\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
+\usepackage{stmaryrd}
\usepackage{latexsym}
\usepackage{ae}
\usepackage{pstricks}
\usepackage{pst-node}
+\usepackage{pst-grad}
%\usepackage{epic}
%\usepackage{eepic}
\usepackage{upgreek}
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+
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+
\begin{document}
\extraslideheight{10in}
% no vertical centering
\centerslidesfalse
-%\ifnum1=0
+\ifnum1=0
% intro
\begin{slide}
+\vspace*{1.8cm}
+
\small
\begin{pspicture}(0,0)(13.5,5)
\end{center}
\begin{pspicture}(0,0)(0,0)
-\rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
+\rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
\begin{minipage}{11cm}
-{\color{red}Diploma thesis}\\
+{\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}
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-\rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
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\begin{minipage}{11cm}
-{\color{blue}Doctoral studies}\\
+{\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
\begin{slide}
+\headdiplom
{\large\bf
Selforganization of nanometric amorphous SiC lamellae
}
\begin{minipage}{12cm}
\includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\
{\scriptsize
-XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si, \degc{150},
+XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si,
+{\color{red}\underline{\degc{150}}},
Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$}
}
\end{minipage}
\begin{slide}
+\headdiplom
{\large\bf
Model displaying the formation of ordered lamellae
}
\begin{slide}
+\headdiplom
{\large\bf
Implementation of the Monte Carlo code
}
\begin{slide}
\begin{minipage}{3.7cm}
+\begin{pspicture}(0,0)(0,0)
+\rput(1.7,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradangle=10,gradmidpoint=1,linestyle=none]{
+\begin{minipage}{3.7cm}
+\hfill
+\vspace{0.7cm}
+\end{minipage}
+}}
+\end{pspicture}
{\large\bf
Results
}
\footnotesize
-\vspace{1.0cm}
+\vspace{1.2cm}
Evolution of the \ldots
\begin{itemize}
\item continuous\\
amorphous layer
\item a/c interface
- \item lamella precipitates
+ \item lamellar precipitates
\end{itemize}
-\ldots reproduced!\\[1.5cm]
+\ldots reproduced!\\[1.4cm]
{\color{blue}
\begin{center}
Experiment \& simulation\\
in good agreement\\[1.0cm]
-Simulation is able to model the whole depth region\\[1.0cm]
+Simulation is able to model the whole depth region\\[1.2cm]
\end{center}
}
\end{minipage}
-\begin{minipage}{0.4cm}
+\begin{minipage}{0.5cm}
\vfill
\end{minipage}
\begin{minipage}{8.0cm}
- \vspace{-0.2cm}
+ \vspace{-0.3cm}
\includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\
\includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps}
\end{minipage}
\begin{slide}
+\headdiplom
{\large\bf
Structural \& compositional details
}
\item C accumulation in the amorphous phase / Origin of stress
\end{itemize}
-\begin{picture}(0,0)(-265,-30)
+\begin{picture}(0,0)(-260,-50)
\framebox{
\begin{minipage}{3cm}
\begin{center}
\end{slide}
-
-\end{document}
-
-% continue here
-\fi
-
-\ifnum1=0
-
\begin{slide}
+\headphd
{\large\bf
- Model displaying the formation of ordered lamellae
+ Formation of epitaxial single crystalline 3C-SiC
}
-\framebox{
- \begin{minipage}{6.3cm}
+\footnotesize
+
+\vspace{0.2cm}
+
+\begin{center}
+\begin{itemize}
+ \item \underline{Implantation step 1}\\[0.1cm]
+ Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
+ $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
+ {\color{blue}precipitates}
+ \item \underline{Implantation step 2}\\[0.1cm]
+ Little remaining dose | \unit[180]{keV} | \degc{250}\\
+ $\Rightarrow$
+ Destruction/Amorphization of precipitates at layer interface
+ \item \underline{Annealing}\\[0.1cm]
+ \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)
+\rnode{box}{
+\psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
+\begin{minipage}{5.3cm}
\begin{center}
{\color{blue}
- Precipitation mechanism not yet fully understood!
