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\usepackage{amsmath}
+\usepackage{stmaryrd}
\usepackage{latexsym}
\usepackage{ae}
\usepackage{pstricks}
\usepackage{pst-node}
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%\usepackage{epic}
%\usepackage{eepic}
\usepackage{upgreek}
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+
\begin{document}
\extraslideheight{10in}
% no vertical centering
\centerslidesfalse
-%\ifnum1=0
-
% intro
\begin{slide}
\end{center}
\begin{pspicture}(0,0)(0,0)
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\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}
\begin{pspicture}(0,0)(0,0)
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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=hred,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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+\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}
+ \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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-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}
\begin{slide}
- \footnotesize
-
-\begin{minipage}{9.5cm}
+\footnotesize
- {\large\bf
- Si self-interstitial point defects in silicon\\
- }
+\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
- 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}\\[0.4cm]
+\end{center}
-\begin{minipage}{4.7cm}
-\includegraphics[width=4.7cm]{e_kin_si_hex.ps}
+\begin{minipage}{3cm}
+\begin{center}
+\underline{Vacancy}\\
+\includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
+\end{center}
\end{minipage}
-\begin{minipage}{4.7cm}
+\begin{minipage}{3cm}
\begin{center}
-{\tiny nearly T $\rightarrow$ T}\\
+\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}
-\includegraphics[width=4.7cm]{nhex_tet.ps}
\end{minipage}\\
\underline{Hexagonal} \hspace{2pt}
\framebox{
\begin{minipage}{2.7cm}
$E_{\text{f}}^*=4.48\text{ eV}$\\
-\includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
+\includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
\end{minipage}
\begin{minipage}{0.4cm}
\begin{center}
\end{minipage}
\begin{minipage}{2.7cm}
$E_{\text{f}}=3.96\text{ eV}$\\
-\includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
+\includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
\end{minipage}
}
-\begin{minipage}{2.9cm}
-\begin{flushright}
-\underline{Vacancy}\\
-\includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
-\end{flushright}
-\end{minipage}
-
-\end{minipage}
-\begin{minipage}{3.5cm}
-
-\begin{flushright}
-\underline{\hkl<1 1 0> dumbbell}\\
-\includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
-\underline{Tetrahedral}\\
-\includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
-\underline{\hkl<1 0 0> dumbbell}\\
-\includegraphics[width=3.0cm]{si_pd_albe/100.eps}
-\end{flushright}
-
+\begin{minipage}{5.5cm}
+\begin{center}
+{\tiny nearly T $\rightarrow$ T}\\
+\end{center}
+\includegraphics[width=6.0cm]{nhex_tet.ps}
\end{minipage}
\end{slide}
\footnotesize
- {\large\bf
- C interstitial point defects in silicon\\[-0.1cm]
- }
+\headphd
+{\large\bf
+ C interstitial point defects in silicon\\
+}
\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\\
+ $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
+ {\color{black} \cs{} \& \si}\\
\hline
- 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} \\
+ \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
+ Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
\hline
\end{tabular}\\[0.1cm]
\framebox{
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
\underline{Hexagonal} \hspace{2pt}
\href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
$E_{\text{f}}^*=9.05\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
\end{minipage}
\begin{minipage}{0.4cm}
\begin{center}
$\Rightarrow$
\end{center}
\end{minipage}
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
\underline{\hkl<1 0 0>}\\
$E_{\text{f}}=3.88\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/100.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
\end{minipage}
}
-\begin{minipage}{2cm}
+\begin{minipage}{1.4cm}
\hfill
\end{minipage}
-\begin{minipage}{3cm}
+\begin{minipage}{3.0cm}
\begin{flushright}
\underline{Tetrahedral}\\
-\includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
+\includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
\end{flushright}
\end{minipage}
\framebox{
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
\underline{Bond-centered}\\
$E_{\text{f}}^*=5.59\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
\end{minipage}
\begin{minipage}{0.4cm}
\begin{center}
$\Rightarrow$
\end{center}
\end{minipage}
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
\underline{\hkl<1 1 0> dumbbell}\\
$E_{\text{f}}=5.18\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/110.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
\end{minipage}
}
-\begin{minipage}{2cm}
+\begin{minipage}{1.4cm}
\hfill
\end{minipage}
-\begin{minipage}{3cm}
+\begin{minipage}{3.0cm}
\begin{flushright}
\underline{Substitutional}\\
-\includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
+\includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
\end{flushright}
\end{minipage}
\begin{slide}
+\headphd
+{\large\bf\boldmath
+ C-Si dimer \& bond-centered interstitial configuration
+}
+
\footnotesize
- {\large\bf\boldmath
- C \hkl<1 0 0> dumbbell interstitial configuration\\
- }
+\vspace{0.1cm}
-{\tiny
-\begin{tabular}{l c c c c c c c c}
-\hline
- Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
-\hline
-Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
-VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
-\hline
-\end{tabular}\\[0.2cm]
-\begin{tabular}{l c c c c }
-\hline
- Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
-\hline
-Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
-VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
-\hline
-\end{tabular}\\[0.2cm]
-\begin{tabular}{l c c c}
-\hline
- Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
-\hline
-Erhart/Albe & 0.084 & -0.091 & 0.175 \\
-VASP & 0.109 & -0.065 & 0.174 \\
-\hline
-\end{tabular}\\[0.6cm]
-}
-
-\begin{minipage}{3.0cm}
+\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=3.0cm]{c_pd_albe/100_cmp.eps}
+\includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
\end{center}
\end{minipage}
-\begin{minipage}{3.0cm}
+\begin{minipage}{2.0cm}
\begin{center}
-\underline{VASP}
-\includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
+\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{picture}(0,0)(-185,10)
-\includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
-\end{picture}
