X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fdefense.tex;h=e800d602821e01d76796c1ca05bb1530d901323e;hp=a8062e86cd38703c420e4980a4e21c592e9f22c8;hb=bfbe6d47f1c27170154c76574acaf7ce8c108fd5;hpb=3f65cf44692d94497ff4a2ac366cb91b97ac3012 diff --git a/posic/talks/defense.tex b/posic/talks/defense.tex index a8062e8..e800d60 100644 --- a/posic/talks/defense.tex +++ b/posic/talks/defense.tex @@ -122,6 +122,7 @@ % layout check %\layout +\ifnum1=0 \begin{slide} \center {\Huge @@ -134,6 +135,7 @@ F\\ E\\ } \end{slide} +\fi % topic @@ -142,23 +144,26 @@ E\\ \vspace{16pt} - {\LARGE\bf - Atomistic simulation study\\[0.2cm] - on silicon carbide precipitation\\[0.2cm] - in silicon + {\Large\bf + \hrule + \vspace{5pt} + Atomistic simulation study on silicon carbide\\[0.2cm] + precipitation in silicon\\ + \vspace{10pt} + \hrule } - \vspace{48pt} + \vspace{60pt} \textsc{Frank Zirkelbach} - \vspace{48pt} + \vspace{60pt} Defense of doctor's thesis \vspace{08pt} - Augsburg, 10. Jan. 2012 + Augsburg, 10.01.2012 \end{center} \end{slide} @@ -166,6 +171,9 @@ E\\ % no vertical centering \centerslidesfalse +% skip for preparation +%\ifnum1=0 + % intro % motivation / properties / applications of silicon carbide @@ -238,156 +246,13 @@ E\\ \end{slide} -% motivation - -\begin{slide} - - {\large\bf - Polytypes of SiC\\[0.4cm] - } - -\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} - -\vspace{0.6cm} - -\footnotesize - -\begin{tabular}{l c c c c c c} -\hline - & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\ -\hline -Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\ -Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\ -Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\ -Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\ -Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\ -Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\ -Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ -\hline -\end{tabular} - -\begin{pspicture}(0,0)(0,0) -\psellipse[linecolor=green](5.7,2.10)(0.4,0.5) -\end{pspicture} -\begin{pspicture}(0,0)(0,0) -\psellipse[linecolor=green](5.6,0.92)(0.4,0.2) -\end{pspicture} -\begin{pspicture}(0,0)(0,0) -\psellipse[linecolor=red](10.45,0.45)(0.4,0.2) -\end{pspicture} - -\end{slide} - % fabrication \begin{slide} -\headphd - {\large\bf - Fabrication of silicon carbide - } - - \small - - \vspace{2pt} - -\begin{center} - {\color{gray} - \emph{Silicon carbide --- Born from the stars, perfected on earth.} - } -\end{center} - -\vspace{2pt} - -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} - -\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{center} -\end{minipage} -\begin{minipage}{3.15cm} - \begin{center} -\includegraphics[width=3cm]{annealing.eps}\\ - {\tiny - Postannealing at $>$ \degc{1200} - } - \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} - -% contents - -\begin{slide} - -\headphd -{\large\bf - Outline -} - - \begin{itemize} - \item Supposed precipitation mechanism of SiC in Si - \item Utilized simulation techniques - \begin{itemize} - \item Molecular dynamics (MD) simulations - \item Density functional theory (DFT) calculations - \end{itemize} - \item C and Si self-interstitial point defects in silicon - \item Silicon carbide precipitation simulations - \item Summary / Conclusion / Outlook - \end{itemize} - -\end{slide} - -\begin{slide} - \headphd {\large\bf - Formation of epitaxial single crystalline 3C-SiC + IBS of epitaxial single crystalline 3C-SiC } \footnotesize @@ -401,7 +266,7 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \& {\color{blue}precipitates} \item \underline{Implantation step 2}\\[0.1cm] - Little remaining dose | \unit[180]{keV} | \degc{250}\\ + Low remaining amount of dose | \unit[180]{keV} | \degc{250}\\ $\Rightarrow$ Destruction/Amorphization of precipitates at layer interface \item \underline{Annealing}\\[0.1cm] @@ -410,36 +275,43 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) \end{itemize} \end{center} -\begin{minipage}{7cm} -\includegraphics[width=7cm]{ibs_3c-sic.eps} +\begin{minipage}{6.9cm} +\includegraphics[width=7cm]{ibs_3c-sic.eps}\\[-0.4cm] +\begin{center} +{\tiny + XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0) +} +\end{center} \end{minipage} \begin{minipage}{5cm} +\begin{center} \begin{pspicture}(0,0)(0,0) \rnode{box}{ \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{ -\begin{minipage}{5.3cm} +\begin{minipage}{3.3cm} \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} +% \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}} +\rput(-5.3,5.5){\pnode{h0}} +\rput(-1.95,5.5){\pnode{h1}} \ncline[linecolor=blue]{-}{h0}{h1} \ncline[linecolor=blue]{->}{h1}{box} \end{pspicture} +\end{center} \end{minipage} \end{slide} @@ -495,7 +367,7 @@ $\rho^*_{\text{Si}}=\unit[97]{\%}$ \begin{minipage}{4.0cm} \begin{center} C-Si dimers (dumbbells)\\[-0.1cm] - on Si interstitial sites + on Si lattice sites \end{center} \end{minipage} \hspace{0.1cm} @@ -673,7 +545,7 @@ r = \unit[2--4]{nm} \begin{itemize} \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./} \begin{itemize} - \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites + \item {\color{blue}Substitutionally} incorporated C on regular Si