+ 3C-SiC precipitation\\
+ not yet fully understood
}
+ \end{center}
+ \vspace*{0.1cm}
\renewcommand\labelitemi{$\Rightarrow$}
- \small
- \underline{Understanding the SiC precipitation}
+ 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
+ \item significant technological progress\\
+ in SiC thin film formation
+ \item perspectives for processes relying\\
+ upon prevention of SiC precipitation
\end{itemize}
- \end{center}
- \end{minipage}
-}
+\end{minipage}
+}}
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+\ncline[linecolor=blue]{->}{h1}{box}
+\end{pspicture}
+\end{minipage}
\end{slide}
\begin{slide}
- {\large\bf
+\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}
+}
\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)
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-\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
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+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}
- \hspace{0.6cm}
- \begin{minipage}{3.8cm}
+ \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{0.1cm}
+ \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)
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-r = 2 - 4 nm
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+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}
\begin{slide}
- {\large\bf
- Molecular dynamics (MD) simulations
- }
-
- \vspace{12pt}
+\headphd
+{\large\bf
+ Utilized computational methods
+}
- \small
+\vspace{0.3cm}
- {\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}
+\small
- \begin{picture}(0,0)(-230,-30)
- \includegraphics[width=5cm]{tersoff_angle.eps}
- \end{picture}
-
-\end{slide}
+{\bf Molecular dynamics (MD)}\\[0.1cm]
+\scriptsize
+\begin{tabular}{| p{4.5cm} | p{7.5cm} |}
+\hline
+System of $N$ particles &
+$N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
+Phase space propagation &
+Velocity Verlet | timestep: \unit[1]{fs} \\
+Analytical interaction potential &
+Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
+(Erhart/Albe)
+$\displaystyle
+E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+ \pot_{ij} = {\color{red}f_C(r_{ij})}
+ \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
+$\\
+Observables: time/ensemble averages &
+NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
+\hline
+\end{tabular}
-\begin{slide}
+\small
- {\large\bf
- Density functional theory (DFT) calculations
- }
+\vspace{0.3cm}
- \small
+{\bf Density functional theory (DFT)}
- Basic ingredients necessary for DFT
+\scriptsize
- \begin{itemize}
- \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
- \begin{itemize}
- \item ... uniquely determines the ground state potential
- / wavefunctions
- \item ... minimizes the systems total energy
- \end{itemize}
- \item \underline{Born-Oppenheimer}
- - $N$ moving electrons in an external potential of static nuclei
-\[
-H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
- +\sum_i^N V_{\text{ext}}(r_i)
- +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
-\]
- \item \underline{Effective potential}
- - averaged electrostatic potential \& exchange and correlation
-\[
+\begin{minipage}[t]{6cm}
+\begin{itemize}
+ \item Hohenberg-Kohn theorem:\\
+ $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
+ \item Kohn-Sham approach:\\
+ Single-particle effective theory
+\end{itemize}
+\hrule
+\begin{itemize}
+\item Code: \textsc{vasp}
+\item Plane wave basis set
+%$\displaystyle
+%\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
+%$\\
+%$\displaystyle
+%E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
+%$
+\item Ultrasoft pseudopotential
+\item Exchange \& correlation: GGA
+\item Brillouin zone sampling: $\Gamma$-point
+\item Supercell: $N=216\pm2$
+\end{itemize}
+\end{minipage}
+\begin{minipage}{6cm}
+\begin{pspicture}(0,0)(0,0)
+\pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
+\rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
+\left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
+$
+}}
+\rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
+n(r)=\sum_i^N|\Phi_i(r)|^2
+$
+}}
+\rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
+V_{\text{XC}}[n(r)]
-\]
- \item \underline{Kohn-Sham system}
- - Schr\"odinger equation of N non-interacting particles
-\[
-\left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
-=\epsilon_i\Phi_i(r)
-\quad
-\Rightarrow
-\quad
-n(r)=\sum_i^N|\Phi_i(r)|^2
-\]
- \item \underline{Self-consistent solution}\\
-$n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
-which in turn depends on $n(r)$
- \item \underline{Variational principle}
- - minimize total energy with respect to $n(r)$
- \end{itemize}
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf
- Density functional theory (DFT) calculations
- }
-
- \small
-
- \vspace*{0.2cm}
-
- Details of applied DFT calculations in this work
-
- \begin{itemize}
- \item \underline{Exchange correlation functional}
- - approximations for the inhomogeneous electron gas
- \begin{itemize}
- \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
- \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
- \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}
- - consider only the valence electrons
- \item \underline{Code} - VASP 4.6
- \end{itemize}
-
- \vspace*{0.2cm}
-
- MD and structural optimization
-
- \begin{itemize}
- \item MD integration: Gear predictor corrector algorithm
- \item Pressure control: Parrinello-Rahman pressure control
- \item Structural optimization: Conjugate gradient method
- \end{itemize}
+$
+}}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
-\begin{pspicture}(0,0)(0,0)
-\psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
\end{pspicture}
+\end{minipage}
\end{slide}
\begin{slide}
+\headphd
{\large\bf
- C and Si self-interstitial point defects in silicon
+ Point defects \& defect migration
}
\small
- \vspace*{0.3cm}
+ \vspace{0.2cm}
-\begin{minipage}{8cm}
-Procedure:\\[0.3cm]
- \begin{pspicture}(0,0)(7,5)
- \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\begin{minipage}[b]{7.5cm}
+{\bf Defect structure}\\
+ \begin{pspicture}(0,0)(7,4.4)
+ \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
\parbox{7cm}{
\begin{itemize}
\item Creation of c-Si simulation volume
\item $T=0\text{ K}$, $p=0\text{ bar}$
\end{itemize}
}}}}
-\rput(3.5,2.1){\rnode{insert}{\psframebox{
+\rput(3.5,1.3){\rnode{insert}{\psframebox{
\parbox{7cm}{
\begin{center}
Insertion of interstitial C/Si atoms
\end{center}
}}}}
- \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
+ \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
\parbox{7cm}{
\begin{center}
Relaxation / structural energy minimization
\ncline[]{->}{insert}{cool}
\end{pspicture}
\end{minipage}
-\begin{minipage}{5cm}
- \includegraphics[width=5cm]{unit_cell_e.eps}\\
+\begin{minipage}[b]{4.5cm}
+\begin{center}
+\includegraphics[width=3.8cm]{unit_cell_e.eps}\\
+\end{center}
+\begin{minipage}{2.21cm}
+{\scriptsize
+{\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
+{\color{green}$\bullet$} Hexagonal\\[-0.1cm]
+{\color{yellow}$\bullet$} \hkl<1 0 0> DB
+}
+\end{minipage}
+\begin{minipage}{2.21cm}
+{\scriptsize
+{\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
+{\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
+{\color{black}$\bullet$} Vac. / Sub.