-\begin{picture}(0,0)(-280,-150)
-\includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
-\end{picture}
-
-\begin{pspicture}(0,0)(0,0)
-\psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
-\psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
-\psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
-\psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
-\end{pspicture}
-
-\end{slide}
-
-\begin{slide}
-
-\small
-
-\begin{minipage}{8.5cm}
-
- {\large\bf
- Bond-centered interstitial configuration\\[-0.1cm]
- }
-
-\begin{minipage}{3.0cm}
-\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
\end{minipage}
-\begin{minipage}{5.2cm}
+\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
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
\end{flushright}
\end{minipage}
\end{minipage}
-}\\[0.1cm]
+}\\[0.4cm]
-\framebox{
-\begin{minipage}{4.5cm}
-\includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
-\end{minipage}
-\begin{minipage}{3.5cm}
+%\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}
-\begin{minipage}{4.2cm}
-\begin{flushright}
-\includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
-{\color{green}$\Box$} {\tiny unoccupied}\\
-{\color{red}$\bullet$} {\tiny occupied}
+%}
+
\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\boldmath
- Migration of the C \hkl<1 0 0> dumbbell interstitial
- }
+\headphd
+{\large\bf\boldmath
+ C interstitial migration --- ab initio
+}
\scriptsize
- {\small Investigated pathways}
+\vspace{0.1cm}
-\begin{minipage}{8.5cm}
-\begin{minipage}{8.3cm}
-\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
-\end{minipage}
-\begin{minipage}{0.4cm}
-$\rightarrow$
-\end{minipage}
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
+\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}{0.4cm}
-$\rightarrow$
-\end{minipage}
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
-\end{minipage}
-\end{minipage}\\
-\begin{minipage}{8.3cm}
-\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
-\end{minipage}
-\begin{minipage}{0.4cm}
+\begin{minipage}{0.2cm}
$\rightarrow$
\end{minipage}
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
+\begin{minipage}{2.0cm}
+\includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
\end{minipage}
-\begin{minipage}{0.4cm}
+\begin{minipage}{0.2cm}
$\rightarrow$
\end{minipage}
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
-\end{minipage}
-\end{minipage}\\
-\begin{minipage}{8.3cm}
-\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
+\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 | $\Delta E=\unit[1.2]{eV}$
+\end{minipage}
+\begin{minipage}{5.4cm}
+\includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
+\end{minipage}\\[0.2cm]
+%\hrule
+%
+\begin{minipage}{6.8cm}
+\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
+\begin{minipage}{2.0cm}
+\includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
\end{minipage}
-\begin{minipage}{0.4cm}
+\begin{minipage}{0.2cm}
$\rightarrow$
\end{minipage}
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
+\begin{minipage}{2.0cm}
+\includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
\end{minipage}
-\begin{minipage}{0.4cm}
+\begin{minipage}{0.2cm}
$\rightarrow$
\end{minipage}
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
-\end{minipage}
-\end{minipage}
+\begin{minipage}{2.0cm}
+\includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
+\end{minipage}\\[0.1cm]
+$\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
+$\Rightarrow$ {\color{red}Migration mechanism identified!}\\
+Note: Change in orientation
\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}
-
-\begin{slide}
-
- {\large\bf\boldmath
- Migration of the C \hkl<1 0 0> dumbbell interstitial
- }
-
-\scriptsize
-
-\framebox{
-\begin{minipage}{5.9cm}
-\begin{flushleft}
-\includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
-\end{flushleft}
-\begin{center}
-\begin{picture}(0,0)(60,0)
-\includegraphics[width=1cm]{vasp_mig/00-1.eps}
-\end{picture}
-\begin{picture}(0,0)(-5,0)
-\includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
-\end{picture}
-\begin{picture}(0,0)(-55,0)
-\includegraphics[width=1cm]{vasp_mig/bc.eps}
-\end{picture}
-\begin{picture}(0,0)(12.5,10)
-\includegraphics[width=1cm]{110_arrow.eps}
-\end{picture}
-\begin{picture}(0,0)(90,0)
-\includegraphics[height=0.9cm]{001_arrow.eps}
-\end{picture}
-\end{center}
-\vspace*{0.35cm}
-\end{minipage}
-}
-\begin{minipage}{0.3cm}
-\hfill
-\end{minipage}
-\framebox{
-\begin{minipage}{5.9cm}
-\begin{flushright}
-\includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
-\end{flushright}
-\begin{center}
-\begin{picture}(0,0)(60,0)
-\includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
-\end{picture}
-\begin{picture}(0,0)(5,0)
-\includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
-\end{picture}
-\begin{picture}(0,0)(-55,0)
-\includegraphics[width=1cm]{vasp_mig/0-10.eps}
-\end{picture}
-\begin{picture}(0,0)(12.5,10)
-\includegraphics[width=1cm]{100_arrow.eps}
-\end{picture}
-\begin{picture}(0,0)(90,0)
-\includegraphics[height=0.9cm]{001_arrow.eps}
-\end{picture}
-\end{center}
-\vspace*{0.3cm}
-\end{minipage}\\
-}
-
-\vspace*{0.05cm}
-
-\framebox{
-\begin{minipage}{5.9cm}
-\begin{flushleft}
-\includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
-\end{flushleft}
+\begin{minipage}{5.4cm}
+\includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
+\end{minipage}\\[0.1cm]
+%
\begin{center}
-\begin{picture}(0,0)(60,0)
-\includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
-\end{picture}
-\begin{picture}(0,0)(10,0)
-\includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
-\end{picture}
-\begin{picture}(0,0)(-60,0)
-\includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
-\end{picture}
-\begin{picture}(0,0)(12.5,10)
-\includegraphics[width=1cm]{100_arrow.eps}
-\end{picture}
-\begin{picture}(0,0)(90,0)
-\includegraphics[height=0.9cm]{001_arrow.eps}
-\end{picture}
+Reorientation pathway composed of two consecutive processes of the above type
\end{center}
-\vspace*{0.3cm}
-\end{minipage}
-}
-\begin{minipage}{0.3cm}
-\hfill
-\end{minipage}
-\begin{minipage}{6.5cm}
-VASP results
-\begin{itemize}
- \item Energetically most favorable path
- \begin{itemize}
- \item Path 2
- \item Activation energy: $\approx$ 0.9 eV
- \item Experimental values: 0.73 ... 0.87 eV
- \end{itemize}
- $\Rightarrow$ {\color{blue}Diffusion} path identified!
- \item Reorientation (path 3)
- \begin{itemize}
- \item More likely composed of two consecutive steps of type 2
- \item Experimental values: 0.77 ... 0.88 eV
- \end{itemize}
- $\Rightarrow$ {\color{blue}Reorientation} transition identified!
