\usepackage{pstricks}
\usepackage{pst-node}
+%\usepackage{epic}
+%\usepackage{eepic}
+
\usepackage{graphicx}
\graphicspath{{../img/}}
% contents
-\begin{slide}
-
- \begin{center}
- {\bf
- Molecular dynamics simulation study\\
- of the silicon carbide precipitation process
- }
- \end{center}
-
- \vspace{16pt}
-
- {\large\bf
- Outline
- }
-
- \vspace{16pt}
-
- \begin{itemize}
- \item Motivation / Introduction
- \item Molecular dynamics simulation details
- \begin{itemize}
- \item Integrator, potential, ensemble control
- \item Simulation sequence
- \end{itemize}
- \item Simulation results
- \begin{itemize}
- \item Interstitials in silicon
- \item SiC-precipitation experiments
- \end{itemize}
- \item Conclusion / Outlook
- \end{itemize}
-\end{slide}
+% no contents for such a short talk!
% start of contents
\vspace{16pt}
- Reasons for investigating C in Si:
+ Reasons for understanding the SiC precipitation process:
\begin{itemize}
\item 3C-SiC wide band gap semiconductor formation
\begin{itemize}
\item Unit cell:
\begin{itemize}
- \item {\color{yellow}fcc} $+$
+ \item {\color{orange}fcc} $+$
\item {\color{gray}fcc shifted $1/4$ of volume diagonal}
\end{itemize}
- \item Lattice constants: $4a_{Si}\approx5a_{SiC}$
+ \item Lattice constants:
+ \[
+ 4a_{Si}\approx5a_{SiC}
+ \]
\item Silicon density:
\[
- \frac{n_{SiC}}{n_{Si}}=
- \frac{4/a_{SiC}^3}{8/a_{Si}^3}=
- \frac{5^3}{2\cdot4^3}={\color{cyan}97,66}\,\%
- \]
+ \frac{n_{SiC}}{n_{Si}}=97,66\,\%
+ \]
\end{itemize}
\end{minipage}
\hspace{8pt}
Experimentally observed:
\begin{itemize}
\item Minimal diameter of precipitation: 4 - 5 nm
- \item (hkl)-planes identical for Si and SiC
+ \item Equal orientation of Si and SiC (hkl)-planes
\end{itemize}
\end{slide}
Application details:
\begin{itemize}
\item Integrator: Velocity Verlet, timestep: $1\, fs$
- \item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$
+ \item Ensemble: NVT, Berendsen thermostat, $\tau=100.0$
\item Potential: Tersoff-like bond order potential\\
\[
E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
\pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
\]
\begin{center}
- {\scriptsize P. Erhart und K. Albe. Phys. Rev. B 71 (2005) 035211}
+ {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211}
\end{center}
\end{itemize}
Simulation details
}
- \vspace{20pt}
-
- Interstitial experiments:
-
- \vspace{12pt}
-
- \begin{itemize}
- \item Initial configuration: $9\times9\times9$ unit cells Si
- \item Periodic boundary conditions
- \item $T=0 \, K$
- \item Insertion of Si / C atom at
- \begin{itemize}
- \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
