From cb6629dfbbe9aaf6a70228e7e9084303686a8f73 Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 28 Sep 2010 16:44:20 +0200 Subject: [PATCH] very first alpha of paper 3 --- posic/publications/sic_prec.tex | 32 ++++++++++++-------------------- 1 file changed, 12 insertions(+), 20 deletions(-) diff --git a/posic/publications/sic_prec.tex b/posic/publications/sic_prec.tex index 614be92..33e0708 100644 --- a/posic/publications/sic_prec.tex +++ b/posic/publications/sic_prec.tex @@ -109,9 +109,7 @@ Integration of equations of motion is realized by the velocity Verlet algorithm\ For structural relaxation of defect structures the same algorith is used with the temperature set to 0 K. The formation energy $E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\text{C}}$ of a defect configuration is defined by chosing SiC as a particle reservoir for the C impurity, i.e. the chemical potentials are determined by the cohesive energies of a perfect Si and SiC supercell after ionic relaxation. -Migration and recombination pathways have been investigated utilizing the constraint conjugate gradient relaxation technique (CRT)\cite{kaukonen98}. -The binding energy of a defect pair is given by the difference of the formation energy of the complex and the sum of the two separated defect configurations. -Accordingly, energetically favorable configurations show binding energies below zero while non-interacting isolated defects result in a binding energy of zero. +Migration and recombination pathways have been investigated utilizing the constraint conjugate gradient relaxation technique\cite{kaukonen98}. \section{Results} @@ -337,7 +335,7 @@ For both structures the C atom appears to reside on a substitutional rather than However, huge amount of damage hampers identification. The alignment of the investigated structures to the c-Si host is lost in many cases, which suggests the necissity of much more time for structural evolution to maintain the topotaptic orientation of the precipitate. -\section{Discussion} +\section{Summary and discussion} Investigations are targeted on the initially stated controversy of SiC precipitation, i.e. whether precipitation occurs abrubtly after ehough C$_{\text{i}}$ agglomerated or a successive agglomeration of C$_{\text{s}}$ on usual Si lattice sites (and Si$_{\text{i}}$) followed by a contraction into incoherent SiC. Results of a previous ab initio study on defects and defect combinations in C implanted Si\cite{zirkelbach10b} sugeest C$_{\text{s}}$ to play a decisive role in the precipitation of SiC in Si. @@ -362,11 +360,17 @@ However, we observed a phase tranisiton of the C$_{\text{i}}$-dominated into a c The amount of substitutionally occupied C atoms increases with increasing temperature. Entropic contributions are assumed to be responsible for these structures at eleveated temperatures that deviate from the ground state at 0 K. Indeed, in a previous ab initio MD simulation\cite{zirkelbach10b} performed at \unit[900]{$^{\circ}$C} we observed the departing of a Si$_{\text{i}}$ \hkl<1 1 0> DB located next to a C$_{\text{s}}$ atom instead of a recombination into the ground state configuration, i.e. a C$_{\text{i}}$ \hkl<1 0 0> DB. -Ci to Cs by increased temperatures ...\cite{eichhorn99} -Increased temperatures during implantation more efficient than postannealing methods, which reflects the present problems of low temperature and low time strcutural evolution ...\cite{eichhorn02} -C-C for low temperatures, postannealing no that efficient as for high C implantations ...\cite{deguchi92} -Thus, we propose an increased participation of C$_{\text{s}}$ already in the initial stages of the precipitation process. +% postannealing less efficient than hot implantation +Experimental studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates\cite{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. +We assume this 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 therefor 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 aplicable 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. @@ -380,18 +384,6 @@ However, agglomeration and rearrangement is enabled by mobile C$_{\text{i}}$, wh 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. -\section{Summary} - -To conclude, we have shown that ab initio calculations on interstitial carbon in silicon are very close to the results expected from experimental data. -The calculations presented in this work agree well with other theoretical results. -So far, the best quantitative agreement with experimental findings has been achieved concerning the interstitial carbon mobility. -For the first time, we have shown that the bond-centered configuration indeed constitutes a real local minimum configuration resulting in a net magnetization if spin polarized calculations are performed. -Classical potentials, however, fail to describe the selected processes. -This has been shown to have two reasons, i.e. the overestimated barrier of migration due to the artificial interaction cut-off on the one hand, and on the other hand the lack of quantum-mechanical effects which are crucial in the problem under study. -% ref mod: language - being investigated -%In order to get more insight on the SiC precipitation mechanism, further ab initio calculations are currently investigated. -In order to get more insight on the SiC precipitation mechanism, further ab initio calculations are currently being performed. - % ---------------------------------------------------- \section*{Acknowledgment} We gratefully acknowledge financial support by the Bayerische Forschungsstiftung (DPA-61/05) and the Deutsche Forschungsgemeinschaft (DFG SCHM 1361/11). -- 2.20.1