\documentclass[portrait,a0b,final]{a0poster}
-\usepackage{epsf,psfig,pstricks,multicol,pst-grad,color}
+\usepackage{epsf,psfig,pstricks,multicol,pst-grad,pst-node,color}
\usepackage{graphicx,amsmath,amssymb}
\graphicspath{{../img/}}
\usepackage[english,german]{babel}
\background{.40 .48 .71}{.99 .99 .99}{0.5}
\newrgbcolor{si-yellow}{.6 .6 0}
+\newrgbcolor{hb}{0.75 0.77 0.89}
+\newrgbcolor{lbb}{0.75 0.8 0.88}
+\newrgbcolor{lachs}{1.0 .93 .81}
% Groesse der einzelnen Spalten als Anteil der Gesamt-Textbreite
\renewcommand{\columnfrac}{.31}
+% potential
+\newcommand{\pot}{\mathcal{V}}
+
% header
+\vspace{-18.5cm}
\begin{header}
\centerline{{\Huge \bfseries Molecular dynamics simulation
of defect formation and precipitation}}
\begin{poster}
+\vspace{-1cm}
\begin{pcolumn}
\begin{pbox}
\section*{Motivation}
- {\bf Reasons for understanding the 3C-SiC precipitation process}
+ {\bf Importance of the 3C-SiC precipitation process in silicon}
\begin{itemize}
- \item Significant technological progress
- in 3C-SiC wide band gap semiconductor thin film formation [1].
- \item New perspectives for processes relying upon prevention of
- precipitation, e.g. fabrication of strained pseudomorphic
- $\text{Si}_{1-y}\text{C}_y$ heterostructures [2].
+ \item SiC is a promising wide band gap material for high-temperature,
+ high-power, high-frequency semiconductor devices [1].
+ \item 3C-SiC epitaxial thin film formation on Si requires detailed
+ knowledge of SiC nucleation.
+ \item Fabrication of high carbon doped, strained pseudomorphic
+ $\text{Si}_{1-y}\text{C}_y$ layers requires suppression of
+ 3C-SiC nucleation [2].
\end{itemize}
{\tiny
[1] J. H. Edgar, J. Mater. Res. 7 (1992) 235.}\\
[2] J. W. Strane, S. R. Lee, H. J. Stein, S. T. Picraux,
J. K. Watanabe, J. W. Mayer, J. Appl. Phys. 79 (1996) 637.}
\end{pbox}
+ \vspace{-0.45cm}
\begin{pbox}
\section*{Crystalline silicon and cubic silicon carbide}
{\bf Lattice types and unit cells:}
\includegraphics[width=10cm]{sic_unit_cell.eps}
\end{minipage}
\end{pbox}
+ \vspace{-0.45cm}
\begin{pbox}
\section*{Supposed Si to 3C-SiC conversion}
{\bf Schematic of the conversion mechanism}\\\\
- \begin{minipage}{7.8cm}
- \includegraphics[width=7.7cm]{sic_prec_seq_01.eps}
+ \begin{minipage}[c]{8.8cm}
+ \includegraphics[width=8.0cm]{sic_prec_seq_01.eps}
\end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{7.8cm}
- \includegraphics[width=7.7cm]{sic_prec_seq_02.eps}
+ \begin{minipage}[c]{8.8cm}
+ \includegraphics[width=8.0cm]{sic_prec_seq_02.eps}
\end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{7.8cm}
- \includegraphics[width=7.7cm]{sic_prec_seq_03.eps}
+ \begin{minipage}[c]{8.1cm}
+ \includegraphics[width=8.0cm]{sic_prec_seq_03.eps}
\end{minipage}
\vspace{1cm}
\begin{enumerate}
\vspace{1cm}
{\bf Experimental observations} [3]
\begin{itemize}
- \item Minimal diameter of precipitation: 2 - 4 nm
+ \item Minimal radius of precipitates: 2 - 4 nm
\item Equal orientation of c-Si and 3C-SiC (hkl)-planes
\end{itemize}
{\tiny
[3] J. K. N. Lindner, Appl. Phys. A 77 (2003) 27.