- \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
- \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
- $\rightarrow$ {\color{yellow}110 dumbbell}
- \item random positions (critical distance check)
- \end{itemize}
- \item Relaxation time: $2\, ps$
- \item Optional heating-up
- \end{itemize}
-
- \begin{picture}(0,0)(-210,-45)
- \includegraphics[width=6cm]{unit_cell.eps}
- \end{picture}
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf
- Simulation details
- }
+ \vspace{8pt}
- \small
+ Interstitial simulations:
- SiC precipitation experiments:
+ \vspace{8pt}
- \begin{pspicture}(0,0)(12,8)
- % nodes
- \rput(4.5,6.5){\rnode{init}{\psframebox{\parbox{7cm}{
+ \begin{pspicture}(0,0)(7,8)
+ \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
+ \parbox{7cm}{
\begin{itemize}
- \item Initial configuration: $31\times31\times31$ unit cells Si
+ \item Initial configuration: $9\times9\times9$ unit cells Si
\item Periodic boundary conditions
- \item $T=450\, ^{\circ}C$
- \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
+ \item $T=0 \, K$
\end{itemize}
}}}}
- \rput(4.5,4.5){\rnode{tc1}{\psframebox[fillstyle=solid,fillcolor=red]{
- $T=450\pm 1\, ^{\circ}C$}}}
- \rput(7,3.5){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
- \parbox{3cm}{
- Insertion of 10 atoms\\
- at random positions}}}}
- \rput(2,3.5){\rnode{adj1}{\psframebox[fillstyle=solid,fillcolor=red]{
- \parbox{3.5cm}{
- Adjusting temperature\\
- for another $100\, fs$}}}}
- \rput(7,2.5){\rnode{nc}{\psframebox[fillstyle=solid,fillcolor=red]{
- $N_{atoms}=6000$}}}
- \rput(4.5,2){\rnode{tc2}{\psframebox[fillstyle=solid,fillcolor=cyan]{
- $T=T_{set}$}}}
- \rput(7,1){\rnode{td}{\psframebox[fillstyle=solid,fillcolor=cyan]{
- $T_{set}:=T_{set}-1\, ^{\circ}C$}}}
- \rput(2,1){\rnode{adj2}{\psframebox[fillstyle=solid,fillcolor=cyan]{
- \parbox{3.5cm}{
- Adjusting temperature\\
- for another $50\, fs$}}}}
- \rput(7,0){\rnode{tc3}{\psframebox[fillstyle=solid,fillcolor=cyan]{
- $T_{set}=20\, ^{\circ}C$}}}
- \rput(10,0){\rnode{end}{\psframebox{End}}}
- % help nodes
- \rput(7,4.5){\pnode{tc1-h}}
- \rput(2,4.5){\pnode{tc1-hh}}
- \rput(4.5,2.5){\pnode{nc-h}}
- \rput(9,2.5){\pnode{nc-hh}}
- \rput(9,2){\pnode{tc2-h}}
- \rput(2,2){\pnode{tc2-hh}}
- \rput(4.5,0){\pnode{tc3-h}}
- % direct lines
- \ncline[]{->}{init}{tc1}
- \ncline[]{->}{adj1}{tc1}
- \ncline[]{->}{insert}{nc}
- \ncline[]{->}{adj2}{tc2}
- \ncline[]{->}{tc2}{td}
- \lput*{0}{yes}
- \ncline[]{->}{td}{tc3}
- \ncline[]{->}{tc3}{end}
- \lput*{0}{yes}
- % lines using help nodes
- \ncline[]{tc1}{tc1-h}
- \lput*{0}{yes}
- \ncline[]{->}{tc1-h}{insert}
- \ncline[]{tc1}{tc1-hh}
- \lput*{0}{no}
- \ncline[]{->}{tc1-hh}{adj1}
