\pdfoutput=0
+%\documentclass[landscape,semhelv,draft]{seminar}
\documentclass[landscape,semhelv]{seminar}
\usepackage{verbatim}
% itemize level ii
\renewcommand\labelitemii{{\color{gray}$\bullet$}}
+% nice phi
+\renewcommand{\phi}{\varphi}
+
+% roman letters
+\newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
+
% colors
\newrgbcolor{si-yellow}{.6 .6 0}
\newrgbcolor{hb}{0.75 0.77 0.89}
\end{pspicture}
-\begin{picture}(0,0)(-10,68)
+\begin{picture}(0,0)(-3,68)
\includegraphics[width=2.6cm]{wide_band_gap.eps}
\end{picture}
-\begin{picture}(0,0)(-295,-165)
-\includegraphics[width=3cm]{sic_led.eps}
+\begin{picture}(0,0)(-285,-162)
+\includegraphics[width=3.38cm]{sic_led.eps}
\end{picture}
-\begin{picture}(0,0)(-215,-165)
-\includegraphics[width=2.5cm]{6h-sic_3c-sic.eps}
+\begin{picture}(0,0)(-195,-162)
+\includegraphics[width=2.8cm]{6h-sic_3c-sic.eps}
\end{picture}
\begin{picture}(0,0)(-313,65)
\includegraphics[width=2.2cm]{infineon_schottky.eps}
\begin{picture}(0,0)(-220,65)
\includegraphics[width=2.9cm]{sic_wechselrichter_ise.eps}
\end{picture}
+\begin{picture}(0,0)(0,-160)
+\includegraphics[width=3.0cm]{sic_proton.eps}
+\end{picture}
+\begin{picture}(0,0)(-60,65)
+\includegraphics[width=3.4cm]{sic_switch.eps}
+\end{picture}
\end{slide}
}
\begin{itemize}
- \item Polyteps and fabrication of silicon carbide
+ \item Polytyps and fabrication of silicon carbide
\item Supposed precipitation mechanism of SiC in Si
\item Utilized simulation techniques
\begin{itemize}
}
\end{minipage}
\end{picture}
+ \begin{picture}(0,0)(-230,-35)
+ \framebox{
+ {\footnotesize\color{blue}\bf Hex: micropipes along c-axis}
+ }
+ \end{picture}
+ \begin{picture}(0,0)(-230,-10)
+ \framebox{
+ \begin{minipage}{3cm}
+ {\footnotesize\color{blue}\bf 3C-SiC fabrication\\
+ less advanced}
+ \end{minipage}
+ }
+ \end{picture}
\end{slide}
\psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
\rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
\psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
+\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+ $4a_{\text{Si}}=5a_{\text{SiC}}$
+ }}}
+\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\hkl(h k l) planes match
+ }}}
\end{pspicture}
-
+
\end{slide}
\begin{slide}
n(r)=\sum_i^N|\Phi_i(r)|^2
\]
\item \underline{Self-consistent solution}\\
-$n(r)$ depends on $\Phi_i$, which depends on $V_{\text{eff}}$,
+$n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
which in turn depends on $n(r)$
\item \underline{Variational principle}
- minimize total energy with respect to $n(r)$
\[
\rightarrow
\text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
+\qquad ({\color{blue}300\text{ eV}})
\]
- \item \underline{$k$-point sampling} - $\Gamma$-point only calculations
+ \item \underline{Brillouin zone sampling} -
+ {\color{blue}$\Gamma$-point only} calculations
\item \underline{Pseudo potential}
- consider only the valence electrons
\item \underline{Code} - VASP 4.6
\item Structural optimization: Conjugate gradient method
\end{itemize}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
+\end{pspicture}
+
\end{slide}
\begin{slide}
\begin{slide}
{\large\bf\boldmath
- Migration involving the C \hkl<1 1 0> dumbbell interstitial
+ Migrations involving the C \hkl<1 1 0> dumbbell interstitial
}
-\scriptsize
+\small
+\vspace*{0.1cm}
+
+VASP
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=6cm]{vasp_mig/110_mig_vasp.ps}
+\end{minipage}
+\begin{minipage}{7cm}
+\underline{Alternative pathway and energies [eV]}\\[0.1cm]
+\hkl<0 -1 0> $\stackrel{0.7}{{\color{red}\longrightarrow}}$
+\hkl<1 1 0> $\stackrel{0.95}{{\color{blue}\longrightarrow}}$
