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+\ifnum1=0
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\center
{\Huge
E\\
}
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+\fi
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-\ifnum1=0
+%\ifnum1=0
% intro
\end{slide}
-% temp
-\fi
-
\begin{slide}
\headphd
\begin{itemize}
\item Stretched coherent SiC structures\\
$\Rightarrow$ Precipitation process involves {\color{blue}\cs}
-\item Explains annealing behavior of high/low T C implantations
- \begin{itemize}
- \item Low T: highly mobile {\color{red}\ci}
- \item High T: stable configurations of {\color{blue}\cs}
- \end{itemize}
\item Role of \si{}
\begin{itemize}
\item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
\ldots Si/SiC interface\\
\ldots within stretched coherent SiC structure
\end{itemize}
+\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}
\end{itemize}
\vspace{0.2cm}
\centering
\end{slide}
+% skip high c conc results
+\ifnum1=0
+
\begin{slide}
{\large\bf
\footnotesize
-\begin{minipage}{6.5cm}
+\begin{minipage}{6.0cm}
\includegraphics[width=6.4cm]{12_pc_thesis.ps}
\end{minipage}
-\begin{minipage}{6.5cm}
+\begin{minipage}{6.0cm}
\includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
\end{minipage}
\end{slide}
+% skip high c conc
+\fi
+
+% for preparation
+%\fi
+
\begin{slide}
\headphd
Summary / Conclusions
}
-\small
+\scriptsize
-\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
+\framebox{
+\begin{minipage}{12.3cm}
+ \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{minipage}
}
-\end{pspicture}\\[0.4cm]
-\begin{pspicture}(0,0)(12,2)
-\psframebox[fillstyle=gradient,gradbegin=hblue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
-\begin{minipage}{11cm}
-{\color{black}Doctoral studies}\\
- Classical potential \underline{molecular dynamics} simulations \ldots\\
- \underline{Density functional theory} calculations \ldots\\[0.2cm]
- \ldots on defect formation and SiC precipitation in Si
+
+\framebox{
+\begin{minipage}[t]{12.3cm}
+ \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}
\end{minipage}
}
-\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}
+
+\begin{center}
+{\color{blue}
+\framebox{Precipitation by successive agglomeration of \cs{}}
}
-\end{pspicture}\\[0.5cm]
+\end{center}
\end{slide}
the interaction is decribed by a Tersoff-like short-range bond order potential,
developed by erhart and albe.
the short range character is achieved by a cutoff function,
-which drops the interaction inbetween the first and second next neighbor atom.
+which drops the interaction inbetween the first and next neighbor atom.
the potential consists of a repulsive and an attractive part associated with
the bonding, which is limited by the bond order term, which takes
into consideration all atoms k influencing the bond of atoms i and j.
slide 21
-now ...
+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,
+into a supercell consisting of 31 Si unit cells in each direction.
+insertion is realized at constant temperature.
+after insertion, the simulation is continued for 100 ps
+follwed by a cooling sequence downto 20 degrees celsius.
+due to the high amount of particles,
+the classical potential is exclusively 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.
+v3 contains the amount of silicon atoms to form such a minimal precipitate.
slide 22
+
+the radial distribution Si-C, C-C and Si-Si bonds of simulations,
+in which C was inserted at 450 dc,
+an operative and efficient temperature in ibs, are shown.
+
+for the low C concentration simulation, i.e. the v1 simulation,
+a clearly 100 C-Si db dominated structure is obtained,
+which is obvious by comparing it to the
+reference distribution generated by a single Ci defect.
+the second peak is a cut-off artifact,
+correpsonding to the Si-C cut-off distance of 0.26 nm.
+the C-C peak at 0.31 nm, as expected in cubic SiC,
+is generated by concatenated, differently oriented Ci dbs.
+the same distance is also expected for the Si atoms, and, indeed,
+the db structure stretches the Si-Si next neighbor distance,
+which is represented by nonzero values in the correlation function.
+
+so, the formation of Ci dumbbells indeed occurs.
+even the C atoms are already found in a separation as expected in cubic SiC.
+
+turning to the high C concentration simulations, i.e. the v1 and v2 simulation,
+a high amount of strongly bound C-C bonds
+as in graphite or diamond are observed.
+an increased defect and damage density is obtained,
+which makes it hard to categorize and trace defect arrangements.
+only short range orde is observed.
+and, indeed, comparing to other distribution data, an amorphous SiC-like
+phase is obtained.
+
slide 23
+
+to summarize, the formation of cubic SiC fails to appear.
+in the v1 simulation, formation of Ci indeed occurs, however,
+agglomeration is missing.
+in the high concentration simulation, an amorphous SiC-like structure,
+which is not expected at 450 dc, is obtained.
+no rearrangemnt into crystalline cubic SiC is indicated.
+
slide 24
+
+having a closer look, there are two obvious reasons for this obstacle.
+
+first of all, there is the time scale problem inherent to md in general.
+to minimize the integration error, the time step must be chosen smaller
+than the reciprocal of the fastes vibrational mode.
+several local minima exist, which are separated by large energy barriers.
+due to the low probability for escaping such a local minimum,
+a transition event correpsonds to a multiple of vibrational periods.
+a phase transition, in turn, consists of many such infrequent transition events.
+new accelerated methods, like temperature accelerated MD and so on,
+have been developed to bypass the time scale problem while retaining proper
+thermodynamic sampling.
+
+in addition, the overestimated diffusion barriers,
+due to the short range character of the potential,
+intensify this problem, which I called:
+potential enhanced slow phase space propagation.
+
+the approach used in this study is to simply increase the temperature, however,
+without possible corrections.
+accelerated methods or higher time scales applied exclusively
+are assumed oto be not sufficient.
+moreover, to legitimate the usage of increased temperatures:
+cubic SiC is also observed for higher temperatures,
+there is definitely a higher temperature inside the sample, and, anyways,
+structural evolution instead of equilibrium properties are matter of interest.
+
slide 25
+
+and indeed, promising changes are observed by comparing,
+again the radial distribution data of Si-C, Si-Si and C-C bonds
+for temperatures up to 2050 dc.
+first of all, the cut-off artifact disappears.
+more important, a transition a 100 db into a Cs dominated structure takes place,
+as can be seen by direct comparison with the respective reference peaks.
+
+the Si-Si rising peak at 0.325 nm is due to two Si atoms next to a Cs atom.
+
+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.
+the amount of bonds due to Ci 100 combinations, represented by dashed arrows,
+decreases accompanied by an increase of bonds due to combinations of
+Ci 100 and Cs and pure Cs combinations, represented by the dashed line and
+solid arrows respectively.
+increasing values in the range between the dashed line and first solid arrow
+correpsond to bonds of a Cs and another Cs with a nearby Si_i atom.
+
slide 26
+
+to conclude, stretched coherent structures of SiC embedded in the Si host
+are directly observed.
+therefore, an increased participation of Cs is suggested
+for implantations at elevated temperatures,
+which simulate the conditions prevalent in ibs that deviate the system
+from thermodynamic equilibrium enabling Ci to turn into Cs.
+
+the emission of Si_i serves several needs:
+as a vehicle to rearrange the Cs,
+realized by recombination into the highly mobile Ci configuration.
+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
+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.
+
+to summarize, the results suggest that Cs plays an important role
+in the precipitation process.
+moreover, high temperatures are necessary to model ibs conditions,
+which are far from equilibrium.
+
slide 27
+to summarize and conclude
+
+slide 28
+
+in the end, I would like to say thank you.
+
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