X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Fthesis%2Fsummary_outlook.tex;h=172572717d7bf1a410cc84600d232e8040ccd736;hb=1c9d7b21ee314037c34aefef556255eedf8eb0a1;hp=66facbe1d81c5c4bc94525ff735d28e1167a614d;hpb=2c91598c223e213c62f9a4356f8db5ed460d8a40;p=lectures%2Flatex.git

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-\chapter{Summary and Outlook}
+\chapter{Summary and conclusions}
 \label{chapter:summary}
 
+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.
+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.
+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.
+Conclusions on the precipitation based on the DFT results are drawn.
+In the second part, classical potential MD simulations are performed, which try to directly reproduce the precipitation.
+Next to the shortcomings of the potential, quirks inherent to MD are discussed and a workaround is proposed.
+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.
+
+Quantum-mechanical results of intrinsic point defects in Si are in good agreement to previous theoretical work on this subject \cite{leung99,al-mushadani03}.
+The \si{} \hkl<1 1 0> DB defect is reproduced as the ground-state configuration followed by the hexagonal and tetrahedral defect.
+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.
+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.
+For the vacancy, the net spin up electron density is localized in caps at the four surrounding Si atoms directed towards the vacant site.
+Results obtained by calculations utilizing the classical EA potential yield formation energies, which are of the same order of magnitude.
+However, EA predicts the tetrahedral configuration to be most stable.
+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.
+Furthermore, the hexagonal defect structure is not stable opposed to results of the authors of the potential \cite{albe_sic_pot}.
+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.
+Obviously, the authors did not check the structure after relaxation still assuming a hexagonal configuration.
+The actual structure equals the tetrahedral configuration, which is slightly displaced along the three coordinate axes.
+Variations exist with displacements along two or a single \hkl<1 0 0> direction indicating a potential artifact.
+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.
+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.
+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}.
+
+HIER WEITER
+
+Defects of C in c-Si are well described by both methods.
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+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.
+