}
\end{pbox}
+ \vspace{-0.45cm}
+ \begin{pbox}
+ \section*{Simulation details}
+ {\bf MD basics:}
+ \begin{itemize}
+ \item Microscopic description of N particles
+ \item Analytical interaction potential
+ \item Propagation rule in 6N-dim. phase space:
+ Hamilton's equations of motion
+ \item Observables obtained by time or ensemble averages
+ \end{itemize}
+ {\bf Application details:}\\[0.5cm]
+ \begin{minipage}{17cm}
+ \begin{itemize}
+ \item Integrator: Velocity Verlet, timestep: 1 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]
+ \[
+ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+ \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
+ \]
+ \end{itemize}
+ \end{minipage}
+ \begin{minipage}{9cm}
+ \includegraphics[width=9cm]{tersoff_angle.eps}
+ \end{minipage}\\[1cm]
+ {\tiny
+ [4] L. Verlet, Phys. Rev. 159 (1967) 98.}\\
+ {\tiny
+ [5] P. Erhart and K. Albe, Phys. Rev. B 71 (2005) 35211.}
+ \end{pbox}
\end{pcolumn}
\begin{pcolumn}
\begin{pbox}
- \section*{Simulation algorithm}
- Hier die Simulation rein!
- \end{pbox}
- \begin{pbox}
- \section*{Results}
- Hier die Resultate!
+ \section*{Interstitial configurations}
+ {\bf Simulation sequence:}\\
+
+\begin{minipage}{15cm}
+{\small
+ \begin{pspicture}(0,0)(14,14)
+ \rput(7,12.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+ \parbox{14cm}{
+ \begin{itemize}
+ \item Initial configuration: $9\times9\times9$ unit cells Si
+ \item Periodic boundary conditions
+ \item $T=0\text{ K}$, $p=0\text{ bar}$
+ \end{itemize}
+ }}}}
+\rput(7,6){\rnode{insert}{\psframebox{
+ \parbox{14cm}{
+ 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 $(-1/8,-1/8,-1/4)$, $(-3/8,-3/8,-1/4)$\\
+ $\rightarrow$ {\color{magenta}110 dumbbell}
+ (${\color{magenta}\Box}$,$\circ$)
+ \item random positions (critical distance check)
+ \end{itemize}
+ }}}}
+ \rput(7,1.5){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
+ \parbox{7cm}{
+ Relaxation time: 2 ps
+ }}}}
+ \ncline[]{->}{init}{insert}
+ \ncline[]{->}{insert}{cool}
+ \end{pspicture}
+}
+\end{minipage}
+\begin{minipage}{10cm}
+ \includegraphics[width=11cm]{unit_cell_s.eps}
+\end{minipage}
+
+ {\bf Si self-interstitial results:}\\
+
+{\small
+ \begin{minipage}[t]{8.5cm}
+ \underline{Tetrahedral}\\
+ $E_f=3.41$ eV\\
+ \includegraphics[width=8cm]{si_self_int_tetra_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{8.5cm}
+ \underline{110 dumbbell}\\
+ $E_f=4.39$ eV\\
+ \includegraphics[width=8cm]{si_self_int_dumbbell_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{8.5cm}
+ \underline{Hexagonal}\\
+ $E_f^{\star}\approx4.48$ eV (unstable!)\\
+ \includegraphics[width=8cm]{si_self_int_hexa_0.eps}
+ \end{minipage}\\[1cm]
+
+ \underline{Random insertion}\\
+
+ \begin{minipage}{8.5cm}
+ $E_f=3.97$ eV\\
+ \includegraphics[width=8cm]{si_self_int_rand_397_0.eps}
+ \end{minipage}
+ \begin{minipage}{8.5cm}
+ $E_f=3.75$ eV\\
+ \includegraphics[width=8cm]{si_self_int_rand_375_0.eps}
