\begin{itemize}
\item total simulation volume {\pnode{in1}}
\item volume of minimal SiC precipitate size {\pnode{in2}}
- \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
+ %\item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
+ \item volume containing Si atoms to form a minimal {\pnode{in3}}\\
precipitate
\end{itemize}
}}}}
\begin{minipage}{6cm}
\vspace{0.1cm}
\centering
-{\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
+{\bf\color{red}Formation of 3C-SiC fails to appear}\\[0.3cm]
\begin{minipage}{0.8cm}
{\bf\boldmath $V_1$:}
\end{minipage}
\end{slide}
-% skip high c conc results
-\ifnum1=0
-
-\begin{slide}
-
- {\large\bf
- Increased temperature simulations at high C concentration
- }
-
-\footnotesize
-
-\begin{minipage}{6.0cm}
-\includegraphics[width=6.4cm]{12_pc_thesis.ps}
-\end{minipage}
-\begin{minipage}{6.0cm}
-\includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
-\end{minipage}
-
-\vspace{0.1cm}
-
-\scriptsize
-
-\framebox{
-\begin{minipage}[t]{6.0cm}
-0.186 nm: Si-C pairs $\uparrow$\\
-(as expected in 3C-SiC)\\[0.2cm]
-0.282 nm: Si-C-C\\[0.2cm]
-$\approx$0.35 nm: C-Si-Si
-\end{minipage}
-}
-\begin{minipage}{0.2cm}
-\hfill
-\end{minipage}
-\framebox{
-\begin{minipage}[t]{6.0cm}
-0.15 nm: C-C pairs $\uparrow$\\
-(as expected in graphite/diamond)\\[0.2cm]
-0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
-0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
-\end{minipage}
-}
-
-\begin{itemize}
-\item Decreasing cut-off artifact
-\item {\color{red}Amorphous} SiC-like phase remains
-\item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
-\item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
-\end{itemize}
-
-\vspace{-0.1cm}
-
-\begin{center}
-{\color{blue}
-\framebox{
-{\color{black}
-High C \& small $V$ \& short $t$
-$\Rightarrow$
-}
-Slow restructuring due to strong C-C bonds
-{\color{black}
-$\Leftarrow$
-High C \& low T implants
-}
-}
-}
-\end{center}
-
-\end{slide}
-
-% skip high c conc
-\fi
-
\begin{slide}
\headphd
\underline{Pecipitation simulations}
\begin{itemize}
\item Problem of potential enhanced slow phase space propagation
+ \item High T necessary to simulate IBS conditions (far from equilibrium)
\item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
\item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
- \item High T necessary to simulate IBS conditions (far from equilibrium)
- \item \cs{} involved in the precipitation process at elevated temperatures
+ / Structures of stretched SiC\\
+ $\Rightarrow$
+ \cs{} involved in the precipitation process at elevated temperatures
\item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
(stretched SiC, interface)
\end{itemize}
\end{slide}
+\begin{slide}
+
+ {\large\bf
+ Increased temperature simulations at high C concentration
+ }
+
+\footnotesize
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=6.4cm]{12_pc_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.0cm}
+\includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
+\end{minipage}
+
+\vspace{0.1cm}
+
+\scriptsize
+
+\framebox{
+\begin{minipage}[t]{5.5cm}
+0.186 nm: Si-C pairs $\uparrow$\\
+(as expected in 3C-SiC)\\[0.2cm]
+0.282 nm: Si-C-C\\[0.2cm]
+$\approx$0.35 nm: C-Si-Si
+\end{minipage}
+}
+\begin{minipage}{0.1cm}
+\hfill
+\end{minipage}
+\framebox{
+\begin{minipage}[t]{5.9cm}
+0.15 nm: C-C pairs $\uparrow$\\
+(as expected in graphite/diamond)\\[0.2cm]
+0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
+0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
+\end{minipage}
+}
+
+\begin{itemize}
+\item Decreasing cut-off artifact
+\item {\color{red}Amorphous} SiC-like phase remains
+\item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
+\item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
+\end{itemize}
+
+\begin{center}
+{\color{blue}
+\framebox{
+{\color{black}
+High C \& small $V$ \& short $t$
+$\Rightarrow$
+}
+\begin{minipage}{4cm}
+\begin{center}
+Slow structural evolution due to strong C-C bonds
+\end{center}
+\end{minipage}
+{\color{black}
+$\Leftarrow$
+High C \& low T implants
+}
+}
+}
+\end{center}
+
+\end{slide}
+
+
+
+\begin{slide}
+
+ {\large\bf
+ Valuation of a practicable temperature limit
+ }
+
+ \small
+
+\vspace{0.1cm}
+
+\begin{center}
+\framebox{
+{\color{blue}
+Recrystallization is a hard task!