+BC $\stackrel{0.25}{\longrightarrow}$ \hkl<0 0 -1>\\[0.3cm]
+Composed of three single transitions\\[0.3cm]
+Activation energy of second transition slightly\\
+higher than direct transition (path 2)\\[0.3cm]
+$\Rightarrow$ very unlikely to happen
+\end{minipage}\\[0.2cm]
+
+Erhart/Albe
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=6cm]{110_mig.ps}
+\end{minipage}
+\begin{minipage}{7cm}
+\underline{Alternative pathway and energies [eV]}\\[0.1cm]
+\hkl<0 0 -1> $\stackrel{2.2}{{\color{green}\longrightarrow}}$
+\hkl<1 1 0> $\stackrel{0.9}{{\color{red}\longrightarrow}}$
+\hkl<0 0 -1>\\[0.3cm]
+Composed of two single transitions\\[0.3cm]
+Compared to direct transition: (2.2 eV \& 0.5 eV)\\[0.3cm]
+$\Rightarrow$ more readily constituting a probable transition
+\end{minipage}
\end{slide}
\begin{slide}
{\large\bf\boldmath
- Combinations of point defects
+ Combinations with a C-Si \hkl<1 0 0>-type interstitial
}
-\scriptsize
+\small
+
+\vspace*{0.1cm}
+
+Binding energy:
+$
+E_{\text{b}}=
+E_{\text{f}}^{\text{defect combination}}-
+E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
+E_{\text{f}}^{\text{2nd defect}}
+$
+
+\vspace*{0.1cm}
+
+{\scriptsize
+\begin{tabular}{l c c c c c c}
+\hline
+ $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
+ \hline
+ \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
+ \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
+ \hkl<0 -1 0> & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl<0 1 0> & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hkl<-1 0 0> & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl<1 0 0> & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hline
+ C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
+ Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
+\hline
+\end{tabular}
+}
+
+\vspace*{0.3cm}
+
+\footnotesize
+
+\begin{minipage}[t]{3.8cm}
+\underline{\hkl<1 0 0> at position 1}\\[0.1cm]
+\includegraphics[width=3.5cm]{00-1dc/2-25.eps}
+\end{minipage}
+\begin{minipage}[t]{3.5cm}
+\underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
+\includegraphics[width=3.2cm]{00-1dc/2-39.eps}
+\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 Stress compensation / increase
+ \item Most favorable: C clustering
+ \item Unfavored: antiparallel orientations
+ \item Indication of energetically favored\\
+ agglomeration
+\end{itemize}
+\end{minipage}
+
+\begin{picture}(0,0)(-295,-130)
+\includegraphics[width=3.5cm]{comb_pos.eps}
+\end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combinations of C-Si \hkl<1 0 0>-type interstitials
+ }
+
+\small
+
+\vspace*{0.1cm}
+
+Energetically most favorable combinations along \hkl<1 1 0>
+
+\vspace*{0.1cm}
+
+{\scriptsize
+\begin{tabular}{l c c c c c c}
+\hline
+ & 1 & 2 & 3 & 4 & 5 & 6\\
+\hline
+$E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
+C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
+Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\
+\hline
+\end{tabular}
+}
+
+\vspace*{0.3cm}
+
+\begin{minipage}{7.0cm}
+\includegraphics[width=7cm]{db_along_110_cc.ps}
+\end{minipage}
+\begin{minipage}{6.0cm}
+\begin{center}
+{\color{blue}
+ Interaction proportional to reciprocal cube of C-C distance
+}\\[0.2cm]
+ Saturation in the immediate vicinity
+\end{center}
+\end{minipage}
+
+\vspace{0.2cm}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
+ }
+
+ \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{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
+\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 Interaction drops quickly to zero\\
