table eof

diff --git a/posic/publications/defect_combos.tex b/posic/publications/defect_combos.tex
index 0b5068bf8298da74d66eb79b61ed488ad17ddd73..a631777e9617665db2367f0c2adc35734e9f7ddb 100644 (file)
--- a/posic/publications/defect_combos.tex
+++ b/posic/publications/defect_combos.tex
@@ -8,7 +8,6 @@
 \usepackage{amsfonts}\r
 \usepackage{amssymb}\r
 \r
-\r
 \begin{document}\r
 \r
 %\title{Mobility of Carbon in Silicon -- a first principles study}\r
@@ -48,7 +47,7 @@ However, in another IBS study Nejim et al. propose a topotactic transformation r
 Solving this controversy and understanding the effective underlying processes will enable significant technological progress in 3C-SiC thin film formation driving the superior polytype for potential applications in high-performance electronic device production\cite{wesch96}.\r
 \r
 Atomistic simulations offer a powerful tool of investigation providing detailed insight not accessible by experiment.\r
-A lot of theoretical work has been done on intrinsic point defects in Si\cite{bar-yam84,bar-yam84_2,car84,batra87,tang97,leung99,colombo02,al-mushadani03,posselt08,ma10}, threshold displacement energies in Si\cite{mazzarolo01,holmstroem08} important in ion implantation, C defects and defect reactions in Si\cite{tersoff90,dal_pino93,capaz94,burnard93,leary97,capaz98,zhu98,mattoni2002,park02,jones04}, the SiC/Si interface\cite{chirita97,kitabatake93,cicero02,pizzagalli03} and defects in SiC\cite{bockstedte03,rauls03a,gao04,posselt06,gao07}.\r
+A lot of theoretical work has been done on intrinsic point defects in Si\cite{bar-yam84,bar-yam84_2,car84,batra87,bloechl93,tang97,leung99,colombo02,goedecker02,al-mushadani03,posselt08,ma10}, threshold displacement energies in Si\cite{mazzarolo01,holmstroem08} important in ion implantation, C defects and defect reactions in Si\cite{tersoff90,dal_pino93,capaz94,burnard93,leary97,capaz98,zhu98,mattoni2002,park02,jones04}, the SiC/Si interface\cite{chirita97,kitabatake93,cicero02,pizzagalli03} and defects in SiC\cite{bockstedte03,rauls03a,gao04,posselt06,gao07}.\r
 However, none of the mentioned studies consistently investigates entirely the relevant defect structures and reactions concentrated on the specific problem of 3C-SiC formation in C implanted Si.\r
 % but mattoni2002 actually did a lot. maybe this should be mentioned!\r
 \r
@@ -59,7 +58,7 @@ In the following a systematic investigation of density functional theory (DFT) c
 %  --------------------------------------------------------------------------------\r
 \section{Methodology}\r
 \r
-The first-principles DFT calculations were performed with the plane-wave based Vienna Ab-initio Simulation Package (VASP)\cite{kresse96}.\r
+The first principles DFT calculations were performed with the plane-wave based Vienna Ab-initio Simulation Package (VASP)\cite{kresse96}.\r
 The Kohn-Sham equations were solved using the generalized-gradient XC-functional approximation proposed by Perdew and Wang (GGA-PW91)\cite{perdew86,perdew92}.\r
 The electron-ion interaction is described by norm-conserving ultra-soft pseudopotentials\cite{hamann79} as implemented in VASP\cite{vanderbilt90}.\r
 Throughout this work an energy cut-off of \unit[300]{eV} was used to expand the wave functions into the plane-wave basis.\r
@@ -77,24 +76,83 @@ The defect formation energy $E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\te
 %Their mobility is the crucial quantity to be investigated.\r
 %However, the implantation process unavoidably creates a variety of further point defects, such as vacancies and silicon self-interstitials.\r
 %Already during implantation and also in the subsequent annealing process, further defects can evolve from these, like pair defects or substitutional carbon.\r
-As mentioned in the introduction the implantation of highly energetic C atoms results in a multiplicity of possible defect configurations.\r
-Next to individual Si$_{\text{i}}$, C$_{\text{i}}$, V and C$_{\text{s}}$ defects combinations of these defects believed to be interesting for the problem under study have been investigated.\r
+The implantation of highly energetic C atoms results in a multiplicity of possible defect configurations.\r
+Next to individual Si$_{\text{i}}$, C$_{\text{i}}$, V and C$_{\text{s}}$ defects, combinations of these defects and their interaction are considered important for the problem under study.\r