- \ncline[]{nc}{nc-h}
- \lput*{0}{no}
- \ncline[]{->}{nc-h}{tc1}
- \ncline[]{nc}{nc-hh}
- \ncline[]{-}{nc-hh}{tc2-h}
- \ncline[]{->}{tc2-h}{tc2}
- \lput*{0}{yes, {\footnotesize $T_{set}:=450\, ^{\circ}C$}}
- \ncline[]{tc2}{tc2-hh}
- \lput*{0}{no}
- \ncline[]{->}{tc2-hh}{adj2}
- \ncline[]{tc3}{tc3-h}
- \lput*{0}{no}
- \ncline[]{->}{tc3-h}{tc2}
- % insertion volumes
- \psframe[fillstyle=solid,fillcolor=white](9.5,1.3)(13.5,5.3)
- \psframe[fillstyle=solid,fillcolor=lightgray](10,1.8)(13,4.8)
- \psframe[fillstyle=solid,fillcolor=gray](10.5,2.3)(12.5,4.3)
- \rput(9.75,3){\pnode{ins1}}
- \rput(10.25,3.3){\pnode{ins2}}
- \rput(10.75,3.6){\pnode{ins3}}
- \ncline[]{-}{insert}{ins1}
- \ncline[]{-}{insert}{ins2}
- \ncline[]{-}{insert}{ins3}
- \psframe[fillstyle=solid,fillcolor=white](9.5,7.6)(13.5,8.1)
- \psframe[fillstyle=solid,fillcolor=lightgray](9.5,6.8)(13.5,7.3)
- \psframe[fillstyle=solid,fillcolor=gray](9.5,6)(13.5,6.5)
- \rput(11.5,7.85){{\tiny Simulation volume:
- $31\times31\times31\, a^3_{Si}$}}
- \rput(11.5,7.05){{\tiny Volume of minimal SiC precipitation}}
- \rput(11.5,6.25){{\tiny Volume of necessary amount of Si}}
+\rput(3.5,3.5){\rnode{insert}{\psframebox{
+ \parbox{7cm}{
+ Insertion of C / Si atom:
+ \begin{itemize}
+ \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
+ \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
+ \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
+ $\rightarrow$ {\color{magenta}110 dumbbell}
+ \item random positions (critical distance check)
+ \end{itemize}
+ }}}}
+ \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ \parbox{3.5cm}{
+ Relaxation time: $2\, ps$
+ }}}}
+ \ncline[]{->}{init}{insert}
+ \ncline[]{->}{insert}{cool}
\end{pspicture}
+ \begin{picture}(0,0)(-210,-45)
+ \includegraphics[width=6cm]{unit_cell.eps}
+ \end{picture}
+
\end{slide}
\begin{slide}
{\large\bf
Results
- }
-
- Si self-interstitial experiments:
-
- {\footnotesize
- {\bf Note:}
- \begin{itemize}
- \item $r_{cutoff}^{Si-Si}=2.96>\frac{5.43}{2}$
- \item Bond length near $r_{cutoff} \Rightarrow$ small bond strength
- \end{itemize}
- }
-
- \vspace{8pt}
+ } - Si self-interstitial runs
\small
- \begin{minipage}[t]{4.0cm}
- \underline{Tetrahedral}
- \begin{itemize}
- \item $E_f=3.41\, eV$
- \item essentialy tetrahedral\\
- bonds
- \end{itemize}
- \end{minipage}
- \hspace{0.3cm}
- \begin{minipage}[t]{4.0cm}
- \underline{110 dumbbell}
- \begin{itemize}
- \item $E_f=4.39\, eV$
- \item essentially 4 bonds
- \end{itemize}
- \end{minipage}
- \hspace{0.3cm}
- \begin{minipage}[t]{4.0cm}
- \underline{Hexagonal}
- \begin{itemize}
- \item $E_f^{\star}\approx4.48\, eV$
- \item unstable!
