\usepackage[setpagesize=false]{hyperref}
+% units
+\usepackage{units}
+
\usepackage{semcolor}
\usepackage{semlayer} % Seminar overlays
\usepackage{slidesec} % Seminar sections and list of slides
\newrgbcolor{hlbb}{0.825 0.88 0.968}
\newrgbcolor{lachs}{1.0 .93 .81}
+% shortcuts
+\newcommand{\si}{Si$_{\text{i}}${}}
+\newcommand{\ci}{C$_{\text{i}}${}}
+\newcommand{\cs}{C$_{\text{sub}}${}}
+\newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
+\newcommand{\distn}[1]{\unit[#1]{nm}{}}
+\newcommand{\dista}[1]{\unit[#1]{\AA}{}}
+\newcommand{\perc}[1]{\unit[#1]{\%}{}}
+
% topic
\begin{slide}
\vspace{48pt}
-Yet another seminar contribution
+Yet another seminar talk
\vspace{08pt}
- Augsburg am 26. Mai 2011
+ Augsburg, 26. Mai 2011
\end{center}
\end{slide}
C interstitial point defects in silicon\\[-0.1cm]
}
-\begin{tabular}{l c c c c c c}
+\begin{tabular}{l c c c c c c r}
\hline
- $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B \\
+ $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
\hline
- VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 \\
- Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & 0.75 & 5.59$^*$ \\
+ VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
+ Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
\hline
\end{tabular}\\[0.1cm]
\scriptsize
+ \vspace{0.1cm}
+
\begin{minipage}{6.5cm}
\framebox{
-\begin{minipage}{5.9cm}
+\begin{minipage}[t]{5.9cm}
\begin{flushleft}
\includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
\end{flushleft}
\item Lowest activation energy: $\approx$ 2.2 eV
\item 2.4 times higher than VASP
\item Different pathway
- \item Transition minima ($\rightarrow$ \hkl<1 1 0> dumbbell)
\end{itemize}
\end{minipage}
\framebox{
\begin{minipage}{5.9cm}
-\begin{flushright}
-\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
-\end{flushright}
-\begin{center}
-\begin{pspicture}(0,0)(0,0)
-\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
-\end{pspicture}
-\begin{picture}(0,0)(60,-5)
-\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
-\end{picture}
-\begin{picture}(0,0)(0,-5)
-\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
-\end{picture}
-\begin{picture}(0,0)(-55,-5)
-\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
-\end{picture}
-\begin{picture}(0,0)(12.5,5)
-\includegraphics[width=1cm]{100_arrow.eps}
-\end{picture}
-\begin{picture}(0,0)(90,0)
-\includegraphics[height=0.9cm]{001_arrow.eps}
-\end{picture}
-\end{center}
-\vspace{0.2cm}
+%\begin{flushright}
+%\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
+%\end{flushright}
+%\begin{center}
+%\begin{pspicture}(0,0)(0,0)
+%\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
+%\end{pspicture}
+%\begin{picture}(0,0)(60,-5)
+%\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
+%\end{picture}
+%\begin{picture}(0,0)(0,-5)
+%\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
+%\end{picture}
+%\begin{picture}(0,0)(-55,-5)
+%\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
+%\end{picture}
+%\begin{picture}(0,0)(12.5,5)
+%\includegraphics[width=1cm]{100_arrow.eps}
+%\end{picture}
+%\begin{picture}(0,0)(90,0)
+%\includegraphics[height=0.9cm]{001_arrow.eps}
+%\end{picture}
+%\end{center}
+%\vspace{0.2cm}
+%\end{minipage}
+%}\\[0.2cm]
+%
+%\framebox{
+%\begin{minipage}{5.9cm}
+\includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
\end{minipage}
-}\\[0.2cm]
+}\\[0.1cm]
-\framebox{
\begin{minipage}{5.9cm}
-\includegraphics[width=5.9cm]{00-1_ip0-10.ps}
+Transition involving \ci{} \hkl<1 1 0>
+\begin{itemize}
+ \item Bond-centered configuration unstable\\
+ $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
+ \item Transition minima of path 2 \& 3\\
+ $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
+ \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
+ \item 2.4 - 3.4 times higher than VASP
+ \item Rotation of dumbbell orientation
+\end{itemize}
\end{minipage}
-}
\end{minipage}
Conclusion of defect / migration / combined defect simulations
}
- \small
+ \footnotesize
\vspace*{0.1cm}
\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
\end{itemize}
-\vspace*{0.2cm}
+
+Migration
\begin{itemize}
- \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
+ \item Consistent with reorientation and diffusion experiments
+\end{itemize}
+\begin{itemize}
+ \item Different path and ...
+ \item overestimated barrier by classical potential calculations
\end{itemize}
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{center}
-{\color{blue}Some results point to a different precipitation mechanism!}
+{\color{blue}Results suggest increased participation of \cs}
\end{center}
-In progress ...
-\begin{itemize}
- \item \hkl<1 0 0> C-Si $\rightarrow$
- C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
- \item \hkl<1 0 0> C-Si combinations: C-C $\rightarrow$ C-...-C
-\end{itemize}
-
\end{slide}
due to temperature\\[0.1cm]
\framebox{
\bf
-Continue with higher temperatures and longer time scales
+Actual SiC precipitation not accessible by MD
}
\end{center}
\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\\
-C-Si-Si $\uparrow$\\
-C-Si-C $\downarrow$
-\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
- Summary / Conclusion / Outlook
+ Summary and Conclusions
}
\scriptsize
\begin{minipage}{12.9cm}
\underline{Defects}
\begin{itemize}
- \item Summary \& conclusion
+ \item DFT / EA
\begin{itemize}
\item Point defects excellently / fairly well described
- by QM / classical potential simulations
+ 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
- \item Agglomeration of point defects energetically favorable
- \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
+ diffusion and reorientation experiments by DFT
+ \item EA fails to describe \ci{} migration:
+ Wrong path \& overestimated barrier
\end{itemize}
- \item In progress
- \begin{itemize}
- \item Migrations separating C-C bond in \hkl<1 0 0> C-Si dumbbell
- interstitial combination
- \item Migration: \hkl<1 0 0> C-Si $\rightarrow$
- C$_{\text{sub}}$ \& Si \hkl<1 1 0> interstitial
- \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)
+ \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{minipage}
\begin{minipage}[t]{12.9cm}
\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}
+ \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}
\end{minipage}
}
- \small
-
\end{slide}
\begin{slide}
\underline{Augsburg}
\begin{itemize}
- \item Prof. B. Stritzker (accepting a simulator at EP \RM{4})
+ \item Prof. B. Stritzker (accomodation at EP \RM{4})
\item Ralf Utermann (EDV)
\end{itemize}
projects / lectures / latex.git / commitdiff