\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
+\usepackage{stmaryrd}
\usepackage{latexsym}
\usepackage{ae}
\end{slide}
-\fi
-
\begin{slide}
\headphd
\vspace{0.2cm}
-\includegraphics[width=7cm]{ibs_3c-sic.eps}\\
-
+\begin{center}
\begin{itemize}
\item \underline{Implantation step 1}\\[0.1cm]
Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
\unit[10]{h} at \degc{1250}\\
$\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
\end{itemize}
+\end{center}
+\begin{minipage}{7cm}
+\includegraphics[width=7cm]{ibs_3c-sic.eps}
+\end{minipage}
+\begin{minipage}{5cm}
\begin{pspicture}(0,0)(0,0)
-\rput(10.0,4.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
+\rnode{box}{
+\psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
\begin{minipage}{5.3cm}
\begin{center}
{\color{blue}
upon prevention of SiC precipitation
\end{itemize}
\end{minipage}
-}}}
+}}
+\rput(-6.8,5.4){\pnode{h0}}
+\rput(-3.0,5.4){\pnode{h1}}
+\ncline[linecolor=blue]{-}{h0}{h1}
+\ncline[linecolor=blue]{->}{h1}{box}
\end{pspicture}
-
+\end{minipage}
\end{slide}
-
-\end{document}
-
-\ifnum1=0
-
-% continue here
-%\fi
-
\begin{slide}
+\headphd
{\large\bf
- Model displaying the formation of ordered lamellae
-}
-
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf
Supposed precipitation mechanism of SiC in Si
- }
+}
\scriptsize
\vspace{0.1cm}
- \begin{minipage}{3.8cm}
- Si \& SiC lattice structure\\[0.2cm]
- \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
- \hrule
+ \framebox{
+ \begin{minipage}{3.6cm}
+ \begin{center}
+ Si \& SiC lattice structure\\[0.1cm]
+ \includegraphics[width=2.3cm]{sic_unit_cell.eps}
+ \end{center}
+{\tiny
+ \begin{minipage}{1.7cm}
+\underline{Silicon}\\
+{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
+$a=\unit[5.429]{\\A}$\\
+$\rho^*_{\text{Si}}=\unit[100]{\%}$
+ \end{minipage}
+ \begin{minipage}{1.7cm}
+\underline{Silicon carbide}\\
+{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
+$a=\unit[4.359]{\\A}$\\
+$\rho^*_{\text{Si}}=\unit[97]{\%}$
+ \end{minipage}
+}
\end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ }
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
\begin{center}
\includegraphics[width=3.3cm]{tem_c-si-db.eps}
\end{center}
\end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
\begin{center}
\includegraphics[width=3.3cm]{tem_3c-sic.eps}
\end{center}
\end{minipage}
- \begin{minipage}{4cm}
+ \vspace{0.1cm}
+
+ \begin{minipage}{4.0cm}
\begin{center}
C-Si dimers (dumbbells)\\[-0.1cm]
on Si interstitial sites
\end{center}
\end{minipage}
- \hspace{0.2cm}
- \begin{minipage}{4.2cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
\begin{center}
Agglomeration of C-Si dumbbells\\[-0.1cm]
$\Rightarrow$ dark contrasts
\end{center}
\end{minipage}
- \hspace{0.2cm}
- \begin{minipage}{4cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
\begin{center}
Precipitation of 3C-SiC in Si\\[-0.1cm]
$\Rightarrow$ Moir\'e fringes\\[-0.1cm]
\end{center}
\end{minipage}
- \begin{minipage}{3.8cm}
+ \vspace{0.1cm}
+
+ \begin{minipage}{4.0cm}
\begin{center}
\includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
\end{center}
\end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
\begin{center}
\includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
\end{center}
\end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
\begin{center}
\includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
\end{center}
\end{minipage}
\begin{pspicture}(0,0)(0,0)
-\psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
-\psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
-\rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
-\psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
-\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
+\psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
+\rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
+\psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
+\rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
$4a_{\text{Si}}=5a_{\text{SiC}}$
}}}
-\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
\hkl(h k l) planes match
}}}
