X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fmpi_app.tex;h=67a4d40b15a25922447fbab4d6eb5581e4812e48;hb=d0ff895e76b30891a3fcd4b9a037eada196e9f95;hp=9931ba16bb1a0f2d05c7b3f9147e1c6a6b0ec785;hpb=448bf217190b3d815e3d749631af50cbcbd21834;p=lectures%2Flatex.git diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex index 9931ba1..67a4d40 100644 --- a/posic/talks/mpi_app.tex +++ b/posic/talks/mpi_app.tex @@ -7,6 +7,7 @@ \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} +\usepackage{stmaryrd} \usepackage{latexsym} \usepackage{ae} @@ -20,6 +21,7 @@ \usepackage{pstricks} \usepackage{pst-node} +\usepackage{pst-grad} %\usepackage{epic} %\usepackage{eepic} @@ -54,6 +56,28 @@ \usepackage{upgreek} +\newcommand{\headdiplom}{ +\begin{pspicture}(0,0)(0,0) +\rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{ +\begin{minipage}{14cm} +\hfill +\vspace{0.7cm} +\end{minipage} +}} +\end{pspicture} +} + +\newcommand{\headphd}{ +\begin{pspicture}(0,0)(0,0) +\rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{ +\begin{minipage}{14cm} +\hfill +\vspace{0.7cm} +\end{minipage} +}} +\end{pspicture} +} + \begin{document} \extraslideheight{10in} @@ -143,6 +167,9 @@ E\\ \end{center} \end{slide} +% no vertical centering +\centerslidesfalse + \ifnum1=0 % intro @@ -182,6 +209,8 @@ R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959) \begin{slide} +\vspace*{1.8cm} + \small \begin{pspicture}(0,0)(13.5,5) @@ -296,7 +325,6 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \end{slide} -\fi % fabrication \begin{slide} @@ -317,7 +345,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \vspace{2pt} -SiC thin film by MBE \& CVD +SiC thin films by MBE \& CVD \begin{itemize} \item Much progress achieved in homo/heteroepitaxial SiC thin film growth \item \underline{Commercially available} semiconductor power devices based on @@ -330,33 +358,33 @@ SiC thin film by MBE \& CVD \includegraphics[width=2.0cm]{cree.eps} \end{picture} -\vspace{-0.4cm} +\vspace{-0.2cm} Alternative approach: Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) +\vspace{0.2cm} + \scriptsize -\begin{minipage}{6.5cm} - \begin{itemize} - \item \underline{Implantation step 1}\\ - 180 keV C$^+$, $D=7.9\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=500\,^{\circ}\mathrm{C}$\\[0.1cm] - Box-like distribution of equally sized \&\\ - epitaxially oriented SiC precipitates - - \item \underline{Implantation step 2}\\ - 180 keV C$^+$, $D=0.6\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=250\,^{\circ}\mathrm{C}$\\[0.1cm] - Destruction of SiC nanocrystals\\ - in growing amorphous interface layers - \item \underline{Annealing}\\ - $T=1250\,^{\circ}\mathrm{C}$, $t=10\,\text{h}$\\[0.1cm] - Homogeneous, stoichiometric SiC layer\\ - with sharp interfaces - \end{itemize} +\framebox{ +\begin{minipage}{3.15cm} + \begin{center} +\includegraphics[width=3cm]{imp.eps}\\ + {\tiny + Carbon implantation + } + \end{center} \end{minipage} -\begin{minipage}{0.3cm} -\hfill +\begin{minipage}{3.15cm} + \begin{center} +\includegraphics[width=3cm]{annealing.eps}\\ + {\tiny + \unit[12]{h} annealing at \degc{1200} + } + \end{center} \end{minipage} +} \begin{minipage}{5.5cm} \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm] \begin{center} @@ -366,26 +394,25 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) \end{center} \end{minipage} -\framebox{ - \begin{minipage}{6.3cm} - \begin{center} - {\color{blue} - Precipitation mechanism not yet fully understood! - } - \renewcommand\labelitemi{$\Rightarrow$} - \small - \underline{Understanding the SiC precipitation} - \begin{itemize} - \item significant technological progress in SiC thin film formation - \item perspectives for processes relying upon prevention of SiC precipitation - \end{itemize} - \end{center} - \end{minipage} +\end{slide} + +% contents + +\begin{slide} + +{\large\bf + Systematic investigation of C implantations into Si } +\vspace{1.7cm} +\begin{center} +\hspace{-1.0cm} +\includegraphics[width=0.75\textwidth]{imp_inv.eps} +\end{center} + \end{slide} -% contents +% outline \begin{slide} @@ -393,75 +420,381 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) Outline } - \begin{itemize} - \item Implantation of C in Si --- Overview of experimental observations - \item Utilized simulation techniques and modeled problems - \begin{itemize} - \item {\color{blue}Diploma thesis}\\ - \underline{Monte Carlo} simulations - modeling the selforganization process - leading to periodic arrays