-For dumbbells oriented along the \hkl<1 1 0> direction and the assumption that there is the possibility of free orientation, an interaction energy proportional to the reciprocal cube of the distance in the far field regime is found.
-These findings support the assumption of the C-Si dumbbell agglomeration proposed by the precipitation model.
-
-Next to the C-Si \hkl<1 0 0> dumbbell interstitial configuration, in which the C atom is sharing a Si lattice site with the corresponding Si atom the C atom could occupy the site of the Si atom, which in turn forms a Si self-interstitial.
-Combinations of substitutional C and a \hkl<1 1 0> Si self-interstitial, which is the ground state configuration for a Si self-interstitial and, thus, assumed to be the energetically most favorable configuration for combined structures, show formation energies 0.5 eV to 1.5 eV greater than that of the C-Si \hkl<1 0 0> interstitial configuration, which remains the energetically most favorable configuration.
-However, the binding energy of substitutional C and the Si self-interstitial quickly drops to zero already for short separations indicating a low interaction capture radius.
-Thus, due to missing attractive interaction forces driving the system to form C-Si \hkl<1 0 0> dumbbell interstitial complexes substitutional C, while thermodynamically not stable, constitutes a most likely configuration occuring in IBS, a process far from equlibrium.
-
-Due to the low interaction capture radius substitutional C can be treated independently of the existence of separated Si self-interstitials.
-This should be also true for combinations of C-Si interstitials next to a vacancy and a further separated Si self-interstitial excluded from treatment, which again is a conveivable configuration in IBS.
-By combination of a \hkl<1 0 0> dumbbell with a vacancy in the absence of the Si self-interstitial it is found that the configuration of substitutional carbon occupying the vacant site is the energetically most favorable configuration.
-Low migration barriers are necessary to obtain this configuration and in contrast comparatively high activation energies necessary for the reverse process.
-Thus, carbon interstitials and vacancies located close together are assumed to end up in such a configuration in which the carbon atom is tetrahedrally coordinated and bound to four silicon atoms as expected in silicon carbide.
-
-While first results support the proposed precipitation model the latter suggest the formation of silicon carbide by succesive creation of substitutional carbon instead of the agglomeration of C-Si dumbbell interstitials followed by an abrupt transition.
-Prevailing conditions in the IBS process at elevated temperatures and the fact that IBS is a nonequilibrium process reinforce the possibility of formation of substitutional C instead of the thermodynamically stable C-Si dumbbell interstitials predicted by simulations at zero Kelvin.
+For dumbbells oriented along the \hkl<1 1 0> bond chain and the assumption that there is the possibility of free orientation, an interaction energy proportional to the reciprocal cube of the distance in the far field regime is found.
+These findings support the assumption of the \ci{} DB agglomeration.
+%
+The ground state configuration is found to consist of a C-C bond, which is responsible for the vast gain in energy.
+However, based on investigations of possible migration pathways, these structures are less likely to arise than structures, in which both C atoms are interconnected by another Si atom, which is due to high activation energies of the respective pathways or alternative pathways featuring less high activation energies, which, however, involve intermediate unfavorable configurations.
+Thus, agglomeration of C$_{\text{i}}$ is expected while the formation of C-C bonds is assumed to fail to appear by thermally activated diffusion processes.
+
+In contrast, C$_{\text{i}}$ and vacancies are found to efficiently react with each other exhibiting activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} resulting in stable C$_{\text{s}}$ configurations.
+In addition, a highly attractive interaction exhibiting a large capture radius, effective independent of the orientation and the direction of separation of the defects, is observed.
+Accordingly, the formation of C$_{\text{s}}$ is very likely to occur.
+Comparatively high energies necessary for the reverse process reveal this configuration to be extremely stable.
+Thus, C interstitials and vacancies located close together are assumed to end up in such a configuration, in which the C atom is tetrahedrally coordinated and bound to four Si atoms as expected in SiC.