+$\Rightarrow$ Avoid melting!
+}
+}
+\end{center}
+
+\vspace{0.1cm}
+
+\footnotesize
+
+\begin{minipage}{6.4cm}
+\includegraphics[width=6.4cm]{fe_and_t.ps}
+\end{minipage}
+\begin{minipage}{5.7cm}
+\underline{Melting does not occur instantly after}\\
+\underline{exceeding the melting point $T_{\text{m}}=2450\text{ K}$}
+\begin{itemize}
+\item required transition enthalpy
+\item hysterisis behaviour
+\end{itemize}
+\underline{Heating up c-Si by 1 K/ps}
+\begin{itemize}
+\item transition occurs at $\approx$ 3125 K
+\item $\Delta E=0.58\text{ eV/atom}=55.7\text{ kJ/mole}$\\
+ (literature: 50.2 kJ/mole)
+\end{itemize}
+\end{minipage}
+
+\vspace{0.1cm}
+
+\framebox{
+\begin{minipage}{4cm}
+Initially chosen temperatures:\\
+$1.0 - 1.2 \cdot T_{\text{m}}$
+\end{minipage}
+}
+\begin{minipage}{2cm}
+\begin{center}
+$\Longrightarrow$
+\end{center}
+\end{minipage}
+\framebox{
+\begin{minipage}{5cm}
+Introduced C (defects)\\
+$\rightarrow$ reduction of transition point\\
+$\rightarrow$ melting already at $T_{\text{m}}$
+\end{minipage}
+}
+
+\vspace{0.4cm}
+
+\begin{center}
+\framebox{
+{\color{blue}
+Maximum temperature used: $0.95\cdot T_{\text{m}}$
+}
+}
+\end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Long time scale simulations at maximum temperature
+ }
+
+\small
+
+\vspace{0.1cm}
+
+\underline{Differences}
+\begin{itemize}
+ \item Temperature set to $0.95 \cdot T_{\text{m}}$
+ \item Cubic insertion volume $\Rightarrow$ spherical insertion volume
+ \item Amount of C atoms: 6000 $\rightarrow$ 5500
+ $\Leftrightarrow r_{\text{prec}}=0.3\text{ nm}$
+ \item Simulation volume: 21 unit cells of c-Si in each direction
+\end{itemize}
+
+\footnotesize
+
+\vspace{0.3cm}
+
+\begin{minipage}[t]{4.3cm}
+\begin{center}
+\underline{Low C concentration, Si-C}
+\includegraphics[width=4.3cm]{c_in_si_95_v1_si-c.ps}\\
+Sharper peaks!
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{4.3cm}
+\begin{center}
+\underline{Low C concentration, C-C}
+\includegraphics[width=4.3cm]{c_in_si_95_v1_c-c.ps}\\
+Sharper peaks!\\
+No C agglomeration!
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{3.4cm}
+\begin{center}
+\underline{High C concentration}
+\includegraphics[width=4.3cm]{c_in_si_95_v2.ps}\\
+No significant changes\\
+iC-Si-Si $\uparrow$\\
+C-Si-C $\downarrow$
+\end{center}
+\end{minipage}
+
+\begin{center}
+\framebox{
+Long time scales and high temperatures most probably not sufficient enough!
