% layout check
%\layout
+\ifnum1=0
\begin{slide}
\center
{\Huge
E\\
}
\end{slide}
+\fi
% topic
\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}
% no vertical centering
\centerslidesfalse
+% skip for preparation
+%\ifnum1=0
+
% intro
% motivation / properties / applications of silicon carbide
\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
$\Rightarrow$ 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]
\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}
\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}
\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./}
\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}
\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
\hrule
\begin{itemize}
\item Code: \textsc{vasp}
-\item Plane wave basis set
+\item Plane wave basis set | $E_{\text{cut}}=\unit[300]{eV}$
%$\displaystyle
%\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
%$\\
\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{
$
$E_{\text{b}}<0$: 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}
\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\\
\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}
\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}
\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}
\headphd
{\large\bf\boldmath
- Defect combinations
+ Defect combinations --- ab inito
}
\footnotesize
{\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:
\headphd
{\large\bf\boldmath
- Defect combinations
+ Defect combinations --- ab inito
}
\footnotesize
{\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 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}
}}}}
\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):\\
\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]
\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):\\
\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]
\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}
\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]
{\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}
\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>
\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}
\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>
\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}
{\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
\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}
}}
\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}
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}
projects / lectures / latex.git / blobdiff