X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fmpi_app.tex;h=e4cdd485901ab5dbde0bc2bf829d7f9e861eaf1f;hp=fe006e21aeb697277e3fec49775e386e4eb0dbeb;hb=ab8104bce0b6ea93877f9a5102a9fa933c4bf17f;hpb=7ae615d57e61e89dfc7e48f34924007ce5ea5f08 diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex index fe006e2..e4cdd48 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} @@ -20,10 +21,13 @@ \usepackage{pstricks} \usepackage{pst-node} +\usepackage{pst-grad} %\usepackage{epic} %\usepackage{eepic} +\usepackage{layout} + \usepackage{graphicx} \graphicspath{{../img/}} @@ -52,20 +56,41 @@ \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} -\slideframe{none} +\slideframe{plain} \pagestyle{empty} % specify width and height -\slidewidth 27.7cm -\slideheight 19.1cm +\slidewidth 26.3cm +\slideheight 19.9cm -% shift it into visual area properly -\def\slideleftmargin{3.3cm} -\def\slidetopmargin{0.6cm} +% margin +\def\slidetopmargin{-0.15cm} \newcommand{\ham}{\mathcal{H}} \newcommand{\pot}{\mathcal{V}} @@ -97,6 +122,24 @@ \newcommand{\dista}[1]{\unit[#1]{\AA}{}} \newcommand{\perc}[1]{\unit[#1]{\%}{}} +% no vertical centering +%\centerslidesfalse + +% layout check +%\layout +\begin{slide} +\center +{\Huge +E\\ +F\\ +G\\ +A B C D E F G H G F E D C B A +G\\ +F\\ +E\\ +} +\end{slide} + % topic \begin{slide} @@ -124,6 +167,11 @@ \end{center} \end{slide} +% no vertical centering +\centerslidesfalse + +\ifnum1=0 + % intro \begin{slide} @@ -134,7 +182,7 @@ \vspace*{0.2cm} -\begin{minipage}{7cm} +\begin{minipage}{6.5cm} \includegraphics[width=6.5cm]{si-c_phase.eps} \begin{center} {\tiny @@ -161,62 +209,69 @@ 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) - \psframe*[linecolor=hb](0,0)(13.5,5) + \psframe*[linecolor=hb](-0.2,0)(12.9,5) - \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.5,1)(7,1)(7,3)(5.5,3) - \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.75,0.5)(8,2)(8,2)(6.75,3.5) + \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3) + \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.4,0.5)(7.7,2)(7.7,2)(6.4,3.5) - \rput[lt](0.2,4.6){\color{gray}PROPERTIES} + \rput[lt](0,4.6){\color{gray}PROPERTIES} - \rput[lt](0.5,4){wide band gap} - \rput[lt](0.5,3.5){high electric breakdown field} - \rput[lt](0.5,3){good electron mobility} - \rput[lt](0.5,2.5){high electron saturation drift velocity} - \rput[lt](0.5,2){high thermal conductivity} + \rput[lt](0.3,4){wide band gap} + \rput[lt](0.3,3.5){high electric breakdown field} + \rput[lt](0.3,3){good electron mobility} + \rput[lt](0.3,2.5){high electron saturation drift velocity} + \rput[lt](0.3,2){high thermal conductivity} - \rput[lt](0.5,1.5){hard and mechanically stable} - \rput[lt](0.5,1){chemically inert} + \rput[lt](0.3,1.5){hard and mechanically stable} + \rput[lt](0.3,1){chemically inert} - \rput[lt](0.5,0.5){radiation hardness} + \rput[lt](0.3,0.5){radiation hardness} - \rput[rt](13.3,4.6){\color{gray}APPLICATIONS} + \rput[rt](12.7,4.6){\color{gray}APPLICATIONS} - \rput[rt](13,3.85){high-temperature, high power} - \rput[rt](13,3.5){and high-frequency} - \rput[rt](13,3.15){electronic and optoelectronic devices} + \rput[rt](12.5,3.85){high-temperature, high power} + \rput[rt](12.5,3.5){and high-frequency} + \rput[rt](12.5,3.15){electronic and optoelectronic devices} - \rput[rt](13,2.35){material suitable for extreme conditions} - \rput[rt](13,2){microelectromechanical systems} - \rput[rt](13,1.65){abrasives, cutting tools, heating elements} + \rput[rt](12.5,2.35){material suitable for extreme conditions} + \rput[rt](12.5,2){microelectromechanical systems} + \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements} - \rput[rt](13,0.85){first wall reactor material, detectors} - \rput[rt](13,0.5){and electronic devices for space} + \rput[rt](12.5,0.85){first wall reactor material, detectors} + \rput[rt](12.5,0.5){and electronic devices for