+}
+\end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Investigation of a silicon carbide precipitate in silicon
+ }
+
+ \scriptsize
+
+\vspace{0.2cm}
+
+\framebox{
+\scriptsize
+\begin{minipage}{5.3cm}
+\[
+\frac{8}{a_{\text{Si}}^3}(
+\underbrace{21^3 a_{\text{Si}}^3}_{=V}
+-\frac{4}{3}\pi x^3)+
+\underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500}
+=21^3\cdot 8
+\]
+\[
+\Downarrow
+\]
+\[
+\frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500
+\Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}}
+\]
+\[
+y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}}
+\]
+\end{minipage}
+}
+\begin{minipage}{0.1cm}
+\hfill
+\end{minipage}
+\begin{minipage}{6.3cm}
+\underline{Construction}
+\begin{itemize}
+ \item Simulation volume: 21$^3$ unit cells of c-Si
+ \item Spherical topotactically aligned precipitate\\
+ $r=3.0\text{ nm}$ $\Leftrightarrow$ $\approx$ 5500 C atoms
+ \item Create c-Si but skipped inside sphere\\
+ of radius $x$
+ \item Create 3C-SiC inside sphere of radius $x$\\
+ and lattice constant $y$
+ \item Strong coupling to heat bath ($T=20\,^{\circ}\mathrm{C}$)
+\end{itemize}
+\end{minipage}
+
+\vspace{0.3cm}
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=6cm]{pc_0.ps}
+\end{minipage}
+\begin{minipage}{6.1cm}
+\underline{Results}
+\begin{itemize}
+ \item Slight increase of c-Si lattice constant!
+ \item C-C peaks\\
+ (imply same distanced Si-Si peaks)
+ \begin{itemize}
+ \item New peak at 0.307 nm: 2$^{\text{nd}}$ NN in 3C-SiC
+ \item Bumps ({\color{green}$\downarrow$}):
+ 4$^{\text{th}}$ and 6$^{\text{th}}$ NN
+ \end{itemize}
+ \item 3C-SiC lattice constant: 4.34 \AA (bulk: 4.36 \AA)\\
+ $\rightarrow$ compressed precipitate
+ \item Interface tension:\\
+ 20.15 eV/nm$^2$ or $3.23 \times 10^{-4}$ J/cm$^2$\\
+ (literature: $2 - 8 \times 10^{-4}$ J/cm$^2$)
+\end{itemize}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Investigation of a silicon carbide precipitate in silicon
+ }
+
+ \footnotesize
+
+\begin{minipage}{7cm}
+\underline{Appended annealing steps}
+\begin{itemize}
+ \item artificially constructed interface\\
+ $\rightarrow$ allow for rearrangement of interface atoms
+ \item check SiC stability
+\end{itemize}
+\underline{Temperature schedule}
+\begin{itemize}
+ \item rapidly heat up structure up to $2050\,^{\circ}\mathrm{C}$\\
+ (75 K/ps)
+ \item slow heating up to $1.2\cdot T_{\text{m}}=2940\text{ K}$
+ by 1 K/ps\\
+ $\rightarrow$ melting at around 2840 K
+ (\href{../video/sic_prec_120.avi}{$\rhd$})
+ \item cooling down structure at 100 \% $T_{\text{m}}$ (1 K/ps)\\
+ $\rightarrow$ no energetically more favorable struture
+\end{itemize}
+\end{minipage}
+\begin{minipage}{5cm}
+\includegraphics[width=5.5cm]{fe_and_t_sic.ps}
+\end{minipage}
+
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{sic_prec/melt_01.eps}
+\end{minipage}
+\begin{minipage}{0.2cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{sic_prec/melt_02.eps}
+\end{minipage}
+\begin{minipage}{0.2cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{3.7cm}
+\includegraphics[width=4cm]{sic_prec/melt_03.eps}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ DFT parameters
+ }
+
+\scriptsize
+
+\vspace{0.1cm}
+
+Equilibrium lattice constants and cohesive energies
+
+\begin{tabular}{l r c c c c c}
+\hline
+\hline
+ & & USPP, LDA & USPP, GGA & PAW, LDA & PAW, GGA & Exp. \\
+\hline
