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\begin{minipage}{14cm}
\hfill
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-\ifnum1=0
-
% intro
\begin{slide}
\end{center}
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\begin{minipage}{11cm}
{\color{black}Diploma thesis}\\
\underline{Monte Carlo} simulation modeling the selforganization process\\
}}}
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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)
-\rput(1.7,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradangle=10,gradmidpoint=1,linestyle=none]{
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\begin{minipage}{3.7cm}
\hfill
\vspace{0.7cm}
\end{slide}
-% continue here
-\fi
-
\begin{slide}
+\headphd
{\large\bf
- Defect combinations
+ Defect combinations of C-Si dimers and vacancies
}
-
\footnotesize
-\vspace{0.1cm}
+\vspace{0.2cm}
-{\bf Combinations of \ci{} \hkl[0 0 -1] and a vacancy}\\
-\begin{minipage}[t]{3cm}
-\underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
-\includegraphics[width=2.8cm]{00-1dc/0-59.eps}
+\begin{minipage}[b]{2.6cm}
+\begin{flushleft}
+\underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
+\includegraphics[width=2.5cm]{00-1dc/0-59.eps}
+\end{flushleft}
\end{minipage}
-
-
-
-\begin{minipage}[t]{7cm}
-\vspace{0.2cm}
-\begin{center}
- Low activation energies\\
- High activation energies for reverse processes\\
- $\Downarrow$\\
- {\color{blue}C$_{\text{sub}}$ very stable}\\
-\vspace*{0.1cm}
- \hrule
-\vspace*{0.1cm}
- Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
- $\Downarrow$\\
- {\color{blue}Formation of SiC by successive substitution by C}
-\end{center}
+\begin{minipage}[b]{7cm}
+\hfill
\end{minipage}
+\begin{minipage}[b]{2.6cm}
+\begin{flushright}
+\underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
+\includegraphics[width=2.5cm]{00-1dc/3-14.eps}
+\end{flushright}
+\end{minipage}\\[0.2cm]
-
-\begin{minipage}[t]{3cm}
-\underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
-\includegraphics[width=2.8cm]{00-1dc/3-14.eps}
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.0cm]{059-539.ps}
+\end{minipage}
+\begin{minipage}{5.7cm}
+\includegraphics[width=6.0cm]{314-539.ps}
\end{minipage}
+\begin{pspicture}(0,0)(0,0)
+\psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
-\framebox{
-\begin{minipage}{5.9cm}
-\includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
+\rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
+\begin{minipage}{6.5cm}
\begin{center}
-\begin{picture}(0,0)(70,0)
-\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
-\end{picture}
-\begin{picture}(0,0)(30,0)
-\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
-\end{picture}
-\begin{picture}(0,0)(-10,0)
-\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
-\end{picture}
-\begin{picture}(0,0)(-48,0)
-\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
-\end{picture}
-\begin{picture}(0,0)(12.5,5)
-\includegraphics[width=1cm]{100_arrow.eps}
-\end{picture}
-\begin{picture}(0,0)(97,-10)
-\includegraphics[height=0.9cm]{001_arrow.eps}
-\end{picture}
-\end{center}
-\vspace{0.1cm}
-\end{minipage}
+IBS: Impinging C creates V \& far away \si\\[0.3cm]
+Low migration barrier towards C$_{\text{sub}}$\\
+\&\\
+High barrier for reverse process\\[0.3cm]
+{\color{blue}
+High probability of stable C$_{\text{sub}}$ configuration
}
-\begin{minipage}{0.3cm}
-\hfill
-\end{minipage}
-\framebox{
-\begin{minipage}{5.9cm}
-\includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
-\begin{center}
-\begin{picture}(0,0)(60,0)
-\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
-\end{picture}
-\begin{picture}(0,0)(25,0)
-\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