space} \end{pspicture} -\begin{picture}(0,0)(0,-162) -\includegraphics[height=2.0cm]{3C_SiC_bs.eps} +\begin{picture}(0,0)(5,-162) +\includegraphics[height=2.2cm]{3C_SiC_bs.eps} \end{picture} -\begin{picture}(0,0)(-130,-162) -\includegraphics[height=2.0cm]{nasa_600c_led.eps} +\begin{picture}(0,0)(-120,-162) +\includegraphics[height=2.2cm]{nasa_600c_led.eps} \end{picture} -\begin{picture}(0,0)(-295,-162) -\includegraphics[height=2.0cm]{6h-sic_3c-sic.eps} +\begin{picture}(0,0)(-270,-162) +\includegraphics[height=2.2cm]{6h-sic_3c-sic.eps} \end{picture} %%%% -\begin{picture}(0,0)(5,65) +\begin{picture}(0,0)(10,65) \includegraphics[height=2.8cm]{sic_switch.eps} \end{picture} -\begin{picture}(0,0)(-145,65) -\includegraphics[height=2.8cm]{infineon_schottky.eps} -\end{picture} -\begin{picture}(0,0)(-260,65) +%\begin{picture}(0,0)(-243,65) +\begin{picture}(0,0)(-110,65) \includegraphics[height=2.8cm]{ise_99.eps} \end{picture} +%\begin{picture}(0,0)(-135,65) +\begin{picture}(0,0)(-100,65) +\includegraphics[height=1.2cm]{infineon_schottky.eps} +\end{picture} +\begin{picture}(0,0)(-233,65) +\includegraphics[height=2.8cm]{solar_car.eps} +\end{picture} \end{slide} @@ -225,12 +280,24 @@ R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959) \begin{slide} {\large\bf - Polytypes of SiC + Polytypes of SiC\\[0.4cm] } - \vspace{4cm} +\includegraphics[width=3.8cm]{cubic_hex.eps}\\ +\begin{minipage}{1.9cm} +{\tiny cubic (twist)} +\end{minipage} +\begin{minipage}{2.9cm} +{\tiny hexagonal (no twist)} +\end{minipage} + +\begin{picture}(0,0)(-150,0) + \includegraphics[width=7cm]{polytypes.eps} +\end{picture} - \small +\vspace{0.6cm} + +\footnotesize \begin{tabular}{l c c c c c c} \hline @@ -246,30 +313,14 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \hline \end{tabular} -{\tiny - Values for $T=300$ K -} - -\begin{picture}(0,0)(-160,-155) - \includegraphics[width=7cm]{polytypes.eps} -\end{picture} -\begin{picture}(0,0)(-10,-185) - \includegraphics[width=3.8cm]{cubic_hex.eps}\\ -\end{picture} -\begin{picture}(0,0)(-10,-175) - {\tiny cubic (twist)} -\end{picture} -\begin{picture}(0,0)(-60,-175) - {\tiny hexagonal (no twist)} -\end{picture} \begin{pspicture}(0,0)(0,0) -\psellipse[linecolor=green](5.7,3.03)(0.4,0.5) +\psellipse[linecolor=green](5.7,2.10)(0.4,0.5) \end{pspicture} \begin{pspicture}(0,0)(0,0) -\psellipse[linecolor=green](5.6,1.68)(0.4,0.2) +\psellipse[linecolor=green](5.6,0.92)(0.4,0.2) \end{pspicture} \begin{pspicture}(0,0)(0,0) -\psellipse[linecolor=red](10.7,1.13)(0.4,0.2) +\psellipse[linecolor=red](10.45,0.45)(0.4,0.2) \end{pspicture} \end{slide} @@ -284,77 +335,64 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \small - \vspace{4pt} + \vspace{2pt} - SiC - \emph{Born from the stars, perfected on earth.} +\begin{center} + {\color{gray} + \emph{Silicon carbide --- Born from the stars, perfected on earth.} + } +\end{center} - IBS also here! - - \vspace{4pt} +\vspace{2pt} - Conventional thin film SiC growth: - \begin{itemize} - \item \underline{Sublimation growth using the modified Lely method} - \begin{itemize} - \item SiC single-crystalline seed at $T=1800 \, ^{\circ} \text{C}$ - \item Surrounded by polycrystalline SiC in a graphite crucible\\ - at $T=2100-2400 \, ^{\circ} \text{C}$ - \item Deposition of supersaturated vapor on cooler seed crystal - \end{itemize} - \item \underline{Homoepitaxial growth using CVD} - \begin{itemize} - \item Step-controlled epitaxy on off-oriented 6H-SiC substrates - \item C$_3$H$_8$/SiH$_4$/H$_2$ at $1100-1500 \, ^{\circ} \text{C}$ - \item Angle, temperature $\rightarrow$ 3C/6H/4H-SiC - \end{itemize} - \item \underline{Heteroepitaxial growth of 3C-SiC on Si using CVD/MBE} - \begin{itemize} - \item Two steps: carbonization and growth - \item $T=650-1050 \, ^{\circ} \text{C}$ - \item SiC/Si lattice mismatch $\approx$ 20 \% - \item Quality and size not yet sufficient - \end{itemize} - \end{itemize} +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 + \underline{\foreignlanguage{greek}{a}-SiC} + \item Production of favored \underline{3C-SiC} material + \underline{less advanced} + \item Quality and size not yet sufficient +\end{itemize} +\begin{picture}(0,0)(-310,-20) + \includegraphics[width=2.0cm]{cree.eps} +\end{picture} - \begin{picture}(0,0)(-280,-65) - \includegraphics[width=3.8cm]{6h-sic_3c-sic.eps} - \end{picture} - \begin{picture}(0,0)(-280,-55) - \begin{minipage}{5cm} - {\tiny - NASA: 6H-SiC and 3C-SiC LED\\[-7pt] - on 6H-SiC substrate - } - \end{minipage} - \end{picture} - \begin{picture}(0,0)(-265,-150) - \includegraphics[width=2.4cm]{m_lely.eps} - \end{picture} - \begin{picture}(0,0)(-333,-175) - \begin{minipage}{5cm} - {\tiny - 1. Lid\\[-7pt] - 2. Heating\\[-7pt] - 3. Source\\[-7pt] - 4. Crucible\\[-7pt] - 5. Insulation\\[-7pt] - 6. Seed crystal - } - \end{minipage} - \end{picture} - \begin{picture}(0,0)(-230,-35) - \framebox{ - {\footnotesize\color{blue}\bf Hex: micropipes along c-axis} +\vspace{-0.2cm} + +Alternative approach: +Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) + +\vspace{0.2cm} + +\scriptsize + +\framebox{ +\begin{minipage}{3.15cm} + \begin{center} +\includegraphics[width=3cm]{imp.eps}\\ + {\tiny + Carbon implantation } - \end{picture} - \begin{picture}(0,0)(-230,-10) - \framebox{ - \begin{minipage}{3cm} - {\footnotesize\color{blue}\bf 3C-SiC fabrication\\ - less advanced} - \end{minipage} + \end{center} +\end{minipage} +\begin{minipage}{3.15cm} + \begin{center} +\includegraphics[width=3cm]{annealing.eps}\\ + {\tiny + \unit[12]{h} annealing at \degc{1200} } - \end{picture} + \end{center} +\end{minipage} +} +\begin{minipage}{5.5cm} + \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm] + \begin{center} + {\tiny + XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0) + } + \end{center} +\end{minipage} \end{slide} @@ -362,130 +400,401 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \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} + +% outline + +\begin{slide} + {\large\bf 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} + +\headdiplom +{\large\bf + Selforganization of nanometric amorphous SiC lamellae +} + +\small +\vspace{0.2cm} -\end{document} +\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 - Fabrication of silicon carbide - } +\headdiplom +{\large\bf + Model displaying the formation of ordered lamellae +} - \small +\vspace{0.1cm} - Alternative approach: - Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) - \begin{itemize} - \item \underline{Implantation step 1}\\ - 180 keV C$^+$, $D=7.9\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=500\,^{\circ}\mathrm{C}$\\ - $\Rightarrow$ box-like distribution of equally sized - and epitactically oriented SiC precipitates - - \item \underline{Implantation step 2}\\ - 180 keV C$^+$, $D=0.6\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=250\,^{\circ}\mathrm{C}$\\ - $\Rightarrow$ destruction of SiC nanocrystals - in growing amorphous interface layers - \item \underline{Annealing}\\ - $T=1250\,^{\circ}\mathrm{C}$, $t=10\,\text{h}$\\ - $\Rightarrow$ homogeneous, stoichiometric SiC layer - with sharp interfaces - \end{itemize} +\begin{center} + \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps} +\end{center} - \begin{minipage}{6.3cm} - \includegraphics[width=6cm]{ibs_3c-sic.eps}\\[-0.2cm] - {\tiny - XTEM micrograph of single crystalline 3C-SiC in Si\hkl(1 0 0) - } - \end{minipage} +\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}{6.3cm} +\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} - Precipitation mechanism not yet fully understood! + 3C-SiC precipitation\\ + not yet fully understood } + \end{center} + \vspace*{0.1cm} \renewcommand\labelitemi{$\Rightarrow$} - \small - \underline{Understanding the SiC precipitation} + 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 + \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} +\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} - {\large\bf +\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} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \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{0.1cm} + \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] @@ -493,37 +802,39 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \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} @@ -531,47 +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] @@ -579,60 +910,81 @@ 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} @@ -641,160 +993,110 @@ r = 2 - 4 nm \begin{slide} - {\large\bf - Molecular dynamics (MD) simulations - } - - \vspace{12pt} +\headphd +{\large\bf + Utilized computational methods +} - \small +\vspace{0.3cm} - {\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} +\small - \begin{picture}(0,0)(-230,-30) - \includegraphics[width=5cm]{tersoff_angle.eps} - \end{picture} - -\end{slide} +{\bf Molecular dynamics (MD)}\\[0.1cm] +\scriptsize +\begin{tabular}{| p{4.5cm} | p{7.5cm} |} +\hline +System of $N$ particles & +$N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\ +Phase space propagation & +Velocity Verlet | timestep: \unit[1]{fs} \\ +Analytical interaction potential & +Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential +(Erhart/Albe) +$\displaystyle +E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad + \pot_{ij} = {\color{red}f_C(r_{ij})} + \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right] +$\\ +Observables: time/ensemble averages & +NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\ +\hline +\end{tabular} -\begin{slide} +\small - {\large\bf - Density functional theory (DFT) calculations - } +\vspace{0.3cm} - \small +{\bf Density functional theory (DFT)} - Basic ingredients necessary for DFT +\scriptsize - \begin{itemize} - \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ... - \begin{itemize} - \item ... uniquely determines the ground state potential - / wavefunctions - \item ... minimizes the systems total energy - \end{itemize} - \item \underline{Born-Oppenheimer} - - $N$ moving electrons in an external potential of static nuclei -\[ -H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2 - +\sum_i^N V_{\text{ext}}(r_i) - +\sum_{i}(3.5,-2.0){2.5}{130}{15} +\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165} +\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310} -\begin{pspicture}(0,0)(0,0) -\psellipse[linecolor=blue](1.5,6.75)(0.5,0.3) \end{pspicture} +\end{minipage} \end{slide} \begin{slide} +\headphd {\large\bf - C and Si self-interstitial point defects in silicon + Point defects \& defect migration } \small - \vspace*{0.3cm} + \vspace{0.2cm} -\begin{minipage}{8cm} -Procedure:\\[0.3cm] - \begin{pspicture}(0,0)(7,5) - \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\begin{minipage}[b]{7.5cm} +{\bf Defect structure}\\ + \begin{pspicture}(0,0)(7,4.4) + \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ \parbox{7cm}{ \begin{itemize} \item Creation of c-Si simulation volume @@ -802,13 +1104,13 @@ Procedure:\\[0.3cm] \item $T=0\text{ K}$, $p=0\text{ bar}$ \end{itemize} }}}} -\rput(3.5,2.1){\rnode{insert}{\psframebox{ +\rput(3.5,1.3){\rnode{insert}{\psframebox{ \parbox{7cm}{ \begin{center} Insertion of interstitial C/Si atoms \end{center} }}}} - \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ + \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ \parbox{7cm}{ \begin{center} Relaxation / structural energy minimization @@ -818,49 +1120,83 @@ Procedure:\\[0.3cm] \ncline[]{->}{insert}{cool} \end{pspicture} \end{minipage} -\begin{minipage}{5cm} - \includegraphics[width=5cm]{unit_cell_e.eps}\\ +\begin{minipage}[b]{4.5cm} +\begin{center} +\includegraphics[width=3.8cm]{unit_cell_e.eps}\\ +\end{center} +\begin{minipage}{2.21cm} +{\scriptsize +{\color{red}$\bullet$} Tetrahedral\\[-0.1cm] +{\color{green}$\bullet$} Hexagonal\\[-0.1cm] +{\color{yellow}$\bullet$} \hkl<1 