+}
+\end{minipage}
\end{minipage}
-\begin{minipage}{9cm}
- \begin{tabular}{l c c}
- \hline
- & size [unit cells] & \# atoms\\
-\hline
-VASP & $3\times 3\times 3$ & $216\pm 1$ \\
-Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
-\hline
- \end{tabular}
+\vspace{0.2cm}
+
+\begin{minipage}[b]{6cm}
+{\bf Defect formation energy}\\
+\framebox{
+$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
+Particle reservoir: Si \& SiC\\[0.2cm]
+{\bf Binding energy}\\
+\framebox{
+$
+E_{\text{b}}=
+E_{\text{f}}^{\text{comb}}-
+E_{\text{f}}^{1^{\text{st}}}-
+E_{\text{f}}^{2^{\text{nd}}}
+$
+}\\[0.1cm]
+\footnotesize
+$E_{\text{b}}<0$: energetically favorable configuration\\
+$E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
\end{minipage}
-\begin{minipage}{4cm}
-{\color{red}$\bullet$} Tetrahedral\\
-{\color{green}$\bullet$} Hexagonal\\
-{\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
-{\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
-{\color{cyan}$\bullet$} Bond-centered\\
-{\color{black}$\bullet$} Vacancy / Substitutional
+\begin{minipage}[b]{6cm}
+{\bf Migration barrier}
+\footnotesize
+\begin{itemize}
+ \item Displace diffusing atom
+ \item Constrain relaxation of (diffusing) atoms
+ \item Record configurational energy
+\end{itemize}
+\begin{picture}(0,0)(-60,-33)
+\includegraphics[width=4.5cm]{crt_mod.eps}
+\end{picture}
\end{minipage}
\end{slide}
+% continue here
+\fi
+
\begin{slide}
\footnotesize
\begin{minipage}{9.5cm}
+\headphd
{\large\bf
- Si self-interstitial point defects in silicon\\
+ Si self-interstitial point defects in silicon\\[0.1cm]
}
\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
- VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
+ \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}\\[0.2cm]
+\end{tabular}\\[0.3cm]
\begin{minipage}{4.7cm}
\includegraphics[width=4.7cm]{e_kin_si_hex.ps}
{\tiny nearly T $\rightarrow$ T}\\
\end{center}
\includegraphics[width=4.7cm]{nhex_tet.ps}
-\end{minipage}\\
+\end{minipage}\\[0.1cm]
\underline{Hexagonal} \hspace{2pt}
\href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
\end{minipage}
\end{minipage}
-\begin{minipage}{3.5cm}
+\begin{minipage}{2.5cm}
\begin{flushright}
+\vspace*{0.2cm}
\underline{\hkl<1 1 0> dumbbell}\\
\includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
\underline{Tetrahedral}\\
\footnotesize
+\headphd
{\large\bf
C interstitial point defects in silicon\\[-0.1cm]
}
+{\scriptsize
\begin{tabular}{l c c c c c c r}
\hline
$E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
\hline
- VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
+ \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
\hline
-\end{tabular}\\[0.1cm]
+\end{tabular}
+}\\[0.1cm]
\framebox{
\begin{minipage}{2.7cm}
\end{slide}
+\end{document}
+\ifnum1=0
+
\begin{slide}
\footnotesize
\end{minipage}
\end{minipage}
\end{minipage}
-\framebox{
-\begin{minipage}{4.2cm}
- {\small Constrained relaxation\\
- technique (CRT) method}\\
-\includegraphics[width=4cm]{crt_orig.eps}
-\begin{itemize}
- \item Constrain diffusing atom
- \item Static constraints
-\end{itemize}
-\vspace*{0.3cm}
- {\small Modifications}\\
-\includegraphics[width=4cm]{crt_mod.eps}
-\begin{itemize}
- \item Constrain all atoms
- \item Update individual\\
- constraints
-\end{itemize}
-\end{minipage}
-}
\end{slide}
projects / lectures / latex.git / blobdiff