- \end{itemize}
- \end{minipage}
-
- \vspace{8pt}
-
\begin{minipage}[t]{4.3cm}
+ \underline{Tetrahedral}\\
+ $E_f=3.41\, eV$\\
\includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
\end{minipage}
\begin{minipage}[t]{4.3cm}
+ \underline{110 dumbbell}\\
+ $E_f=4.39\, eV$\\
\includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
\end{minipage}
\begin{minipage}[t]{4.3cm}
+ \underline{Hexagonal} \hspace{4pt}
+ \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
+ $E_f^{\star}\approx4.48\, eV$ (unstable!)\\
\includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
- \begin{center}
- \href{../video/si_self_int_hexa.avi}{$\rhd$}
- \end{center}
\end{minipage}
-\end{slide}
-
-\begin{slide}
-
- {\large\bf
- Results
- }
-
- \vspace{8pt}
-
- Si self-interstitial \underline{random insertion} experiments:
-
- \small
-
- \vspace{8pt}
-
- \begin{minipage}[t]{4.0cm}
- \begin{itemize}
- \item $E_f=3.97\, eV$
- \item 3 identical weak bonds
- \item displaced in volume\\ diagonal
- \end{itemize}
- \end{minipage}
- \hspace{0.3cm}
- \begin{minipage}[t]{4.0cm}
- \begin{itemize}
- \item $E_f=3.75\, eV$
- \item 4 identical weak bonds
- \item displaced in plane\\ diagonal
- \end{itemize}
- \end{minipage}
- \hspace{0.3cm}
- \begin{minipage}[t]{4.0cm}
- \begin{itemize}
- \item $E_f=3.56\, eV$
- \item single weak bond
- \item displaced along\\ $x$-direction
- \item closest to tetrahedral\\ configuration
- \end{itemize}
- \end{minipage}
-
- \vspace{8pt}
+ \underline{Random insertion}
\begin{minipage}{4.3cm}
+ $E_f=3.97\, eV$\\
\includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
\end{minipage}
\begin{minipage}{4.3cm}
+ $E_f=3.75\, eV$\\
\includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
\end{minipage}
\begin{minipage}{4.3cm}
+ $E_f=3.56\, eV$\\
\includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
\end{minipage}
- \vspace{8pt}
-
- \begin{center}
- {\footnotesize
- {\bf Note:} Displacements relative to tetrahedral configuration
- }
- \end{center}
-
\end{slide}
\begin{slide}
{\large\bf
Results
- }
-
- \vspace{8pt}
-
- Carbon interstitial experiments:
-
- \vspace{12pt}
+ } - Carbon interstitial runs
\small
- \begin{minipage}[t]{4.0cm}
- \underline{Tetrahedral}
- \begin{itemize}
- \item $E_f=2.67\, eV$
- \item tetrahedral bond
- \end{itemize}
- \end{minipage}
- \hspace{0.3cm}
- \begin{minipage}[t]{4.0cm}
- \underline{110 dumbbell}
- \begin{itemize}
- \item $E_f=1.76\, eV$
- \item C forms 3 bonds
- \end{itemize}
- \end{minipage}
- \hspace{0.3cm}
- \begin{minipage}[t]{4.0cm}
- \underline{Hexagonal}
- \begin{itemize}
- \item $E_f^{\star}\approx5.6\, eV$
- \item unstable!
- \end{itemize}
- \end{minipage}
-
- \vspace{8pt}
-
\begin{minipage}[t]{4.3cm}
+ \underline{Tetrahedral}\\
+ $E_f=2.67\, eV$\\
\includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
\end{minipage}
\begin{minipage}[t]{4.3cm}
+ \underline{110 dumbbell}\\
+ $E_f=1.76\, eV$\\
\includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
\end{minipage}
\begin{minipage}[t]{4.3cm}
+ \underline{Hexagonal} \hspace{4pt}
+ \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
+ $E_f^{\star}\approx5.6\, eV$ (unstable!)\\
\includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
- \begin{center}
- \href{../video/c_in_si_int_hexa.avi}{$\rhd$}
- \end{center}
\end{minipage}
+ \underline{Random insertion}
+
+ \footnotesize
+
+\begin{minipage}[t]{3.3cm}
+ $E_f=0.47\, eV$\\
+ \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
