The calculations aim at a comprehensive, microscopic understanding of the precipitation mechanism in the context of controversial discussions in the literature.
%
For the quantum-mechanical treatment, basic processes assumed in the precipitation process are calculated in feasible systems of small size.
-The migration mechanism of a carbon \hkl<1 0 0> interstitial and silicon \hkl<1 1 0> self-interstitial in otherwise defect-free silicon using density functional theory calculations are investigated.
+The migration mechanism of a carbon \hkl<1 0 0> interstitial and silicon \hkl<1 1 0> self-interstitial in otherwise defect-free silicon are investigated using density functional theory calculations.
The influence of a nearby vacancy, another carbon interstitial and a substitutional defect as well as a silicon self-interstitial has been investigated systematically.
Interactions of various combinations of defects have been characterized including a couple of selected migration pathways within these configurations.
Almost all of the investigated pairs of defects tend to agglomerate allowing for a reduction in strain.
A long range capture radius has been observed for pairs of interstitial carbon as well as interstitial carbon and vacancies.
A rather small capture radius is predicted for substitutional carbon and silicon self-interstitials.
%
-We derive conclusions on the precipitation mechanism of silicon carbide in bulk silicon and discuss conformability to experimental findings.
+%We derive conclusions on the precipitation mechanism of silicon carbide in bulk silicon and discuss conformability to experimental findings.
+Initial assumptions regarding the precipitation mechanism of silicon carbide in bulk silicon are established and conformability to experimental findings is discussed.
%
Furthermore, results of the accurate first-principles calculations on defects and carbon diffusion in silicon are compared to results of classical potential simulations revealing significant limitations of the latter method.
An approach to work around this problem is proposed.
-Finally, results of the classical potential molecular dynamics simulations of large systems are discussed, which allow to draw further conclusions on the precipitation mechanism of silicon carbide in silicon.
+Finally, results of the classical potential molecular dynamics simulations of large systems are examined, which reinforce previous assumptions and give further insight into basic processes involved in the silicon carbide transition.
+%Finally, results of the classical potential molecular dynamics simulations of large systems are discussed, which allow to draw further conclusions on the precipitation mechanism of silicon carbide in silicon.
\end{abstract}
\keywords{point defects, migration, interstitials, first-principles calculations, classical potentials, molecular dynamics, silicon carbide, ion implantation}
Atomistic simulations offer a powerful tool to study materials on a microscopic level providing detailed insight not accessible by experiment.
%
A lot of theoretical work has been done on intrinsic point defects in Si\cite{bar-yam84,bar-yam84_2,car84,batra87,bloechl93,tang97,leung99,colombo02,goedecker02,al-mushadani03,hobler05,sahli05,posselt08,ma10}, threshold displacement energies in Si\cite{mazzarolo01,holmstroem08} important in ion implantation, C defects and defect reactions in Si\cite{tersoff90,dal_pino93,capaz94,burnard93,leary97,capaz98,zhu98,mattoni2002,park02,jones04}, the SiC/Si interface\cite{chirita97,kitabatake93,cicero02,pizzagalli03} and defects in SiC\cite{bockstedte03,rauls03a,gao04,posselt06,gao07}.
-However, none of the mentioned studies consistently investigates entirely the relevant defect structures and reactions concentrated on the specific problem of 3C-SiC formation in C implanted Si.
+However, none of the mentioned studies comprehenisvely investigates all the relevant defect structures and reactions concentrated on the specific problem of 3C-SiC formation in C implanted Si.
% but mattoni2002 actually did a lot. maybe this should be mentioned!^M
In fact, in a combined analytical potential molecular dynamics and ab initio study\cite{mattoni2002} the interaction of substitutional C with Si self-interstitials and C interstitials is evaluated.
However, investigations are, first of all, restricted to interaction chains along the \hkl[1 1 0] and \hkl[-1 1 0] direction, secondly lacking combinations of C interstitials and, finally, not considering migration barriers providing further information on the probability of defect agglomeration.