lattice sites \item \si{} reacting with further C in cleared volume \end{itemize} \item Annealing behavior {\tiny\color{gray}/Serre~et~al./} @@ -683,11 +555,11 @@ r = \unit[2--4]{nm} \end{itemize} $\Rightarrow$ mobile {\color{red}\ci} opposed to stable {\color{blue}\cs{}} configurations -\item Strained silicon \& Si/SiC heterostructures +\item Strained Si$_{1-y}$C$_y$/Si heterostructures {\tiny\color{gray}/Strane~et~al./Guedj~et~al./} \begin{itemize} - \item {\color{blue}Coherent} SiC precipitates (tensile strain) - \item Incoherent SiC (strain relaxation) + \item Initial {\color{blue}coherent} SiC structures (tensile strain) + \item Incoherent SiC nanocrystals (strain relaxation) \end{itemize} \end{itemize} \vspace{0.1cm} @@ -705,6 +577,35 @@ r = \unit[2--4]{nm} \begin{slide} +% contents + +\headphd +{\large\bf + Outline +} + + \begin{itemize} + {\color{gray} + \item Introduction / Motivation + \item Assumed SiC precipitation mechanisms / Controversy + } + \item Utilized simulation techniques + \begin{itemize} + \item Molecular dynamics (MD) simulations + \item Density functional theory (DFT) calculations + \end{itemize} + \item Simulation results + \begin{itemize} + \item C and Si self-interstitial point defects in silicon + \item Silicon carbide precipitation simulations + \end{itemize} + \item Summary / Conclusion + \end{itemize} + +\end{slide} + +\begin{slide} + \headphd {\large\bf Utilized computational methods @@ -753,7 +654,7 @@ NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\ \hrule \begin{itemize} \item Code: \textsc{vasp} -\item Plane wave basis set +\item Plane wave basis set | $E_{\text{cut}}=\unit[300]{eV}$ %$\displaystyle %\Phi_i=\sum_{|G+k| DB & H & T & \hkl<1 0 0> DB & V \\ -\hline - \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\ - Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\ -\hline -\end{tabular}\\[0.4cm] -\end{center} - -\begin{minipage}{3cm} -\begin{center} -\underline{Vacancy}\\ -\includegraphics[width=2.8cm]{si_pd_albe/vac.eps} -\end{center} -\end{minipage} -\begin{minipage}{3cm} -\begin{center} -\underline{\hkl<1 1 0> DB}\\ -\includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps} -\end{center} -\end{minipage} -\begin{minipage}{3cm} -\begin{center} -\underline{\hkl<1 0 0> DB}\\ -\includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps} -\end{center} -\end{minipage} -\begin{minipage}{3cm} -\begin{center} -\underline{Tetrahedral}\\ -\includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps} -\end{center} -\end{minipage}\\ - -\underline{Hexagonal} \hspace{2pt} -\href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm] -\framebox{ -\begin{minipage}{2.7cm} -$E_{\text{f}}^*=4.48\text{ eV}$\\ -\includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps} -\end{minipage} -\begin{minipage}{0.4cm} -\begin{center} -$\Rightarrow$ -\end{center} -\end{minipage} -\begin{minipage}{2.7cm} -$E_{\text{f}}=3.96\text{ eV}$\\ -\includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps} -\end{minipage} -} -\begin{minipage}{5.5cm} -\begin{center} -{\tiny nearly T $\rightarrow$ T}\\ -\end{center} -\includegraphics[width=6.0cm]{nhex_tet.ps} -\end{minipage} - -\end{slide} - -\begin{slide} - -\footnotesize - \headphd {\large\bf C interstitial point defects in silicon\\ @@ -1038,173 +869,38 @@ $E_{\text{f}}=5.18\text{ eV}$\\ \headphd {\large\bf\boldmath - C-Si dimer \& bond-centered interstitial configuration + C interstitial migration --- ab initio } -\footnotesize +\scriptsize -\vspace{0.1cm} +\vspace{0.3cm} -\begin{minipage}[t]{4.1cm} -{\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm] +\begin{minipage}{6.8cm} +\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\ \begin{minipage}{2.0cm} -\begin{center} -\underline{Erhart/Albe} -\includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps} -\end{center} +\includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps} +\end{minipage} +\begin{minipage}{0.2cm} +$\rightarrow$ \end{minipage} \begin{minipage}{2.0cm} -\begin{center} -\underline{\textsc{vasp}} -\includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps} -\end{center} -\end{minipage}\\[0.2cm] -Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\ -$\Rightarrow$ $sp$ hybridization\\[0.1cm] -Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\ -$\Rightarrow$ $sp^2$ hybridization -\begin{center} -\includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm] -{\tiny Charge density isosurface} -\end{center} +\includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps} \end{minipage} \begin{minipage}{0.2cm} -\hfill -\end{minipage} -\begin{minipage}[t]{8.1cm} -\begin{flushright} -{\bf Bond-centered interstitial}\\[0.1cm] -\begin{minipage}{4.4cm} -%\scriptsize -\begin{itemize} - \item Linear Si-C-Si bond - \item Si: one C \& 3 Si neighbours - \item Spin polarized calculations - \item No saddle point!