-\end{picture}
-\begin{picture}(0,0)(-20,0)
-\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
-\end{picture}
-\begin{picture}(0,0)(-55,0)
-\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
-\end{picture}
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-\includegraphics[width=1cm]{100_arrow.eps}
-\end{picture}
-\begin{picture}(0,0)(95,0)
-\includegraphics[height=0.9cm]{001_arrow.eps}
-\end{picture}
\end{center}
-\vspace{0.1cm}
\end{minipage}
-}
+}}}
+\end{pspicture}
\end{slide}
-\end{document}
-\ifnum1=0
-
\begin{slide}
- {\large\bf\boldmath
- Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
- }
-
- \scriptsize
+\headphd
+{\large\bf
+ Combinations of substitutional C and Si self-interstitials
+}
-\begin{minipage}{6.0cm}
-\includegraphics[width=5.8cm]{c_sub_si110.ps}
-\end{minipage}
-\begin{minipage}{7cm}
\scriptsize
+
+\vspace{0.3cm}
+
+\begin{minipage}{6.2cm}
+\begin{center}
+{\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
\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 Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
- \item Less favorable than C-Si \hkl<1 0 0> dumbbell
+ \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
+ \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
\item Interaction drops quickly to zero\\
$\rightarrow$ 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{minipage}{0.2cm}
+\hfill
+\end{minipage}
+\begin{minipage}{6.0cm}
+\begin{center}
+{\bf Transition from the ground state}
\begin{itemize}
- \item Low migration barrier
+ \item Low transition barrier
+ \item Barrier smaller than \ci{} migration barrier
+ \item Low \si{} migration barrier (\unit[0.67]{eV})\\
+ $\rightarrow$ Separation of \cs{} \& \si{} most probable
\end{itemize}
+\end{center}
+\end{minipage}\\[0.3cm]
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=6.0cm]{c_sub_si110.ps}
\end{minipage}
-\begin{minipage}{6.5cm}
+\begin{minipage}{0.4cm}
+\hfill
+\end{minipage}
+\begin{minipage}{6.0cm}
+\begin{flushright}
+\includegraphics[width=6.0cm]{162-097.ps}
+\end{flushright}
+\end{minipage}
+
+\begin{pspicture}(0,0)(0,0)
+\psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
+\rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
+\begin{minipage}{8cm}
\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
+\vspace{0.1cm}
+{\color{black}
+\cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
+IBS --- process far from equilibrium\\
}
+\end{center}
\end{minipage}
+}}}
+\end{pspicture}
\end{slide}
\begin{slide}
- {\large\bf
- Conclusion of defect / migration / combined defect simulations
- }
+\headphd
+{\large\bf
+ Combinations of substitutional C and Si self-interstitials
+}
- \footnotesize
+\scriptsize
-\vspace*{0.1cm}
+\vspace{0.3cm}
-Defect structures
+\begin{minipage}{6.2cm}
+\begin{center}
+{\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
\begin{itemize}
- \item Accurately described by quantum-mechanical simulations
- \item Less accurate description by classical potential simulations
- \item Underestimated formation energy of \cs{} by classical approach
- \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
+ \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
+ \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
+ \item Interaction drops quickly to zero\\
+ $\rightarrow$ low capture radius
\end{itemize}
-
-Migration
-\begin{itemize}
- \item C migration pathway in Si identified
- \item Consistent with reorientation and diffusion experiments
-\end{itemize}
+\end{center}
+\end{minipage}
+\begin{minipage}{0.2cm}
+\hfill
+\end{minipage}
+\begin{minipage}{6.0cm}
+\begin{center}
+{\bf Transition from the ground state}
\begin{itemize}
- \item Different path and ...