+In the following the structure and energetics of separated defects are presented.\r
+The investigations proceed with pairs of the ground state and, thus, most probable defect configurations that are believed to be fundamental in the Si to SiC transition.\r
 \r
 \subsection{Separated defects in silicon}\r
-% we need both: Si self-int & C int ground state configuration\r
-\r
-Several geometries have been calculated to be stable for intrinsic and carbon interstitials.\r
-Fig.\ref{fig:interstitials} shows the obtained structures.\r
-Table \ref{table:formation} summarizes the formation energies of the geometries a carbon interstitial can take in an otherwise perfect Si \r
-crystal. \r
+% we need both: Si self-int & C int ground state configuration (for combos)\r
+\r
+Several geometries have been calculated to be stable for individual intrinsic and C related defects in Si.\r
+Fig.~\ref{fig:sep_def} shows the obtained structures while the corresponding energies of formation are summarized and compared to values from literature in table~\ref{table:sep_eof}.\r
+\begin{figure}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{Si $\langle 1 1 0 \rangle$ DB}\\\r
+\includegraphics[width=\columnwidth]{si110.eps}\r
+\end{minipage}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{Si hexagonal}\\\r
+\includegraphics[width=\columnwidth]{sihex.eps}\r
+\end{minipage}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{Si tetrahedral}\\\r
+\includegraphics[width=\columnwidth]{sitet.eps}\r
+\end{minipage}\\\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{Si $\langle 1 0 0 \rangle$ DB}\\\r
+\includegraphics[width=\columnwidth]{si100.eps}\r
+\end{minipage}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{Vacancy}\\\r
+\includegraphics[width=\columnwidth]{sivac.eps}\r
+\end{minipage}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{Substitutional}\\\r
+\includegraphics[width=\columnwidth]{csub.eps}\r
+\end{minipage}\\\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{C $\langle 1 0 0 \rangle$ DB}\\\r
+\includegraphics[width=\columnwidth]{c100.eps}\r
+\end{minipage}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{C $\langle 1 1 0 \rangle$ DB}\\\r
+\includegraphics[width=\columnwidth]{c110.eps}\r
+\end{minipage}\r
+\begin{minipage}[t]{0.32\columnwidth}\r
+\underline{C bond-centered}\\\r
+\includegraphics[width=\columnwidth]{cbc.eps}\r
+\end{minipage}\r
+\caption{Configurations of silicon and carbon point defects in silicon. Silicon and carbon atoms are illustrated by yellow and grey spheres respectively. Blue lines are bonds drawn whenever considered appropriate to ease identifying defect structures for the reader. Dumbbell configurations are abbreviated by DB.}\r
+\label{fig:sep_def}\r
+\end{figure}\r
+\begin{table*}\r
+\begin{ruledtabular}\r
+\begin{tabular}{l c c c c c c c c c}\r
+ & Si $\langle1 1 0\rangle$ DB & Si H & Si T & Si $\langle 1 0 0\rangle$ DB & V & C$_{\text{s}}$ & C $\langle1 0 0\rangle$ DB & C $\langle1 1 0\rangle$ DB & C BC \\\r
+\hline\r
+ This work & 3.39 & 3.42 & 3.77 & 4.41 & 3.63 & 1.95 & 3.72 & 4.16 & 4.66 \\\r
+ References & 3.40\cite{al-mushadani03}, 3.31\cite{leung99} & 3.45\cite{al-mushadani03}, 3.31\cite{leung99} & 3.43\cite{leung99} & - & 3.53\cite{al-mushadani03} & 1.89\cite{dal_pino93} & x & - & x+2.1\cite{capaz94}\r
+\end{tabular}\r
+\end{ruledtabular}\r
+\caption{Formation energies of silicon and carbon point defects in crystalline silicon. The formation energies are given in eV. T denotes the tetrahedral, H the hexagonal and BC the bond-centered interstitial configuration. V corresponds to the vacancy configuration. Dumbbell configurations are abbreviated by DB.}\r
+\label{tab:sep_eof}\r
+\end{table*}\r
+\r
+The ground state configurations of a Si self-interstitial and a C interstitial is the $\langle 1 1 0 \rangle$ and $\langle 1 0 0 \rangle$ dumbbell respectively.\r
 \r
 %%  Kurze Beschreibung der Migration - auch wie im anderen paper, auch nur DFT.   Und:   \cite{zirkelbach10} ... to be published (2010). \r
 \r
 \subsection{C$_I$ next to further C interstitials}\r
+\r
 \subsection{C$_I$ next to C$_{\text{s}}$}\r
+\r
 \subsection{C$_I$ next to vacancies}\r
+\r
 \subsection{C$_{\text{s}}$ next to Si self interstitials}\r
 \r
+Non-zeor temperature, entropy, spatial separation of these defects possible, indeed observed in ab initio MD run.\r
+\r
 %% Viele Bilder... da kann ich zunächst gar nicht soviel zu schreiben....  \r
 \r
 \section{Discussion}\r