+ (low interaction capture radius)
+\end{itemize}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Migration in C-Si \hkl<1 0 0> and vacancy combinations
+ }
+
+ \footnotesize
+
+\vspace{0.1cm}
+
+\begin{minipage}[t]{3cm}
+\underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
+\includegraphics[width=2.8cm]{00-1dc/0-59.eps}
+\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}
+\end{minipage}
+\begin{minipage}[t]{3cm}
+\underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
+\includegraphics[width=2.8cm]{00-1dc/3-14.eps}
+\end{minipage}
+
+\framebox{
+\begin{minipage}{5.9cm}
+\includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
+\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}
+}
+\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}
+\begin{picture}(0,0)(12.5,5)
+\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{slide}
\begin{slide}
{\large\bf
- Silicon carbide precipitation simulations
+ Conclusion of defect / migration / combined defect simulations
}
\small
+\vspace*{0.1cm}
+
+Defect structures
+\begin{itemize}
+ \item Accurately described by quantum-mechanical simulations
+ \item Less correct description by classical potential simulations
+\end{itemize}
+\vspace*{0.2cm}
+\begin{itemize}
+ \item Consistent with solubility data of C in Si
+ \item \hkl<1 0 0> C-Si dumbbell interstitial ground state configuration
+ \item Consistent with reorientation and diffusion experiments
+ \item C migration pathway in Si identified
+\end{itemize}
+
+\vspace*{0.2cm}
+
+Concerning the precipitation mechanism
+\begin{itemize}
+ \item Agglomeration of C-Si dumbbells energetically favorable
+ \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 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}
+
+\vspace*{0.1cm}
+\begin{center}
+{\color{blue}Some results point to a different precipitation mechanism!}
+\end{center}
+
\end{slide}
\begin{slide}
{\large\bf
- Investigation of a silicon carbide precipitate in silicon
+ Silicon carbide precipitation simulations
+ }
+
+ \small
+
+{\scriptsize
+ \begin{pspicture}(0,0)(12,6.5)
+ % nodes
+ \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+ \parbox{7cm}{
+ \begin{itemize}
+ \item Create c-Si volume
+ \item Periodc boundary conditions
+ \item Set requested $T$ and $p=0\text{ bar}$
+ \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
+ \end{itemize}
+ }}}}
+ \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
+ \parbox{7cm}{
+ 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 consisting of Si atoms to form a minimal {\pnode{in3}}\\
+ precipitate
+ \end{itemize}
+ }}}}
+ \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
+ \parbox{7.0cm}{
+ Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
+ }}}}
+ \ncline[]{->}{init}{insert}
+ \ncline[]{->}{insert}{cool}
+ \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
+ \rput(7.8,6){\footnotesize $V_1$}
+ \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 $V_3$}
+ \rput(7.9,3.2){\pnode{ins1}}
+ \rput(9.22,2.8){\pnode{ins2}}
+ \rput(11.0,2.4){\pnode{ins3}}
+ \ncline[]{->}{in1}{ins1}
+ \ncline[]{->}{in2}{ins2}
+ \ncline[]{->}{in3}{ins3}
+ \end{pspicture}
+}
+
+\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
+ (238328 Si atoms)
+\end{itemize}
+
+\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}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Limitations of molecular dynamics and short range potentials
+ }
+
+\footnotesize
+
+\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
+ of vibrational periods\\
+$\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
+ infrequent transition events\\[0.1cm]