0 0> DB +} +\end{minipage} +\begin{minipage}{2.21cm} +{\scriptsize +{\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm] +{\color{cyan}$\bullet$} Bond-centered\\[-0.1cm] +{\color{black}$\bullet$} Vac. / Sub. +} +\end{minipage} \end{minipage} -\begin{minipage}{9cm} - \begin{tabular}{l c c} - \hline - & size [unit cells] & \# atoms\\ -\hline -VASP & $3\times 3\times 3$ & $216\pm 1$ \\ -Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\ -\hline - \end{tabular} +\vspace{0.2cm} + +\begin{minipage}[b]{6cm} +{\bf Defect formation energy}\\ +\framebox{ +$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm] +Particle reservoir: Si \& SiC\\[0.2cm] +{\bf Binding energy}\\ +\framebox{ +$ +E_{\text{b}}= +E_{\text{f}}^{\text{comb}}- +E_{\text{f}}^{1^{\text{st}}}- +E_{\text{f}}^{2^{\text{nd}}} +$ +}\\[0.1cm] +\footnotesize +$E_{\text{b}}<0$: energetically favorable configuration\\ +$E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\ \end{minipage} -\begin{minipage}{4cm} -{\color{red}$\bullet$} Tetrahedral\\ -{\color{green}$\bullet$} Hexagonal\\ -{\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\ -{\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\ -{\color{cyan}$\bullet$} Bond-centered\\ -{\color{black}$\bullet$} Vacancy / Substitutional +\begin{minipage}[b]{6cm} +{\bf Migration barrier} +\footnotesize +\begin{itemize} + \item Displace diffusing atom + \item Constrain relaxation of (diffusing) atoms + \item Record configurational energy +\end{itemize} +\begin{picture}(0,0)(-60,-33) +\includegraphics[width=4.5cm]{crt_mod.eps} +\end{picture} \end{minipage} \end{slide} +% continue here +\fi + \begin{slide} \footnotesize \begin{minipage}{9.5cm} +\headphd {\large\bf - Si self-interstitial point defects in silicon\\ + Si self-interstitial point defects in silicon\\[0.1cm] } \begin{tabular}{l c c c c c} \hline $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\ \hline - VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\ + \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\ Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\ \hline -\end{tabular}\\[0.2cm] +\end{tabular}\\[0.3cm] \begin{minipage}{4.7cm} \includegraphics[width=4.7cm]{e_kin_si_hex.ps} @@ -870,7 +1206,7 @@ Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\ {\tiny nearly T $\rightarrow$ T}\\ \end{center} \includegraphics[width=4.7cm]{nhex_tet.ps} -\end{minipage}\\ +\end{minipage}\\[0.1cm] \underline{Hexagonal} \hspace{2pt} \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm] @@ -897,9 +1233,10 @@ $E_{\text{f}}=3.96\text{ eV}$\\ \end{minipage} \end{minipage} -\begin{minipage}{3.5cm} +\begin{minipage}{2.5cm} \begin{flushright} +\vspace*{0.2cm} \underline{\hkl<1 1 0> dumbbell}\\ \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\ \underline{Tetrahedral}\\ @@ -916,18 +1253,21 @@ $E_{\text{f}}=3.96\text{ eV}$\\ \footnotesize +\headphd {\large\bf C interstitial point defects in silicon\\[-0.1cm] } +{\scriptsize \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 & \cs{} \& \si\\ \hline - VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\ + \textsc{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] +\end{tabular} +}\\[0.1cm] \framebox{ \begin{minipage}{2.7cm} @@ -986,6 +1326,9 @@ $E_{\text{f}}=5.18\text{ eV}$\\ \end{slide} +\end{document} +\ifnum1=0 + \begin{slide} \footnotesize @@ -1219,25 +1562,6 @@ $\rightarrow$ \end{minipage} \end{minipage} \end{minipage} -\framebox{ -\begin{minipage}{4.2cm} - {\small Constrained relaxation\\ - technique (CRT) method}\\ -\includegraphics[width=4cm]{crt_orig.eps} -\begin{itemize} - \item Constrain diffusing atom - \item Static constraints -\end{itemize} -\vspace*{0.3cm} - {\small Modifications}\\ -\includegraphics[width=4cm]{crt_mod.eps} -\begin{itemize} - \item Constrain all atoms - \item Update individual\\ - constraints -\end{itemize} -\end{minipage} -} \end{slide}