-\end{itemize}
-\end{minipage}
\end{slide}
\begin{slide}
- {\large\bf\boldmath
- Migration of the C \hkl<1 0 0> dumbbell interstitial
- }
+\headphd
+{\large\bf\boldmath
+ C interstitial migration --- analytical potential
+}
\scriptsize
- \vspace{0.1cm}
-
-\begin{minipage}{6.5cm}
-
-\framebox{
-\begin{minipage}[t]{5.9cm}
-\begin{flushleft}
-\includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
-\end{flushleft}
-\begin{center}
-\begin{pspicture}(0,0)(0,0)
-\psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
-\end{pspicture}
-\begin{picture}(0,0)(60,-50)
-\includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
-\end{picture}
-\begin{picture}(0,0)(5,-50)
-\includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
-\end{picture}
-\begin{picture}(0,0)(-55,-50)
-\includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
-\end{picture}
-\begin{picture}(0,0)(12.5,-40)
-\includegraphics[width=1cm]{110_arrow.eps}
-\end{picture}
-\begin{picture}(0,0)(90,-45)
-\includegraphics[height=0.9cm]{001_arrow.eps}
-\end{picture}\\
-\begin{pspicture}(0,0)(0,0)
-\psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
-\end{pspicture}
-\begin{picture}(0,0)(60,-15)
-\includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
-\end{picture}
-\begin{picture}(0,0)(35,-15)
-\includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
-\end{picture}
-\begin{picture}(0,0)(-5,-15)
-\includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
-\end{picture}
-\begin{picture}(0,0)(-55,-15)
-\includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
-\end{picture}
-\begin{picture}(0,0)(12.5,-5)
-\includegraphics[width=1cm]{100_arrow.eps}
-\end{picture}
-\begin{picture}(0,0)(90,-15)
-\includegraphics[height=0.9cm]{010_arrow.eps}
-\end{picture}
-\end{center}
-\end{minipage}
-}\\[0.1cm]
+\vspace{0.3cm}
-\begin{minipage}{5.9cm}
-Erhart/Albe results
+\begin{minipage}[t]{6.0cm}
+{\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
+\includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
\begin{itemize}
- \item Lowest activation energy: $\approx$ 2.2 eV
- \item 2.4 times higher than VASP
+ \item Lowermost migration barrier
+ \item $\Delta E \approx \unit[2.2]{eV}$
+ \item 2.4 times higher than ab initio result
\item Different pathway
\end{itemize}
\end{minipage}
-
-\end{minipage}
-\begin{minipage}{6.5cm}
-
-\framebox{
-\begin{minipage}{5.9cm}
-%\begin{flushright}
-%\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
-%\end{flushright}
-%\begin{center}
-%\begin{pspicture}(0,0)(0,0)
-%\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
-%\end{pspicture}
-%\begin{picture}(0,0)(60,-5)
-%\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
-%\end{picture}
-%\begin{picture}(0,0)(0,-5)
-%\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
-%\end{picture}
-%\begin{picture}(0,0)(-55,-5)
-%\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
-%\end{picture}
-%\begin{picture}(0,0)(12.5,5)
-%\includegraphics[width=1cm]{100_arrow.eps}
-%\end{picture}
-%\begin{picture}(0,0)(90,0)
-%\includegraphics[height=0.9cm]{001_arrow.eps}
-%\end{picture}
-%\end{center}
-%\vspace{0.2cm}
-%\end{minipage}
-%}\\[0.2cm]
-%
-%\framebox{
-%\begin{minipage}{5.9cm}
-\includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
+\begin{minipage}[t]{0.2cm}
+\hfill
\end{minipage}
-}\\[0.1cm]
-
-\begin{minipage}{5.9cm}
-Transition involving \ci{} \hkl<1 1 0>
+\begin{minipage}[t]{6.0cm}
+{\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
+\vspace{0.1cm}
\begin{itemize}
\item Bond-centered configuration unstable\\
$\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
- \item Transition minima of path 2 \& 3\\
- $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
- \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
- \item 2.4 - 3.4 times higher than VASP
- \item Rotation of dumbbell orientation
+ \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
+ $\rightarrow$ \ci{} \hkl<1 1 0> DB
\end{itemize}
\vspace{0.1cm}
+\includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
+\begin{itemize}
+ \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
+ \item 2.4 -- 3.4 times higher than ab initio result
+ \item After all: Change of the DB orientation
+\end{itemize}
+\end{minipage}
+
+\vspace{0.5cm}
\begin{center}
-{\color{blue}Overestimated diffusion barrier}
+{\color{red}\bf Drastically overestimated diffusion barrier}
\end{center}
-\end{minipage}
-\end{minipage}
+\begin{pspicture}(0,0)(0,0)
+\psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
+\end{pspicture}
\end{slide}
\begin{slide}
- {\large\bf\boldmath
- Combinations with a C-Si \hkl<1 0 0>-type interstitial
- }
-
-\small
-
-\vspace*{0.1cm}
+\headphd
+{\large\bf\boldmath
+ Defect combinations
+}
-Binding energy:
-$
-E_{\text{b}}=
-E_{\text{f}}^{\text{defect combination}}-
-E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
-E_{\text{f}}^{\text{2nd defect}}
-$
+\footnotesize
-\vspace*{0.1cm}
+\vspace{0.3cm}
+\begin{minipage}{9cm}
+{\bf
+ Summary of combinations}\\[0.1cm]
{\scriptsize
\begin{tabular}{l c c c c c c}
\hline
$E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
\hline
- \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
- \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
- \hkl<0 -1 0> & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
- \hkl<0 1 0> & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
- \hkl<-1 0 0> & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
- \hkl<1 0 0> & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
+ \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
+ \hkl[0 -1 0] & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl[0 1 0] & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hkl[-1 0 0] & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl[1 0 0] & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
\hline
- C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
- Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
+ C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
+ Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
\hline
\end{tabular}
}
+\vspace{0.2cm}
+\begin{center}
+{\color{blue}
+ $E_{\text{b}}$ explainable by stress compensation / increase
+}
+\end{center}
+\end{minipage}
+\begin{minipage}{3cm}
+\includegraphics[width=3.5cm]{comb_pos.eps}
+\end{minipage}