+{\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}
+
+\framebox{
+\color{red}
+Potential enhanced problem of slow phase space propagation
+}
+
+\vspace{0.3cm}
+
+\underline{Approach to the (twofold) problem}\\[0.2cm]
+Increased temperature simulations without TAD corrections\\
+(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}
+\end{minipage}
+}
+\end{picture}
+
+\begin{picture}(0,0)(-305,-155)
+\framebox{
+\begin{minipage}{2.5cm}
+\tiny
+\begin{center}
+retain proper\\
+thermodynmic sampling
+\end{center}
+\end{minipage}
+}
+\end{picture}
+
+\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}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Increased temperature simulations at high C concentration
+ }
+
+\footnotesize
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{12_pc_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\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}
+
+\framebox{
+\begin{minipage}[t]{6.0cm}
+0.186 nm: Si-C pairs $\uparrow$\\
+(as expected in 3C-SiC)\\[0.2cm]
+0.282 nm: Si-C-C\\[0.2cm]
+$\approx$0.35 nm: C-Si-Si
+\end{minipage}
+}
+\begin{minipage}{0.2cm}
+\hfill
+\end{minipage}
+\framebox{
+\begin{minipage}[t]{6.0cm}
+0.15 nm: C-C pairs $\uparrow$\\
+(as expected in graphite/diamond)\\[0.2cm]
+0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
+0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
+\end{minipage}
+}
+
+\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]
+\framebox{
+\bf
+Continue with higher temperatures and longer time scales
+}
+\end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Valuation of a practicable temperature limit
+ }
+
+ \small
+
+\vspace{0.1cm}
+
+\begin{center}
+\framebox{
+{\color{blue}
+Recrystallization is a hard task!
+$\Rightarrow$ Avoid melting!
+}
+}
+\end{center}
+
+\vspace{0.1cm}
+
+\footnotesize
+
+\begin{minipage}{7.5cm}
+\includegraphics[width=7cm]{fe_and_t.ps}
+\end{minipage}
+\begin{minipage}{5.5cm}
+\underline{Melting does not occur instantly after}\\
+\underline{exceeding the melting point $T_{\text{m}}=2450\text{ K}$}
+\begin{itemize}
+\item required transition enthalpy
+\item hysterisis behaviour
+\end{itemize}
+\underline{Heating up c-Si by 1 K/ps}
+\begin{itemize}
+\item transition occurs at $\approx$ 3125 K
+\item $\Delta E=0.58\text{ eV/atom}=55.7\text{ kJ/mole}$\\
+ (literature: 50.2 kJ/mole)
+\end{itemize}
+\end{minipage}
+
+\vspace{0.1cm}
+
+\framebox{
+\begin{minipage}{4cm}
+Initially chosen temperatures:\\
+$1.0 - 1.2 \cdot T_{\text{m}}$
+\end{minipage}
+}
+\begin{minipage}{3cm}
+\begin{center}
+$\Longrightarrow$
+\end{center}
+\end{minipage}
+\framebox{
+\begin{minipage}{5cm}
+Introduced C (defects)\\
+$\rightarrow$ reduction of transition point\\
+$\rightarrow$ melting already at $T_{\text{m}}$
+\end{minipage}
+}
+
+\vspace{0.4cm}
+
+\begin{center}
+\framebox{
+{\color{blue}
+Maximum temperature used: $0.95\cdot T_{\text{m}}$
+}
+}
+\end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Long time scale simulations at maximum temperature
+ }
+
+\small
+
+\vspace{0.1cm}
+
+\underline{Differences}
+\begin{itemize}
+ \item Temperature set to $0.95 \cdot T_{\text{m}}$
+ \item Cubic insertion volume $\Rightarrow$ spherical insertion volume
+ \item Amount of C atoms: 6000 $\rightarrow$ 5500
+ $\Leftrightarrow r_{\text{prec}}=0.3\text{ nm}$
+ \item Simulation volume: 21 unit cells of c-Si in each direction
+\end{itemize}
+
+\footnotesize
+
+\vspace{0.3cm}
+
+\begin{minipage}[t]{4.5cm}
+\begin{center}
+\underline{Low C concentration, Si-C}
+\includegraphics[width=4.5cm]{c_in_si_95_v1_si-c.ps}\\
+Sharper peaks!
