\end{slide}
- \small
+\begin{slide}
+
+ {\large\bf
+ SiC-Ausscheidungsvorgang
+ }
+
+ \vspace{64pt}
+
+ Hier die aus experimentellen Untersuchungen heraus vermuteten
+ Ausscheidungsvorgaenge rein.
+
+\end{slide}
+
\begin{slide}
{\large\bf
}
\small
+
\vspace{6pt}
- Vermuteter SiC-Ausscheidungsvorgang in Si:
+ Vermuteter 3C-SiC-Ausscheidungsvorgang in c-Si:
\vspace{8pt}
\end{minipage}
\hspace{0.6cm}
\begin{minipage}{3.8cm}
- Ausscheidung von 3C-SiC + Erzeugung von Si-Zwischengitteratomen\\
+ Ausscheidung von 3C-SiC + Erzeugung von Si-Zwischengitteratomen
\end{minipage}
\vspace{12pt}
- \begin{minipage}{7cm}
- Experimentally observed [3]:
+ Aus experimentellen Untersuchungen:
\begin{itemize}
- \item Minimal diameter of precipitation: 4 - 5 nm
- \item Equal orientation of Si and SiC (hkl)-planes
+ \item kritischer Durchmesser einer Ausscheidung: 4 - 5 nm
+ \item gleiche Orientierung der c-Si and 3C-SiC (hkl)-Ebenen
\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}
-\end{document}
-
\begin{slide}
{\large\bf
- Simulation details
+ Details der MD-Simulation
}
+ \vspace{12pt}
\small
- {\bf MD basics:}
+ {\bf MD-Grundlagen:}
\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 or ensemble averages
+ \item Mikroskopische Beschreibung eines N-Teilchensystems
+ \item Analytisches Wechselwirkungspotential
+ \item Numerische Integration der Newtonschen Bewegungsgleichung\\
+ als Propagationsvorschrift im 6N-dimensionalen Phasenraum
+ \item Observablen sind die Zeit- und/oder Ensemblemittelwerte
\end{itemize}
- {\bf Application details:}
+ {\bf Details der Simulation:}
\begin{itemize}
- \item Integrator: Velocity Verlet, timestep: $1\text{ fs}$
- \item Ensemble: isothermal-isobaric NPT [4]
+ \item Integration: Velocity Verlet, Zeitschritt: $1\text{ fs}$
+ \item Ensemble: NpT, isothermal-isobares Ensemble
\begin{itemize}
- \item Berendsen thermostat:
+ \item Berendsen Thermostat:
$\tau_{\text{T}}=100\text{ fs}$
- \item Brendsen barostat:\\
+ \item Berendsen Barostat:\\
$\tau_{\text{P}}=100\text{ fs}$,
$\beta^{-1}=100\text{ GPa}$
\end{itemize}
- \item Potential: Tersoff-like bond order potential [5]
+ \item Potential: Tersoff-"ahnliches 'bond order' Potential
+ \vspace*{12pt}
\[
E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
\pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
\]
\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)
+ \begin{picture}(0,0)(-230,-30)
\includegraphics[width=5cm]{tersoff_angle.eps}
\end{picture}
\begin{slide}
{\large\bf
- Simulation sequence
+ Zwischengitter-Konfigurationen
}
\vspace{8pt}
- Interstitial configurations:
+ Simulationssequenz:\\
\vspace{8pt}
\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 initiale Konfiguration:\\
+ $9\times9\times9$ Einheitszellen c-Si
+ \item periodische Randbedingungen
\item $T=0\text{ K}$, $p=0\text{ bar}$
\end{itemize}
}}}}
\rput(3.5,3.5){\rnode{insert}{\psframebox{
\parbox{7cm}{
- Insertion of C / Si atom:
+ Einf"ugen der C/Si Atome:
\begin{itemize}
- \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
+ \item $(0,0,0)$ $\rightarrow$ {\color{red}tetraedrisch}
(${\color{red}\triangleleft}$)
\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}
