\end{slide}
+
\begin{slide}
{\large\bf
\rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
r = 2 - 4 nm
}}}
-\rput(6.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=lachs]{
+\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
\begin{minipage}{10cm}
\small
-IBS studies revealing controversial views\\
+{\color{red}\bf Controversial views}
\begin{itemize}
-\item Nejim et al.
+\item Implantations at high T (Nejim et al.)
\begin{itemize}
\item Topotactic transformation based on \cs
- \item \si as supply reacting with further C in cleared volume
+ \item \si{} as supply reacting with further C in cleared volume
+ \end{itemize}
+\item Annealing behavior (Serre et al.)
+ \begin{itemize}
+ \item Room temperature implants $\rightarrow$ highly mobile C
+ \item Elevated T implants $\rightarrow$ no/low C redistribution/migration\\
+ (indicate stable \cs{} configurations)
\end{itemize}
-\item Serre, Reeson, Lindner ...
+\item Strained silicon \& Si/SiC heterostructures
\begin{itemize}
- \item RT implants: highly mobile C
- \item elevated T implants: no/low C redistribution/migration
+ \item Coherent SiC precipitates (tensile strain)
+ \item Incoherent SiC (strain relaxation)
\end{itemize}
\end{itemize}
\end{minipage}
\vspace*{12pt}
\[
E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
- \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
+ \pot_{ij} = {\color{red}f_C(r_{ij})}
+ \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
\]
\end{itemize}
\item 2.4 - 3.4 times higher than VASP
\item Rotation of dumbbell orientation
\end{itemize}
+\vspace{0.1cm}
+\begin{center}
+{\color{blue}Overestimated diffusion barrier}
+\end{center}
\end{minipage}
\end{minipage}
\end{minipage}
\begin{minipage}[t]{5.5cm}
\begin{itemize}
- \item Restricted to VASP simulations
- \item $E_{\text{b}}=0$ for isolated non-interacting defects
- \item $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
+ \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
+ $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
\item Stress compensation / increase
- \item Most favorable: C clustering
\item Unfavored: antiparallel orientations
\item Indication of energetically favored\\
agglomeration
+ \item Most favorable: C clustering
+ \item However: High barrier ($>4\,\text{eV}$)
+ \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
+ (Entropy)
\end{itemize}
\end{minipage}
\includegraphics[width=7cm]{db_along_110_cc.ps}
\end{minipage}
\begin{minipage}{6.0cm}
+\begin{itemize}
+ \item Interaction proportional to reciprocal cube of C-C distance
+ \item Saturation in the immediate vicinity
+ \renewcommand\labelitemi{$\Rightarrow$}
+ \item Agglomeration of \ci{} expected
+ \item Absence of C clustering
+\end{itemize}
\begin{center}
{\color{blue}
- Interaction proportional to reciprocal cube of C-C distance
-}\\[0.2cm]
- Saturation in the immediate vicinity
+ Consisten with initial precipitation model
+}
\end{center}
\end{minipage}
\scriptsize
-\begin{center}
-\begin{minipage}{3.2cm}
-\includegraphics[width=3cm]{sub_110_combo.eps}
-\end{minipage}
-\begin{minipage}{7.8cm}
-\begin{tabular}{l c c c c c c}
-\hline
-C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
- \hkl<1 0 1> & \hkl<-1 0 1> \\
-\hline
-1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
-2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
-3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
-4 & \RM{4} & B & D & E & E & D \\
-5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
-\hline
-\end{tabular}
-\end{minipage}
-\end{center}
+%\begin{center}
+%\begin{minipage}{3.2cm}
+%\includegraphics[width=3cm]{sub_110_combo.eps}
+%\end{minipage}
+%\begin{minipage}{7.8cm}
+%\begin{tabular}{l c c c c c c}
+%\hline
+%C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
+% \hkl<1 0 1> & \hkl<-1 0 1> \\
+%\hline
+%1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
+%2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
+%3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
+%4 & \RM{4} & B & D & E & E & D \\
+%5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