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{4.5cm}
+\begin{center}
+\underline{Low C concentration, C-C}
+\includegraphics[width=4.5cm]{c_in_si_95_v1_c-c.ps}\\
+Sharper peaks!\\
+No C agglomeration!
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{4cm}
+\begin{center}
+\underline{High C concentration}
+\includegraphics[width=4.5cm]{c_in_si_95_v2.ps}\\
+No significant changes
+\end{center}
+\end{minipage}
+
+\begin{center}
+\framebox{
+Long time scales and high temperatures most probably not sufficient enough!
+}
+\end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Investigation of a silicon carbide precipitate in silicon
+ }
+
+ \footnotesize
+
+\vspace{0.2cm}
+
+\framebox{
+\scriptsize
+\begin{minipage}{5.3cm}
+\[
+\frac{8}{a_{\text{Si}}^3}(
+\underbrace{21^3 a_{\text{Si}}^3}_{=V}
+-\frac{4}{3}\pi x^3)+
+\underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500}
+=21^3\cdot 8
+\]
+\[
+\Downarrow
+\]
+\[
+\frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500
+\Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}}
+\]
+\[
+y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}}
+\]
+\end{minipage}
+}
+\begin{minipage}{0.3cm}
+\hfill
+\end{minipage}
+\begin{minipage}{7.0cm}
+\underline{Construction}
+\begin{itemize}
+ \item Simulation volume: 21$^3$ unit cells of c-Si
+ \item Spherical topotactically aligned precipitate\\
+ $r=3.0\text{ nm}$ $\Leftrightarrow$ $\approx$ 5500 C atoms
+ \item Create c-Si but skipped inside sphere of radius $x$
+ \item Create 3C-SiC inside sphere of radius $x$\\
+ and lattice constant $y$
+ \item Strong coupling to heat bath ($T=20\,^{\circ}\mathrm{C}$)
+\end{itemize}
+\end{minipage}
+
+\vspace{0.3cm}
+
+\begin{minipage}{6.2cm}
+\includegraphics[width=6cm]{pc_0.ps}
+\end{minipage}
+\begin{minipage}{6.8cm}
+\underline{Results}
+\begin{itemize}
+ \item Slight increase of c-Si lattice constant!
+ \item C-C peaks (imply same distanced Si-Si peaks)
+ \begin{itemize}
+ \item New peak at 0.307 nm: 2$^{\text{nd}}$ NN in 3C-SiC
+ \item Bumps ({\color{green}$\downarrow$}):
+ 4$^{\text{th}}$ and 6$^{\text{th}}$ NN
+ \end{itemize}
+ \item 3C-SiC lattice constant: 4.34 \AA (bulk: 4.36 \AA)\\
+ $\rightarrow$ compressed precipitate
+ \item Interface tension:\\
+ 20.15 eV/nm$^2$ or $3.23 \times 10^{-4}$ J/cm$^2$\\
+ (literature: $2 - 8 \times 10^{-4}$ J/cm$^2$)
+\end{itemize}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Investigation of a silicon carbide precipitate in silicon
+ }
+
+ \footnotesize
+
+\begin{minipage}{7cm}
+\underline{Appended annealing steps}
+\begin{itemize}
+ \item artificially constructed interface\\
+ $\rightarrow$ allow for rearrangement of interface atoms
+ \item check SiC stability
+\end{itemize}
+\underline{Temperature schedule}
+\begin{itemize}
+ \item rapidly heat up structure up to $2050\,^{\circ}\mathrm{C}$\\
+ (75 K/ps)
+ \item slow heating up to $1.2\cdot T_{\text{m}}=2940\text{ K}$
+ by 1 K/ps\\
+ $\rightarrow$ melting at around 2840 K
+ (\href{../video/sic_prec_120.avi}{$\rhd$})
+ \item cooling down structure at 100 \% $T_{\text{m}}$ (1 K/ps)\\
+ $\rightarrow$ no energetically more favorable struture