-\rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
-r = 2 - 4 nm
+\rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+r = \unit[2--4]{nm}
}}}
\end{pspicture}
\begin{slide}
- {\large\bf
- Supposed precipitation mechanism of SiC in Si
- }
+\headphd
+{\large\bf
+ Supposed precipitation mechanism of SiC in Si
+}
\scriptsize
\vspace{0.1cm}
- \begin{minipage}{3.8cm}
- Si \& SiC lattice structure\\[0.2cm]
- \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
- \hrule
+ \framebox{
+ \begin{minipage}{3.6cm}
+ \begin{center}
+ Si \& SiC lattice structure\\[0.1cm]
+ \includegraphics[width=2.3cm]{sic_unit_cell.eps}
+ \end{center}
+{\tiny
+ \begin{minipage}{1.7cm}
+\underline{Silicon}\\
+{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
+$a=\unit[5.429]{\\A}$\\
+$\rho^*_{\text{Si}}=\unit[100]{\%}$
+ \end{minipage}
+ \begin{minipage}{1.7cm}
+\underline{Silicon carbide}\\
+{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
+$a=\unit[4.359]{\\A}$\\
+$\rho^*_{\text{Si}}=\unit[97]{\%}$
\end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+}
+ \end{minipage}
+ }
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
\begin{center}
\includegraphics[width=3.3cm]{tem_c-si-db.eps}
\end{center}
\end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
\begin{center}
\includegraphics[width=3.3cm]{tem_3c-sic.eps}
\end{center}
\end{minipage}
- \begin{minipage}{4cm}
+ \vspace{0.1cm}
+
+ \begin{minipage}{4.0cm}
\begin{center}
C-Si dimers (dumbbells)\\[-0.1cm]
on Si interstitial sites
\end{center}
\end{minipage}
- \hspace{0.2cm}
- \begin{minipage}{4.2cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
\begin{center}
Agglomeration of C-Si dumbbells\\[-0.1cm]
$\Rightarrow$ dark contrasts
\end{center}
\end{minipage}
- \hspace{0.2cm}
- \begin{minipage}{4cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
\begin{center}
Precipitation of 3C-SiC in Si\\[-0.1cm]
$\Rightarrow$ Moir\'e fringes\\[-0.1cm]
\end{center}
\end{minipage}
- \begin{minipage}{3.8cm}
+ \vspace{0.1cm}
+
+ \begin{minipage}{4.0cm}
\begin{center}
\includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
\end{center}
\end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.1cm}
\begin{center}
\includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
\end{center}
\end{minipage}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \hspace{0.1cm}
+ \begin{minipage}{4.0cm}
\begin{center}
\includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
\end{center}
\end{minipage}
\begin{pspicture}(0,0)(0,0)
-\psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
-\psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
-\rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
-\psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
-\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
+\psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
+\rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
+\psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
+\rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
$4a_{\text{Si}}=5a_{\text{SiC}}$
}}}
-\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
\hkl(h k l) planes match
}}}
-\rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
-r = 2 - 4 nm
+\rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+r = \unit[2--4]{nm}
}}}
-\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
+% controversial view!
+\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
+\begin{minipage}{14cm}
+\hfill
+\vspace{12cm}
+\end{minipage}
+}}
+\rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
\begin{minipage}{10cm}
\small
-{\color{red}\bf Controversial views}
+\vspace*{0.2cm}
+\begin{center}
+{\color{gray}\bf Controversial findings}
+\end{center}
\begin{itemize}
-\item Implantations at high T (Nejim et al.)
+\item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
\begin{itemize}
- \item Topotactic transformation based on \cs
- \item \si{} as supply reacting with further C in cleared volume
+ \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
+ \item \si{} reacting with further C in cleared volume
\end{itemize}
-\item Annealing behavior (Serre et al.)