\\ - Real local minimum! -\end{itemize} -\end{minipage} -\begin{minipage}{2.7cm} -%\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\ -\vspace{0.2cm} -\includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\ -\end{minipage} - -\framebox{ - \tiny - \begin{minipage}[t]{6.5cm} - \begin{minipage}[t]{1.2cm} - {\color{red}Si}\\ - {\tiny sp$^3$}\\[0.8cm] - \underline{${\color{black}\uparrow}$} - \underline{${\color{black}\uparrow}$} - \underline{${\color{black}\uparrow}$} - \underline{${\color{red}\uparrow}$}\\ - sp$^3$ - \end{minipage} - \begin{minipage}[t]{1.4cm} - \begin{center} - {\color{red}M}{\color{blue}O}\\[0.8cm] - \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\ - $\sigma_{\text{ab}}$\\[0.5cm] - \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\ - $\sigma_{\text{b}}$ - \end{center} - \end{minipage} - \begin{minipage}[t]{1.0cm} - \begin{center} - {\color{blue}C}\\ - {\tiny sp}\\[0.2cm] - \underline{${\color{white}\uparrow\uparrow}$} - \underline{${\color{white}\uparrow\uparrow}$}\\ - 2p\\[0.4cm] - \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$} - \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\ - sp - \end{center} - \end{minipage} - \begin{minipage}[t]{1.4cm} - \begin{center} - {\color{blue}M}{\color{green}O}\\[0.8cm] - \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\ - $\sigma_{\text{ab}}$\\[0.5cm] - \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\ - $\sigma_{\text{b}}$ - \end{center} - \end{minipage} - \begin{minipage}[t]{1.2cm} - \begin{flushright} - {\color{green}Si}\\ - {\tiny sp$^3$}\\[0.8cm] - \underline{${\color{green}\uparrow}$} - \underline{${\color{black}\uparrow}$} - \underline{${\color{black}\uparrow}$} - \underline{${\color{black}\uparrow}$}\\ - sp$^3$ - \end{flushright} - \end{minipage} - \end{minipage} -}\\[0.4cm] - -%\framebox{ -\begin{minipage}{3.0cm} -%\scriptsize -\underline{Charge density}\\ -{\color{gray}$\bullet$} Spin up\\ -{\color{green}$\bullet$} Spin down\\ -{\color{blue}$\bullet$} Resulting spin up\\ -{\color{yellow}$\bullet$} Si atoms\\ -{\color{red}$\bullet$} C atom -\end{minipage} -\begin{minipage}{3.6cm} -\includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps} -\end{minipage} -%} - -\end{flushright} - -\end{minipage} -\begin{pspicture}(0,0)(0,0) -\psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0) -\end{pspicture} - -\end{slide} - -\begin{slide} - -\headphd -{\large\bf\boldmath - C interstitial migration --- ab initio -} - -\scriptsize - -\vspace{0.1cm} - -\begin{minipage}{6.8cm} -\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\ -\begin{minipage}{2.0cm} -\includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps} -\end{minipage} -\begin{minipage}{0.2cm} -$\rightarrow$ -\end{minipage} -\begin{minipage}{2.0cm} -\includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps} -\end{minipage} -\begin{minipage}{0.2cm} -$\rightarrow$ +$\rightarrow$ \end{minipage} \begin{minipage}{2.0cm} \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps} \end{minipage}\\[0.1cm] -Spin polarization\\ -$\Rightarrow$ BC configuration constitutes local minimum\\ +Symmetry:\\ +$\Rightarrow$ Sufficient to consider \hkl[00-1] to BC transition\\ $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$ \end{minipage} \begin{minipage}{5.4cm} \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps} -\end{minipage}\\[0.2cm] +%\end{minipage}\\[0.2cm] +\end{minipage}\\[0.4cm] %\hrule % \begin{minipage}{6.8cm} @@ -1232,9 +928,9 @@ Note: Change in orientation \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps} \end{minipage}\\[0.1cm] % -\begin{center} -Reorientation pathway composed of two consecutive processes of the above type -\end{center} +%\begin{center} +%Reorientation pathway composed of two consecutive processes of the above type +%\end{center} \end{slide} @@ -1268,7 +964,7 @@ Reorientation pathway composed of two consecutive processes of the above type \begin{itemize} \item Bond-centered configuration unstable\\ $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell - \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\ + \item Minimum of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\ $\rightarrow$ \ci{} \hkl<1 1 0> DB \end{itemize} \vspace{0.1cm} @@ -1295,7 +991,7 @@ Reorientation pathway composed of two consecutive processes of the above type \headphd {\large\bf\boldmath - Defect combinations + Defect combinations --- ab inito } \footnotesize @@ -1338,17 +1034,23 @@ Reorientation pathway composed of two consecutive processes of the above type {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm] \begin{minipage}[t]{3.2cm} \underline{\hkl[1 0 0] at position 1}\\[0.1cm] +{\color{cyan} +\framebox{ \includegraphics[width=2.8cm]{00-1dc/2-25.eps} +}} \end{minipage} \begin{minipage}[t]{3.0cm} \underline{\hkl[0 -1 0] at position 1}\\[0.1cm] -\includegraphics[width=2.8cm]{00-1dc/2-39.eps} +{\color{orange} +\framebox{ +\includegraphics[width=2.5cm]{00-1dc/2-39.eps} +}} \end{minipage} \begin{minipage}[t]{6.1cm} \vspace{0.7cm} \begin{itemize} \item \ci{} agglomeration energetically favorable - \item Most favorable: C clustering\\ + \item Most favorable: strong C-C bond\\ {\color{red}However \ldots}\\ \ldots high migration barrier ($>4\,\text{eV}$)\\ \ldots entropy: @@ -1366,7 +1068,7 @@ Reorientation pathway composed of two consecutive processes of the above type \headphd {\large\bf\boldmath - Defect combinations + Defect combinations --- ab inito } \footnotesize @@ -1409,11 +1111,17 @@ Reorientation pathway composed