of nanometric amorphous SiC - precipitates - \item {\color{blue}Doctoral studies}\\ - Classical potential \underline{molecular dynamics} simulations - \ldots\\ - \underline{Density functional theory} calculations - \ldots\\[0.2cm] - \ldots on defects and SiC precipitation in Si - \end{itemize} - \item Summary / Conclusion / Outlook - \end{itemize} +\vspace{1.7cm} +\begin{center} +\hspace{-1.0cm} +\includegraphics[width=0.75\textwidth]{imp_inv.eps} +\end{center} + +\begin{pspicture}(0,0)(0,0) +\rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{ +\begin{minipage}{11cm} +{\color{black}Diploma thesis}\\ + \underline{Monte Carlo} simulation modeling the selforganization process\\ + leading to periodic arrays of nanometric amorphous SiC precipitates +\end{minipage} +}}} +\end{pspicture} +\begin{pspicture}(0,0)(0,0) +\rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{ +\begin{minipage}{11cm} +{\color{black}Doctoral studies}\\ + Classical potential \underline{molecular dynamics} simulations \ldots\\ + \underline{Density functional theory} calculations \ldots\\[0.2cm] + \ldots on defect formation and SiC precipitation in Si +\end{minipage} +}}} +\end{pspicture} +\begin{pspicture}(0,0)(0,0) +\psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0) +\end{pspicture} +\begin{pspicture}(0,0)(0,0) +\psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6) +\end{pspicture} \end{slide} +\begin{slide} -\end{document} -\ifnum1=0 +\headdiplom +{\large\bf + Selforganization of nanometric amorphous SiC lamellae +} +\small + +\vspace{0.2cm} + +\begin{itemize} + \item Regularly spaced, nanometric spherical\\ + and lamellar amorphous inclusions\\ + at the upper a/c interface + \item Carbon accumulation\\ + in amorphous volumes +\end{itemize} + +\vspace{0.4cm} + +\begin{minipage}{12cm} +\includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\ +{\scriptsize +XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si, +{\color{red}\underline{\degc{150}}}, +Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$} +} +\end{minipage} + +\begin{picture}(0,0)(-182,-215) +\begin{minipage}{6.5cm} +\begin{center} +\includegraphics[width=6.5cm]{../../nlsop/img/eftem.eps}\\[-0.2cm] +{\scriptsize +XTEM bright-field and respective EFTEM C map +} +\end{center} +\end{minipage} +\end{picture} + +\end{slide} \begin{slide} - {\large\bf - Supposed precipitation mechanism of SiC in Si +\headdiplom +{\large\bf + Model displaying the formation of ordered lamellae +} + +\vspace{0.1cm} + +\begin{center} + \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps} +\end{center} + +\footnotesize + +\begin{itemize} +\item Supersaturation of C in c-Si\\ + $\rightarrow$ {\bf Carbon induced} nucleation of spherical + SiC$_x$-precipitates +\item High interfacial energy between 3C-SiC and c-Si\\ + $\rightarrow$ {\bf Amorphous} precipitates +\item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\ + $\rightarrow$ {\bf Lateral strain} (black arrows) +\item Implantation range near surface\\ + $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component} +\item Reduction of the carbon supersaturation in c-Si\\ + $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina + (white arrows) +\item Remaining lateral strain\\ + $\rightarrow$ {\bf Strain enhanced} lateral amorphisation +\item Absence of crystalline neighbours (structural information)\\ + $\rightarrow$ {\bf Stabilization} of amorphous inclusions + {\bf against recrystallization} +\end{itemize} + +\end{slide} + +\begin{slide} + +\headdiplom +{\large\bf + Implementation of the Monte Carlo code +} + +\small + +\begin{enumerate} + \item \underline{Amorphization / Recrystallization}\\ + Ion collision in discretized target determined by random numbers + distributed according to nuclear energy loss. + Amorphization/recrystallization probability: +\[ +p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}} +\] +\begin{itemize} + \item {\color{green} $p_b$} normal `ballistic' amorphization + \item {\color{blue} $p_c$} carbon induced amorphization + \item {\color{red} $p_s$} stress enhanced amorphization +\end{itemize} +\[ +p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,} +\] +\[ +\delta (\vec r) = \left\{ +\begin{array}{ll} + 1 & \textrm{if volume at position $\vec r$ is amorphous} \\ + 0 & \textrm{otherwise} \\ +\end{array} +\right. +\] + \item \underline{Carbon incorporation}\\ + Incorporation volume determined according to implantation profile + \item \underline{Diffusion / Sputtering} + \begin{itemize} + \item Transfer fraction of C atoms + of crystalline into neighbored amorphous volumes + \item Remove surface layer + \end{itemize} +\end{enumerate} + +\end{slide} + +\begin{slide} + +\begin{minipage}{3.7cm} +\begin{pspicture}(0,0)(0,0) +\rput(1.7,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradangle=10,gradmidpoint=1,linestyle=none]{ +\begin{minipage}{3.7cm} +\hfill +\vspace{0.7cm} +\end{minipage} +}} +\end{pspicture} +{\large\bf + Results +} + +\footnotesize + +\vspace{1.2cm} + +Evolution of the \ldots +\begin{itemize} + \item continuous\\ + amorphous layer + \item a/c interface + \item lamellar precipitates +\end{itemize} +\ldots reproduced!\\[1.4cm] + +{\color{blue} +\begin{center} +Experiment \& simulation\\ +in good agreement\\[1.0cm] + +Simulation is able to model the whole depth region\\[1.2cm] +\end{center} +} + +\end{minipage} +\begin{minipage}{0.5cm} +\vfill +\end{minipage} +\begin{minipage}{8.0cm} + \vspace{-0.3cm} + \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\ + \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headdiplom +{\large\bf + Structural \& compositional details +} + +\begin{minipage}[t]{7.5cm} +\includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\ +\end{minipage} +\begin{minipage}[t]{5.0cm} +\includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps} +\end{minipage} + +\footnotesize + +\vspace{-0.1cm} + +\begin{itemize} + \item Fluctuation of C concentration in lamellae region + \item \unit[8--10]{at.\%} C saturation limit + within the respective conditions + \item Complementarily arranged and alternating sequence of layers\\ + with a high and low amount of amorphous regions + \item C accumulation in the amorphous phase / Origin of stress +\end{itemize} + +\begin{picture}(0,0)(-260,-50) +\framebox{ +\begin{minipage}{3cm} +\begin{center} +{\color{blue} +Precipitation process\\ +gets traceable\\ +by simulation! +} +\end{center} +\end{minipage} +} +\end{picture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Formation of epitaxial single crystalline 3C-SiC +} + +\footnotesize + +\vspace{0.2cm} + +\begin{center} +\begin{itemize} + \item \underline{Implantation step 1}\\[0.1cm] + Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\ + $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \& + {\color{blue}precipitates} + \item \underline{Implantation step 2}\\[0.1cm] + Little remaining dose | \unit[180]{keV} | \degc{250}\\ + $\Rightarrow$ + Destruction/Amorphization of precipitates at layer interface + \item \underline{Annealing}\\[0.1cm] + \unit[10]{h} at \degc{1250}\\ + $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces +\end{itemize} +\end{center} + +\begin{minipage}{7cm} +\includegraphics[width=7cm]{ibs_3c-sic.eps} +\end{minipage} +\begin{minipage}{5cm} +\begin{pspicture}(0,0)(0,0) +\rnode{box}{ +\psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{ +\begin{minipage}{5.3cm} + \begin{center} + {\color{blue} + 3C-SiC precipitation\\ + not yet fully understood } + \end{center} + \vspace*{0.1cm} + \renewcommand\labelitemi{$\Rightarrow$} + Details of the SiC precipitation + \begin{itemize} + \item significant technological progress\\ + in SiC thin film formation + \item perspectives for processes relying\\ + upon prevention of SiC precipitation + \end{itemize} +\end{minipage} +}} +\rput(-6.8,5.4){\pnode{h0}} +\rput(-3.0,5.4){\pnode{h1}} +\ncline[linecolor=blue]{-}{h0}{h1} +\ncline[linecolor=blue]{->}{h1}{box} +\end{pspicture} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Supposed precipitation mechanism of SiC in Si +} \scriptsize \vspace{0.1cm} - \begin{minipage}{3.8cm} - Si \& SiC lattice structure\\[0.2cm] - \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm] - \hrule + \framebox{ + \begin{minipage}{3.6cm} + \begin{center} + Si \& SiC lattice structure\\[0.1cm] + \includegraphics[width=2.3cm]{sic_unit_cell.eps} + \end{center} +{\tiny + \begin{minipage}{1.7cm} +\underline{Silicon}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\ +$a=\unit[5.429]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[100]{\%}$ + \end{minipage} + \begin{minipage}{1.7cm} +\underline{Silicon carbide}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\ +$a=\unit[4.359]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[97]{\%}$ + \end{minipage} +} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + } + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} \includegraphics[width=3.3cm]{tem_c-si-db.