X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fseminar_2011.tex;h=ca198d57b88c4563444d7121e6b8e3eb27e41276;hp=988543e3c59268fc70c0371f08784e87b0f087c3;hb=918b064821da48aed61c671f936f699d7a14edae;hpb=8f332a5618a1846f72c914e5aaa7e960ecd540aa diff --git a/posic/talks/seminar_2011.tex b/posic/talks/seminar_2011.tex index 988543e..ca198d5 100644 --- a/posic/talks/seminar_2011.tex +++ b/posic/talks/seminar_2011.tex @@ -31,6 +31,9 @@ \usepackage[setpagesize=false]{hyperref} +% units +\usepackage{units} + \usepackage{semcolor} \usepackage{semlayer} % Seminar overlays \usepackage{slidesec} % Seminar sections and list of slides @@ -85,6 +88,15 @@ \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} @@ -103,11 +115,11 @@ \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} @@ -385,6 +397,93 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \end{slide} + +\begin{slide} + + {\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 + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + \begin{center} + \includegraphics[width=3.3cm]{tem_c-si-db.eps} + \end{center} + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + \begin{center} + \includegraphics[width=3.3cm]{tem_3c-sic.eps} + \end{center} + \end{minipage} + + \begin{minipage}{4cm} + \begin{center} + C-Si dimers (dumbbells)\\[-0.1cm] + on Si interstitial sites + \end{center} + \end{minipage} + \hspace{0.2cm} + \begin{minipage}{4.2cm} + \begin{center} + Agglomeration of C-Si dumbbells\\[-0.1cm] + $\Rightarrow$ dark contrasts + \end{center} + \end{minipage} + \hspace{0.2cm} + \begin{minipage}{4cm} + \begin{center} + Precipitation of 3C-SiC in Si\\[-0.1cm] + $\Rightarrow$ Moir\'e fringes\\[-0.1cm] + \& release of Si self-interstitials + \end{center} + \end{minipage} + + \begin{minipage}{3.8cm} + \begin{center} + \includegraphics[width=3.3cm]{sic_prec_seq_01.eps} + \end{center} + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + \begin{center} + \includegraphics[width=3.3cm]{sic_prec_seq_02.eps} + \end{center} + \end{minipage} + \hspace{0.6cm} + \begin{minipage}{3.8cm} + \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]{ + $4a_{\text{Si}}=5a_{\text{SiC}}$ + }}} +\rput(12.2,8){\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 + }}} +\end{pspicture} + +\end{slide} + \begin{slide} {\large\bf @@ -467,6 +566,30 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ r = 2 - 4 nm }}} +\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{ +\begin{minipage}{10cm} +\small +{\color{red}\bf Controversial views} +\begin{itemize} +\item Implantations at high T (Nejim et al.) + \begin{itemize} + \item Topotactic transformation based on \cs + \item \si{} as supply reacting with further C in cleared volume + \end{itemize} +\item Annealing behavior (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) + \end{itemize} +\item Strained silicon \& Si/SiC heterostructures + \begin{itemize} + \item Coherent SiC precipitates (tensile strain) + \item Incoherent SiC (strain relaxation) + \end{itemize} +\end{itemize} +\end{minipage} + }}} \end{pspicture} \end{slide} @@ -504,7 +627,8 @@ r = 2 - 4 nm \vspace*{12pt} \[ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad - \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] + \pot_{ij} = {\color{red}f_C(r_{ij})} + \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right] \] \end{itemize} @@ -751,12 +875,12 @@ $E_{\text{f}}=3.96\text{ eV}$\\ 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] @@ -1193,10 +1317,12 @@ VASP results \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} @@ -1250,7 +1376,6 @@ Erhart/Albe results \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} @@ -1259,38 +1384,55 @@ Erhart/Albe results \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} +\vspace{0.1cm} +\begin{center} +{\color{blue}Overestimated diffusion barrier} +\end{center} \end{minipage} -} \end{minipage} @@ -1348,14 +1490,16 @@ $ \end{minipage} \begin{minipage}[t]{5.5cm} \begin{itemize} - \item Restricted to VASP simulations - \item $E_{\text{b}}=0$ for isolated non-interacting defects - \item $E_{\text{b}} \rightarrow 0$ for increasing distance (R) + \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\ + $E_{\text{b}} \rightarrow 0$ for increasing distance (R) \item Stress compensation / increase - \item Most favorable: C clustering \item Unfavored: antiparallel orientations \item Indication of energetically favored\\ agglomeration + \item Most favorable: C clustering + \item However: High barrier ($>4\,\text{eV}$) + \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$ + (Entropy) \end{itemize} \end{minipage} @@ -1397,11 +1541,17 @@ Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \h \includegraphics[width=7cm]{db_along_110_cc.ps} \end{minipage} \begin{minipage}{6.0cm} +\begin{itemize} + \item Interaction proportional to reciprocal cube of C-C distance + \item Saturation in the immediate vicinity + \renewcommand\labelitemi{$\Rightarrow$} + \item Agglomeration of \ci{} expected + \item Absence of C clustering +\end{itemize} \begin{center} {\color{blue} - Interaction proportional to reciprocal cube of C-C distance -}\\[0.2cm] - Saturation in the immediate vicinity + Consisten with initial precipitation model +} \end{center} \end{minipage} @@ -1417,55 +1567,80 @@ Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \h \scriptsize -\begin{center} -\begin{minipage}{3.2cm} -\includegraphics[width=3cm]{sub_110_combo.eps} -\end{minipage} -\begin{minipage}{7.8cm} -\begin{tabular}{l c c c c c c} -\hline -C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> & - \hkl<1 0 1> & \hkl<-1 0 1> \\ -\hline -1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\ -2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\ -3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\ -4 & \RM{4} & B & D & E & E & D \\ -5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\ -\hline -\end{tabular} -\end{minipage} -\end{center} - -\begin{center} -\begin{tabular}{l c c c c c c c c c c} -\hline -Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\ -\hline -$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\ -$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\ -$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\ -\hline -\end{tabular} -\end{center} +%\begin{center} +%\begin{minipage}{3.2cm} +%\includegraphics[width=3cm]{sub_110_combo.eps} +%\end{minipage} +%\begin{minipage}{7.8cm} +%\begin{tabular}{l c c c c c c} +%\hline +%C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> & +% \hkl<1 0 1> & \hkl<-1 0 1> \\ +%\hline +%1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\ +%2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\ +%3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\ +%4 & \RM{4} & B & D & E & E & D \\ +%5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\ +%\hline +%\end{tabular} +%\end{minipage} +%\end{center} + +%\begin{center} +%\begin{tabular}{l c c c c c c c c c c} +%\hline +%Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\ +%\hline +%$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\ +%$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\ +%$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\ +%\hline +%\end{tabular} +%\end{center} \begin{minipage}{6.0cm} \includegraphics[width=5.8cm]{c_sub_si110.ps} \end{minipage} \begin{minipage}{7cm} -\small +\scriptsize \begin{itemize} \item IBS: C may displace Si\\ $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial \item Assumption:\\ \hkl<1 1 0>-type $\rightarrow$ favored combination \renewcommand\labelitemi{$\Rightarrow$} - \item Less favorable than C-Si \hkl<1 0 0> dumbbell\\ - ($E_{\text{f}}=3.88\text{ eV}$) + \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{} + \item Less favorable than C-Si \hkl<1 0 0> dumbbell \item Interaction drops quickly to zero\\ - (low interaction capture radius) + $\rightarrow$ low capture radius +\end{itemize} +\begin{center} + {\color{blue} + IBS process far from equilibrium\\ + \cs{} \& \si{} instead of thermodynamic ground state + } +\end{center} +\end{minipage} + +\begin{minipage}{6.5cm} +\includegraphics[width=6.0cm]{162-097.ps} +\begin{itemize} + \item Low migration barrier \end{itemize} \end{minipage} +\begin{minipage}{6.5cm} +\begin{center} +Ab initio MD at \degc{900}\\ +\includegraphics[width=3.3cm]{md_vasp_01.eps} +$t=\unit[2230]{fs}$\\ +\includegraphics[width=3.3cm]{md_vasp_02.eps} +$t=\unit[2900]{fs}$ +\end{center} +{\color{blue} +Contribution of entropy to structural formation +} +\end{minipage} \end{slide} @@ -1569,7 +1744,7 @@ $r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 Conclusion of defect / migration / combined defect simulations } - \small + \footnotesize \vspace*{0.1cm} @@ -1577,34 +1752,36 @@ Defect structures \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} @@ -1708,6 +1885,66 @@ Only short range order observable\\ \end{slide} +\begin{slide} + + {\large\bf\boldmath + Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS + } + + \small + +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps} +\end{minipage} +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{sic_prec_450_energy.ps} +\end{minipage} + +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{sic_prec_450_si-c.ps} +\end{minipage} +\begin{minipage}{6.5cm} +\scriptsize +\underline{Low C concentration ($V_1$)}\\ +\hkl<1 0 0> C-Si dumbbell dominated structure +\begin{itemize} + \item Si-C bumbs around 0.19 nm + \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\ + concatenated dumbbells of various orientation + \item Si-Si NN distance stretched to 0.3 nm +\end{itemize} +{\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\ +\underline{High C concentration ($V_2$, $V_3$)}\\ +High amount of strongly bound C-C bonds\\ +Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\ +Only short range order observable\\ +{\color{blue}$\Rightarrow$ amorphous SiC-like phase} +\end{minipage} + +\begin{pspicture}(0,0)(0,0) +\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{ +\begin{minipage}{10cm} +\small +{\color{red}\bf 3C-SiC formation fails to appear} +\begin{itemize} +\item Low C concentration simulations + \begin{itemize} + \item Formation of \ci{} indeed occurs + \item Agllomeration not observed + \end{itemize} +\item High C concentration simulations + \begin{itemize} + \item Amorphous SiC-like structure\\ + (not expected at prevailing temperatures) + \item Rearrangement and transition into 3C-SiC structure missing + \end{itemize} +\end{itemize} +\end{minipage} + }}} +\end{pspicture} + +\end{slide} + \begin{slide} {\large\bf @@ -1846,6 +2083,85 @@ in c-Si \end{slide} +\begin{slide} + + {\large\bf + Increased temperature simulations at low C concentration + } + +\small + +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{tot_pc_thesis.ps} +\end{minipage} +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{tot_pc3_thesis.ps} +\end{minipage} + +\begin{minipage}{6.5cm} +\includegraphics[width=6.4cm]{tot_pc2_thesis.ps} +\end{minipage} +\begin{minipage}{6.5cm} +\scriptsize + \underline{Si-C bonds:} + \begin{itemize} + \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$) + \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$ + \end{itemize} + \underline{Si-Si bonds:} + {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0> + ($\rightarrow$ 0.325 nm)\\[0.1cm] + \underline{C-C bonds:} + \begin{itemize} + \item C-C next neighbour pairs reduced (mandatory) + \item Peak at 0.3 nm slightly shifted + \begin{itemize} + \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\ + $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$ + combinations (|)\\ + $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations} + ($\downarrow$) + \item Range [|-$\downarrow$]: + {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$ + with nearby Si$_{\text{I}}$} + \end{itemize} + \end{itemize} +\end{minipage} + +%\begin{picture}(0,0)(-330,-74) +%\color{blue} +%\framebox{ +%\begin{minipage}{1.6cm} +%\tiny +%\begin{center} +%stretched SiC\\[-0.1cm] +%in c-Si +%\end{center} +%\end{minipage} +%} +%\end{picture} + +\begin{pspicture}(0,0)(0,0) +\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{ +\begin{minipage}{10cm} +\small +{\color{blue}\bf Stretched SiC in c-Si} +\begin{itemize} +\item Consistent to precipitation model involving \cs{} +\item Explains annealing behavior of high/low T C implants + \begin{itemize} + \item Low T: highly mobiel \ci{} + \item High T: stable configurations of \cs{} + \end{itemize} +\end{itemize} +$\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\ +$\Rightarrow$ Precipitation mechanism involving \cs{} +\end{minipage} + }}} +\end{pspicture} + +\end{slide} + \begin{slide} {\large\bf @@ -1861,14 +2177,10 @@ in c-Si \includegraphics[width=6.4cm]{12_pc_c_thesis.ps} \end{minipage} -\begin{center} -Decreasing cut-off artifact\\ -High amount of {\color{red}damage} \& alignement to c-Si host matrix lost -$\Rightarrow$ hard to categorize -\end{center} - \vspace{0.1cm} +\scriptsize + \framebox{ \begin{minipage}[t]{6.0cm} 0.186 nm: Si-C pairs $\uparrow$\\ @@ -1889,72 +2201,28 @@ $\approx$0.35 nm: C-Si-Si \end{minipage} } -\vspace{0.1cm} - -\begin{center} -{\color{red}Amorphous} SiC-like phase remains\\ -Slightly sharper peaks -$\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} -due to temperature\\[0.1cm] -\framebox{ -\bf -Continue with higher temperatures and longer time scales -} -\end{center} - -\end{slide} - -\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 +\item Decreasing cut-off artifact +\item {\color{red}Amorphous} SiC-like phase remains +\item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost +\item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature \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} +\vspace{-0.1cm} \begin{center} +{\color{blue} \framebox{ -Long time scales and high temperatures most probably not sufficient enough! +{\color{black} +High C \& small $V$ \& short $t$ +$\Rightarrow$ +} +Slow restructuring due to strong C-C bonds +{\color{black} +$\Leftarrow$ +High C \& low T implants +} +} } \end{center} @@ -1963,71 +2231,65 @@ Long time scales and high temperatures most probably not sufficient enough! \begin{slide} {\large\bf - Summary / Conclusion / Outlook + Summary and Conclusions } \scriptsize -\vspace{0.1cm} +%\vspace{0.1cm} \framebox{ -\begin{minipage}{12.9cm} - \underline{Defects} +\begin{minipage}[t]{12.9cm} + \underline{Pecipitation simulations} \begin{itemize} - \item Summary \& conclusion - \begin{itemize} - \item Point defects excellently / fairly well described - by QM / classical potential simulations - \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) - \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) - \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} } -\vspace{0.2cm} +%\vspace{0.1cm} \framebox{ -\begin{minipage}[t]{12.9cm} - \underline{Pecipitation simulations} +\begin{minipage}{12.9cm} + \underline{Defects} \begin{itemize} - \item Summary \& conclusion + \item DFT / EA \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 + \item Point defects excellently / fairly well described + 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 by DFT + \item EA fails to describe \ci{} migration: + Wrong path \& overestimated barrier \end{itemize} - \item Todo - \begin{itemize} - \item Accelerated method: self-guided MD - \item Activation relaxation technique - \item Constrainted transition path + \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} } - \small +\begin{center} +{\color{blue} +\framebox{Precipitation by successive agglomeration of \cs{}} +} +\end{center} \end{slide} @@ -2045,7 +2307,7 @@ Long time scales and high temperatures most probably not sufficient enough! \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}