X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Fposter%2Femrs2008.tex;h=1226f1bda2a65b9f6d1db8f915b6bd89c2439989;hp=5945eac895ef73d19ff7c5102956a9a480781a2a;hb=17d5c879c418790a154098e51c524eca183c4d98;hpb=b05b08319c0aedb26856e20f744a54215a196003

diff --git a/posic/poster/emrs2008.tex b/posic/poster/emrs2008.tex
index 5945eac..1226f1b 100644
--- a/posic/poster/emrs2008.tex
+++ b/posic/poster/emrs2008.tex
@@ -1,5 +1,5 @@
 \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}
@@ -22,11 +22,18 @@
 \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}}
@@ -65,16 +72,19 @@
 
 \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.}\\
@@ -82,6 +92,7 @@
      [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:}
@@ -107,19 +118,18 @@
       \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}
@@ -130,39 +140,293 @@
     \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}