\chapter{Summary and conclusions}
\label{chapter:summary}
-\paragraph{To summarize,}
+{\setlength{\parindent}{0pt}
+%\paragraph{To summarize,}
+{\bf To summarize},
in a short review of the C/Si compound and the fabrication of the technologically promising semiconductor SiC by IBS, two controversial assumptions of the precipitation mechanism of 3C-SiC in c-Si are elaborated.
+}
These propose the precipitation of SiC by agglomeration of \ci{} DBs followed by a sudden formation of SiC and otherwise a formation by successive accumulation of \cs{} via intermediate stretched SiC structures, which are coherent to the Si lattice.
To solve this controversy and contribute to the understanding of SiC precipitation in c-Si, a series of atomistic simulations is carried out.
-In the first part, intrinsic and C related point defects in c-Si as well as some selected diffusion processes of the C defect are investigated by means of first-principles quatum-mechanical calculations based on DFT and classical potential calculations employing a Tersoff-like analytical bond order potential.
+In the first part, intrinsic and C related point defects in c-Si as well as some selected diffusion processes of the C defect are investigated by means of first-principles quantum-mechanical calculations based on DFT and classical potential calculations employing a Tersoff-like analytical bond order potential.
Shortcomings of the computationally efficient though less accurate classical potential approach compared to the quantum-mechanical treatment are revealed.
The study proceeds investigating combinations of defect structures and related diffusion processes exclusively by the first-principles method.
The applicability of the utilized bond order potential for subsequent MD simulations is discussed.
Defects of C in Si are well described by both methods.
The \ci{} \hkl<1 0 0> DB is found to constitute the most favorable interstitial configuration in agreement with several theoretical \cite{burnard93,leary97,dal_pino93,capaz94,jones04} and experimental \cite{watkins76,song90} investigations.
Almost equal formation energies are predicted by the EA and DFT calculations for this defect.
-A small discrepancy in the resulting equilibrium structure with respect to the DFT method exists due to missing quantum-mechanical effects within the calssical treatment.
+A small discrepancy in the resulting equilibrium structure with respect to the DFT method exists due to missing quantum-mechanical effects within the classical treatment.
The high formation energies of the tetrahedral and hexagonal configuration obtained by classical potentials act in concert with the fact that these configurations are found unstable by the first-principles description.
The BC configuration turns out to be unstable relaxing into the \ci{} \hkl<1 1 0> DB configuration within the EA approach.
-This is supported by another {\em ab inito} study \cite{capaz94}, which in turn finds the BC configuration to be an intermediate saddle point structure of a possible migration path, which is \unit[2.1]{eV} higher than the \ci{} \hkl<1 0 0> DB structure.
+This is supported by another {\em ab initio} study \cite{capaz94}, which in turn finds the BC configuration to be an intermediate saddle point structure of a possible migration path, which is \unit[2.1]{eV} higher than the \ci{} \hkl<1 0 0> DB structure.
By quantum-mechanical calculations performed in this work, however, it turns out that the BC configuration constitutes a real local minimum if the electron spin is fully accounted for.
Indeed, spin polarization is absolutely necessary for the BC configuration resulting in a net magnetization of two electrons accompanied by a reduction of the total energy by \unit[0.3]{eV}.
The resulting spin up density is localized in a torus around the C perpendicular to the linear Si-C-Si bond.
Based on the above findings, it is concluded that modeling of the SiC precipitation by the EA potential might lead to trustable results.
Quantum-mechanical investigations of the mobility of the \ci{} \hkl<1 0 0> DB yield a migration barrier of \unit[0.9]{eV}, which excellently agrees to experimental values ranging from \unit[0.70]{eV} to \unit[0.87]{eV} \cite{lindner06,song90,tipping87}.
-The respective path correpsonds to a \ci{} \hkl[0 0 -1] DB migrating towards the next neighbored Si atom located in \hkl[1 1 -1] direction forming a \ci{} \hkl[0 -1 0] DB.
+The respective path corresponds to a \ci{} \hkl[0 0 -1] DB migrating towards the next neighbored Si atom located in \hkl[1 1 -1] direction forming a \ci{} \hkl[0 -1 0] DB.
The identified migration path involves a change in orientation of the DB.
-Thus, the same path explains the experimentally determined activation energies for reorientation of the DB ranging from \unit[0.77]{eV} \cite{watkins76} upto \unit[0.88]{eV} \cite{song90}.
+Thus, the same path explains the experimentally determined activation energies for reorientation of the DB ranging from \unit[0.77]{eV} \cite{watkins76} up to \unit[0.88]{eV} \cite{song90}.
Investigations based on the EA bond order potential suggest a migration involving an intermediate \ci{} \hkl<1 1 0> DB configuration.
