Structures of maximum configurational energy do not necessarily constitute saddle point configurations, i .e. the method does not guarantee to find the true minimum energy path.
Whether a saddle point configuration and, thus, the minimum energy path is obtained by the CRT method, needs to be verified by caculating the respective vibrational modes.
-Modifications used to add the CRT feature to the VASP code and a short instruction on how to use it can be found in appendix \ref{app:patch_vasp}.
+Modifications used to add the CRT feature to the {\textsc vasp} code and a short instruction on how to use it can be found in appendix \ref{app:patch_vasp}.
% todo - advantages of pw basis concenring hf forces
% todo - sync with conclusion chapter
-These findings allow to draw conclusions on the mechanisms involved in the process of SiC conversion in Si.
+These findings allow to draw conclusions on the mechanisms involved in the process of SiC conversion in Si, which is elaborated in more detail within the comprehensive description in chapter~\ref{chapter:summary}.
Agglomeration of C$_{\text{i}}$ is energetically favored and enabled by a low activation energy for migration.
Although ion implantation is a process far from thermodynamic equilibrium, which might result in phases not described by the Si/C phase diagram, i.e. a C phase in Si, high activation energies are believed to be responsible for a low probability of the formation of C-C clusters.
On the other hand, the conversion of some region of Si into SiC by \cs{} is accompanied by a reduction of the volume since SiC exhibits a \unit[20]{\%} smaller lattice constant than Si.
The reduction in volume is compensated by excess Si$_{\text{i}}$ serving as building blocks for the surrounding Si host or a further formation of SiC.
-To conclude, precipitation occurs by successive agglomeration of C$_{\text{s}}$.
+To conclude, the available results suggest precipitation by successive agglomeration of C$_{\text{s}}$.
However, the agglomeration and rearrangement of C$_{\text{s}}$ is only possible by mobile C$_{\text{i}}$, which has to be present at the same time.
Accordingly, the process is governed by both, C$_{\text{s}}$ accompanied by Si$_{\text{i}}$ as well as C$_{\text{i}}$.
It is worth to mention that there is no contradiction to results of the HREM studies \cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}.
% rt implantation + annealing
Furthermore, C implanted at room temperature was found to be able to migrate towards the surface and form C-rich clusters in contrast to implantations at elevated temperatures, which form stable epitaxially aligned 3C-SiC precipitates \cite{serre95}.
In simulation, low temperatures result in configurations of highly mobile \ci{} \hkl<1 0 0> DBs whereas elevated temperatures show configurations of \cs{}, which constitute an extremely stable configuration that is unlikely to migrate.
+%
+% added
+This likewise agrees to results of IBS experiments utilizing implantation temperatures of \degc{550}, which require annealing temperatures as high as \degc{1405} for C segregation due to the stability of \cs{} \cite{reeson87}.
+%
Indeed, in the optimized recipe to form 3C-SiC by IBS \cite{lindner99}, elevated temperatures are used to improve the epitaxial orientation together with a low temperature implant to destroy stable SiC nanocrystals at the interface, which are unable to migrate during thermal annealing resulting in a rough surface.
Furthermore, the improvement of the epitaxial orientation of the precipitate with increasing temperature in experiment perfectly conforms to the increasing occurrence of \cs{} in simulation.
%
-% todo add sync here starting from werner96 (Similar, implan ...)
+% todo add sync here starting from strane93, werner96 ...
+Moreover, implantations of an understoichiometric dose into preamorphized Si followed by an annealing step at \degc{700} result in Si$_{1-x}$C$_x$ layers with C residing on substitutional Si lattice sites \cite{strane93}.
+For implantations of an understoichiometric dose into c-Si at room temperature followed by thermal annealing below and above \degc{700}, the formation of small C$_{\text{i}}$ agglomerates and SiC precipitates was observed respectively \cite{werner96}.
+However, increased implantation temperatures were found to be more efficient than postannealing methods resulting in the formation of SiC precipitates for implantations at \unit[450]{$^{\circ}$C} \cite{lindner99,lindner01}.
%
-At elevated temperatures, implanted C is therefore expected to occupy substitutionally usual Si lattice sites right from the start.
+Thus, at elevated temperatures, implanted C is expected to occupy substitutionally usual Si lattice sites right from the start.
+These findings, which are outlined in more detail within the comprehensive description in chapter~\ref{chapter:summary}, are in perfect agreement with previous results of the quantum-mechanical investigations.
Thus, elevated temperatures are considered to constitute a necessary condition to deviate the system from equilibrium, as it is the case in IBS.
It is concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.~\cite{nejim95}.