-\vspace*{0.3cm}
-
-\footnotesize
+\vspace{0.2cm}
-\begin{minipage}[t]{3.8cm}
-\underline{\hkl<1 0 0> at position 1}\\[0.1cm]
-\includegraphics[width=3.5cm]{00-1dc/2-25.eps}
+{\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]
+\includegraphics[width=2.8cm]{00-1dc/2-25.eps}
\end{minipage}
-\begin{minipage}[t]{3.5cm}
-\underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
-\includegraphics[width=3.2cm]{00-1dc/2-39.eps}
+\begin{minipage}[t]{3.0cm}
+\underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
+\includegraphics[width=2.8cm]{00-1dc/2-39.eps}
\end{minipage}
-\begin{minipage}[t]{5.5cm}
+\begin{minipage}[t]{6.1cm}
+\vspace{0.7cm}
\begin{itemize}
- \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
- $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
- \item Stress compensation / increase
- \item Unfavored: antiparallel orientations
- \item Indication of energetically favored\\
- agglomeration
- \item Most favorable: C clustering
- \item However: High barrier ($>4\,\text{eV}$)
- \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
- (Entropy)
+ \item \ci{} agglomeration energetically favorable
+ \item Most favorable: C clustering\\
+ {\color{red}However \ldots}\\
+ \ldots high migration barrier ($>4\,\text{eV}$)\\
+ \ldots entropy:
+ $4\times{\color{cyan}[-2.25]}$ versus
+ $2\times{\color{orange}[-2.39]}$
\end{itemize}
+\begin{center}
+{\color{blue}\ci{} agglomeration / no C clustering}
+\end{center}
\end{minipage}
-\begin{picture}(0,0)(-295,-130)
-\includegraphics[width=3.5cm]{comb_pos.eps}
-\end{picture}
-
\end{slide}
\begin{slide}
- {\large\bf\boldmath
- Combinations of C-Si \hkl<1 0 0>-type interstitials
- }
-
-\small
-
-\vspace*{0.1cm}
+\headphd
+{\large\bf\boldmath
+ Defect combinations
+}
-Energetically most favorable combinations along \hkl<1 1 0>
+\footnotesize
-\vspace*{0.1cm}
+\vspace{0.3cm}
+\begin{minipage}{9cm}
+{\bf
+ Summary of combinations}\\[0.1cm]
{\scriptsize
\begin{tabular}{l c c c c c c}
\hline
- & 1 & 2 & 3 & 4 & 5 & 6\\
-\hline
-$E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
-C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
-Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\
+ $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
+ \hline
+ \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
+ \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
+ \hkl[0 -1 0] & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl[0 1 0] & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hkl[-1 0 0] & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl[1 0 0] & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hline
+ C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
+ Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
\hline
\end{tabular}
}
+\vspace{0.2cm}
+\begin{center}
+{\color{blue}
+ $E_{\text{b}}$ explainable by stress compensation / increase
+}
+\end{center}
+\end{minipage}
+\begin{minipage}{3cm}
+\includegraphics[width=3.5cm]{comb_pos.eps}
+\end{minipage}
-\vspace*{0.3cm}
+\vspace{0.2cm}
-\begin{minipage}{7.0cm}
-\includegraphics[width=7cm]{db_along_110_cc.ps}
+{\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]
+\includegraphics[width=2.8cm]{00-1dc/2-25.eps}
\end{minipage}
-\begin{minipage}{6.0cm}
+\begin{minipage}[t]{3.0cm}
+\underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
+\includegraphics[width=2.8cm]{00-1dc/2-39.eps}
+\end{minipage}
+\begin{minipage}[t]{6.1cm}
+\vspace{0.7cm}
\begin{itemize}
- \item Interaction proportional to reciprocal cube of C-C distance
- \item Saturation in the immediate vicinity
- \renewcommand\labelitemi{$\Rightarrow$}
- \item Agglomeration of \ci{} expected
- \item Absence of C clustering
+ \item \ci{} agglomeration energetically favorable
+ \item Most favorable: C clustering\\
+ {\color{red}However \ldots}\\
+ \ldots high migration barrier ($>4\,\text{eV}$)\\
+ \ldots entropy:
+ $4\times{\color{cyan}[-2.25]}$ versus
+ $2\times{\color{orange}[-2.39]}$
\end{itemize}
\begin{center}
-{\color{blue}
- Consisten with initial precipitation model
-}
+{\color{blue}\ci{} agglomeration / no C clustering}
\end{center}
\end{minipage}
+% insert graph ...
+\begin{pspicture}(0,0)(0,0)
+\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}{8cm}
+\begin{center}
\vspace{0.2cm}
+\scriptsize
+Interaction along \hkl[1 1 0]
+\includegraphics[width=7cm]{db_along_110_cc.ps}
+\end{center}
+\end{minipage}
+}}}
+\end{pspicture}
\end{slide}
\begin{slide}
- {\large\bf\boldmath
- Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
- }
-
- \scriptsize
+\headphd
+{\large\bf
+ Defect combinations of C-Si dimers and vacancies
+}
+\footnotesize
-%\begin{center}
-%\begin{minipage}{3.2cm}
-%\includegraphics[width=3cm]{sub_110_combo.eps}
-%\end{minipage}
-%\begin{minipage}{7.8cm}
-%\begin{tabular}{l c c c c c c}
-%\hline
-%C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
-% \hkl<1 0 1> & \hkl<-1 0 1> \\
-%\hline
-%1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
-%2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
-%3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
-%4 & \RM{4} & B & D & E & E & D \\
-%5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
-%\hline
-%\end{tabular}
-%\end{minipage}
-%\end{center}
-
-%\begin{center}
-%\begin{tabular}{l c c c c c c c c c c}
-%\hline
-%Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
-%\hline
-%$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
-%$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
-%$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
-%\hline
-%\end{tabular}
-%\end{center}
+\vspace{0.2cm}
-\begin{minipage}{6.0cm}
-\includegraphics[width=5.8cm]{c_sub_si110.ps}
+\begin{minipage}[b]{2.6cm}
+\begin{flushleft}
+\underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
+\includegraphics[width=2.5cm]{00-1dc/0-59.eps}
+\end{flushleft}
\end{minipage}
-\begin{minipage}{7cm}
-\scriptsize
-\begin{itemize}
- \item IBS: C may displace Si\\
- $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
- \item Assumption:\\
- \hkl<1 1 0>-type $\rightarrow$ favored combination
- \renewcommand\labelitemi{$\Rightarrow$}
- \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
- \item Less favorable than C-Si \hkl<1 0 0> dumbbell
- \item Interaction drops quickly to zero\\
- $\rightarrow$ low capture radius
-\end{itemize}