+Si (dia) & $a$ [\AA] & 5.389 & 5.455 & - & - & 5.429 \\
+ & $\Delta_a$ [\%] & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - & - & - \\
+ & $E_{\text{coh}}$ [eV] & -5.277 & -4.591 & - & - & -4.63 \\
+ & $\Delta_E$ [\%] & \unit[{\color{red}14.0}]{\%} & \unit[{\color{green}0.8}]{\%} & - & - & - \\
+\hline
+C (dia) & $a$ [\AA] & 3.527 & 3.567 & - & - & 3.567 \\
+ & $\Delta_a$ [\%] & \unit[{\color{green}1.1}]{\%} & \unit[{\color{green}0.01}]{\%} & - & - & - \\
+ & $E_{\text{coh}}$ [eV] & -8.812 & -7.703 & - & - & -7.374 \\
+ & $\Delta_E$ [\%] & \unit[{\color{red}19.5}]{\%} & \unit[{\color{orange}4.5}]{\%} & - & - & - \\
+\hline
+3C-SiC & $a$ [\AA] & 4.319 & 4.370 & 4.330 & 4.379 & 4.359 \\
+ & $\Delta_a$ [\%] & \unit[{\color{green}0.9}]{\%} & \unit[{\color{green}0.3}]{\%} & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - \\
+ & $E_{\text{coh}}$ [eV] & -7.318 & -6.426 & -7.371 & -6.491 & -6.340 \\
+ & $\Delta_E$ [\%] & \unit[{\color{red}15.4}]{\%} & \unit[{\color{green}1.4}]{\%} & \unit[{\color{red}16.3}]{\%} & \unit[{\color{orange}2.4}]{\%} & - \\
+\hline
+\hline
+\end{tabular}
+
+\vspace{0.3cm}
+
+\begin{minipage}{7cm}
+\begin{center}
+\begin{tabular}{l c c c}
+\hline
+\hline
+ & Si (dia) & C (dia) & 3C-SiC \\
+\hline
+$a$ [\AA] & 5.458 & 3.562 & 4.365 \\
+$\Delta_a$ [\%] & 0.5 & 0.1 & 0.1 \\
+\hline
+$E_{\text{coh}}$ [eV] & -4.577 & -7.695 & -6.419 \\
+$\Delta_E$ [\%] & 1.1 & 4.4 & 1.2 \\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\end{minipage}
+\begin{minipage}{5cm}
+$\leftarrow$ entire parameter set
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ DFT parameters\\
+ }
+
+\footnotesize
+
+\begin{minipage}{6cm}
+\begin{center}
+\includegraphics[width=6cm]{sic_32pc_gamma_cutoff_lc.ps}
+\end{center}
+\end{minipage}
+\begin{minipage}{6cm}
+\begin{center}
+Lattice constants with respect to the PW cut-off energy
+\end{center}
+\end{minipage}
+
+\begin{minipage}{6cm}
+\begin{center}
+\includegraphics[width=6cm]{si_self_int_thesis.ps}
+\end{center}
+\end{minipage}
+\begin{minipage}{6cm}
+\begin{center}
+Defect formation energy with respect to the size of the supercell\\[0.1cm]
+\end{center}
+
+\end{minipage}
+
+\end{slide}
+
\end{document}
slide 15
-in addition, it is instructive to look at combinations of Cs and Si_i,
-again, a situation which is very likely to arise in ibs.
-Cs located right next to the 110 Si db within the 110 chain
-constitutes the energetically most favirable configuration,
-which, however, is still less favorable than the Ci 100 ground state.
+in addition, it is instructive to look at combinations of Cs and Si_i.
+the most favorable configuration is obtained for
+Cs located right next to the 110 Si db within the 110 chain.
+this configuration is still less favorable than the Ci 100 ground state.
however, the interaction of C_s and Si_i drops quickly to zero
indicating a low capture radius.
in ibs, configurations exceedinig this separation distance are easily produced.
as a last task, reproducing the SiC precipitation is attempted
by successive insertion of 6000 C atoms,
-the number necessary to form a precipitate with a radius of approximately 3 nm,
+the number necessary to form a minimal precipitate,
into a supercell consisting of 31 Si unit cells in each direction.
insertion is realized at constant temperature.
due to the high amount of particles,
-the classical potential is exclusively used.