of two consecutive processes of the above type {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm] \begin{minipage}[t]{3.2cm} \underline{\hkl[1 0 0] at position 1}\\[0.1cm] +{\color{cyan} +\framebox{ \includegraphics[width=2.8cm]{00-1dc/2-25.eps} +}} \end{minipage} \begin{minipage}[t]{3.0cm} \underline{\hkl[0 -1 0] at position 1}\\[0.1cm] -\includegraphics[width=2.8cm]{00-1dc/2-39.eps} +{\color{orange} +\framebox{ +\includegraphics[width=2.5cm]{00-1dc/2-39.eps} +}} \end{minipage} \begin{minipage}[t]{6.1cm} \vspace{0.7cm} @@ -1701,7 +1409,8 @@ Contribution of entropy to structural formation\\[0.1cm] \begin{itemize} \item total simulation volume {\pnode{in1}} \item volume of minimal SiC precipitate size {\pnode{in2}} - \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\ + %\item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\ + \item volume containing Si atoms to form a minimal {\pnode{in3}}\\ precipitate \end{itemize} }}}} @@ -1773,7 +1482,7 @@ $\rightarrow$ Consider $V_2$ and $V_3$ \begin{minipage}{6.1cm} \scriptsize \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm] -\hkl<1 0 0> C-Si dumbbell dominated structure +\ci{} \hkl<1 0 0> dumbbell dominated structure \begin{itemize} \item Si-C bumbs around \unit[0.19]{nm} \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\ @@ -1785,7 +1494,7 @@ $\rightarrow$ Consider $V_2$ and $V_3$ \begin{minipage}{6cm} \centering Formation of \ci{} dumbbells\\ -C atoms in proper 3C-SiC distance first +C atoms separated as expected in 3C-SiC \end{minipage} }} \end{pspicture}\\[0.1cm] @@ -1833,7 +1542,7 @@ Amorphous SiC-like phase \begin{minipage}{6.1cm} \scriptsize \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm] -\hkl<1 0 0> C-Si dumbbell dominated structure +\ci{} \hkl<1 0 0> dumbbell dominated structure \begin{itemize} \item Si-C bumbs around \unit[0.19]{nm} \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\ @@ -1845,7 +1554,7 @@ Amorphous SiC-like phase \begin{minipage}{6cm} \centering Formation of \ci{} dumbbells\\ -C atoms in proper 3C-SiC distance first +C atoms separated as expected in 3C-SiC \end{minipage} }} \end{pspicture}\\[0.1cm] @@ -1869,7 +1578,7 @@ Amorphous SiC-like phase \begin{minipage}{6cm} \vspace{0.1cm} \centering -{\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm] +{\bf\color{red}Formation of 3C-SiC fails to appear}\\[0.3cm] \begin{minipage}{0.8cm} {\bf\boldmath $V_1$:} \end{minipage} @@ -1904,7 +1613,7 @@ No rearrangement/transition into 3C-SiC \vspace{0.2cm} {\bf Time scale problem of MD}\\[0.2cm] -Precise integration \& thermodynamic sampling\\ +Minimize integration error \& precise thermodynamic sampling\\ $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$, $\omega$: vibrational mode\\ $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm] @@ -1920,8 +1629,7 @@ $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}} {\bf Limitations related to the short range potential}\\[0.2cm] Cut-off function limits interaction to next neighbours\\ -$\Rightarrow$ Overestimated unphysical high forces of next neighbours - (factor: 2.4--3.4) +$\Rightarrow$ Overestimated diffusion barrier (factor: 2.4--3.4) \vspace{1.4cm} @@ -1988,7 +1696,8 @@ equilibrium properties \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$_{\text{sub}}$ + \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$ + {\color{blue}\cs{}} \end{itemize} \underline{Si-Si bonds:} {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0> @@ -1996,17 +1705,11 @@ equilibrium properties \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} + \item Peak at 0.3 nm slightly shifted\\[0.05cm] + $\searrow$ \ci{} combinations (dashed arrows)\\ + $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\ + $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm] + Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si} \end{itemize} \end{minipage} @@ -2038,7 +1741,8 @@ equilibrium properties \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$_{\text{sub}}$ + \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$ + {\color{blue}\cs{}} \end{itemize} \underline{Si-Si bonds:} {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0> @@ -2046,17 +1750,11 @@ equilibrium properties \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} + \item Peak at 0.3 nm slightly shifted\\[0.05cm] + $\searrow$ \ci{} combinations (dashed arrows)\\ + $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\ + $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm] + Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si} \end{itemize} \end{minipage} @@ -2077,14 +1775,14 @@ equilibrium properties {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\ \end{center} \begin{itemize} -\item Stretched coherent SiC structures\\ -$\Rightarrow$ Precipitation process involves {\color{blue}\cs} -\item Explains annealing behavior of high/low T C implantations - \begin{itemize} - \item Low T: highly mobile {\color{red}\ci} - \item High T: stable configurations of {\color{blue}\cs} - \end{itemize} -\item Role of \si{} +\item Stretched coherent SiC structures directly observed\\ +\psframebox[linecolor=blue,linewidth=0.05cm]{ +\begin{minipage}{7cm} +\centering +\cs{} involved