+ \begin{picture}(0,0)(-15,-3)
+ 001 dumbbell
+ \end{picture}
+\end{minipage}
+\begin{minipage}[t]{3.3cm}
+ $E_f=1.62\, eV$\\
+ \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
+\end{minipage}
+\begin{minipage}[t]{3.3cm}
+ $E_f=2.39\, eV$\\
+ \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
+\end{minipage}
+\begin{minipage}[t]{3.0cm}
+ $E_f=3.41\, eV$\\
+ \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
+\end{minipage}
+
\end{slide}
\begin{slide}
{\large\bf
- Results
+ Simulation details
}
+ \small
+
\vspace{8pt}
- Carbon \underline{random insertion} experiments:
+ SiC precipitation simulations:
\vspace{8pt}
- bar
+ \begin{pspicture}(0,0)(12,8)
+ % nodes
+ \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
+ \parbox{7cm}{
+ \begin{itemize}
+ \item Initial configuration: $31\times31\times31$ unit cells Si
+ \item Periodic boundary conditions
+ \item $T=450\, ^{\circ}C$
+ \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
+ \end{itemize}
+ }}}}
+ \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
+ \parbox{7cm}{
+ Insertion of $6000$ carbon atoms at constant\\
+ temperature into:
+ \begin{itemize}
+ \item Total simulation volume {\pnode{in1}}
+ \item Volume of minimal SiC precipitation {\pnode{in2}}
+ \item Volume of necessary amount of Si {\pnode{in3}}
+ \end{itemize}
+ }}}}
+ \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ \parbox{3.5cm}{
+ Cooling down to $20\, ^{\circ}C$
+ }}}}
+ \ncline[]{->}{init}{insert}
+ \ncline[]{->}{insert}{cool}
+ \psframe[fillstyle=solid,fillcolor=white](7.5,1.8)(13.5,7.8)
+ \psframe[fillstyle=solid,fillcolor=lightgray](9,3.3)(12,6.3)
+ \psframe[fillstyle=solid,fillcolor=gray](9.25,3.55)(11.75,6.05)
+ \rput(7.9,4.8){\pnode{ins1}}
+ \rput(9.22,4.4){\pnode{ins2}}
+ \rput(10.5,4.8){\pnode{ins3}}
+ \ncline[]{->}{in1}{ins1}
+ \ncline[]{->}{in2}{ins2}
+ \ncline[]{->}{in3}{ins3}
+ \end{pspicture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Very first results of the SiC precipitation runs
+ }
+
+ \footnotesize
+
+ \begin{minipage}[b]{6.9cm}
+ \includegraphics[width=6.3cm]{../plot/sic_prec_energy.ps}
+ \includegraphics[width=6.3cm]{../plot/sic_prec_temp.ps}
+ \end{minipage}
+ \begin{minipage}[b]{5.5cm}
+ \begin{itemize}
+ \item {\color{red} Total simulation volume}
+ \item {\color{green} Volume of minimal SiC precipitation}
+ \item {\color{blue} Volume of necessary amount of Si}
+ \end{itemize}
+ \vspace{40pt}
+ \includegraphics[width=6.3cm]{../plot/foo150.ps}
+ \end{minipage}
\end{slide}
\begin{slide}
{\large\bf
- Results
+ Very first results of the SiC precipitation runs
}
- SiC-precipitation experiments:
+ \begin{minipage}[t]{6.9cm}
+ \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
+ \includegraphics[width=6.3cm]{../plot/foo_end.ps}
+ \hspace{12pt}
+ \end{minipage}
+ \begin{minipage}[c]{5.5cm}
+ \includegraphics[width=6.0cm]{sic_si-c-n.eps}
+ \end{minipage}
\end{slide}
\begin{slide}
{\large\bf
- Conclusion / Outlook
+ Summary / Outlook
}
+\vspace{24pt}
+
+\begin{itemize}
+ \item Importance of understanding the SiC precipitation mechanism
+ \item Interstitial configurations in silicon using the Albe potential
+ \item Indication of SiC precipitation
+\end{itemize}
+
+\vspace{24pt}
+
+\begin{itemize}
+ \item Displacement and stress calculations
+ \item Refinement of simulation sequence to create 3C-SiC
+ \item Analyzing self-designed Si/SiC interface
+\end{itemize}
+
\end{slide}
\end{document}
projects / lectures / latex.git / blobdiff