+ $\rightarrow$ {\color{magenta}110 Dumbbell}
(${\color{magenta}\Box}$,$\circ$)
- \item random positions (critical distance check)
+ \item zuf"allige Position (Minimalabstand)
\end{itemize}
}}}}
\rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
\parbox{3.5cm}{
- Relaxation time: $2\, ps$
+ Relaxation ($>2$ ps)
}}}}
\ncline[]{->}{init}{insert}
\ncline[]{->}{insert}{cool}
\begin{slide}
{\large\bf
- Results
- } - Si self-interstitial runs
+ Zwischengitter-Konfigurationen
+ }
\small
\begin{minipage}[t]{4.3cm}
- \underline{Tetrahedral}\\
+ \underline{Tetraedrisch}\\
$E_f=3.41$ eV\\
\includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
\end{minipage}
\begin{minipage}[t]{4.3cm}
- \underline{110 dumbbell}\\
+ \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!)\\
+ $E_f^{\star}\approx4.48$ eV (nicht stabil!)\\
\includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
\end{minipage}
- \underline{Random insertion}
+ \underline{zuf"allige Positionen}
\begin{minipage}{4.3cm}
$E_f=3.97$ eV\\
\begin{slide}
{\large\bf
- Results
- } - Carbon interstitial runs
+ Zwischengitter-Konfigurationen
+ }
\small
\begin{minipage}[t]{4.3cm}
- \underline{Tetrahedral}\\
+ \underline{Tetraedrisch}\\
$E_f=2.67$ eV\\
\includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
\end{minipage}
\begin{minipage}[t]{4.3cm}
- \underline{110 dumbbell}\\
+ \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!)\\
+ $E_f^{\star}\approx5.6$ eV (nicht stabil!)\\
\includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
\end{minipage}
- \underline{Random insertion}
+ \underline{zuf"allige Positionen}
\footnotesize
$E_f=0.47$ eV\\
\includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
\begin{picture}(0,0)(-15,-3)
- 100 dumbbell
+ 100 Dumbbell
\end{picture}
\end{minipage}
\begin{minipage}[t]{3.3cm}
\begin{slide}
{\large\bf
- Results
- } - <100> dumbbell configuration
+ Zwischengitter-Konfigurationen
+ }
+
+ Das 100 Dumbbell
\vspace{8pt}
\begin{slide}
{\large\bf
- Simulation sequence
+ Simulationen zum Ausscheidungsvorgang
}
\small
\vspace{8pt}
- SiC precipitation simulations:
+ Simulationssequenz:\\
\vspace{8pt}
\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 initiale Konfiguration:\\
+ $31\times31\times31$ c-Si Einheitszellen
+ \item periodsche Randbedingungen
\item $T=450\, ^{\circ}\text{C}$, $p=0\text{ bar}$
- \item Equilibration of $E_{kin}$ and $E_{pot}$
+ \item "Aquilibrierung von $E_{\text{kin}}$ and $E_{\text{pot}}$
\end{itemize}
}}}}
\rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
\parbox{7cm}{
- Insertion of 6000 carbon atoms at constant\\
- temperature into:
+ Einf"ugen von 6000 C-Atomen bei konstanter Temperatur\\
\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}}
+ \item gesamte Simulationsvolumen {\pnode{in1}}
+ \item Volumen einer minimal SiC-Ausscheidung {\pnode{in2}}
+ \item Bereich der ben"otigten Si-Atome {\pnode{in3}}
\end{itemize}
}}}}
\rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
\parbox{3.5cm}{
- Cooling down to $20\, ^{\circ}C$
+ Abk"uhlen auf $20\, ^{\circ}\textrm{C}$
}}}}
\ncline[]{->}{init}{insert}
\ncline[]{->}{insert}{cool}
\end{slide}
+\end{document}
+
\begin{slide}
{\large\bf
projects / lectures / latex.git / commitdiff