+
+Investigating configurations of C$_{\text{s}}$ and Si$_{\text{i}}$, formation energies higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB were obtained keeping up previously derived assumptions concerning the ground state of C$_{\text{i}}$ in otherwise perfect Si.
+However, a small capture radius is identified for the respective interaction that might prevent the recombination of defects exceeding a separation of \unit[0.6]{nm} into the ground state configuration.
+In addition, a rather small activation energy of \unit[0.77]{eV} allows for the formation of a C$_{\text{s}}$-Si$_{\text{i}}$ pair originating from the C$_{\text{i}}$ \hkl<1 0 0> DB structure by thermally activated processes.
+Thus, elevated temperatures might lead to thermodynamically unstable configurations of C$_{\text{s}}$ and a remaining Si atom in the near interstitial lattice, which is supported by the result of an {\em ab initio} molecular dynamics run.
+%Thus, due to missing attractive interaction forces driving the system to form C-Si \hkl<1 0 0> dumbbell interstitial complexes substitutional C, while thermodynamically not stable, constitutes a most likely configuration occuring in IBS, a process far from equlibrium.
+
+% todo
+% maybe move above stuff to conclusion chapter, at least shorten!
+% see remember in sic chapter
+
+These findings allow to draw conclusions on the mechanisms involved in the process of SiC conversion in Si.
+Agglomeration of C$_{\text{i}}$ is energetically favored and enabled by a low activation energy for migration.
+Although ion implantation is a process far from thermodynamic equilibrium, which might result in phases not described by the Si/C phase diagram, i.e. a C phase in Si, high activation energies are believed to be responsible for a low probability of the formation of C-C clusters.
+
+In the context of the initially stated controversy present in the precipitation model, these findings suggest an increased participation of C$_{\text{s}}$ already in the initial stage due to its high probability of incidence.
+In addition, thermally activated, C$_{\text{i}}$ might turn into C$_{\text{s}}$.
+The associated emission of Si$_{\text{i}}$ serves two needs: as a vehicle for other C$_{\text{s}}$ atoms and as a supply of Si atoms needed elsewhere to form the SiC structure.
+As for the vehicle, Si$_{\text{i}}$ is believed to react with C$_{\text{s}}$ turning it into highly mobile C$_{\text{i}}$ again, allowing for the rearrangement of the C atom.
+The rearrangement is crucial to end up in a configuration of C atoms only occupying substitutionally the lattice sites of one of the two fcc lattices that build up the diamond lattice.
+On the other hand, the conversion of some region of Si into SiC by \cs{} is accompanied by a reduction of the volume since SiC exhibits a \unit[20]{\%} smaller lattice constant than Si.
+The reduction in volume is compensated by excess Si$_{\text{i}}$ serving as building blocks for the surrounding Si host or a further formation of SiC.
+
+To conclude, precipitation occurs by successive agglomeration of C$_{\text{s}}$.
+However, the agglomeration and rearrangement of C$_{\text{s}}$ is only possible by mobile C$_{\text{i}}$, which has to be present at the same time.
+Accordingly, the process is governed by both, C$_{\text{s}}$ accompanied by Si$_{\text{i}}$ as well as C$_{\text{i}}$.
+It is worth to mention that there is no contradiction to results of the HREM studies \cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}.
+Regions showing dark contrasts in an otherwise undisturbed Si lattice are attributed to C atoms in the interstitial lattice.
+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 regions are either composed of stretched coherent SiC and interstitials or of already contracted incoherent SiC surrounded by Si and interstitials, 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.
+
+Furthermore, the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate is satisfied by the mechanism of successive positioning of C$_{\text{s}}$.
+In contrast, 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.
+
+%Prevailing conditions in the IBS process at elevated temperatures and the fact that IBS is a nonequilibrium process reinforce the possibility of formation of substitutional C instead of the thermodynamically stable C-Si dumbbell interstitials predicted by simulations at zero Kelvin.
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