Although different, starting and final configuration as well as the change in orientation of the \hkl<1 0 0> DB are equal to the identified pathway by the {\em ab initio} calculations.
However, barrier heights, which are overestimated by a factor of 2.4 to 3.5 depending on the character of migration, i.e. a single step or two step process, compared to the DFT results, are obtained.
Results of combinations of \ci{} and \cs{} revealed two additional metastable structures different to these obtained by a naive relaxation.
Small displacements result in a structure of a \hkl<1 1 0> C-C DB and in a structure of a twofold coordinated Si atom located in between two substitutional C atoms residing on regular Si lattice sites.
-Both structures are lower in energy compared to the respetive counterparts.
+Both structures are lower in energy compared to the respective counterparts.
These results, for the most part, compare well with results gained in previous studies \cite{leary97,capaz98,liu02} and show an astonishingly good agreement with experiment \cite{song90_2}.
Again, spin polarized calculations are revealed necessary.
A net magnetization of two electrons is observed for the \hkl<1 1 0> C-C DB configuration, which constitutes the ground state.
Limitations of the MD technique in addition to overestimated bond strengths due to the short range potential are identified to be responsible.
The approach of using increased temperatures during C insertion is followed to work around this problem termed {\em potential enhanced slow phase space propagation}.
-Higher temperatures are justified for severeal reasons.
-Elevated temperatures are expected to compensate the overestimated diffusion barriers and accelerate strcutural evolution.
-In addition, formation of SiC is also observed at higher implantation temperatures \cite{nejim95,lindner01} and temperatures in the implantation region is definetly higher than the temperature determined experimentally at the surface of the sample.
+Higher temperatures are justified for several reasons.
+Elevated temperatures are expected to compensate the overestimated diffusion barriers and accelerate structural evolution.
+In addition, formation of SiC is also observed at higher implantation temperatures \cite{nejim95,lindner01} and temperatures in the implantation region is definitely higher than the temperature determined experimentally at the surface of the sample.
Furthermore, the present study focuses on structural transitions in a system far from equilibrium.
No significant change is observed for high C concentrations at increased temperatures.
The amorphous phase is maintained.
The huge amount of damage hampers identification of investigated structures, which in many cases lost the alignment to the c-Si host.
-Obviously, inccorporation of a high quantity of C into a small volume within a short period of time creates damage, which decelerates structural evolution.
+Obviously, incorporation of a high quantity of C into a small volume within a short period of time creates damage, which decelerates structural evolution.
For the low C concentrations, time scales are still too low to observe C agglomeration.
However, a phase transition of the C$_{\text{i}}$-dominated into a clearly C$_{\text{s}}$-dominated structure is observed.
The amount of \cs{} increases with increasing temperature.
\si{} is often found in the direct surrounding.
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}
+%\paragraph{Conclusions}
+{\bf Conclusions}
concerning the SiC conversion mechanism are derived from results of both, first-principles and classical potential calculations.
Although classical potential MD calculations fail to directly simulate the precipitation of SiC, obtained results, on the one hand, reinforce previous findings of the first-principles investigations and, on the other hand, allow further conclusions on the SiC precipitation in Si.
Initially, quantum-mechanical investigations suggest agglomeration of \ci{} defects that form energetically favorable configurations by an effective stress compensation.
Low barriers of migration are found except for transitions into the ground-state configuration, which is composed of a strong C-C bond.
-Thus, agglomeration of \ci{} in the absence of C clsutering is expected.
-These initial results suggest a conversion mechansim based on the agglomeration of \ci{} defects followed by a sudden precipitation once a critical size is reached.
-However, subsequent investigations of structures that are particularly conceivable under conditions prevalant in IBS and at elevated temperatures show \cs{} to occur in all probability.
+Thus, agglomeration of \ci{} in the absence of C clustering is expected.
+These initial results suggest a conversion mechanism based on the agglomeration of \ci{} defects followed by a sudden precipitation once a critical size is reached.
+However, subsequent investigations of structures that are particularly conceivable under conditions prevalent in IBS and at elevated temperatures show \cs{} to occur in all probability.
The transition from the ground state of a single C atom incorporated into otherwise perfect c-Si, i.e. the \ci{} \hkl<1 0 0> DB, into a configuration of \cs{} next to a \si{} atom exhibits an activation energy lower than the one for the diffusion of the highly mobile \ci{} defect.
Considering additionally the likewise lower diffusion barrier of \si{}, configurations of separated \cs{} and \si{} will occur in all probability.
-This is reinforced by the {\em ab initio} MD run at non-zero temperature, which shows structures of separating instead of recombining \cs{} and \si{} defetcs.
+This is reinforced by the {\em ab initio} MD run at non-zero temperature, which shows structures of separating instead of recombining \cs{} and \si{} defects.
This suggests increased participation of \cs{} already in the initial stages of the implantation process.