- \item overestimated barrier by classical potential calculations
-\end{itemize}
+ \item Low transition barrier
+ \item Barrier smaller than \ci{} migration barrier
+ \item Low \si{} migration barrier (\unit[0.67]{eV})\\
+ $\rightarrow$ Separation of \cs{} \& \si{} most probable
+\end{itemize}
+\end{center}
+\end{minipage}\\[0.3cm]
-Concerning the precipitation mechanism
-\begin{itemize}
- \item Agglomeration of C-Si dumbbells energetically favorable
- (stress compensation)
- \item C-Si indeed favored compared to
- C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
- \item Possible low interaction capture radius of
- C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
- \item Low barrier for
- \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
- \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
- C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
-\end{itemize}
+\begin{minipage}{6.0cm}
+\includegraphics[width=6.0cm]{c_sub_si110.ps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+\hfill
+\end{minipage}
+\begin{minipage}{6.0cm}
+\begin{flushright}
+\includegraphics[width=6.0cm]{162-097.ps}
+\end{flushright}
+\end{minipage}
+
+\begin{pspicture}(0,0)(0,0)
+\psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
+\rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
+\begin{minipage}{8cm}
\begin{center}
-{\color{blue}Results suggest increased participation of \cs}
+\vspace{0.1cm}
+{\color{black}
+\cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
+IBS --- process far from equilibrium\\
+}
\end{center}
+\end{minipage}
+}}}
+\end{pspicture}
+
+% md support
+\begin{pspicture}(0,0)(0,0)
+\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
+\begin{minipage}{14cm}
+\hfill
+\vspace{14cm}
+\end{minipage}
+}}
+\rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
+\begin{minipage}{11cm}
+\begin{center}
+\vspace{0.2cm}
+\scriptsize
+Ab initio MD at \degc{900}\\[0.4cm]
+\begin{minipage}{5.4cm}
+\centering
+\includegraphics[width=4.3cm]{md01_bonds.eps}\\
+$t=\unit[2230]{fs}$
+\end{minipage}
+\begin{minipage}{5.4cm}
+\centering
+\includegraphics[width=4.3cm]{md02_bonds.eps}\\
+$t=\unit[2900]{fs}$
+\end{minipage}\\[0.5cm]
+{\color{blue}
+Contribution of entropy to structural formation\\[0.1cm]
+}
+\end{center}
+\end{minipage}
+}}}
+\end{pspicture}
\end{slide}
\begin{slide}
- {\large\bf
- Silicon carbide precipitation simulations
- }
+\headphd
+{\large\bf
+ Silicon carbide precipitation simulations
+}
- \small
+\small
+
+\vspace{0.2cm}
+
+{\bf Procedure}
{\scriptsize
\begin{pspicture}(0,0)(12,6.5)
Insertion of C atoms at constant T
\begin{itemize}
\item total simulation volume {\pnode{in1}}
- \item volume of minimal SiC precipitate {\pnode{in2}}
+ \item volume of minimal SiC precipitate size {\pnode{in2}}
\item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
precipitate
\end{itemize}
}}}}
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\ncline[]{->}{insert}{cool}
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- \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
- \rput(9.2,4.85){\tiny $V_2$}
- \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
- \rput(9.55,4.45){\footnotesize $V_3$}
+ \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
+ \rput(7.6,6){\footnotesize $V_1$}
+ \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
+ \rput(8.9,4.85){\tiny $V_2$}
+ \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
+ \rput(9.25,4.45){\footnotesize $V_3$}
\rput(7.9,3.2){\pnode{ins1}}
- \rput(9.22,2.8){\pnode{ins2}}
- \rput(11.0,2.4){\pnode{ins3}}
+ \rput(8.92,2.8){\pnode{ins2}}
+ \rput(10.8,2.4){\pnode{ins3}}
\ncline[]{->}{in1}{ins1}
\ncline[]{->}{in2}{ins2}
\ncline[]{->}{in3}{ins3}
\end{pspicture}
}
+\vspace{-0.5cm}
+
+{\bf Note}
+
+\footnotesize
+
+\begin{minipage}{5.7cm}
\begin{itemize}
- \item Restricted to classical potential simulations
- \item $V_2$ and $V_3$ considered due to low diffusion
- \item Amount of C atoms: 6000
- ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
- \item Simulation volume: $31\times 31\times 31$ unit cells
+ \item Amount of C atoms: 6000\\
+ ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
+ \item Simulation volume: $31^3$ Si unit cells\\
(238328 Si atoms)
\end{itemize}
+\end{minipage}
+\begin{minipage}{0.3cm}
+\hfill
+\end{minipage}
+\framebox{
+\begin{minipage}{6.0cm}
+Restricted to classical potential caclulations\\
+$\rightarrow$ Low C diffusion / overestimated barrier\\
+$\rightarrow$ Consider $V_2$ and $V_3$
+%\begin{itemize}
+% \item $V_2$ and $V_3$ considered due to expected low C diffusion
+%\end{itemize}
+\end{minipage}
+}
\end{slide}
\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}
+\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}
\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}
\end{document}
-\fi
projects / lectures / latex.git / blobdiff