+\end{itemize}
+\end{minipage}
+\begin{minipage}{6cm}
+\includegraphics[width=6.7cm]{fe_and_t_sic.ps}
+\end{minipage}
+
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{sic_prec/melt_01.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{sic_prec/melt_02.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{sic_prec/melt_03.eps}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Summary / Conclusion / Outlook
+ }
+
+ \scriptsize
+
+\vspace{0.1cm}
+
+\framebox{
+\begin{minipage}{12.9cm}
+ \underline{Defects}
+ \begin{itemize}
+ \item Summary \& conclusion
+ \begin{itemize}
+ \item Point defects excellently / fairly well described
+ by QM / classical potential simulations
+ \item Identified migration path explaining
+ diffusion and reorientation experiments
+ \item Agglomeration of point defects energetically favorable
+ \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
+ \end{itemize}
+ \item Todo
+ \begin{itemize}
+ \item Discussions concerning interpretation of QM results (Paderborn)
+ \item Compare migration barrier of
+ \hkl<1 1 0> Si and C-Si \hkl<1 0 0> dumbbell
+ \item Combination: Vacancy \& \hkl<1 1 0> Si self-interstitial \&
+ C-Si \hkl<1 0 0> dumbbell (IBS)
+ \end{itemize}
+ \end{itemize}
+\end{minipage}
+}
+
+\vspace{0.2cm}
+
+\framebox{
+\begin{minipage}[t]{6.2cm}
+ \underline{Pecipitation simulations}
+ \begin{itemize}
+ \item Summary \& conclusion
+ \begin{itemize}
+ \item Low T
+ $\rightarrow$ C-Si \hkl<1 0 0> dumbbell\\
+ dominated structure
+ \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
+ \item High C concentration\\
+ $\rightarrow$ amorphous SiC like phase
+ \end{itemize}
+ \item Todo
+ \begin{itemize}
+ \item Accelerated method: self-guided MD
+ \item Activation relaxation technique
+ \item Constrainted transition path
+ \end{itemize}
+ \end{itemize}
+\end{minipage}
+}
+\framebox{
+\begin{minipage}[t]{6.2cm}
+ \underline{Constructed 3C-SiC precipitate}
+ \begin{itemize}
+ \item Summary \& conclusion
+ \begin{itemize}
+ \item Small / stable / compressed 3C-SiC\\
+ precipitate in slightly stretched\\
+ c-Si matrix
+ \item Interface tension matches experiemnts
+ \end{itemize}
+ \item Todo
+ \begin{itemize}
+ \item Try to improve interface
+ \item Precipitates of different size
+ \end{itemize}
+ \end{itemize}
+\end{minipage}
+}
+
+ \small
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Acknowledgements
+ }
+
+ \vspace{0.1cm}
+
+ \small
+
+ Thanks to \ldots
+
+ \underline{Augsburg}
+ \begin{itemize}
+ \item Prof. B. Stritzker (accepting a simulator at EP \RM{4})
+ \item Ralf Utermann (EDV)
+ \end{itemize}
+
+ \underline{Helsinki}
+ \begin{itemize}
+ \item Prof. K. Nordlund (MD)
+ \end{itemize}
+
+ \underline{Munich}
+ \begin{itemize}
+ \item Bayerische Forschungsstiftung (financial support)
+ \end{itemize}
+
+ \underline{Paderborn}
+ \begin{itemize}
+ \item Prof. J. Lindner (SiC)
+ \item Prof. G. Schmidt (DFT + financial support)
+ \item Dr. E. Rauls (DFT + SiC)
+ \end{itemize}
+
+\vspace{0.2cm}
+
+\begin{center}
+\framebox{
+\bf Thank you for your attention!
+}
+\end{center}
+
\end{slide}
\end{document}
projects / lectures / latex.git / blobdiff