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-
% intro
\begin{slide}
\end{center}
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\begin{minipage}{11cm}
{\color{black}Diploma thesis}\\
\underline{Monte Carlo} simulation modeling the selforganization process\\
}}}
\end{pspicture}
\begin{pspicture}(0,0)(0,0)
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\begin{minipage}{11cm}
{\color{black}Doctoral studies}\\
Classical potential \underline{molecular dynamics} simulations \ldots\\
\begin{minipage}{3.7cm}
\begin{pspicture}(0,0)(0,0)
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\begin{minipage}{3.7cm}
\hfill
\vspace{0.7cm}
\end{slide}
-% continue here
-\fi
-
\begin{slide}
\headphd
\small
-\begin{minipage}{6.2cm}
-\hspace{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
-\hfill
-\end{minipage}
-\begin{minipage}{6.2cm}
-\includegraphics[width=6.5cm]{sic_prec_450_energy.ps}
-\end{minipage}
-
-\begin{minipage}{6.2cm}
-\hspace{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}
+\begin{minipage}{6.3cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
\hfill
\end{minipage}
-\begin{minipage}{6.2cm}
+\begin{minipage}{6.1cm}
\scriptsize
-\underline{Low C concentration ($V_1$)}\\
+\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
\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
+ \item Si-C bumbs around \unit[0.19]{nm}
+ \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
+ concatenated differently oriented \ci{} DBs
+ \item Si-Si NN distance stretched to \unit[0.3]{nm}
+\end{itemize}
+\begin{pspicture}(0,0)(6.0,1.0)
+\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{6cm}
+\centering
+Formation of \ci{} dumbbells\\
+C atoms in proper 3C-SiC distance first
+\end{minipage}
+}}
+\end{pspicture}\\[0.1cm]
+\underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
+\begin{itemize}
+\item High amount of strongly bound C-C bonds
+\item Increased defect \& damage density\\
+ $\rightarrow$ Arrangements hard to categorize and trace
+\item Only short range order observable
\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}
+\begin{pspicture}(0,0)(6.0,0.8)
+\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{6cm}
+\centering
+Amorphous SiC-like phase
+\end{minipage}
+}}
+\end{pspicture}\\[0.3cm]
+\begin{pspicture}(0,0)(6.0,2.0)
+\rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
+\begin{minipage}{6cm}
+\hfill
+\vspace{2.5cm}
+\end{minipage}
+}}
+\end{pspicture}
\end{minipage}
\end{slide}
-\end{document}
-\ifnum1=0
-
\begin{slide}
- {\large\bf\boldmath
- Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
- }
-
- \small
+\headphd
+{\large\bf\boldmath
+ Silicon carbide precipitation simulations at \degc{450} as in IBS
+}
-\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}
+\small
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
+\begin{minipage}{6.3cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
+\begin{minipage}{6.1cm}
\scriptsize
-\underline{Low C concentration ($V_1$)}\\
+\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
\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
+ \item Si-C bumbs around \unit[0.19]{nm}
+ \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
+ concatenated differently oriented \ci{} DBs
+ \item Si-Si NN distance stretched to \unit[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{pspicture}(0,0)(6.0,1.0)
+\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{6cm}
+\centering
+Formation of \ci{} dumbbells\\
+C atoms in proper 3C-SiC distance first
+\end{minipage}
+}}
+\end{pspicture}\\[0.1cm]
+\underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
\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}
+\item High amount of strongly bound C-C bonds
+\item Increased defect \& damage density\\
+ $\rightarrow$ Arrangements hard to categorize and trace
+\item Only short range order observable
\end{itemize}
+\begin{pspicture}(0,0)(6.0,0.8)
+\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{6cm}
+\centering
+Amorphous SiC-like phase
\end{minipage}
- }}}
+}}
+\end{pspicture}\\[0.3cm]
+\begin{pspicture}(0,0)(6.0,2.0)
+\rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
+\begin{minipage}{6cm}
+\vspace{0.1cm}
+\centering
+{\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
+\begin{minipage}{0.8cm}
+{\bf\boldmath $V_1$:}
+\end{minipage}
+\begin{minipage}{5.1cm}
+Formation of \ci{} indeed occurs\\
+Agllomeration not observed
+\end{minipage}\\[0.3cm]
+\begin{minipage}{0.8cm}
+{\bf\boldmath $V_{2,3}$:}
+\end{minipage}
+\begin{minipage}{5.1cm}
+Amorphous SiC-like structure\\
+(not expected at \degc{450})\\[0.05cm]
+No rearrangement/transition into 3C-SiC
+\end{minipage}\\[0.1cm]
+\end{minipage}
+}}
\end{pspicture}
+\end{minipage}
\end{slide}
\begin{slide}
- {\large\bf
- Limitations of molecular dynamics and short range potentials
- }
+\headphd
+{\large\bf
+ Limitations of MD and short range potentials
+}
-\footnotesize
+\small
\vspace{0.2cm}
-\underline{Time scale problem of MD}\\[0.2cm]
-Minimize integration error\\
-$\Rightarrow$ discretization considerably smaller than
- reciprocal of fastest vibrational mode\\[0.1cm]
-Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
-$\Rightarrow$ suitable choice of time step:
- $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
-$\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
-Several local minima in energy surface separated by large energy barriers\\
-$\Rightarrow$ transition event corresponds to a multiple
+{\bf Time scale problem of MD}\\[0.2cm]
+Precise integration \& thermodynamic sampling\\
+$\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
+ $\omega$: vibrational mode\\
+$\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