%\usepackage[resetlabels]{multibib}
\newcites{pub}{List of publications}
+% box around verbatim text
+\usepackage{fancyvrb}
+
% miller
\usepackage{miller}
\label{app:patch_vasp}
\section{Description}
-The modifications to the VASP code allow to rotate all atom coordinates individually in the particle position evaluation routine of VASP.
-In that way constraints for every atom can be applied independently of the chosen basis.
-A patch against version 4.6 of the VASP code containing these modifications is available for download\footnote{http://www.physik.uni-augsburg.de/\~{}zirkelfr/download/posic/sd\_rot\_all-atoms.patch}.
+In the {\textsc vasp} code, the {\em selective dynamics} mode provides a feature to allow or constrain the change of each of the three coordinates for every single atom.
+By this, however, applied constraints are restricted to the chosen basis.
+For the investigation of migration pathways utilizing the constrained relaxation technique as detailed in section~\ref{section:basics:migration}, the required constraint not necessarily corresponds to one of the coordinate axes as defined by the basis, which, in turn, is determined to enable a construction within the supercell approach.
-\section{Usage}
+Thus, the functionality of the {\em selective dynamics} mode had to be extended by modifications in the particle position evaluation routine of {\textsc vasp}.
+These modifications allow for a rotation of all atom coordinates individually before respective constraints are applied and a following, final inverse transformation.
+In that way, constraints for every single atom can be applied independently of the chosen basis.
+A patch against version 4.6 of the {\textsc vasp} code containing these modifications is available for download\footnote{http://www.physik.uni-augsburg.de/\~{}zirkelfr/download/posic/sd\_rot\_all-atoms.patch}.
-Since this feature only makes sense in selective dynamics mode, it can be switched on by adding the word {\em Transformed} in front of the {\em selective dynamics} switch.
-This feature only works in direct mode.
+\section{Mode of operation}
+
+The extended capabilities can only be used within the {\em selective dynamics} mode.
+It is enabled by adding the word {\em transformed} in front of the {\em selective dynamics} switch.
+This feature only works in {\em direct} mode.
Two values of angles need to be added after the extra flags of each atom.
The first angle corresponds to the rotation of the basis about the $z$-axis.
The second angle determines the rotation about the transformed $x$-axis, $x'$.
All values have to be supplied in degrees.
-All these information is given in the POSCAR file as can be seen in the follwing example:
-\begin{verbatim}
-cubic diamond
- 5.48000000000000
- 2.9909698580839312 0.0039546630279804 -0.0039658085666586
- 0.0039548953566878 2.9909698596656376 -0.0039660323646892
- -0.0039680658132861 -0.0039674231313905 2.9909994291263242
- 216 1
-Transformed selective dynamics
-Direct
- 0.994174 0.994174 -0.000408732 T F T 45 36.5145
- 0.182792 0.182792 0.981597 T F T -135 -5.95043
- ...
- 0.119896 0.119896 0.0385525 T F T -135 21.8036
-\end{verbatim}
-In case of the first atom the basis is transformed by a rotation of $45^{\circ}$ and $36.5145^{\circ}$ about the $z$ and $x'$ axis.
-Relaxation of this atom is constrained to the $y''$-axis.
+The entire information is given in the POSCAR file as can be seen in the example displayed in Fig.~\ref{fig:vasp_input}.
+\begin{figure}[t]
+\begin{Verbatim}[frame=single]
+cubic diamond
+ 5.429
+ 1.00000 0.00000 0.00000
+ 0.00000 1.00000 0.00000
+ 0.00000 0.00000 1.00000
+ 8
+transformed selective dynamics
+direct
+ 0.00000 0.00000 0.00000 T F T 45.0 30.0
+ 0.50000 0.50000 0.00000 T T T 0.0 0.0
+ 0.50000 0.00000 0.50000 T T T 0.0 0.0
+ 0.00000 0.50000 0.50000 T T T 0.0 0.0
+ 0.25000 0.25000 0.25000 T F T 135.0 -10.0
+ 0.75000 0.75000 0.25000 T T T 0.0 0.0
+ 0.75000 0.25000 0.75000 T T T 0.0 0.0
+ 0.25000 0.75000 0.75000 T T T 0.0 0.0
+\end{Verbatim}
+\caption{Example {\textsc vasp} input file utilizing the {\em transformed selective dynamics} mode of operation.}
+\label{fig:vasp_input}
+\end{figure}
+In case of the first atom, the basis is transformed by a rotation of $45^{\circ}$ and $30^{\circ}$ about the $z$ and $x'$ axis.
+The basis of the fifth atom is likewise rotated by $135^{\circ}$ and $-10^{\circ}$ respectively.
+Relaxation of both atoms is only allowed within the plane perpendicular to the $y''$-axis.
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