-\begin{center}
- {\color{blue}
- IBS process far from equilibrium\\
- \cs{} \& \si{} instead of thermodynamic ground state
- }
-\end{center}
+\begin{minipage}[b]{7cm}
+\hfill
\end{minipage}
+\begin{minipage}[b]{2.6cm}
+\begin{flushright}
+\underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
+\includegraphics[width=2.5cm]{00-1dc/3-14.eps}
+\end{flushright}
+\end{minipage}\\[0.2cm]
\begin{minipage}{6.5cm}
-\includegraphics[width=6.0cm]{162-097.ps}
-\begin{itemize}
- \item Low migration barrier
-\end{itemize}
+\includegraphics[width=6.0cm]{059-539.ps}
\end{minipage}
+\begin{minipage}{5.7cm}
+\includegraphics[width=6.0cm]{314-539.ps}
+\end{minipage}
+
+\begin{pspicture}(0,0)(0,0)
+\psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
+
+\rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
\begin{minipage}{6.5cm}
\begin{center}
-Ab initio MD at \degc{900}\\
-\includegraphics[width=3.3cm]{md_vasp_01.eps}
-$t=\unit[2230]{fs}$\\
-\includegraphics[width=3.3cm]{md_vasp_02.eps}
-$t=\unit[2900]{fs}$
-\end{center}
+IBS: Impinging C creates V \& far away \si\\[0.3cm]
+Low migration barrier towards C$_{\text{sub}}$\\
+\&\\
+High barrier for reverse process\\[0.3cm]
{\color{blue}
-Contribution of entropy to structural formation
+High probability of stable C$_{\text{sub}}$ configuration
}
+\end{center}
\end{minipage}
+}}}
+\end{pspicture}
\end{slide}
\begin{slide}
- {\large\bf\boldmath
- Migration in C-Si \hkl<1 0 0> and vacancy combinations
- }
+\headphd
+{\large\bf
+ Combinations of substitutional C and Si self-interstitials
+}
- \footnotesize
+\scriptsize
-\vspace{0.1cm}
+\vspace{0.3cm}
-\begin{minipage}[t]{3cm}
-\underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
-\includegraphics[width=2.8cm]{00-1dc/0-59.eps}
-\end{minipage}
-\begin{minipage}[t]{7cm}
-\vspace{0.2cm}
+\begin{minipage}{6.2cm}
\begin{center}
- Low activation energies\\
- High activation energies for reverse processes\\
- $\Downarrow$\\
- {\color{blue}C$_{\text{sub}}$ very stable}\\
-\vspace*{0.1cm}
- \hrule
-\vspace*{0.1cm}
- Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
- $\Downarrow$\\
- {\color{blue}Formation of SiC by successive substitution by C}
-
+{\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
+\begin{itemize}
+ \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
+ \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
+ \item Interaction drops quickly to zero\\
+ $\rightarrow$ low capture radius
+\end{itemize}
\end{center}
\end{minipage}
-\begin{minipage}[t]{3cm}
-\underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
-\includegraphics[width=2.8cm]{00-1dc/3-14.eps}
+\begin{minipage}{0.2cm}
+\hfill
\end{minipage}
-
-
-\framebox{
-\begin{minipage}{5.9cm}
-\includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
+\begin{minipage}{6.0cm}
\begin{center}
-\begin{picture}(0,0)(70,0)
-\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
-\end{picture}
-\begin{picture}(0,0)(30,0)
-\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
-\end{picture}
-\begin{picture}(0,0)(-10,0)
-\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
-\end{picture}
-\begin{picture}(0,0)(-48,0)
-\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
-\end{picture}
-\begin{picture}(0,0)(12.5,5)
-\includegraphics[width=1cm]{100_arrow.eps}
-\end{picture}
-\begin{picture}(0,0)(97,-10)
-\includegraphics[height=0.9cm]{001_arrow.eps}
-\end{picture}
+{\bf Transition from the ground state}
+\begin{itemize}
+ \item Low transition barrier
+ \item Barrier smaller than \ci{} migration barrier
+ \item Low \si{} migration barrier (\unit[0.67]{eV})\\
+ $\rightarrow$ Separation of \cs{} \& \si{} most probable
+\end{itemize}
\end{center}
-\vspace{0.1cm}
+\end{minipage}\\[0.3cm]
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=6.0cm]{c_sub_si110.ps}
\end{minipage}
-}
-\begin{minipage}{0.3cm}
+\begin{minipage}{0.4cm}
\hfill
\end{minipage}
-\framebox{
-\begin{minipage}{5.9cm}
-\includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
-\begin{center}
-\begin{picture}(0,0)(60,0)
-\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
-\end{picture}
-\begin{picture}(0,0)(25,0)
-\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
-\end{picture}
-\begin{picture}(0,0)(-20,0)
-\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
-\end{picture}
-\begin{picture}(0,0)(-55,0)
-\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
-\end{picture}
-\begin{picture}(0,0)(12.5,5)
-\includegraphics[width=1cm]{100_arrow.eps}
-\end{picture}
-\begin{picture}(0,0)(95,0)
-\includegraphics[height=0.9cm]{001_arrow.eps}
-\end{picture}
-\end{center}
-\vspace{0.1cm}
+\begin{minipage}{6.0cm}
+\begin{flushright}
+\includegraphics[width=6.0cm]{162-097.ps}
+\end{flushright}
\end{minipage}
+
+\begin{pspicture}(0,0)(0,0)
+\psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
+\rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
+\begin{minipage}{8cm}
+\begin{center}
+\vspace{0.1cm}
+{\color{black}
+\cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
+IBS --- process far from equilibrium\\
}
+\end{center}
+\end{minipage}
+}}}
+\end{pspicture}
\end{slide}
\begin{slide}
- {\large\bf
- Conclusion of defect / migration / combined defect simulations
- }
+\headphd
+{\large\bf
+ Combinations of substitutional C and Si self-interstitials
+}
- \footnotesize
+\scriptsize
-\vspace*{0.1cm}
+\vspace{0.3cm}
-Defect structures
+\begin{minipage}{6.2cm}
+\begin{center}
+{\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
\begin{itemize}
- \item Accurately described by quantum-mechanical simulations
- \item Less accurate description by classical potential simulations
- \item Underestimated formation energy of \cs{} by classical approach
- \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
+ \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
+ \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
+ \item Interaction drops quickly to zero\\
+ $\rightarrow$ low capture radius
\end{itemize}
-
-Migration
-\begin{itemize}
- \item C migration pathway in Si identified
- \item Consistent with reorientation and diffusion experiments
-\end{itemize}
+\end{center}
+\end{minipage}
+\begin{minipage}{0.2cm}
+\hfill
+\end{minipage}
+\begin{minipage}{6.0cm}
+\begin{center}
+{\bf Transition from the ground state}
\begin{itemize}
- \item Different path and ...