+Several local minima separated by large energy barriers\\
+$\Rightarrow$ Transition event corresponds to a multiple
of vibrational periods\\
-$\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
- infrequent transition events\\[0.1cm]
+$\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
+ infrequent transition events\\[0.2cm]
{\color{blue}Accelerated methods:}
\underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
-\vspace{0.3cm}
-
-\underline{Limitations related to the short range potential}\\[0.2cm]
-Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
-and 2$^{\text{nd}}$ next neighbours\\
-$\Rightarrow$ overestimated unphysical high forces of next neighbours
-
-\vspace{0.3cm}
+\vspace{0.2cm}
-\framebox{
-\color{red}
-Potential enhanced problem of slow phase space propagation
-}
+{\bf Limitations related to the short range potential}\\[0.2cm]
+Cut-off function limits interaction to next neighbours\\
+$\Rightarrow$ Overestimated unphysical high forces of next neighbours
+ (factor: 2.4--3.4)
-\vspace{0.3cm}
+\vspace{1.4cm}
-\underline{Approach to the (twofold) problem}\\[0.2cm]
+{\bf Approach to the (twofold) problem}\\[0.2cm]
Increased temperature simulations without TAD corrections\\
-(accelerated methods or higher time scales exclusively not sufficient)
+Accelerated methods or higher time scales exclusively not sufficient!
-\begin{picture}(0,0)(-260,-30)
-\framebox{
-\begin{minipage}{4.2cm}
-\tiny
-\begin{center}
-\vspace{0.03cm}
-\underline{IBS}
-\end{center}
-\begin{itemize}
-\item 3C-SiC also observed for higher T
-\item higher T inside sample
-\item structural evolution vs.\\
- equilibrium properties
-\end{itemize}
+\begin{pspicture}(0,0)(0,0)
+\rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
+\begin{minipage}{7.5cm}
+\centering
+\vspace{0.05cm}
+Potential enhanced slow phase space propagation
\end{minipage}
-}
-\end{picture}
-
-\begin{picture}(0,0)(-305,-155)
-\framebox{
-\begin{minipage}{2.5cm}
+}}
+\rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{2.7cm}
\tiny
-\begin{center}
+\centering
retain proper\\
-thermodynmic sampling
-\end{center}
+thermodynamic sampling
\end{minipage}
-}
-\end{picture}
+}}
+\psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
+\rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{3.6cm}
+\tiny
+\centering
+\underline{IBS}\\[0.1cm]
+3C-SiC also observed for higher T\\[0.1cm]
+Higher T inside sample\\[0.1cm]
+Structural evolution vs.\\
+equilibrium properties
+\end{minipage}
+}}
+\psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
+\end{pspicture}
\end{slide}
\begin{slide}
- {\large\bf
- Increased temperature simulations at low C concentration
- }
+\headphd
+{\large\bf\boldmath
+ Increased temperature simulations --- $V_1$
+}
\small
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc_thesis.ps}
+\begin{minipage}{6.2cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
+\begin{minipage}{6.2cm}
+\includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
\end{minipage}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
+\begin{minipage}{6.2cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
+\begin{minipage}{6.3cm}
\scriptsize
\underline{Si-C bonds:}
\begin{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}
-
\end{slide}
\begin{slide}
- {\large\bf
- Increased temperature simulations at low C concentration
- }
+\headphd
+{\large\bf\boldmath
+ Increased temperature simulations --- $V_1$
+}
\small
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc_thesis.ps}
+\begin{minipage}{6.2cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
+\begin{minipage}{6.2cm}
+\includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
\end{minipage}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
+\begin{minipage}{6.2cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
+\begin{minipage}{6.3cm}
\scriptsize
\underline{Si-C bonds:}
\begin{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}
-
+% conclusions
\begin{pspicture}(0,0)(0,0)
-\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
-\begin{minipage}{10cm}
+\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
+\begin{minipage}{14cm}
+\hfill
+\vspace{14cm}
+\end{minipage}
+}}
+\rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
+\begin{minipage}{9cm}
+\vspace{0.2cm}
\small
-{\color{blue}\bf Stretched SiC in c-Si}
+\begin{center}
+{\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
+{\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
+\end{center}
\begin{itemize}
-\item Consistent to precipitation model involving \cs{}
-\item Explains annealing behavior of high/low T C implants
+\item Stretched coherent SiC structures\\
+$\Rightarrow$ Precipitation process involves {\color{blue}\cs}
+\item Explains annealing behavior of high/low T C implantations
+ \begin{itemize}
+ \item Low T: highly mobile {\color{red}\ci}
+ \item High T: stable configurations of {\color{blue}\cs}
+ \end{itemize}
+\item Role of \si{}
\begin{itemize}
- \item Low T: highly mobiel \ci{}
- \item High T: stable configurations of \cs{}
+ \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
+ \item Building block for surrounding Si host \& further SiC
+ \item Strain compensation \ldots\\
+ \ldots Si/SiC interface\\
+ \ldots within stretched coherent SiC structure
\end{itemize}
\end{itemize}
-$\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
-$\Rightarrow$ Precipitation mechanism involving \cs{}
+\vspace{0.2cm}
+\centering
+\psframebox[linecolor=blue,linewidth=0.05cm]{
+\begin{minipage}{7cm}
+\centering
+Precipitation mechanism involving \cs\\
+High T $\leftrightarrow$ IBS conditions far from equilibrium\\
\end{minipage}
- }}}
+}
+\end{minipage}
+\vspace{0.2cm}
+}}
\end{pspicture}
\end{slide}
+% skip high T / C conc ... only here!