+the classical potential must be used.
since low carbon diffusion due to the overestimated barriers is expected,
insertion volumes v2 and v3 next to the total volume v1 are considered.
v2 corresponds to the minimal precipiatte size.
to summarize, the formation of cubic SiC fails to appear.
neither agglomeration of C interstitials
-nor a transition into crystalline SiC can be identified.
+nor a transition into SiC can be identified.
slide 20
however, in addition, the overestimated diffusion barriers,
due to the short range character of the potential,
-intensify this problem, which I called:
+intensify this problem, which I termed:
potential enhanced slow phase space propagation.
the approach used in this study is to simply increase the temperature, however,
along a 110 direction.
the C-C next neighbor pairs are reduced,
-which is mandatory for cubic SiC formation.
-the peak at roughly 0.3 nm gets slightly shifter to higher distances,
+which is mandatory for SiC formation.
+the peak at roughly 0.3 nm gets slightly shifted to higher distances,
due to a decrease of interstitial carbon combinations accompanied by an
increase in interstitial and substitutional as well as pure substitutional
combinations.
increasing values in this range
-correpsond to bonds of Cs and another Cs with a nearby Si_i atom.
+correspond to bonds of Cs and another Cs with a nearby Si_i atom.
slide 22
-to conclude, stretched coherent structures of SiC embedded in the Si host
-are directly observed.
-therefore, it is concluded that Cs is extensively involved
+to conclude, stretched coherent structures are directly observed.
+therefore, it is expected that Cs is extensively involved
in the precipitation process for implantations at elevated temperatures.
the emission of Si_i serves several needs:
as a vehicle to rearrange stable Cs,
-furthermore, it serves as a building block for the surrounding Si host
-or further SiC formation.
-finally, it may compensate stress at the Si/SiC interface
+as a building block for the surrounding Si host or further SiC formation.
+and for strain compensation either at the Si/SiC interface
or in the stretched SiC structure, which, again,
was diretly observed in simulation.
this perfectly explains the results of the annealing experiments
stated in the beginning of this talk.
-at low temperatures highly mobile Ci whereas at high temperatures stable Cs
-configurations are formed.
+at low temperatures highly mobile Ci
+whereas at high temperatures stable Cs configurations are formed.
-it is further concluded that high temperatures are necessary to model
+thus, it is further concluded that high temperatures are necessary to model
ibs conditions, which are far from equilibrium.
the high temperatures deviate the system from thermodynamic equilibrium
enabling Ci to turn into Cs.
slide 23
to summarize and conclude ...
-defect structures were described by both methods.
+point defects were investigated by both methods.
the interstitial carbon mmigration path was identified.
-it turned out that the the diffusion barrier is drastically overestimated
+it turned out that the diffusion barrier is drastically overestimated
within the ea description.
combinations of defects were investigated by first principles methods.
however, substitutional carbon arises in all probability.
even transitions from the ground state are very likely to occur.
-concerning the precipitation simulations, the problem of the potential
-enhanced slow phase space propagation was discussed.
-by comparing with experiment it is concluded
-that high temperatures are necessary to model simultae ibs conditions.
-at elevated temperatures stretched structures of SiC were directly observed
-in simulation.
+concerning the precipitation simulations, the problem of
+potential enhanced slow phase space propagation was discussed.
+high temperatures are assumed necessary to simulate ibs conditions.
+at low temperatures a dumbbell dominated structure is obatined
+whereas
+it is expected that
+Stretched structures of SiC were observed at elevated temperatures.
it is thus concluded that
substitutional carbon is heavily involved in the precipitation process.
-the role of the Si_i was outlined and in one case also directly observed
-in simulation.
+the role of the Si_i was outlined.
-in total, it is my feeling, that cubic SiC precipitation occurs by successive
-agglomeration of substitutional C.
+in total, these results suggest,
+that cubic SiC precipitation occurs by successive agglomeration of Cs.
slide 24
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