X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fdefense.tex;h=2a0b5633cb10d87084afc7789dcc4b4e3cfc05a2;hp=00f1c5a20929fd5a4c661453e1a19268526e1b70;hb=1b919ddeeb86bac15cb95ef2efaccaf7c94365b2;hpb=348f10f39655e4efc37eb22f88ac02c75ec60c23 diff --git a/posic/talks/defense.tex b/posic/talks/defense.tex index 00f1c5a..2a0b563 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 @@ -170,7 +172,7 @@ E\\ \centerslidesfalse % skip for preparation -\ifnum1=0 +%\ifnum1=0 % intro @@ -244,147 +246,10 @@ E\\ \end{slide} -% motivation - -\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} - % 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{-0.5cm} - -\begin{center} -\color{red} -\framebox{ -{\footnotesize\color{black} - Mismatch in \underline{thermal expansion coeefficient} - and \underline{lattice parameter} w.r.t. substrate -} -} -\end{center} - -\vspace{0.1cm} - -{\bf Alternative approach}\\ -Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) - -\vspace{0.1cm} - -\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} -\begin{center} -{\footnotesize -No surface bending effects\\ -High areal homogenity\\[0.1cm] -$\Downarrow$\\[0.1cm] -Synthesis of large area SiC films possible -} -\end{center} -\end{minipage} - -\end{slide} - -\begin{slide} - \headphd {\large\bf IBS of epitaxial single crystalline 3C-SiC @@ -401,7 +266,7 @@ Synthesis of large area SiC films possible $\Rightarrow$ 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] @@ -419,42 +284,38 @@ Synthesis of large area SiC films possible \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(-6.8,5.5){\pnode{h0}} -\rput(-3.0,5.5){\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} -%\end{document} -% temp -%\ifnum1=0 - -% contents - \begin{slide} \headphd @@ -684,7 +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./} @@ -694,11 +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} @@ -714,10 +575,10 @@ r = \unit[2--4]{nm} \end{slide} -\fi - \begin{slide} +% contents + \headphd {\large\bf Outline @@ -892,13 +753,13 @@ $ \end{minipage} \end{minipage} -\vspace{0.2cm} +\vspace{0.3cm} -\begin{minipage}[b]{6cm} +\begin{minipage}[t]{6cm} {\bf Defect formation energy}\\ \framebox{ -$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm] -Particle reservoir: Si \& SiC\\[0.2cm] +$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.5cm] +%Particle reservoir: Si \& SiC\\[0.2cm] {\bf Binding energy}\\ \framebox{ $ @@ -912,7 +773,8 @@ $ $E_{\text{b}}<0$: energetically favorable configuration\\ $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\ \end{minipage} -\begin{minipage}[b]{6cm} +\begin{minipage}[t]{6cm} +\vspace{1.4cm} {\bf Migration barrier} \footnotesize \begin{itemize} @@ -931,77 +793,6 @@ $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\ \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} - -\footnotesize - \headphd {\large\bf C interstitial point defects in silicon\\ @@ -1074,180 +865,42 @@ $E_{\text{f}}=5.18\text{ eV}$\\ \end{slide} -\end{document} -\ifnum1=0 - \begin{slide} \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} +$\rightarrow$ \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} -$\rightarrow$ -\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\\ -$\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$ +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps} +\end{minipage}\\[0.1cm] +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} @@ -1275,9 +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} @@ -1311,7 +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} @@ -1338,7 +991,7 @@ Reorientation pathway composed of two consecutive processes of the above type \headphd {\large\bf\boldmath - Defect combinations + Defect combinations --- ab inito } \footnotesize @@ -1409,7 +1062,7 @@ Reorientation pathway composed of two consecutive processes of the above type \headphd {\large\bf\boldmath - Defect combinations + Defect combinations --- ab inito } \footnotesize @@ -1816,7 +1469,7 @@ $\rightarrow$ 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):\\ @@ -1828,7 +1481,7 @@ $\rightarrow$ 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] @@ -1876,7 +1529,7 @@ 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):\\ @@ -1888,7 +1541,7 @@ 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] @@ -1947,7 +1600,7 @@ 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] @@ -1963,8 +1616,7 @@ $\Rightarrow$ 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} @@ -2031,7 +1683,8 @@ 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> @@ -2039,17 +1692,11 @@ 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} @@ -2081,7 +1728,8 @@ 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> @@ -2089,17 +1737,11 @@ 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} @@ -2120,14 +1762,14 @@ 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 @@ -2135,16 +1777,18 @@ $\Rightarrow$ 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} }} @@ -2152,7 +1796,7 @@ High T $\leftrightarrow$ IBS conditions far from equilibrium\\ \end{slide} -% skip high T / C conc ... only here! +% skip high c conc results \ifnum1=0 \begin{slide} @@ -2163,10 +1807,10 @@ High T $\leftrightarrow$ IBS conditions far from equilibrium\\ \footnotesize -\begin{minipage}{6.5cm} +\begin{minipage}{6.0cm} \includegraphics[width=6.4cm]{12_pc_thesis.ps} \end{minipage} -\begin{minipage}{6.5cm} +\begin{minipage}{6.0cm} \includegraphics[width=6.4cm]{12_pc_c_thesis.ps} \end{minipage} @@ -2221,64 +1865,71 @@ High C \& low T implants \end{slide} -% skipped high T / C conc +% skip high c conc \fi \begin{slide} +\headphd {\large\bf - Summary / Outlook + Summary and Conclusions } -\small +\footnotesize -\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 +\vspace{0.1cm} + +\framebox{ +\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} } -\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 + +\framebox{ +\begin{minipage}[t]{12.3cm} + \underline{Pecipitation simulations} + \begin{itemize} + \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 \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} } -\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} + +\begin{center} +{\color{blue}\bf +\framebox{IBS: 3C-SiC precipitation occurs by successive agglomeration of \cs{}} } -\end{pspicture}\\[0.5cm] +\end{center} \end{slide} \begin{slide} - {\large\bf - Acknowledgements - } +\headphd +{\large\bf + Acknowledgements +} \vspace{0.1cm} @@ -2286,39 +1937,311 @@ 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} -\end{document} -\fi + + + + + +\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} + +\end{document}