+\ifnum1=0
+
\begin{slide}
{\large\bf
\end{slide}
-\begin{slide}
+% skipped high T / C conc
+\fi
- {\large\bf
- Summary and Conclusions
- }
+\begin{slide}
- \scriptsize
+{\large\bf
+ Summary / Outlook
+}
-%\vspace{0.1cm}
+\small
-\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}
+\begin{pspicture}(0,0)(12,1.0)
+\psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
+\begin{minipage}{11cm}
+{\color{black}Diploma thesis}\\
+ \underline{Monte Carlo} simulation modeling the selforganization process\\
+ leading to periodic arrays of nanometric amorphous SiC precipitates
\end{minipage}
}
-
-%\vspace{0.1cm}
-
-\framebox{
-\begin{minipage}{12.9cm}
- \underline{Defects}
- \begin{itemize}
- \item DFT / EA
- \begin{itemize}
- \item Point defects excellently / fairly well described
- by DFT / EA
- \item C$_{\text{sub}}$ drastically underestimated by EA
- \item EA predicts correct ground state:
- C$_{\text{sub}}$ \& \si{} $>$ \ci{}
- \item Identified migration path explaining
- diffusion and reorientation experiments by DFT
- \item EA fails to describe \ci{} migration:
- Wrong path \& overestimated barrier
- \end{itemize}
- \item Combinations of defects
- \begin{itemize}
- \item Agglomeration of point defects energetically favorable
- by compensation of stress
- \item Formation of C-C unlikely
- \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
- \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
- Low barrier (\unit[0.77]{eV}) \& low capture radius
- \end{itemize}
- \end{itemize}
+\end{pspicture}\\[0.4cm]
+\begin{pspicture}(0,0)(12,2)
+\psframebox[fillstyle=gradient,gradbegin=hblue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
+\begin{minipage}{11cm}
+{\color{black}Doctoral studies}\\
+ Classical potential \underline{molecular dynamics} simulations \ldots\\
+ \underline{Density functional theory} calculations \ldots\\[0.2cm]
+ \ldots on defect formation and SiC precipitation in Si
\end{minipage}
}
-
-\begin{center}
-{\color{blue}
-\framebox{Precipitation by successive agglomeration of \cs{}}
+\end{pspicture}\\[0.5cm]
+\begin{pspicture}(0,0)(12,3)
+\psframebox[fillstyle=solid,fillcolor=white,linestyle=solid]{
+\begin{minipage}{11cm}
+\vspace{0.2cm}
+{\color{black}\bf How to proceed \ldots}\\[0.1cm]
+MC $\rightarrow$ empirical potential MD $\rightarrow$ Ground-state DFT \ldots
+\begin{itemize}
+ \renewcommand\labelitemi{$\ldots$}
+ \item beyond LDA/GGA methods \& ground-state DFT
+\end{itemize}
+Investigation of structure \& structural evolution \ldots
+\begin{itemize}
+ \renewcommand\labelitemi{$\ldots$}
+ \item electronic/optical properties
+ \item electronic correlations
+ \item non-equilibrium systems
+\end{itemize}
+\end{minipage}
}
-\end{center}
+\end{pspicture}\\[0.5cm]
\end{slide}
\item Prof. J. Lindner (SiC)
\item Prof. G. Schmidt (DFT + financial support)
\item Dr. E. Rauls (DFT + SiC)
- \item Dr. S. Sanna (VASP)
\end{itemize}
-\vspace{0.2cm}
-
+ \underline{Stuttgart}
\begin{center}
\framebox{
-\bf Thank you for your attention!
+\bf Thank you for your attention / invitation!
}
\end{center}
\end{document}
-\fi