From 537c302265dd73722c04f8b867ba58b090e0f8b9 Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 22 Sep 2010 16:32:02 +0200 Subject: [PATCH] almost finished results --- posic/publications/sic_prec.tex | 49 +++++++++++++++++++++++++++++---- 1 file changed, 43 insertions(+), 6 deletions(-) diff --git a/posic/publications/sic_prec.tex b/posic/publications/sic_prec.tex index 0524c1a..8a6d36d 100644 --- a/posic/publications/sic_prec.tex +++ b/posic/publications/sic_prec.tex @@ -278,20 +278,40 @@ Due to the potential enhanced problem of slow phase space propagation, pushing t Instead higher temperatures are utilized to compensate overestimated diffusion barriers. These are overestimated by a factor of 2.4 to 3.5. Scaling the absolute temperatures accordingly results in maximum temperatures of \unit[1460-2260]{$^{\circ}$C}. -Since melting already occurs shortly below the melting point of the potetnial (2450 K) due to the defects, a maximum temperature of \unit[2050]{$^{\circ}$C} is used. -Fig.~\ref{fig:tot} shows the resulting bonds for various temperatures. +Since melting already occurs shortly below the melting point of the potetnial (2450 K)\cite{albe_sic_pot} due to the presence of defects, a maximum temperature of \unit[2050]{$^{\circ}$C} is used. + +Fig.~\ref{fig:tot} shows the resulting radial distribution functions for various temperatures. \begin{figure} \begin{center} \includegraphics[width=\columnwidth]{../img/tot_pc_thesis.ps}\\ \includegraphics[width=\columnwidth]{../img/tot_pc3_thesis.ps}\\ \includegraphics[width=\columnwidth]{../img/tot_pc2_thesis.ps} \end{center} -\caption{Radial distribution function for Si-C (top), Si-Si (center) and C-C (bottom) pairs for the C insertion into $V_1$ at elevated temperatures. In the latter case dashed arrows mark C-C distances occuring from C$_{\text{i}}$ \hkl<1 0 0> DB combinations, solid arrows mark C-C distances of pure C$_{\text{s}}$ combinations and the dashed line marks C-C distances of a C$_{\text{i}}$ and C$_{\text{s}}$ combination.} +\caption{Radial distribution function for Si-C (top), Si-Si (center) and C-C (bottom) pairs for the C insertion into $V_1$ at elevated temperatures. For the Si-C distribution resulting Si-C distances of a C$_{\text{s}}$ configuration are plotted. In the C-C distribution dashed arrows mark C-C distances occuring from C$_{\text{i}}$ \hkl<1 0 0> DB combinations, solid arrows mark C-C distances of pure C$_{\text{s}}$ combinations and the dashed line marks C-C distances of a C$_{\text{i}}$ and C$_{\text{s}}$ combination.} \label{fig:tot} \end{figure} -Obviously a phase transition occurs ... WEITER - -Barfoo ... +The first noticeable and promising change observed for the Si-C bonds is the successive decline of the artificial peak at the cut-off distance with increasing temperature. +Obviously enough kinetic energy is provided to affected atoms that are enabled to escape the cut-off region. +Additionally a more important structural change was observed, which is illustrated in the two shaded areas of the graph. +Obviously the structure obtained at \unit[450]{$^{\circ}$C}, which was found to be dominated by C$_{\text{i}}$, transforms into a C$_{\text{s}}$ dominated structure with increasing temperature. +Comparing the radial distribution at \unit[2050]{$^{\circ}$C} to the resulting bonds of C$_{\text{s}}$ in c-Si excludes all possibility of doubt. + +The phase transformation is accompanied by an arising Si-Si peak at \unit[0.325]{nm}, which corresponds to the distance of second next neighbored Si atoms alonga \hkl<1 1 0> boind chain with C$_{\text{s}}$ inbetween. +Since the expected distance of these Si pairs in 3C-SiC is \unit[0.308]{nm} the existing SiC structures embedded in the c-Si host are stretched. + +According to the C-C radial distribution agglomeration of C fails to appear even for elevated temperatures as can be seen on the total amount of C pairs within the investigated separation range, wich does not change significantly. +However, a small decrease in the amount of next neighboured C pairs can be observed with increasing temperature. +This high temperature behavior is promising since breaking of these diomand- and graphite-like bonds is mandatory for the formation of 3C-SiC. +Obviously acceleration of the dynamics occured by supplying additional kinetic energy. +A slight shift towards higher distances can be observed for the maximum located shortly above \unit[0.3]{nm}. +Arrows with dashed lines mark C-C distances resulting from C$_{\text{i}}$ \hkl<1 0 0> DB combinations while arrows with solid lines mark distances arising from combinations of C$_{\text{s}}$. +The continuous dashed line corresponds to the distance of C$_{\text{s}}$ and a next neighboured C$_{\text{i}}$ DB. +Obviously the shift of the peak is caused by the advancing transformation of the C$_{\text{i}}$ DB into the C$_{\text{s}}$ defect. +Quite high g(r) values are obtained for distances inbetween the continuous dashed line and the first arrow with a solid line. +For the most part these structures can be identified as configurations of C$_{\text{s}}$ with either another C atom that basically occupies a Si lattice site but is displaced by a Si interstitial residing in the very next surrounding or a C atom that nearly occupies a Si lattice site forming a defect other than the \hkl<1 0 0>-type with the Si atom. +Again, this is a quite promising result since the C atoms are taking the appropriate coordination as expected in 3C-SiC. + +Fig.~\ref{fig:v2} displays the radial distribution for high C concentrations. \begin{figure} \begin{center} \includegraphics[width=\columnwidth]{../img/12_pc_thesis.ps}\\ @@ -300,9 +320,26 @@ Barfoo ... \caption{Radial distribution function for Si-C (top) and C-C (bottom) pairs for the C insertion into $V_2$ at elevated temperatures.} \label{fig:v2} \end{figure} +The amorphous SiC-like phase remains. +No significant change in structure is observed. +However, the decrease of the cut-off artifact and slightly sharper peaks observed with increasing temperature, in turn, indicate a slight acceleration of the dynamics realized by the supply of kinetic energy. +However, it is not sufficient to enable the amorphous to crystalline transition. +In contrast, even though next neighbored C bonds could be partially dissolved in the system exhibiting low C concentrations the amount of next neighbored C pairs even increased in the latter case. +Moreover the peak at \unit[0.252]{nm}, which gets slightly more distinct, equals the second next neighbor distance in diamond and indeed is made up by a structure of two C atoms interconnected by a third C atom. +Obviously conducive rearrangements of C are hindered in a system, in which high amounts of C are incoorporated within a too short period of time. +Thus, for these systems even larger time scales are necessary for an amorphous to crystalline transition and structural evolution in general, which is not accessible by the traditional MD technique. +% maybe put description of bonds in here ... + + + \section{Discussion} + +Sii stress compensation ... + +Both, low and high, acceleration not enough to either observe C agglomeration or amorphous to crystalline transition ... + The first-principles results are in good agreement to previous work on this subject\cite{burnard93,leary97,dal_pino93,capaz94}. The C-Si \hkl<1 0 0> dumbbell interstitial is found to be the ground state configuration of a C defect in Si. The lowest migration path already proposed by Capaz et~al.\cite{capaz94} is reinforced by an additional improvement of the quantitative conformance of the barrier height calculated in this work (\unit[0.9]{eV}) with experimentally observed values (\unit[0.70]{eV} -- \unit[0.87]{eV})\cite{lindner06,song90,tipping87}. -- 2.20.1