+%\hline
+%\end{tabular}
+%\end{minipage}
+%\end{center}
-\begin{center}
-\begin{tabular}{l c c c c c c c c c c}
-\hline
-Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
-\hline
-$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
-$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
-$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
-\hline
-\end{tabular}
-\end{center}
+%\begin{center}
+%\begin{tabular}{l c c c c c c c c c c}
+%\hline
+%Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
+%\hline
+%$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
+%$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
+%$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
+%\hline
+%\end{tabular}
+%\end{center}
\begin{minipage}{6.0cm}
\includegraphics[width=5.8cm]{c_sub_si110.ps}
\end{minipage}
\begin{minipage}{7cm}
-\small
+\scriptsize
\begin{itemize}
\item IBS: C may displace Si\\
$\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
\item Assumption:\\
\hkl<1 1 0>-type $\rightarrow$ favored combination
\renewcommand\labelitemi{$\Rightarrow$}
- \item Less favorable than C-Si \hkl<1 0 0> dumbbell\\
- ($E_{\text{f}}=3.88\text{ eV}$)
+ \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
+ \item Less favorable than C-Si \hkl<1 0 0> dumbbell
\item Interaction drops quickly to zero\\
- (low interaction capture radius)
+ $\rightarrow$ low capture radius
\end{itemize}
+\begin{center}
+ {\color{blue}
+ IBS process far from equilibrium\\
+ \cs{} \& \si{} instead of thermodynamic ground state
+ }
+\end{center}
+\end{minipage}
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.0cm]{162-097.ps}
+\begin{itemize}
+ \item Low migration barrier
+\end{itemize}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\begin{center}
+Ab initio MD at \degc{900}\\
+\includegraphics[width=3.3cm]{md_vasp_01.eps}
+$t=\unit[2230]{fs}$\\
+\includegraphics[width=3.3cm]{md_vasp_02.eps}
+$t=\unit[2900]{fs}$
+\end{center}
+{\color{blue}
+Contribution of entropy to structural formation
+}
\end{minipage}
\end{slide}
\end{slide}
+\begin{slide}
+
+ {\large\bf\boldmath
+ Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
+ }
+
+ \small
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
+\end{minipage}
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\scriptsize
+\underline{Low C concentration ($V_1$)}\\
+\hkl<1 0 0> C-Si dumbbell dominated structure
+\begin{itemize}
+ \item Si-C bumbs around 0.19 nm
+ \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
+ concatenated dumbbells of various orientation
+ \item Si-Si NN distance stretched to 0.3 nm
+\end{itemize}
+{\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
+\underline{High C concentration ($V_2$, $V_3$)}\\
+High amount of strongly bound C-C bonds\\
+Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
+Only short range order observable\\
+{\color{blue}$\Rightarrow$ amorphous SiC-like phase}
+\end{minipage}
+
+\begin{pspicture}(0,0)(0,0)
+\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
+\begin{minipage}{10cm}
+\small
+{\color{red}\bf 3C-SiC formation fails to appear}
+\begin{itemize}
+\item Low C concentration simulations
+ \begin{itemize}
+ \item Formation of \ci{} indeed occurs
+ \item Agllomeration not observed
+ \end{itemize}
+\item High C concentration simulations
+ \begin{itemize}
+ \item Amorphous SiC-like structure\\
+ (not expected at prevailing temperatures)
+ \item Rearrangement and transition into 3C-SiC structure missing
+ \end{itemize}
+\end{itemize}
+\end{minipage}
+ }}}
+\end{pspicture}
+
+\end{slide}
+
\begin{slide}
{\large\bf
\end{slide}
+\begin{slide}
+
+ {\large\bf
+ Increased temperature simulations at low C concentration
+ }
+
+\small
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{tot_pc_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
+\end{minipage}
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\scriptsize
+ \underline{Si-C bonds:}
+ \begin{itemize}
+ \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
+ \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
+ \end{itemize}