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{tem_3c-sic.eps} \end{center} \end{minipage} - \begin{minipage}{4cm} + \vspace{0.1cm} + + \begin{minipage}{4.0cm} \begin{center} C-Si dimers (dumbbells)\\[-0.1cm] on Si interstitial sites \end{center} \end{minipage} - \hspace{0.2cm} - \begin{minipage}{4.2cm} + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} Agglomeration of C-Si dumbbells\\[-0.1cm] $\Rightarrow$ dark contrasts \end{center} \end{minipage} - \hspace{0.2cm} - \begin{minipage}{4cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} Precipitation of 3C-SiC in Si\\[-0.1cm] $\Rightarrow$ Moir\'e fringes\\[-0.1cm] @@ -469,37 +802,39 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) \end{center} \end{minipage} - \begin{minipage}{3.8cm} + \vspace{0.1cm} + + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_01.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_02.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_03.eps} \end{center} \end{minipage} \begin{pspicture}(0,0)(0,0) -\psline[linewidth=4pt]{->}(8.5,2)(9.0,2) -\psellipse[linecolor=blue](11.5,5.8)(0.3,0.5) -\rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)} -\psline[linewidth=4pt]{->}(4.0,2)(4.5,2) -\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\psline[linewidth=2pt]{->}(8.3,2)(8.8,2) +\psellipse[linecolor=blue](11.1,6.0)(0.3,0.5) +\rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)} +\psline[linewidth=2pt]{->}(3.9,2)(4.4,2) +\rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ $4a_{\text{Si}}=5a_{\text{SiC}}$ }}} -\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ \hkl(h k l) planes match }}} -\rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ -r = 2 - 4 nm +\rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +r = \unit[2--4]{nm} }}} \end{pspicture} @@ -507,47 +842,67 @@ r = 2 - 4 nm \begin{slide} - {\large\bf - Supposed precipitation mechanism of SiC in Si - } +\headphd +{\large\bf + Supposed precipitation mechanism of SiC in Si +} \scriptsize \vspace{0.1cm} - \begin{minipage}{3.8cm} - Si \& SiC lattice structure\\[0.2cm] - \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm] - \hrule + \framebox{ + \begin{minipage}{3.6cm} + \begin{center} + Si \& SiC lattice structure\\[0.1cm] + \includegraphics[width=2.3cm]{sic_unit_cell.eps} + \end{center} +{\tiny + \begin{minipage}{1.7cm} +\underline{Silicon}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\ +$a=\unit[5.429]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[100]{\%}$ + \end{minipage} + \begin{minipage}{1.7cm} +\underline{Silicon carbide}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\ +$a=\unit[4.359]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[97]{\%}$ \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} +} + \end{minipage} + } + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} \includegraphics[width=3.3cm]{tem_c-si-db.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{tem_3c-sic.eps} \end{center} \end{minipage} - \begin{minipage}{4cm} + \vspace{0.1cm} + + \begin{minipage}{4.0cm} \begin{center} C-Si dimers (dumbbells)\\[-0.1cm] on Si interstitial sites \end{center} \end{minipage} - \hspace{0.2cm} - \begin{minipage}{4.2cm} + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} Agglomeration of C-Si dumbbells\\[-0.1cm] $\Rightarrow$ dark contrasts \end{center} \end{minipage} - \hspace{0.2cm} - \begin{minipage}{4cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} Precipitation of 3C-SiC in Si\\[-0.1cm] $\Rightarrow$ Moir\'e fringes\\[-0.1cm] @@ -555,118 +910,184 @@ r = 2 - 4 nm \end{center} \end{minipage} - \begin{minipage}{3.8cm} + \vspace{0.1cm} + + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_01.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_02.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_03.eps} \end{center} \end{minipage} \begin{pspicture}(0,0)(0,0) -\psline[linewidth=4pt]{->}(8.5,2)(9.0,2) -\psellipse[linecolor=blue](11.5,5.8)(0.3,0.5) -\rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)} -\psline[linewidth=4pt]{->}(4.0,2)(4.5,2) -\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\psline[linewidth=2pt]{->}(8.3,2)(8.8,2) +\psellipse[linecolor=blue](11.1,6.0)(0.3,0.5) +\rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)} +\psline[linewidth=2pt]{->}(3.9,2)(4.4,2) +\rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ $4a_{\text{Si}}=5a_{\text{SiC}}$ }}} -\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ \hkl(h k l) planes match }}} -\rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ -r = 2 - 4 nm +\rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +r = \unit[2--4]{nm} }}} -\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{ +% controversial view! +\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{ +\begin{minipage}{14cm} +\hfill +\vspace{12cm} +\end{minipage} +}} +\rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{ \begin{minipage}{10cm} \small -{\color{red}\bf Controversial views} +\vspace*{0.2cm} +\begin{center} +{\color{gray}\bf Controversial findings} +\end{center} \begin{itemize} -\item Implantations at high T (Nejim et al.) +\item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./} \begin{itemize} - \item Topotactic transformation based on \cs - \item \si{} as supply reacting with further C in cleared volume + \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites + \item \si{} reacting with further C in cleared volume \end{itemize} -\item Annealing behavior (Serre et al.) +\item Annealing behavior {\tiny\color{gray}/Serre~et~al./} \begin{itemize} - \item Room temperature implants $\rightarrow$ highly mobile C - \item Elevated T implants $\rightarrow$ no/low C redistribution/migration\\ - (indicate stable \cs{} configurations) + \item Room temperature implantation $\rightarrow$ high C diffusion + \item Elevated temperature implantation $\rightarrow$ no C redistribution \end{itemize} + $\Rightarrow$ mobile {\color{red}\ci} opposed to + stable {\color{blue}\cs{}} configurations \item Strained silicon \& Si/SiC heterostructures + {\tiny\color{gray}/Strane~et~al./Guedj~et~al./} \begin{itemize} - \item Coherent SiC precipitates (tensile strain) + \item {\color{blue}Coherent} SiC precipitates (tensile strain) \item Incoherent SiC (strain relaxation) \end{itemize} \end{itemize} +\vspace{0.1cm} +\begin{center} +{\Huge${\lightning}$} \hspace{0.3cm} +{\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm} +{\Huge${\lightning}$} +\end{center} +\vspace{0.2cm} \end{minipage} }}} \end{pspicture} \end{slide} +% continue here +\fi + \begin{slide} - {\large\bf - Molecular dynamics (MD) simulations - } +\headphd +{\large\bf + Utilized computational methods +} - \vspace{12pt} +\vspace{0.2cm} - \small +\small - {\bf MD basics:} - \begin{itemize} - \item Microscopic description of N particle system - \item Analytical interaction potential - \item Numerical integration using Newtons equation of motion\\ - as a propagation rule in 6N-dimensional phase space - \item Observables obtained by time and/or ensemble averages - \end{itemize} - {\bf Details of the simulation:} - \begin{itemize} - \item Integration: Velocity Verlet, timestep: $1\text{ fs}$ - \item Ensemble: NpT (isothermal-isobaric) - \begin{itemize} - \item Berendsen thermostat: - $\tau_{\text{T}}=100\text{ fs}$ - \item Berendsen barostat:\\ - $\tau_{\text{P}}=100\text{ fs}$, - $\beta^{-1}=100\text{ GPa}$ - \end{itemize} - \item Erhart/Albe potential: Tersoff-like bond order potential - \vspace*{12pt} - \[ - E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad - \pot_{ij} = {\color{red}f_C(r_{ij})} - \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right] - \] - \end{itemize} +{\bf Molecular dynamics (MD)}\\ +\scriptsize +\begin{tabular}{p{4.5cm} p{7.5cm}} +Basics & Details\\ +\hline +System of $N$ particles & +$N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\ +\hline +Phase space propagation & +Velocity Verlet | timestep: \unit[1]{fs} \\ +\hline +Analytical interaction potential & +Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential +(Erhart/Albe) +$\displaystyle +E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad + \pot_{ij} = {\color{red}f_C(r_{ij})} + \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right] +$\\ +\hline +Observables: time/ensemble averages & +NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\ +\hline +\end{tabular} + +\small + +\vspace{0.1cm} + +{\bf Density functional theory (DFT)} + +\scriptsize + +\begin{minipage}[t]{6cm} +\underline{Basics} +\begin{itemize} + \item Born-Oppenheimer approximation:\\ + Decouple electronic \& ionic motion + \item Hohenberg-Kohn theorem:\\ + $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$ + $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$} +\end{itemize} +\underline{Details} +\begin{itemize} +\item Code: \textsc{vasp} +\item Plane wave basis set $\{\phi_j\}$\\[0.1cm] +$\displaystyle +\Phi_i=\sum_{|G+k|