Crystalline silicon and cubic silicon carbide
}
+ \vspace{8pt}
+
{\bf Lattice types and unit cells:}
\begin{itemize}
\item Crystalline silicon (c-Si) has diamond structure\\
$\Rightarrow {\color{si-yellow}\bullet}$ are Si atoms,
${\color{gray}\bullet}$ are C atoms
\end{itemize}
+ \vspace{8pt}
\begin{minipage}{8cm}
{\bf Lattice constants:}
\[
\vspace{12pt}
- Experimentally observed:
+ \begin{minipage}{7cm}
+ Experimentally observed [3]:
\begin{itemize}
\item Minimal diameter of precipitation: 4 - 5 nm
\item Equal orientation of Si and SiC (hkl)-planes
\end{itemize}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \vspace{32pt}
+ \hspace{16pt}
+ {\tiny [3] J. K. N. Lindner, Appl. Phys. A 77 (2003) 27.}
+ \end{minipage}
\end{slide}
Simulation details
}
- \vspace{12pt}
+ \small
- MD basics:
+ {\bf MD basics:}
\begin{itemize}
\item Microscopic description of N particle system
\item Analytical interaction potential
\item Hamilton's equations of motion as propagation rule\\
in 6N-dimensional phase space
- \item Observables obtained by time average
+ \item Observables obtained by time or ensemble averages
\end{itemize}
-
- \vspace{12pt}
-
- Application details:
+ {\bf Application details:}
\begin{itemize}
- \item Integrator: Velocity Verlet, timestep: $1\, fs$
- \item Ensemble: NVT, Berendsen thermostat, $\tau=100.0$
- \item Potential: Tersoff-like bond order potential\\
+ \item Integrator: Velocity Verlet, timestep: $1\text{ fs}$
+ \item Ensemble: isothermal-isobaric NPT [4]
+ \begin{itemize}
+ \item Berendsen thermostat:
+ $\tau_{\text{T}}=100\text{ fs}$
+ \item Brendsen barostat:\\
+ $\tau_{\text{P}}=100\text{ fs}$,
+ $\beta^{-1}=100\text{ GPa}$
+ \end{itemize}
+ \item Potential: Tersoff-like bond order potential [5]
\[
E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
\pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
\]
- \begin{center}
- {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211}
- \end{center}
\end{itemize}
+ {\tiny
+ [4] L. Verlet, Phys. Rev. 159 (1967) 98.}\\
+ {\tiny
+ [5] P. Erhart and K. Albe, Phys. Rev. B 71 (2005) 35211.}
\begin{picture}(0,0)(-240,-70)
\includegraphics[width=5cm]{tersoff_angle.eps}
\begin{slide}
{\large\bf
- Simulation details
+ Simulation sequence
}
\vspace{8pt}
- Interstitial simulations:
+ Interstitial configurations:
\vspace{8pt}
\begin{pspicture}(0,0)(7,8)
- \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
+ \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
\parbox{7cm}{
\begin{itemize}
\item Initial configuration: $9\times9\times9$ unit cells Si
\item Periodic boundary conditions
- \item $T=0 \, K$
+ \item $T=0\text{ K}$, $p=0\text{ bar}$
\end{itemize}
}}}}
\rput(3.5,3.5){\rnode{insert}{\psframebox{
Insertion of C / Si atom:
\begin{itemize}
\item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
+ (${\color{red}\triangleleft}$)
\item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
+ (${\color{green}\triangleright}$)
\item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
$\rightarrow$ {\color{magenta}110 dumbbell}
+ (${\color{magenta}\Box}$,$\circ$)
\item random positions (critical distance check)
\end{itemize}
}}}}
- \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
\parbox{3.5cm}{
Relaxation time: $2\, ps$
}}}}
\end{pspicture}
\begin{picture}(0,0)(-210,-45)
- \includegraphics[width=6cm]{unit_cell.eps}
+ \includegraphics[width=6cm]{unit_cell_s.eps}
\end{picture}
\end{slide}
\begin{slide}
{\large\bf
- Simulation details
+ Simulation sequence
}
\small
\begin{pspicture}(0,0)(12,8)
% nodes
- \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
+ \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
\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 $600\, fs$
+ \item $T=450\, ^{\circ}\text{C}$, $p=0\text{ bar}$
+ \item Equilibration of $E_{kin}$ and $E_{pot}$
\end{itemize}
}}}}
- \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
+ \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
\parbox{7cm}{
- Insertion of $6000$ carbon atoms at constant\\
+ Insertion of 6000 carbon atoms at constant\\
temperature into:
\begin{itemize}
\item Total simulation volume {\pnode{in1}}
\item Volume of necessary amount of Si {\pnode{in3}}
\end{itemize}
}}}}
- \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
\parbox{3.5cm}{
Cooling down to $20\, ^{\circ}C$
}}}}
\begin{slide}
{\large\bf
- Very first results of the SiC precipitation runs
- }
+ Results
+ } - SiC precipitation runs
\footnotesize