+ \underline{Si-Si bonds:}
+ {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
+ ($\rightarrow$ 0.325 nm)\\[0.1cm]
+ \underline{C-C bonds:}
+ \begin{itemize}
+ \item C-C next neighbour pairs reduced (mandatory)
+ \item Peak at 0.3 nm slightly shifted
+ \begin{itemize}
+ \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
+ $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
+ combinations (|)\\
+ $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
+ ($\downarrow$)
+ \item Range [|-$\downarrow$]:
+ {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
+ with nearby Si$_{\text{I}}$}
+ \end{itemize}
+ \end{itemize}
+\end{minipage}
+
+%\begin{picture}(0,0)(-330,-74)
+%\color{blue}
+%\framebox{
+%\begin{minipage}{1.6cm}
+%\tiny
+%\begin{center}
+%stretched SiC\\[-0.1cm]
+%in c-Si
+%\end{center}
+%\end{minipage}
+%}
+%\end{picture}
+
+\begin{pspicture}(0,0)(0,0)
+\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
+\begin{minipage}{10cm}
+\small
+{\color{blue}\bf Stretched SiC in c-Si}
+\begin{itemize}
+\item Consistent to precipitation model involving \cs{}
+\item Explains annealing behavior of high/low T C implants
+ \begin{itemize}
+ \item Low T: highly mobiel \ci{}
+ \item High T: stable configurations of \cs{}
+ \end{itemize}
+\end{itemize}
+$\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
+$\Rightarrow$ Precipitation mechanism involving \cs{}
+\end{minipage}
+ }}}
+\end{pspicture}
+
+\end{slide}
+
\begin{slide}
{\large\bf
\includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
\end{minipage}
-\begin{center}
-Decreasing cut-off artifact\\
-High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
-$\Rightarrow$ hard to categorize
-\end{center}
-
\vspace{0.1cm}
+\scriptsize
+
\framebox{
\begin{minipage}[t]{6.0cm}
0.186 nm: Si-C pairs $\uparrow$\\
\end{minipage}
}
-\vspace{0.1cm}
+\begin{itemize}
+\item Decreasing cut-off artifact
+\item {\color{red}Amorphous} SiC-like phase remains
+\item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
+\item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
+\end{itemize}
+
+\vspace{-0.1cm}
\begin{center}
-{\color{red}Amorphous} SiC-like phase remains\\
-Slightly sharper peaks
-$\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics}
-due to temperature\\[0.1cm]
+{\color{blue}
\framebox{
-\bf
-Actual SiC precipitation not accessible by MD
+{\color{black}
+High C \& small $V$ \& short $t$
+$\Rightarrow$
+}
+Slow restructuring due to strong C-C bonds
+{\color{black}
+$\Leftarrow$
+High C \& low T implants
+}
+}
}
\end{center}
\scriptsize
-\vspace{0.1cm}
+%\vspace{0.1cm}
+
+\framebox{
+\begin{minipage}[t]{12.9cm}
+ \underline{Pecipitation simulations}
+ \begin{itemize}
+ \item High C concentration $\rightarrow$ amorphous SiC like phase
+ \item Problem of potential enhanced slow phase space propagation
+ \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
+ \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
+ \item High T necessary to simulate IBS conditions (far from equilibrium)
+ \item Precipitation by successive agglomeration of \cs (epitaxy)
+ \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
+ (stretched SiC, interface)
+ \end{itemize}
+\end{minipage}
+}
+
+%\vspace{0.1cm}
\framebox{
\begin{minipage}{12.9cm}
\end{minipage}
}
-\vspace{0.2cm}
-
-\framebox{
-\begin{minipage}[t]{12.9cm}
- \underline{Pecipitation simulations}
- \begin{itemize}
- \item High C concentration $\rightarrow$ amorphous SiC like phase
- \item Problem of potential enhanced slow phase space propagation
- \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
- \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
- \item High T necessary to simulate IBS conditions (far from equilibrium)
- \item Precipitation by successive agglomeration of \cs (epitaxy)
- \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
- (stretched SiC, interface)
- \end{itemize}
-\end{minipage}
+\begin{center}
+{\color{blue}
+\framebox{Precipitation by successive agglomeration of \cs{}}
}
+\end{center}
\end{slide}
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