- \item overestimated barrier by classical potential calculations
-\end{itemize}
+ \item Low transition barrier
+ \item Barrier smaller than \ci{} migration barrier
+ \item Low \si{} migration barrier (\unit[0.67]{eV})\\
+ $\rightarrow$ Separation of \cs{} \& \si{} most probable
+\end{itemize}
+\end{center}
+\end{minipage}\\[0.3cm]
-Concerning the precipitation mechanism
-\begin{itemize}
- \item Agglomeration of C-Si dumbbells energetically favorable
- (stress compensation)
- \item C-Si indeed favored compared to
- C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
- \item Possible low interaction capture radius of
- C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
- \item Low barrier for
- \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
- \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
- C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
-\end{itemize}
+\begin{minipage}{6.0cm}
+\includegraphics[width=6.0cm]{c_sub_si110.ps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+\hfill
+\end{minipage}
+\begin{minipage}{6.0cm}
+\begin{flushright}
+\includegraphics[width=6.0cm]{162-097.ps}
+\end{flushright}
+\end{minipage}
+
+\begin{pspicture}(0,0)(0,0)
+\psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
+\rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
+\begin{minipage}{8cm}
+\begin{center}
+\vspace{0.1cm}
+{\color{black}
+\cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
+IBS --- process far from equilibrium\\
+}
+\end{center}
+\end{minipage}
+}}}
+\end{pspicture}
+
+% md support
+\begin{pspicture}(0,0)(0,0)
+\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
+\begin{minipage}{14cm}
+\hfill
+\vspace{14cm}
+\end{minipage}
+}}
+\rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
+\begin{minipage}{11cm}
\begin{center}
-{\color{blue}Results suggest increased participation of \cs}
+\vspace{0.2cm}
+\scriptsize
+Ab initio MD at \degc{900}\\[0.4cm]
+\begin{minipage}{5.4cm}
+\centering
+\includegraphics[width=4.3cm]{md01_bonds.eps}\\
+$t=\unit[2230]{fs}$
+\end{minipage}
+\begin{minipage}{5.4cm}
+\centering
+\includegraphics[width=4.3cm]{md02_bonds.eps}\\
+$t=\unit[2900]{fs}$
+\end{minipage}\\[0.5cm]
+{\color{blue}
+Contribution of entropy to structural formation\\[0.1cm]
+}
\end{center}
+\end{minipage}
+}}}
+\end{pspicture}
\end{slide}
\begin{slide}
- {\large\bf
- Silicon carbide precipitation simulations
- }
+\headphd
+{\large\bf
+ Silicon carbide precipitation simulations
+}
- \small
+\small
+
+\vspace{0.2cm}
+
+{\bf Procedure}
{\scriptsize
\begin{pspicture}(0,0)(12,6.5)
Insertion of C atoms at constant T
\begin{itemize}
\item total simulation volume {\pnode{in1}}
- \item volume of minimal SiC precipitate {\pnode{in2}}
+ \item volume of minimal SiC precipitate size {\pnode{in2}}
\item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
precipitate
\end{itemize}
}}}}
\ncline[]{->}{init}{insert}
\ncline[]{->}{insert}{cool}
- \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
- \rput(7.8,6){\footnotesize $V_1$}
- \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
- \rput(9.2,4.85){\tiny $V_2$}
- \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
- \rput(9.55,4.45){\footnotesize $V_3$}
+ \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
+ \rput(7.6,6){\footnotesize $V_1$}
+ \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
+ \rput(8.9,4.85){\tiny $V_2$}
+ \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
+ \rput(9.25,4.45){\footnotesize $V_3$}
\rput(7.9,3.2){\pnode{ins1}}
- \rput(9.22,2.8){\pnode{ins2}}
- \rput(11.0,2.4){\pnode{ins3}}
+ \rput(8.92,2.8){\pnode{ins2}}
+ \rput(10.8,2.4){\pnode{ins3}}
\ncline[]{->}{in1}{ins1}
\ncline[]{->}{in2}{ins2}
\ncline[]{->}{in3}{ins3}
\end{pspicture}
}
+\vspace{-0.5cm}
+
+{\bf Note}
+
+\footnotesize
+
+\begin{minipage}{5.7cm}
\begin{itemize}
- \item Restricted to classical potential simulations
- \item $V_2$ and $V_3$ considered due to low diffusion
- \item Amount of C atoms: 6000
- ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
- \item Simulation volume: $31\times 31\times 31$ unit cells
+ \item Amount of C atoms: 6000\\
+ ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
+ \item Simulation volume: $31^3$ Si unit cells\\
(238328 Si atoms)
\end{itemize}
+\end{minipage}
+\begin{minipage}{0.3cm}
+\hfill
+\end{minipage}
+\framebox{
+\begin{minipage}{6.0cm}
+Restricted to classical potential caclulations\\
+$\rightarrow$ Low C diffusion / overestimated barrier\\
+$\rightarrow$ Consider $V_2$ and $V_3$
+%\begin{itemize}
+% \item $V_2$ and $V_3$ considered due to expected low C diffusion
+%\end{itemize}
+\end{minipage}
+}
\end{slide}
\begin{slide}
- {\large\bf\boldmath
- Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
- }
-
- \small
+\headphd
+{\large\bf\boldmath
+ Silicon carbide precipitation simulations at \degc{450} as in IBS
+}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
-\end{minipage}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
-\end{minipage}
+\small
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
+\begin{minipage}{6.3cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
+\begin{minipage}{6.1cm}
\scriptsize
-\underline{Low C concentration ($V_1$)}\\
+\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
\hkl<1 0 0> C-Si dumbbell dominated structure
\begin{itemize}
- \item Si-C bumbs around 0.19 nm
- \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
- concatenated dumbbells of various orientation
- \item Si-Si NN distance stretched to 0.3 nm
+ \item Si-C bumbs around \unit[0.19]{nm}
+ \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
+ concatenated differently oriented \ci{} DBs
+ \item Si-Si NN distance stretched to \unit[0.3]{nm}
+\end{itemize}
+\begin{pspicture}(0,0)(6.0,1.0)
+\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{6cm}
+\centering
+Formation of \ci{} dumbbells\\
+C atoms in proper 3C-SiC distance first
+\end{minipage}
+}}
+\end{pspicture}\\[0.1cm]
+\underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
+\begin{itemize}
+\item High amount of strongly bound C-C bonds
+\item Increased defect \& damage density\\
+ $\rightarrow$ Arrangements hard to categorize and trace
+\item Only short range order observable
\end{itemize}
-{\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
-\underline{High C concentration ($V_2$, $V_3$)}\\
-High amount of strongly bound C-C bonds\\
-Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
-Only short range order observable\\
-{\color{blue}$\Rightarrow$ amorphous SiC-like phase}
+\begin{pspicture}(0,0)(6.0,0.8)
+\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{6cm}
+\centering
+Amorphous SiC-like phase
+\end{minipage}
+}}
+\end{pspicture}\\[0.3cm]
+\begin{pspicture}(0,0)(6.0,2.0)
+\rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
+\begin{minipage}{6cm}
+\hfill
+\vspace{2.5cm}
+\end{minipage}
+}}
+\end{pspicture}
\end{minipage}
\end{slide}
\begin{slide}
- {\large\bf\boldmath
- Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
- }
-
- \small
+\headphd
+{\large\bf\boldmath
+ Silicon carbide precipitation simulations at \degc{450} as in IBS
+}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
-\end{minipage}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
-\end{minipage}
+\small
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
+\begin{minipage}{6.3cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
+\begin{minipage}{6.1cm}
\scriptsize
-\underline{Low C concentration ($V_1$)}\\
+\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
\hkl<1 0 0> C-Si dumbbell dominated structure
\begin{itemize}
- \item Si-C bumbs around 0.19 nm
- \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
- concatenated dumbbells of various orientation
- \item Si-Si NN distance stretched to 0.3 nm
+ \item Si-C bumbs around \unit[0.19]{nm}
+ \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
+ concatenated differently oriented \ci{} DBs
+ \item Si-Si NN distance stretched to \unit[0.3]{nm}
\end{itemize}
-{\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
-\underline{High C concentration ($V_2$, $V_3$)}\\
-High amount of strongly bound C-C bonds\\
-Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
-Only short range order observable\\
-{\color{blue}$\Rightarrow$ amorphous SiC-like phase}
-\end{minipage}
-
-\begin{pspicture}(0,0)(0,0)
-\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
-\begin{minipage}{10cm}
-\small
-{\color{red}\bf 3C-SiC formation fails to appear}
+\begin{pspicture}(0,0)(6.0,1.0)
+\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{6cm}
+\centering
+Formation of \ci{} dumbbells\\
+C atoms in proper 3C-SiC distance first
+\end{minipage}
+}}
+\end{pspicture}\\[0.1cm]
+\underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
\begin{itemize}
-\item Low C concentration simulations
- \begin{itemize}
- \item Formation of \ci{} indeed occurs
- \item Agllomeration not observed
- \end{itemize}
-\item High C concentration simulations
- \begin{itemize}
- \item Amorphous SiC-like structure\\
- (not expected at prevailing temperatures)
- \item Rearrangement and transition into 3C-SiC structure missing
- \end{itemize}
+\item High amount of strongly bound C-C bonds
+\item Increased defect \& damage density\\
+ $\rightarrow$ Arrangements hard to categorize and trace
+\item Only short range order observable
\end{itemize}
+\begin{pspicture}(0,0)(6.0,0.8)
+\rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{6cm}
+\centering
+Amorphous SiC-like phase
\end{minipage}
- }}}
+}}
+\end{pspicture}\\[0.3cm]
+\begin{pspicture}(0,0)(6.0,2.0)
+\rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
+\begin{minipage}{6cm}
+\vspace{0.1cm}
+\centering
+{\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
+\begin{minipage}{0.8cm}
+{\bf\boldmath $V_1$:}
+\end{minipage}
+\begin{minipage}{5.1cm}
+Formation of \ci{} indeed occurs\\
+Agllomeration not observed
+\end{minipage}\\[0.3cm]
+\begin{minipage}{0.8cm}
+{\bf\boldmath $V_{2,3}$:}
+\end{minipage}
+\begin{minipage}{5.1cm}
+Amorphous SiC-like structure\\
+(not expected at \degc{450})\\[0.05cm]
+No rearrangement/transition into 3C-SiC
+\end{minipage}\\[0.1cm]
+\end{minipage}
+}}
\end{pspicture}
+\end{minipage}
\end{slide}
\begin{slide}
- {\large\bf
- Limitations of molecular dynamics and short range potentials
- }
+\headphd
+{\large\bf
+ Limitations of MD and short range potentials
+}
-\footnotesize
+\small
\vspace{0.2cm}
-\underline{Time scale problem of MD}\\[0.2cm]
-Minimize integration error\\
-$\Rightarrow$ discretization considerably smaller than
- reciprocal of fastest vibrational mode\\[0.1cm]
-Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
-$\Rightarrow$ suitable choice of time step:
- $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
-$\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
-Several local minima in energy surface separated by large energy barriers\\
-$\Rightarrow$ transition event corresponds to a multiple
+{\bf Time scale problem of MD}\\[0.2cm]
+Precise integration \& thermodynamic sampling\\
+$\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
+ $\omega$: vibrational mode\\
+$\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
+Several local minima separated by large energy barriers\\
+$\Rightarrow$ Transition event corresponds to a multiple
of vibrational periods\\
-$\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
- infrequent transition events\\[0.1cm]
+$\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
+ infrequent transition events\\[0.2cm]
{\color{blue}Accelerated methods:}
\underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
-\vspace{0.3cm}
-
-\underline{Limitations related to the short range potential}\\[0.2cm]
-Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
-and 2$^{\text{nd}}$ next neighbours\\
-$\Rightarrow$ overestimated unphysical high forces of next neighbours
-
-\vspace{0.3cm}
+\vspace{0.2cm}
-\framebox{
-\color{red}
-Potential enhanced problem of slow phase space propagation
-}
+{\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)
-\vspace{0.3cm}
+\vspace{1.4cm}
-\underline{Approach to the (twofold) problem}\\[0.2cm]
+{\bf Approach to the (twofold) problem}\\[0.2cm]
Increased temperature simulations without TAD corrections\\
-(accelerated methods or higher time scales exclusively not sufficient)
-
-\begin{picture}(0,0)(-260,-30)
-\framebox{
-\begin{minipage}{4.2cm}
-\tiny
-\begin{center}
-\vspace{0.03cm}
-\underline{IBS}
-\end{center}
-\begin{itemize}
-\item 3C-SiC also observed for higher T
-\item higher T inside sample
-\item structural evolution vs.\\
- equilibrium properties
-\end{itemize}
-\end{minipage}
-}
-\end{picture}
+Accelerated methods or higher time scales exclusively not sufficient!