+\item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
\begin{itemize}
- \item Room temperature implants $\rightarrow$ highly mobile C
- \item Elevated T implants $\rightarrow$ no/low C redistribution/migration\\
- (indicate stable \cs{} configurations)
+ \item Room temperature implantation $\rightarrow$ high C diffusion
+ \item Elevated temperature implantation $\rightarrow$ no C redistribution
\end{itemize}
+ $\Rightarrow$ mobile {\color{red}\ci} opposed to
+ stable {\color{blue}\cs{}} configurations
\item Strained silicon \& Si/SiC heterostructures
+ {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
\begin{itemize}
- \item Coherent SiC precipitates (tensile strain)
+ \item {\color{blue}Coherent} SiC precipitates (tensile strain)
\item Incoherent SiC (strain relaxation)
\end{itemize}
\end{itemize}
+\vspace{0.1cm}
+\begin{center}
+{\Huge${\lightning}$} \hspace{0.3cm}
+{\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
+{\Huge${\lightning}$}
+\end{center}
+\vspace{0.2cm}
\end{minipage}
}}}
\end{pspicture}
\end{slide}
+% continue here
+\fi
+
\begin{slide}
- {\large\bf
- Molecular dynamics (MD) simulations
- }
+\headphd
+{\large\bf
+ Utilized computational methods
+}
- \vspace{12pt}
+\vspace{0.2cm}
- \small
+\small
- {\bf MD basics:}
- \begin{itemize}
- \item Microscopic description of N particle system
- \item Analytical interaction potential
- \item Numerical integration using Newtons equation of motion\\
- as a propagation rule in 6N-dimensional phase space
- \item Observables obtained by time and/or ensemble averages
- \end{itemize}
- {\bf Details of the simulation:}
- \begin{itemize}
- \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
- \item Ensemble: NpT (isothermal-isobaric)
- \begin{itemize}
- \item Berendsen thermostat:
- $\tau_{\text{T}}=100\text{ fs}$
- \item Berendsen barostat:\\
- $\tau_{\text{P}}=100\text{ fs}$,
- $\beta^{-1}=100\text{ GPa}$
- \end{itemize}
- \item Erhart/Albe potential: Tersoff-like bond order potential
- \vspace*{12pt}
- \[
- E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
- \pot_{ij} = {\color{red}f_C(r_{ij})}
- \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
- \]
- \end{itemize}
+{\bf Molecular dynamics (MD)}\\
+\scriptsize
+\begin{tabular}{p{4.5cm} p{7.5cm}}
+Basics & Details\\
+\hline
+System of $N$ particles &
+$N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
+\hline
+Phase space propagation &
+Velocity Verlet | timestep: \unit[1]{fs} \\
+\hline
+Analytical interaction potential &
+Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
+(Erhart/Albe)
+$\displaystyle
+E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+ \pot_{ij} = {\color{red}f_C(r_{ij})}
+ \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
+$\\
+\hline
+Observables: time/ensemble averages &
+NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
+\hline
+\end{tabular}
+
+\small
+
+\vspace{0.1cm}
+
+{\bf Density functional theory (DFT)}
+
+\scriptsize
+
+\begin{minipage}[t]{6cm}
+\underline{Basics}
+\begin{itemize}
+ \item Born-Oppenheimer approximation:\\
+ Decouple electronic \& ionic motion
+ \item Hohenberg-Kohn theorem:\\
+ $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$
+ $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$}
+\end{itemize}
+\underline{Details}
+\begin{itemize}
+\item Code: \textsc{vasp}
+\item Plane wave basis set $\{\phi_j\}$\\[0.1cm]
+$\displaystyle
+\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r)
+$\\
+$\displaystyle
+E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
+$
+\item Ultrasoft pseudopotential
+\item Brillouin zone sampling: $\Gamma$-point
+\end{itemize}
+\end{minipage}
+\begin{minipage}[t]{6cm}
+
+\[
+\left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
+\]
+\[
+n(r)=\sum_i^N|\Phi_i(r)|^2
+\]
+\[
+V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
+ +V_{\text{XC}}[n(r)]
+\]
+
+\end{minipage}
- \begin{picture}(0,0)(-230,-30)
- \includegraphics[width=5cm]{tersoff_angle.eps}
- \end{picture}
-
\end{slide}
+\end{document}
+\ifnum1=0
+
\begin{slide}
+ \small
{\large\bf
Density functional theory (DFT) calculations
}
- \small
-
Basic ingredients necessary for DFT
\begin{itemize}
\end{itemize}
\item \underline{Plane wave basis set}
- approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
-\[
-\rightarrow
-\text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
-\qquad ({\color{blue}300\text{ eV}})
-\]
\item \underline{Brillouin zone sampling} -
{\color{blue}$\Gamma$-point only} calculations
\item \underline{Pseudo potential}
projects / lectures / latex.git / blobdiff