in the precipitation mechanism\\ +\end{minipage} +} +\item Emission of \si{} serves several needs: \begin{itemize} \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci] \item Building block for surrounding Si host \& further SiC @@ -2092,16 +1790,18 @@ $\Rightarrow$ Precipitation process involves {\color{blue}\cs} \ldots Si/SiC interface\\ \ldots within stretched coherent SiC structure \end{itemize} -\end{itemize} -\vspace{0.2cm} -\centering +\item Explains annealing behavior of high/low T C implantations + \begin{itemize} + \item Low T: highly mobile {\color{red}\ci} + \item High T: stable configurations of {\color{blue}\cs} + \end{itemize} \psframebox[linecolor=blue,linewidth=0.05cm]{ \begin{minipage}{7cm} \centering -Precipitation mechanism involving \cs\\ High T $\leftrightarrow$ IBS conditions far from equilibrium\\ \end{minipage} } +\end{itemize} \end{minipage} \vspace{0.2cm} }} @@ -2109,133 +1809,70 @@ High T $\leftrightarrow$ IBS conditions far from equilibrium\\ \end{slide} -% skip high T / C conc ... only here! -\ifnum1=0 - \begin{slide} - {\large\bf - Increased temperature simulations at high C concentration - } +\headphd +{\large\bf + Summary and Conclusions +} \footnotesize -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{12_pc_thesis.ps} -\end{minipage} -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{12_pc_c_thesis.ps} -\end{minipage} - \vspace{0.1cm} -\scriptsize - \framebox{ -\begin{minipage}[t]{6.0cm} -0.186 nm: Si-C pairs $\uparrow$\\ -(as expected in 3C-SiC)\\[0.2cm] -0.282 nm: Si-C-C\\[0.2cm] -$\approx$0.35 nm: C-Si-Si +\begin{minipage}{12.3cm} + \underline{Defects} + \begin{itemize} + \item DFT / EA + \begin{itemize} + \item Point defects excellently / fairly well described + by DFT / EA + \item Identified \ci{} migration path + \item EA drastically overestimates the diffusion barrier + \end{itemize} + \item Combinations of defects (DFT) + \begin{itemize} + \item Agglomeration of point defects energetically favorable + \item C$_{\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} } -\begin{minipage}{0.2cm} -\hfill -\end{minipage} + \framebox{ -\begin{minipage}[t]{6.0cm} -0.15 nm: C-C pairs $\uparrow$\\ -(as expected in graphite/diamond)\\[0.2cm] -0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm] -0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C +\begin{minipage}[t]{12.3cm} + \underline{Pecipitation simulations} + \begin{itemize} + \item Problem of potential enhanced slow phase space propagation + \item High T necessary to simulate IBS conditions (far from equilibrium) + \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure + \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure + / Structures of stretched SiC\\ + $\Rightarrow$ + \cs{} involved in the precipitation process at elevated temperatures + \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation + (stretched SiC, interface) + \end{itemize} \end{minipage} } -\begin{itemize} -\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} - -\vspace{-0.1cm} - \begin{center} -{\color{blue} -\framebox{ -{\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 -} -} +{\color{blue}\bf +\framebox{IBS: 3C-SiC precipitation occurs by successive agglomeration of \cs{}} } \end{center} \end{slide} -% skipped high T / C conc -\fi - \begin{slide} +\headphd {\large\bf - Summary / Outlook -} - -\small - -\begin{pspicture}(0,0)(12,1.0) -\psframebox[fillstyle=gradient,gradbegin=hred,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}\\[0.4cm] -\begin{pspicture}(0,0)(12,2) -\psframebox[fillstyle=gradient,gradbegin=hblue,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} + Acknowledgements } -\end{pspicture}\\[0.5cm] -\begin{pspicture}(0,0)(12,3) -\psframebox[fillstyle=solid,fillcolor=white,linestyle=solid]{ -\begin{minipage}{11cm} -\vspace{0.2cm} -{\color{black}\bf How to proceed \ldots}\\[0.1cm] -MC $\rightarrow$ empirical potential MD $\rightarrow$ Ground-state DFT \ldots -\begin{itemize} - \renewcommand\labelitemi{$\ldots$} - \item beyond LDA/GGA methods \& ground-state DFT -\end{itemize} -Investigation of structure \& structural evolution \ldots -\begin{itemize} - \renewcommand\labelitemi{$\ldots$} - \item electronic/optical properties - \item electronic correlations - \item non-equilibrium systems -\end{itemize} -\end{minipage} -} -\end{pspicture}\\[0.5cm] - -\end{slide} - -\begin{slide} - - {\large\bf - Acknowledgements - } \vspace{0.1cm} @@ -2243,37 +1880,728 @@ Investigation of structure \& structural evolution \ldots Thanks to \ldots +\begin{minipage}[t]{6cm} \underline{Augsburg} \begin{itemize} - \item Prof. B. Stritzker (accomodation at EP \RM{4}) - \item Ralf Utermann (EDV) + \item Prof. B. Stritzker + \item Ralf Utermann + \item EP \RM{4} \end{itemize} \underline{Helsinki} \begin{itemize} - \item Prof. K. Nordlund (MD) + \item Prof. K. Nordlund \end{itemize} \underline{Munich} \begin{itemize} - \item Bayerische Forschungsstiftung (financial support) + \item Bayerische Forschungsstiftung \end{itemize} \underline{Paderborn} \begin{itemize} - \item Prof. J. Lindner (SiC) - \item Prof. G. Schmidt (DFT + financial support) - \item Dr. E. Rauls (DFT + SiC) + \item Prof. J. Lindner + \item Prof. G. Schmidt + \item Dr. E. Rauls \end{itemize} +\end{minipage} +\begin{minipage}[t]{6cm} +\underline{Referees} + \begin{itemize} + \item PD V. Eyert + \item Prof. F. Haider + \end{itemize} +\end{minipage} - \underline{Stuttgart} +\vspace{0.5cm} \begin{center} \framebox{ -\bf Thank you for your attention / invitation! +\Large\bf Thank you for your attention! } \end{center} \end{slide} + + + + + + +\begin{slide} + +\headphd + {\large\bf + Polytypes of SiC\\[0.6cm] + } + +\vspace{0.6cm} + +\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} + +\vspace{0.6cm} + +\footnotesize + +\begin{tabular}{l c c c c c c} +\hline + & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\ +\hline +Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\ +Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\ +Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\ +Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\ +Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\ +Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\ +Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ +\hline +\end{tabular} + +\begin{pspicture}(0,0)(0,0) +\psellipse[linecolor=green](5.7,2.05)(0.4,0.50) +\end{pspicture} +\begin{pspicture}(0,0)(0,0) +\psellipse[linecolor=green](5.6,0.89)(0.4,0.20) +\end{pspicture} +\begin{pspicture}(0,0)(0,0) +\psellipse[linecolor=red](10.45,0.42)(0.4,0.20) +\end{pspicture} + +\end{slide} + +\begin{slide} + +\footnotesize + +\headphd +{\large\bf + Si self-interstitial point defects in silicon\\[0.1cm] +} + +\begin{center} +\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 + \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}\\[0.4cm] +\end{center} + +\begin{minipage}{3cm} +\begin{center} +\underline{Vacancy}\\ +\includegraphics[width=2.8cm]{si_pd_albe/vac.eps} +\end{center} +\end{minipage} +\begin{minipage}{3cm} +\begin{center} +\underline{\hkl<1 1 0> DB}\\ +\includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps} +\end{center} +\end{minipage} +\begin{minipage}{3cm} +\begin{center} +\underline{\hkl<1 0 0> DB}\\ +\includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps} +\end{center} +\end{minipage} +\begin{minipage}{3cm} +\begin{center} +\underline{Tetrahedral}\\ +\includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps} +\end{center} +\end{minipage}\\ + +\underline{Hexagonal} \hspace{2pt} +\href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm] +\framebox{ +\begin{minipage}{2.7cm} +$E_{\text{f}}^*=4.48\text{ eV}$\\ +\includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps} +\end{minipage} +\begin{minipage}{0.4cm} +\begin{center} +$\Rightarrow$ +\end{center} +\end{minipage} +\begin{minipage}{2.7cm} +$E_{\text{f}}=3.96\text{ eV}$\\ +\includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps} +\end{minipage} +} +\begin{minipage}{5.5cm} +\begin{center} +{\tiny nearly T $\rightarrow$ T}\\ +\end{center} +\includegraphics[width=6.0cm]{nhex_tet.ps} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf\boldmath + C-Si dimer \& bond-centered interstitial configuration +} + +\footnotesize + +\vspace{0.1cm} + +\begin{minipage}[t]{4.1cm} +{\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm] +\begin{minipage}{2.0cm} +\begin{center} +\underline{Erhart/Albe} +\includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps} +\end{center} +\end{minipage} +\begin{minipage}{2.0cm} +\begin{center} +\underline{\textsc{vasp}} +\includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps} +\end{center} +\end{minipage}\\[0.2cm] +Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\ +$\Rightarrow$ $sp$ hybridization\\[0.1cm] +Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\ +$\Rightarrow$ $sp^2$ hybridization +\begin{center} +\includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm] +{\tiny Charge density isosurface} +\end{center} +\end{minipage} +\begin{minipage}{0.2cm} +\hfill +\end{minipage} +\begin{minipage}[t]{8.1cm} +\begin{flushright} +{\bf Bond-centered interstitial}\\[0.1cm] +\begin{minipage}{4.4cm} +%\scriptsize +\begin{itemize} + \item Linear Si-C-Si bond + \item Si: one C \& 3 Si neighbours + \item Spin polarized calculations + \item No saddle point!\\ + Real local minimum! +\end{itemize} +\end{minipage} +\begin{minipage}{2.7cm} +%\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\ +\vspace{0.2cm} +\includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\ +\end{minipage} + +\framebox{ + \tiny + \begin{minipage}[t]{6.5cm} + \begin{minipage}[t]{1.2cm} + {\color{red}Si}\\ + {\tiny sp$^3$}\\[0.8cm] + \underline{${\color{black}\uparrow}$} + \underline{${\color{black}\uparrow}$} + \underline{${\color{black}\uparrow}$} + \underline{${\color{red}\uparrow}$}\\ + sp$^3$ + \end{minipage} + \begin{minipage}[t]{1.4cm} + \begin{center} + {\color{red}M}{\color{blue}O}\\[0.8cm] + \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\ + $\sigma_{\text{ab}}$\\[0.5cm] + \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\ + $\sigma_{\text{b}}$ + \end{center} + \end{minipage} + \begin{minipage}[t]{1.0cm} + \begin{center} + {\color{blue}C}\\ + {\tiny sp}\\[0.2cm] + \underline{${\color{white}\uparrow\uparrow}$} + \underline{${\color{white}\uparrow\uparrow}$}\\ + 2p\\[0.4cm] + \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$} + \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\ + sp + \end{center} + \end{minipage} + \begin{minipage}[t]{1.4cm} + \begin{center} + {\color{blue}M}{\color{green}O}\\[0.8cm] + \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\ + $\sigma_{\text{ab}}$\\[0.5cm] + \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\ + $\sigma_{\text{b}}$ + \end{center} + \end{minipage} + \begin{minipage}[t]{1.2cm} + \begin{flushright} + {\color{green}Si}\\ + {\tiny sp$^3$}\\[0.8cm] + \underline{${\color{green}\uparrow}$} + \underline{${\color{black}\uparrow}$} + \underline{${\color{black}\uparrow}$} + \underline{${\color{black}\uparrow}$}\\ + sp$^3$ + \end{flushright} + \end{minipage} + \end{minipage} +}\\[0.4cm] + +%\framebox{ +\begin{minipage}{3.0cm} +%\scriptsize +\underline{Charge density}\\ +{\color{gray}$\bullet$} Spin up\\ +{\color{green}$\bullet$} Spin down\\ +{\color{blue}$\bullet$} Resulting spin up\\ +{\color{yellow}$\bullet$} Si atoms\\ +{\color{red}$\bullet$} C atom +\end{minipage} +\begin{minipage}{3.6cm} +\includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps} +\end{minipage} +%} + +\end{flushright} + +\end{minipage} +\begin{pspicture}(0,0)(0,0) +\psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0) +\end{pspicture} + +\end{slide} + +\begin{slide} + + {\large\bf + Increased temperature simulations at high C concentration + } + +\footnotesize + +\begin{minipage}{6.0cm} +\includegraphics[width=6.4cm]{12_pc_thesis.ps} +\end{minipage} +\begin{minipage}{6.0cm} +\includegraphics[width=6.4cm]{12_pc_c_thesis.ps} +\end{minipage} + +\vspace{0.1cm} + +\scriptsize + +\framebox{ +\begin{minipage}[t]{5.5cm} +0.186 nm: Si-C pairs $\uparrow$\\ +(as expected in 3C-SiC)\\[0.2cm] +0.282 nm: Si-C-C\\[0.2cm] +$\approx$0.35 nm: C-Si-Si +\end{minipage} +} +\begin{minipage}{0.1cm} +\hfill +\end{minipage} +\framebox{ +\begin{minipage}[t]{5.9cm} +0.15 nm: C-C pairs $\uparrow$\\ +(as expected in graphite/diamond)\\[0.2cm] +0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm] +0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C +\end{minipage} +} + +\begin{itemize} +\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} + +\begin{center} +{\color{blue} +\framebox{ +{\color{black} +High C \& small $V$ \& short $t$ +$\Rightarrow$ +} +\begin{minipage}{4cm} +\begin{center} +Slow structural evolution due to strong C-C bonds +\end{center} +\end{minipage} +{\color{black} +$\Leftarrow$ +High C \& low T implants +} +} +} +\end{center} + +\end{slide} + + + +\begin{slide} + + {\large\bf + Valuation of a practicable temperature limit + } + + \small + +\vspace{0.1cm} + +\begin{center} +\framebox{ +{\color{blue} +Recrystallization is a hard task! +$\Rightarrow$ Avoid melting! +} +} +\end{center} + +\vspace{0.1cm} + +\footnotesize + +\begin{minipage}{6.4cm} +\includegraphics[width=6.4cm]{fe_and_t.ps} +\end{minipage} +\begin{minipage}{5.7cm} +\underline{Melting does not occur instantly after}\\ +\underline{exceeding the melting point $T_{\text{m}}=2450\text{ K}$} +\begin{itemize} +\item required transition enthalpy +\item hysterisis behaviour +\end{itemize} +\underline{Heating up c-Si by 1 K/ps} +\begin{itemize} +\item transition occurs at $\approx$ 3125 K +\item $\Delta E=0.58\text{ eV/atom}=55.7\text{ kJ/mole}$\\ + (literature: 50.2 kJ/mole) +\end{itemize} +\end{minipage} + +\vspace{0.1cm} + +\framebox{ +\begin{minipage}{4cm} +Initially chosen temperatures:\\ +$1.0 - 1.2 \cdot T_{\text{m}}$ +\end{minipage} +} +\begin{minipage}{2cm} +\begin{center} +$\Longrightarrow$ +\end{center} +\end{minipage} +\framebox{ +\begin{minipage}{5cm} +Introduced C (defects)\\ +$\rightarrow$ reduction of transition point\\ +$\rightarrow$ melting already at $T_{\text{m}}$ +\end{minipage} +} + +\vspace{0.4cm} + +\begin{center} +\framebox{ +{\color{blue} +Maximum temperature used: $0.95\cdot T_{\text{m}}$ +} +} +\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 +\end{itemize} + +\footnotesize + +\vspace{0.3cm} + +\begin{minipage}[t]{4.3cm} +\begin{center} +\underline{Low C concentration, Si-C} +\includegraphics[width=4.3cm]{c_in_si_95_v1_si-c.ps}\\ +Sharper peaks! +\end{center} +\end{minipage} +\begin{minipage}[t]{4.3cm} +\begin{center} +\underline{Low C concentration, C-C} +\includegraphics[width=4.3cm]{c_in_si_95_v1_c-c.ps}\\ +Sharper peaks!\\ +No C agglomeration! +\end{center} +\end{minipage} +\begin{minipage}[t]{3.4cm} +\begin{center} +\underline{High C concentration} +\includegraphics[width=4.3cm]{c_in_si_95_v2.ps}\\ +No significant changes\\ +iC-Si-Si $\uparrow$\\ +C-Si-C $\downarrow$ +\end{center} +\end{minipage} + +\begin{center} +\framebox{ +Long time scales and high temperatures most probably not sufficient enough! +} +\end{center} + +\end{slide} + +\begin{slide} + + {\large\bf + Investigation of a silicon carbide precipitate in silicon + } + + \scriptsize + +\vspace{0.2cm} + +\framebox{ +\scriptsize +\begin{minipage}{5.3cm} +\[ +\frac{8}{a_{\text{Si}}^3}( +\underbrace{21^3 a_{\text{Si}}^3}_{=V} +-\frac{4}{3}\pi x^3)+ +\underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500} +=21^3\cdot 8 +\] +\[ +\Downarrow +\] +\[ +\frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500 +\Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}} +\] +\[ +y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}} +\] +\end{minipage} +} +\begin{minipage}{0.1cm} +\hfill +\end{minipage} +\begin{minipage}{6.3cm} +\underline{Construction} +\begin{itemize} + \item Simulation volume: 21$^3$ unit cells of c-Si + \item Spherical topotactically aligned precipitate\\ + $r=3.0\text{ nm}$ $\Leftrightarrow$ $\approx$ 5500 C atoms + \item Create c-Si but skipped inside sphere\\ + of radius $x$ + \item Create 3C-SiC inside sphere of radius $x$\\ + and lattice constant $y$ + \item Strong coupling to heat bath ($T=20\,^{\circ}\mathrm{C}$) +\end{itemize} +\end{minipage} + +\vspace{0.3cm} + +\begin{minipage}{6.0cm} +\includegraphics[width=6cm]{pc_0.ps} +\end{minipage} +\begin{minipage}{6.1cm} +\underline{Results} +\begin{itemize} + \item Slight increase of c-Si lattice constant! + \item C-C peaks\\ + (imply same distanced Si-Si peaks) + \begin{itemize} + \item New peak at 0.307 nm: 2$^{\text{nd}}$ NN in 3C-SiC + \item Bumps ({\color{green}$\downarrow$}): + 4$^{\text{th}}$ and 6$^{\text{th}}$ NN + \end{itemize} + \item 3C-SiC lattice constant: 4.34 \AA (bulk: 4.36 \AA)\\ + $\rightarrow$ compressed precipitate + \item Interface tension:\\ + 20.15 eV/nm$^2$ or $3.23 \times 10^{-4}$ J/cm$^2$\\ + (literature: $2 - 8 \times 10^{-4}$ J/cm$^2$) +\end{itemize} +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + Investigation of a silicon carbide precipitate in silicon + } + + \footnotesize + +\begin{minipage}{7cm} +\underline{Appended annealing steps} +\begin{itemize} + \item artificially constructed interface\\ + $\rightarrow$ allow for rearrangement of interface atoms + \item check SiC stability +\end{itemize} +\underline{Temperature schedule} +\begin{itemize} + \item rapidly heat up structure up to $2050\,^{\circ}\mathrm{C}$\\ + (75 K/ps) + \item slow heating up to $1.2\cdot T_{\text{m}}=2940\text{ K}$ + by 1 K/ps\\ + $\rightarrow$ melting at around 2840 K + (\href{../video/sic_prec_120.avi}{$\rhd$}) + \item cooling down structure at 100 \% $T_{\text{m}}$ (1 K/ps)\\ + $\rightarrow$ no energetically more favorable struture +\end{itemize} +\end{minipage} +\begin{minipage}{5cm} +\includegraphics[width=5.5cm]{fe_and_t_sic.ps} +\end{minipage} + +\begin{minipage}{4cm} +\includegraphics[width=4cm]{sic_prec/melt_01.eps} +\end{minipage} +\begin{minipage}{0.2cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{4cm} +\includegraphics[width=4cm]{sic_prec/melt_02.eps} +\end{minipage} +\begin{minipage}{0.2cm} +$\rightarrow$ +\end{minipage} +\begin{minipage}{3.7cm} +\includegraphics[width=4cm]{sic_prec/melt_03.eps} +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + DFT parameters + } + +\scriptsize + +\vspace{0.1cm} + +Equilibrium lattice constants and cohesive energies + +\begin{tabular}{l r c c c c c} +\hline +\hline + & & USPP, LDA & USPP, GGA & PAW, LDA & PAW, GGA & Exp. \\ +\hline +Si (dia) & $a$ [\AA] & 5.389 & 5.455 & - & - & 5.429 \\ + & $\Delta_a$ [\%] & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - & - & - \\ + & $E_{\text{coh}}$ [eV] & -5.277 & -4.591 & - & - & -4.63 \\ + & $\Delta_E$ [\%] & \unit[{\color{red}14.0}]{\%} & \unit[{\color{green}0.8}]{\%} & - & - & - \\ +\hline +C (dia) & $a$ [\AA] & 3.527 & 3.567 & - & - & 3.567 \\ + & $\Delta_a$ [\%] & \unit[{\color{green}1.1}]{\%} & \unit[{\color{green}0.01}]{\%} & - & - & - \\ + & $E_{\text{coh}}$ [eV] & -8.812 & -7.703 & - & - & -7.374 \\ + & $\Delta_E$ [\%] & \unit[{\color{red}19.5}]{\%} & \unit[{\color{orange}4.5}]{\%} & - & - & - \\ +\hline +3C-SiC & $a$ [\AA] & 4.319 & 4.370 & 4.330 & 4.379 & 4.359 \\ + & $\Delta_a$ [\%] & \unit[{\color{green}0.9}]{\%} & \unit[{\color{green}0.3}]{\%} & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - \\ + & $E_{\text{coh}}$ [eV] & -7.318 & -6.426 & -7.371 & -6.491 & -6.340 \\ + & $\Delta_E$ [\%] & \unit[{\color{red}15.4}]{\%} & \unit[{\color{green}1.4}]{\%} & \unit[{\color{red}16.3}]{\%} & \unit[{\color{orange}2.4}]{\%} & - \\ +\hline +\hline +\end{tabular} + +\vspace{0.3cm} + +\begin{minipage}{7cm} +\begin{center} +\begin{tabular}{l c c c} +\hline +\hline + & Si (dia) & C (dia) & 3C-SiC \\ +\hline +$a$ [\AA] & 5.458 & 3.562 & 4.365 \\ +$\Delta_a$ [\%] & 0.5 & 0.1 & 0.1 \\ +\hline +$E_{\text{coh}}$ [eV] & -4.577 & -7.695 & -6.419 \\ +$\Delta_E$ [\%] & 1.1 & 4.4 & 1.2 \\ +\hline +\hline +\end{tabular} +\end{center} +\end{minipage} +\begin{minipage}{5cm} +$\leftarrow$ entire parameter set +\end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf + DFT parameters\\ + } + +\footnotesize + +\begin{minipage}{6cm} +\begin{center} +\includegraphics[width=6cm]{sic_32pc_gamma_cutoff_lc.ps} +\end{center} +\end{minipage} +\begin{minipage}{6cm} +\begin{center} +Lattice constants with respect to the PW cut-off energy +\end{center} +\end{minipage} + +\begin{minipage}{6cm} +\begin{center} +\includegraphics[width=6cm]{si_self_int_thesis.ps} +\end{center} +\end{minipage} +\begin{minipage}{6cm} +\begin{center} +Defect formation energy with respect to the size of the supercell\\[0.1cm] +\end{center} + +\end{minipage} + +\end{slide} + \end{document}