1 \chapter{Summary and conclusions}
2 \label{chapter:summary}
4 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.
5 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.
6 To solve this controversy and contribute to the understanding of SiC precipitation in c-Si, a series of atomistic simulations is carried out.
7 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.
8 Shortcomings of the computationally efficient though less accurate classical potential approach compared to the quantum-mechanical treatment are revealed.
9 The study proceeds investigating combinations of defect structures and related diffusion processes exclusively by the first-principles method.
10 The applicability of the utilized bond order potential for subsequent MD simulations is discussed.
11 Conclusions on the precipitation based on the DFT results are drawn.
12 In the second part, classical potential MD simulations are performed, which try to directly reproduce the precipitation.
13 Next to the shortcomings of the potential, quirks inherent to MD are discussed and a workaround is proposed.
14 Although direct formation of SiC fails to appear, the obtained results indicate a mechanism of precipitation, which is consistent with previous quantum-mechanical conclusions as well as experimental findings.
16 Quantum-mechanical results of intrinsic point defects in Si are in good agreement to previous theoretical work on this subject \cite{leung99,al-mushadani03}.
17 The \si{} \hkl<1 1 0> DB defect is reproduced as the ground-state configuration followed by the hexagonal and tetrahedral defect.
18 Spin polarized calculations are required for the \si{} \hkl<1 0 0> DB and vacancy whereas no other of the investigated intrinsic defects is affected.
19 For the \si{} \hkl<1 0 0> DB, the net spin up density is localized in two caps at each of the two DB atoms perpendicularly aligned to the bonds to the other two Si atoms.
20 For the vacancy, the net spin up electron density is localized in caps at the four surrounding Si atoms directed towards the vacant site.
21 Results obtained by calculations utilizing the classical EA potential yield formation energies, which are of the same order of magnitude.
22 However, EA predicts the tetrahedral configuration to be most stable.
23 The particular problem is due to the cut-off and the fact that the second neighbors are only slightly more distant than the first neighbors within the tetrahedral configuration.
24 Furthermore, the hexagonal defect structure is not stable opposed to results of the authors of the potential \cite{albe_sic_pot}.
25 The obtained structure after relaxation, which is similar to the tetrahedral configuration, has a formation energy equal to the one given by the authors for the hexagonal one.
26 Obviously, the authors did not check the structure after relaxation still assuming a hexagonal configuration.
27 The actual structure equals the tetrahedral configuration, which is slightly displaced along the three coordinate axes.
28 Variations exist with displacements along two or a single \hkl<1 0 0> direction indicating a potential artifact.
29 However, finite temperature simulations are not affected by this artifact due to a low activation energy necessary for a transition into the energetically more favorable tetrahedral configuration.
30 Next to the known problem of the underestimated formation energy of the tetrahedral configuration \cite{tersoff90}, the energetic sequence of the defect structures is well reproduced by the EA calculations.
31 Migration barriers of \si{} investigated by quantum-mechanical calculations are found to be of the same order of magnitude than values derived in other ab initio studies \cite{bloechl93,sahli05}.
33 Defects of C in Si are well described by both methods.
34 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.
35 Almost equal formation energies are predicted by the EA and DFT calculations for this defect.
36 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.
37 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.
38 The BC configuration turns out to be unstable relaxing into the \ci{} \hkl<1 1 0> DB configuration within the EA approach.
39 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.
40 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.
41 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}.
42 The resulting spin up density is localized in a torus around the C perpendicular to the linear Si-C-Si bond.
43 No other configuration is affected by spin polarization.
44 The underestimated formation energy of \cs{} is a definite drawback of the classical potential.
45 However, the creation of \cs{} is necessarily accompanied by a \si{} in a perfect Si crystal, in which a C atom is incorporated.
46 Fortunately, the energetics of combinations of \cs{} and \si{} are quite well described by the EA potential.
47 Thus, the underestimated formation energy does not pose a serious limitation.
48 Based on the above findings, it is concluded that modeling of the SiC precipitation by the EA potential might lead to trustable results.
50 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}.
51 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.
52 The identified migration path involves a change in orientation of the DB.
53 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}.
54 Investigations based on the EA bond order potential suggest a migration involving an intermediate \ci{} \hkl<1 1 0> DB configuration.
55 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.
56 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.
57 Obviously, the EA potential fails to describe \ci{} diffusion yielding a drastically overestimated activation energy, which has to be taken into account in subsequent investigations.
59 Quantum-mechanical investigations of two \ci{} defects of the \hkl<1 0 0>-type for varying separations and orientations state a rather attractive interaction between these interstitials.
60 Primiraly, energetically favorable configurations of two interstitials are found.
61 This is due to strain compensation enabled by the combination of such defects in certain orientations.
62 An interaction energy proportional to the reciprocal cube of the distance in the far field regime is found supporting the assumption of \ci{} DB agglomeration.
63 The energetically most favorable configuration consists of a C-C bond.
64 However, due to high activation energies of respective pathways or alternative pathways featuring less high activation energies, which, however, involve intermediate unfavorable configurations, this structure is less likely to arise than structures of C atoms that are interconnected by another Si atom.
65 Thus, agglomeration of C$_{\text{i}}$ is expected whereas the formation of C-C bonds is assumed to fail to appear by thermally activated diffusion processes.
70 % for c_s c_i combos ...
71 %Obtaind results for the most part compare well with results gained in previous studies \cite{leary97,capaz98,mattoni2002,liu02} and show an astonishingly good agreement with experiment \cite{song90}.
74 Experimental studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates \cite{kimura82,eichhorn02}.
75 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.
76 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.
77 % rt implantation + annealing
78 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}.
79 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}.
80 Implanted C is therefore expected to occupy substitutionally usual Si lattice sites right from the start.
82 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}.
83 Thermally activated, C$_{\text{i}}$ is enabled to turn into C$_{\text{s}}$ accompanied by Si$_{\text{i}}$.
84 The associated emission of Si$_{\text{i}}$ is needed for several reasons.
85 For the agglomeration and rearrangement of C, Si$_{\text{i}}$ is needed to turn C$_{\text{s}}$ into highly mobile C$_{\text{i}}$ again.
86 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.
87 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.
88 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.
90 It is, thus, concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.\cite{nejim95}.
91 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.
92 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$_{\text{i}}$.
93 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.
94 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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