> that compare with taking the energies of each defect in a
> supercell.
-We would like to remind the referee that the properties of isolated,
-non-intertacting defects were modeled in separate simulation runs. It
-is not our purpose to separate defects by a large distance in order to
-approximate the situation of isolated defects. We are rather
-interested in interacting defects. However, we did find that for
-increasing defect distances, configurations appear, which converge to
-the energetics of two isolated defects. This is indicated by the
-(absolute value of the) binding energy, which is approaching zero with
-increasing distance. From this, we conclude a decrease in
-interaction, which is already observable for defect separation
-distances accessible in our simulations. Combinations of defects with
-similar distances were already successfully modeled in a supercell
-containing 216 atoms as described in PRB 66, 195214 (2002).
+The calculations criticized by the referee did not aim at the
+properties of isolated, non-intertacting defects, but rather at the
+defect-defect interaction. Single defects were modeled in separate
+simulation runs. However, we did find that for increasing defect
+distances, configurations appear, which converge to the energetics of
+two isolated defects. This is indicated by the (absolute value of the)
+binding energy, which is approaching zero with increasing distance.
+From this, we conclude a decrease in interaction, which is already
+observable for defect separation distances accessible in our
+simulations. Combinations of defects with similar distances were
+already successfully modeled in a supercell containing 216 atoms as
+described in PRB 66, 195214 (2002).
+
+% We would like to remind the referee that the properties of isolated,
+% non-intertacting defects were modeled in separate simulation runs. It
+% is not our purpose to separate defects by a large distance in order to
+% approximate the situation of isolated defects. We are rather
+% interested in interacting defects. However, we did find that for
+% increasing defect distances, configurations appear, which converge to
+% the energetics of two isolated defects. This is indicated by the
+% (absolute value of the) binding energy, which is approaching zero with
+% increasing distance. From this, we conclude a decrease in
+% interaction, which is already observable for defect separation
+% distances accessible in our simulations. Combinations of defects with
+% similar distances were already successfully modeled in a supercell
+% containing 216 atoms as described in PRB 66, 195214 (2002).
An explanation of the binding energy and the relation to the
interaction of defects was added (Change 8).
> are seen for constant volume calculations (on a few simple
> examples, say)?
-Differences are supposed to be negligible small since only small
-changes in volume are detected. However, in experiment, substrate
-swelling is observed. Thus, to allow for full relaxation, simulations
-were performed in the NpT ensemble. However, for the above-mentioned
-reason, no fundamental differences are expected for single defect
-configurations in the canonical and isothermal-isobaric ensemble with
-respect to energy.
+% Differences are supposed to be negligible small since only small
+% changes in volume are detected. However, in experiment, substrate
+% swelling is observed. Thus, to allow for full relaxation, simulations
+% were performed in the NpT ensemble. However, for the above-mentioned
+% reason, no fundamental differences are expected for single defect
+% configurations in the canonical and isothermal-isobaric ensemble with
+% respect to energy.
+
+In experiment, substrate swelling is observed for high-dose carbon
+implantation into silicon. Indeed, for a single defect, the change in
+volume is less than 0.2% in simulation. Due to this, results of single
+defects within an isothermal-isobaric simulation are expected to not
+drastically differ to results of constant volume simulations. Based on the
+experimentally observed change in volume for high-dose carbon
+implantations, however, the respective relaxation is allowed for in
+simulation for both, single defect calulations as well as the high carbon
+concentration simulations.
A respective statement was added to the methodology section
(Change 4).
appropriately consider the overestimated barrier heights for
diffusion.
-Indeed the cut-off effect increases if the system is driven away from
-the equilibrium (such as by modeling IBS). Since this is to some
+Indeed, the cut-off effect increases if the system is driven away from
+the equilibrium, such as it is the case in IBS. Since this is to some
extent cured by increasing the simulation temperature, the work-around
is particularly helpful for short range potentials.
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