+ \end{minipage}
+ \begin{minipage}{8.5cm}
+ $E_f=3.56$ eV\\
+ \includegraphics[width=8cm]{si_self_int_rand_356_0.eps}
+ \end{minipage}\\[1cm]
+}
+
+ {\bf C in Si interstitial results:}\\
+
+{\small
+ \begin{minipage}[t]{8.5cm}
+ \underline{Tetrahedral}\\
+ $E_f=2.67$ eV\\
+ \includegraphics[width=8cm]{c_in_si_int_tetra_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{8.5cm}
+ \underline{110 dumbbell}\\
+ $E_f=1.76$ eV\\
+ \includegraphics[width=8cm]{c_in_si_int_dumbbell_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{8.5cm}
+ \underline{Hexagonal}\\
+ $E_f^{\star}\approx5.6$ eV (unstable!)\\
+ \includegraphics[width=8cm]{c_in_si_int_hexa_0.eps}
+ \end{minipage}\\[1cm]
+}
+\begin{minipage}{17cm}
+\underline{\flq100\frq{} dumbbell configuration}
+\begin{itemize}
+ \item $E_f=0.47$ eV
+ \item Very often observed
+ \item Most energetically favorable configuration
+ \item Experimental evidence [6]
+\end{itemize}
+\end{minipage}
+\begin{minipage}{8cm}
+\includegraphics[width=8cm]{c_in_si_int_001db_0.eps}
+\end{minipage}\\[1cm]
+\begin{center}
+\includegraphics[width=26cm]{100-c-si-db_s.eps}\\[0.35cm]
+\end{center}
+{\tiny
+ [6] G. D. Watkins and K. L. Brower, Phys. Rev. Lett. 36 (1976) 1329.}
+
\end{pbox}
+
\end{pcolumn}
\begin{pcolumn}
\begin{pbox}
- \section*{Structural/compositional information}
- blabla
+ \section*{High C concentration simulations}
+
+ {\bf Simulation sequence:}\\
+
+{\small
+ \begin{pspicture}(0,0)(30,13)
+ % nodes
+ \rput(7.5,11){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+ \parbox{15cm}{
+ \begin{itemize}
+ \item Initial configuration: $31\times31\times31$ unit cells Si
+ \item Periodic boundary conditions
+ \item $T=450\, ^{\circ}\textrm{C}$, $p=0\text{ bar}$
+ \item Equilibration of $E_{kin}$ and $E_{pot}$
+ \end{itemize}
+ }}}}
+ \rput(7.5,5){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
+ \parbox{15cm}{
+ Insertion of 6000 carbon atoms at constant\\
+ temperature into $V_1$ or $V_2$ or $V_3$:
+ \begin{itemize}
+ \item Total simulation volume $V_1$
+ \item Volume of minimal 3C-SiC precipitation $V_2$
+ \item Volume of necessary amount of Si $V_3$
+ \end{itemize}
+ }}}}
+ \rput(7.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
+ \parbox{8cm}{
+ Cooling down to $20\, ^{\circ}\textrm{C}$
+ }}}}
+ \ncline[]{->}{init}{insert}
+ \ncline[]{->}{insert}{cool}
+ \psframe[fillstyle=solid,fillcolor=white](16,2.6)(26,12.6)
+ \psframe[fillstyle=solid,fillcolor=lightgray](18,4.6)(24,10.6)
+ \psframe[fillstyle=solid,fillcolor=gray](18.5,5.1)(23.5,10.1)
+ \rput(9,5.4){\pnode{in1}}
+ \rput(15,5.4){\pnode{in-1}}
+ \rput(17,7.2){\pnode{ins1}}
+ \rput(14,4.2){\pnode{in2}}
+ \rput(15,4.2){\pnode{in-2}}
+ \rput(18.25,6.88){\pnode{ins2}}
+ \rput(12,3.0){\pnode{in3}}
+ \rput(15,3.0){\pnode{in-3}}
+ \rput(21,7.6){\pnode{ins3}}
+ \ncline[linewidth=0.05]{->}{in-1}{ins1}
+ \ncline[linewidth=0.05]{->}{in-2}{ins2}
+ \ncline[linewidth=0.05]{->}{in-3}{ins3}
