X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Fpublications%2Fsic_prec.tex;h=860fe77659247fd3516ef7ac6b74f525717da0a1;hp=0524c1ab7e30831fe3502e38e8218c52db5002e1;hb=d0720ff0926e68d25a95f89a8f0f703799402754;hpb=2bd27ac8e684decc7ceb349ea7b2b220ba71efb0

diff --git a/posic/publications/sic_prec.tex b/posic/publications/sic_prec.tex
index 0524c1a..860fe77 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}\\
@@ -300,35 +320,53 @@ 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 C-C 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 processes that appear to be non-conducive are likewise accelerated in a system, in which high amounts of C are incoorporated within a short period of time, which is accompanied by a concurrent introduction of accumulating, for the reason of time non-degradable, damage.
+% non-degradable, non-regenerative, non-recoverable
+Thus, for these systems even larger time scales, which are not accessible within traditional MD, must be assumed for an amorphous to crystalline transition or structural evolution in general.
+% maybe put description of bonds in here ...
+Nevertheless, some results likewiese indicate the acceleration of other processes that, again, involve C$_{\text{s}}$.
+The increasingly pronounced Si-C peak at \unit[0.35]{nm} corresponds to the distance of a C and a Si atom interconnected by another Si atom.
+Additionally the C-C peak at \unit[0.31]{nm} corresponds to the distance of two C atoms bound to a central Si atom.
+For both structures the C atom appears to reside on a substitutional rather than an interstitial lattice site.
+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}
 
-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}.
-However, it turns out that the bond-centered configuration is not a saddle point configuration as proposed by Capaz et~al.\cite{capaz94} but constitutes a real local minimum if the electron spin is properly accounted for.
-A net magnetization of two electrons, which is already clear by simple molecular orbital theory considerations on the bonding of the sp hybridized C atom, is settled.
-By investigating the charge density isosurface it turns out that the two resulting spin up electrons are localized in a torus around the C atom.
-With an activation energy of \unit[0.9]{eV} the C$_{\text{i}}$ carbon interstitial can be expected to be highly mobile at prevailing temperatures in the process under investigation, i.e. IBS.
-
-We found that the description of the same processes fails if classical potential methods are used.
-Already the geometry of the most stable dumbbell configuration differs considerably from that obtained by first-principles calculations.
-The classical approach is unable to reproduce the correct character of bonding due to the deficiency of quantum-mechanical effects in the potential.
-%ref mod: language - energy / order 
-%Nevertheless, both methods predict the same type of interstitial as the ground state configuration, and also the order in energy of the remaining defects is reproduced fairly well.
-Nevertheless, both methods predict the same type of interstitial as the ground state configuration.
-Furthermore, the relative energies of the other defects are reproduced fairly well.
-From this, a description of defect structures by classical potentials looks promising.
-% ref mod: language - changed
-%However, focussing on the description of diffusion processes the situation is changing completely.
-However, focussing on the description of diffusion processes the situation has changed completely.
-Qualitative and quantitative differences exist.
-First of all, a different pathway is suggested as the lowest energy path, which again might be attributed to the absence of quantum-mechanical effects in the classical interaction model.
-Secondly, the activation energy is overestimated by a factor of 2.4 compared to the more accurate quantum-mechanical methods and experimental findings.
-This is attributed to the sharp cut-off of the short range potential.
-As already pointed out in a previous study\cite{mattoni2007} the short cut-off is responsible for overestimated and unphysical high forces of next neighbor atoms.
-The overestimated migration barrier, however, affects the diffusion behavior of the C interstitials.
-By this artifact the mobility of the C atoms is tremendously decreased resulting in an inaccurate description or even absence of the dumbbell agglomeration as proposed by the precipitation model.
+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.
+To support previous assumptions MD simulations, which are capable of modeling the necessary amount of atoms, i.e. the precipitate and the surrounding c-Si structure, have been employed in the current study.
+
+In a previous comparative study\cite{zirkelbach10a} we have schown that the utilized empirical potential fails to describe some selected processes.
+Thus, limitations of the employed potential have been further investigated and taken into account in the present study.
+We focussed on two major shortcomings: the overestimated activation energy and the improper description of intrinsic and C point defects in Si.
+Overestimated forces between next neighbor atoms that are expected for short range potentials\cite{mattoni2007} have been confirmed to influence the C$_{\text{i}}$ diffusion.
+The migration barrier was estimated to be larger by a factor of 2.4 to 3.5 compared to highly accurate quantum-mechanical calculations\cite{zirkelbach10a}.
+Concerning point defects the drastically underestimated formation energy of C$_{\text{s}}$ and deficiency in the description of the Si$_{\text{i}}$ ground state necessitated further investigations on structures that are considered important for the problem under study.
+It turned out that the EA potential still favors a C$_{\text{i}}$ \hkl<1 0 0> DB over a C$_{\text{s}}$-Si$_{\text{i}}$ configuration, which, thus, does not constitute any limitation for the simulations aiming to resolve the present controversy of the proposed SiC precipitation models.
+
+MD simulations at temperatures used in IBS resulted in structures that were dominated by the C$_{\text{i}}$ \hkl<1 0 0> DB and its combinations if C is inserted into the total volume.
+Incoorporation into volmes $V_2$ and $V_3$ led to an amorphous SiC-like structure within the respective volume.
+To ensure correct diffusion behavior simulations at elevated temperatures have been performed.
+Although ...
+
+entropic contribution.
+as in \cite{zirkelbach10b}, next neighbored Cs and Sii did not recombine, but departed from each other.
+
+Sii stress compensation ...
+Thus, we prpopose (support) the follwing model ...
+
+Concluded that C sub is very probable ...
+Alignment lost, successive substitution more probable to end up with topotactic 3C-SiC.
+
+Both, low and high, acceleration not enough to either observe C agglomeration or amorphous to crystalline transition ...
+
 
 \section{Summary}