The highly mobile \si{} is assumed to constitute a vehicle for the rearrangement of other \cs{} atoms onto proper lattice sites, i.e. lattice sites of one of the the two fcc lattices composing the diamond structure.
-This way, stretched SiC strcutures, which are coherently aligned to the c-Si host, are formed by agglomeration of \cs.
+This way, stretched SiC structures, which are coherently aligned to the c-Si host, are formed by agglomeration of \cs.
Precipitation into an incoherent and partially strain-compensated SiC nucleus occurs once the increasing strain energy surpasses the interfacial energy of the incoherent 3C-SiC precipitate and the c-Si substrate.
As already assumed by Nejim~et~al.~\cite{nejim95}, \si{} serves as supply for subsequently implanted C atoms to form further SiC in the resulting free space due to the accompanied volume reduction.
%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 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.
+Due to this, the occurrence 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 of the strongly damaged region, can be mapped to a system of low temperature, which lacks the kinetic energy required for the restructuring process.
This is assumed to be related to the problem of slow structural evolution encountered in the high C concentration simulations.
%
%Considering the efficiency of high implantation temperatures, experimental arguments exist, which point to the precipitation mechanism based on the agglomeration of \cs.
-More substantially, understoichiometric implantations at room temperature into preamorphized Si followed by a solid phase epitaxial regrowth step at \degc{700} result in Si$_{1-x}$C$_x$ layers in the diamond cubic phase with C residing on substitutional Si lattice sites \cite{strane93}.
+More substantially, understoichiometric implantations at room temperature into preamorphized Si followed by a solid-phase epitaxial regrowth step at \degc{700} result in Si$_{1-x}$C$_x$ layers in the diamond cubic phase with C residing on substitutional Si lattice sites \cite{strane93}.
The strained structure is found to be stable up to \degc{810}.
Coherent clustering followed by precipitation is suggested if these structures are annealed at higher temperatures.
%
-Similar, implantations of an understoichiometric dose into c-Si 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.
+Similar, implantations of an understoichiometric dose into c-Si 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 observed for as-implanted samples \cite{lindner99,lindner01} in implantations performed at \unit[450]{$^{\circ}$C}.
-Thus, implanted C is likewise expected to occupy substitutionally regular Si lattice sites right from the start for implantations into c-Si at elevated temperatures.
+According to this, implanted C is likewise expected to occupy substitutionally regular Si lattice sites right from the start for implantations into c-Si at elevated temperatures.
%
%
% 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.
+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 satisfies 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
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.
+In any case, the precipitation mechanism by accumulation of \cs{} obviously satisfies 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 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: as a vehicle to rearrange the \cs{} atoms, as a building block for the surrounding Si host or further SiC and for strain compensation, either in the stretched SiC structure or at the interface of the SiC precipitate and the Si matrix.
-% todo \si reduced interfacial energy
-%
-Results of the atomistic simulation study indicating the respective precipitation mechanism conform well with other experimental findings.
+Elevated temperatures result in increased entropic contributions to structural formation.
+Moreover, conditions prevalent in IBS deviate the system from thermodynamic equilibrium.
+Thereby, C$_{\text{i}}$ is enabled to turn into C$_{\text{s}}$ accompanied by the emission of Si$_{\text{i}}$.
+\si{}, which is likewise existent, serves several needs: as a vehicle to rearrange the \cs{} atoms, as a building block for the surrounding Si host or further SiC and for strain compensation.
+The \si{} vehicle turns \cs{} into highly mobile \ci.
+This way, C can be easily rearranged in order to end up in a configuration of C atoms that occupy substitutionally the lattice sites of one of the fcc lattices of the diamond structure.
+Stretched SiC structures arise, which are coherently aligned to the Si matrix.
+\si{} is believed to likewise compensate the tensile strain within these structures.
+This is followed by the precipitation into incoherent 3C-SiC once the strain energy of the coherent structure surpasses the interfacial energy of the incoherent precipitate and the c-Si substrate.
+The associated volume reduction is compensated by \si{} that may serve as a supply for further SiC or as a building block for the surrounding Si host and likewise reduce existing strain in the interface region.
%
-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.
-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 amounts of strain are assumed to reside in the coherent as well as at the surface of the incoherent structure.
-Si$_{\text{i}}$ serves either as a supply of Si atoms needed in the surrounding of the contracted precipitates or as an 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 and Si$_{\text{i}}$ located in the vicinity.
+Results of the atomistic simulation study that indicate the respective precipitation mechanism conform well with other experimental findings.
+By verification, the derived conclusions with respect to the precipitation mechanism are reinforced.
+Furthermore, experimental results that suggest a precipitation mechanism based on the agglomeration of \ci{} do not conflict with the proposed model of precipitation as concluded in the present study.
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