast to assumptions of an abrupt precipitation of an agglomerate of C$_{\text{i}}$\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}, however, structural evolution is believed to occur by a successive occupation of usual Si lattice sites with substitutional C.
+This mechanism satisfies the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate, whereas there is no obvious reason for the topotactic orientation of an agglomerate consisting exclusively of C-Si dimers, which would necessarily involve a much more profound change in structure for the transition into SiC.
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\section*{Acknowledgment}
projects / lectures / latex.git / blobdiff