\chapter{Summary and conclusions}
\label{chapter:summary}
+{\setlength{\parindent}{0pt}
\paragraph{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.
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.
+This is likewise suggested by IBS experiments utilizing implantation temperatures of \degc{550} followed by incoherent lamp annealing at temperatures as high as \degc{1405} required for the C segregation due to the stability of \cs{} \cite{reeson87}.
+% 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}.
+%
+Particularly 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.
+%
+%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}.
+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.
+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}.
+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.
+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.
-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.
-
-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 initio study on defects in C implanted Si\cite{zirkelbach11a}, 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.
+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.
+%
+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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