+ \ncline[linewidth=0.05]{-}{in1}{in-1}
+ \ncline[linewidth=0.05]{-}{in2}{in-2}
+ \ncline[linewidth=0.05]{-}{in3}{in-3}
+ \end{pspicture}
+}
+ {\bf Results:}\\
+ Si-C and C-C pair correlation function:\\
+ \hspace*{1.3cm} \includegraphics[width=22cm]{pc_si-c_c-c.eps}
+ \begin{center}
+ {\tiny
+ {\bf Dashed vertical lines:} Further calculated C-Si distances
+ in the \flq100\frq{} C-Si dumbbell interstitial configuration}\\[0.5cm]
+ \end{center}
+ Si-Si pair correlation function:\\
+ \hspace*{1.3cm} \includegraphics[width=22cm]{pc_si-si.eps}\\
+ {\bf Interpretation:}
+ {\small
+ \begin{itemize}
+ \item C-C peak at 0.15 nm similar to next neighbour distance of graphite
+ or diamond\\
+ $\Rightarrow$ Formation of strong C-C bonds
+ (almost only for high C concentrations)
+ \item Si-C peak at 0.19 nm similar to next neighbour distance in 3C-SiC
+ \item C-C peak at 0.31 nm equals C-C distance in 3C-SiC\\
+ (due to concatenated, differently oriented
+ \flq100\frq{} dumbbell interstitials)
+ \item Si-Si shows non-zero g(r) values around 0.31 nm like in 3C-SiC\\
+ and a decrease at regular distances\\
+ (no clear peak,
+ interval of enhanced g(r) corresponds to C-C peak width)
+ \item Low C concentration (i.e. $V_1$):
+ The \flq100\frq{} dumbbell configuration
+ \begin{itemize}
+ \item is identified to stretch the Si-Si next neighbour distance
+ to 0.3 nm
+ \item is identified to contribute to the Si-C peak at 0.19 nm
+ \item explains further C-Si peaks (dashed vertical lines)
+ \end{itemize}
+ $\Rightarrow$ C atoms are first elements arranged at distances
+ expected for 3C-SiC\\
+ $\Rightarrow$ C atoms pull the Si atoms into the right
+ configuration at a later stage
+ \item High C concentration (i.e. $V_2$ and $V_3$):
+ \begin{itemize}
+ \item High amount of damage introduced into the system
+ \item Short range order observed but almost no long range order
+ \end{itemize}
+ $\Rightarrow$ Start of amorphous SiC-like phase formation\\
+ $\Rightarrow$ Higher temperatures required for proper SiC formation
+ \end{itemize}
+ }
+
\end{pbox}
+ \vspace{-2cm}
\begin{pbox}
- \section*{Recipe for thick films of ordered lamellae}
- blabla
+ \section*{Conclusion}
+ \begin{itemize}
+ \item \flq100\frq{} C-Si dumbbell interstitial configuration is observed
+ to be the energetically most favorable configuration
+ \item For low C concentrations C atoms introduced as differently
+ oriented C-Si dumbbells in c-Si are properly arranged
+ for 3C-SiC formation
+ \item For high C concentrations an amorphous SiC-like phase is observed
+ which suggests higher temperature simulation runs for proper
+ 3C-SiC formation
+ \end{itemize}
\end{pbox}
+ \vspace{-2cm}
\begin{pbox}
- \section*{Conclusions}
- Hier die Zusammenfassung
+ One of us (F. Z.) wants to acknowledge financial support by the\\
+ {\bf Bayerische Forschungsstiftung} (DPA-61/05).
\end{pbox}
\end{pcolumn}
projects / lectures / latex.git / blobdiff