-\begin{picture}(0,0)(-305,-155)
-\framebox{
-\begin{minipage}{2.5cm}
+\begin{pspicture}(0,0)(0,0)
+\rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
+\begin{minipage}{7.5cm}
+\centering
+\vspace{0.05cm}
+Potential enhanced slow phase space propagation
+\end{minipage}
+}}
+\rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{2.7cm}
\tiny
-\begin{center}
+\centering
retain proper\\
-thermodynmic sampling
-\end{center}
+thermodynamic sampling
\end{minipage}
-}
-\end{picture}
+}}
+\psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
+\rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
+\begin{minipage}{3.6cm}
+\tiny
+\centering
+\underline{IBS}\\[0.1cm]
+3C-SiC also observed for higher T\\[0.1cm]
+Higher T inside sample\\[0.1cm]
+Structural evolution vs.\\
+equilibrium properties
+\end{minipage}
+}}
+\psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
+\end{pspicture}
\end{slide}
\begin{slide}
- {\large\bf
- Increased temperature simulations at low C concentration
- }
+\headphd
+{\large\bf\boldmath
+ Increased temperature simulations --- $V_1$
+}
\small
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc_thesis.ps}
+\begin{minipage}{6.2cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
+\begin{minipage}{6.2cm}
+\includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
\end{minipage}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
+\begin{minipage}{6.2cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
+\begin{minipage}{6.3cm}
\scriptsize
\underline{Si-C bonds:}
\begin{itemize}
\end{itemize}
\end{minipage}
-\begin{picture}(0,0)(-330,-74)
-\color{blue}
-\framebox{
-\begin{minipage}{1.6cm}
-\tiny
-\begin{center}
-stretched SiC\\[-0.1cm]
-in c-Si
-\end{center}
-\end{minipage}
-}
-\end{picture}
-
\end{slide}
\begin{slide}
- {\large\bf
- Increased temperature simulations at low C concentration
- }
+\headphd
+{\large\bf\boldmath
+ Increased temperature simulations --- $V_1$
+}
\small
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc_thesis.ps}
+\begin{minipage}{6.2cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
+\begin{minipage}{6.2cm}
+\includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
\end{minipage}
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
+\begin{minipage}{6.2cm}
+\hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
+\hfill
\end{minipage}
-\begin{minipage}{6.5cm}
+\begin{minipage}{6.3cm}
\scriptsize
\underline{Si-C bonds:}
\begin{itemize}
\end{itemize}
\end{minipage}
-%\begin{picture}(0,0)(-330,-74)
-%\color{blue}
-%\framebox{
-%\begin{minipage}{1.6cm}
-%\tiny
-%\begin{center}
-%stretched SiC\\[-0.1cm]
-%in c-Si
-%\end{center}
-%\end{minipage}
-%}
-%\end{picture}
-
+% conclusions
\begin{pspicture}(0,0)(0,0)
-\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
-\begin{minipage}{10cm}
+\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
+\begin{minipage}{14cm}
+\hfill
+\vspace{14cm}
+\end{minipage}
+}}
+\rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
+\begin{minipage}{9cm}
+\vspace{0.2cm}
\small
-{\color{blue}\bf Stretched SiC in c-Si}
+\begin{center}
+{\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
+{\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
+\end{center}
\begin{itemize}
-\item Consistent to precipitation model involving \cs{}
-\item Explains annealing behavior of high/low T C implants
+\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{}
\begin{itemize}
- \item Low T: highly mobiel \ci{}
- \item High T: stable configurations of \cs{}
+ \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
+ \item Building block for surrounding Si host \& further SiC
+ \item Strain compensation \ldots\\
+ \ldots Si/SiC interface\\
+ \ldots within stretched coherent SiC structure
\end{itemize}
\end{itemize}
-$\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
-$\Rightarrow$ Precipitation mechanism involving \cs{}
+\vspace{0.2cm}
+\centering
+\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{minipage}
+\vspace{0.2cm}
+}}
\end{pspicture}
\end{slide}
+% skip high T / C conc ... only here!
+\ifnum1=0
+
\begin{slide}
{\large\bf
\end{slide}
-\begin{slide}
+% skipped high T / C conc
+\fi
- {\large\bf
- Summary and Conclusions
- }
+\begin{slide}
- \scriptsize
+{\large\bf
+ Summary / Outlook
+}
-%\vspace{0.1cm}
+\small
-\framebox{
-\begin{minipage}[t]{12.9cm}
- \underline{Pecipitation simulations}
- \begin{itemize}
- \item High C concentration $\rightarrow$ amorphous SiC like phase
- \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 Precipitation by successive agglomeration of \cs (epitaxy)
- \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
- (stretched SiC, interface)
- \end{itemize}
+\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}
}
-
-%\vspace{0.1cm}
-
-\framebox{
-\begin{minipage}{12.9cm}
- \underline{Defects}
- \begin{itemize}
- \item DFT / EA
- \begin{itemize}
- \item Point defects excellently / fairly well described
- by DFT / EA
- \item C$_{\text{sub}}$ drastically underestimated by EA
- \item EA predicts correct ground state:
- C$_{\text{sub}}$ \& \si{} $>$ \ci{}
- \item Identified migration path explaining
- diffusion and reorientation experiments by DFT
- \item EA fails to describe \ci{} migration:
- Wrong path \& overestimated barrier
- \end{itemize}
- \item Combinations of defects
- \begin{itemize}
- \item Agglomeration of point defects energetically favorable
- by compensation of stress
- \item Formation of C-C unlikely
- \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{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}
}
-
-\begin{center}
-{\color{blue}
-\framebox{Precipitation by successive agglomeration of \cs{}}
+\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{center}
+\end{pspicture}\\[0.5cm]
\end{slide}
\end{document}
-\fi
projects / lectures / latex.git / blobdiff