Utilized and enhanced, ion beam synthesis (IBS) has become a promising method to form thin SiC layers of high quality and exclusively of the 3C polytype embedded in and epitactically aligned to the Si host featuring a sharp interface\cite{lindner99,lindner01,lindner02}.
However, only little is known about the SiC conversion in C implanted Si.
-High resolution transmission electron microscopy (HREM) studies\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03} suggest the formation of C-Si dimers (dumbbells) on regular Si lattice sites, which agglomerate into large clusters indicated by dark contrasts and otherwise undisturbed Si lattice fringes in HREM.
-A topotactic transformation into a 3C-SiC precipitate occurs once a critical radius of 2 nm to 4 nm is reached, which is manifested by the disappearance of the dark contrasts in favor of Moir\'e patterns due to the lattice mismatch of \unit[20]{\%} of the 3C-SiC precipitate and c-Si.
+\begin{figure}
+\begin{center}
+\subfigure[]{\label{fig:hrem:c-si}\includegraphics[width=0.48\columnwidth]{../img/tem_c-si-db.eps}}
+\subfigure[]{\label{fig:hrem:sic}\includegraphics[width=0.48\columnwidth]{../img/tem_3c-sic.eps}}
+\end{center}
+\caption{High resolution transmission electron microscopy (HREM) micrographs\cite{lindner99_2} of agglomerates of C-Si dimers showing dark contrasts and otherwise undisturbed Si lattice fringes (a) and equally sized Moir\'e patterns indicating 3C-SiC precipitates (b).}
+\label{fig:hrem}
+\end{figure}
+High resolution transmission electron microscopy (HREM) studies\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03} suggest the formation of C-Si dimers (dumbbells) on regular Si lattice sites, which agglomerate into large clusters indicated by dark contrasts and otherwise undisturbed Si lattice fringes in HREM, as can be seen in Fig.~\ref{fig:hrem:c-si}.
+A topotactic transformation into a 3C-SiC precipitate occurs once a critical radius of 2 nm to 4 nm is reached, which is manifested by the disappearance of the dark contrasts in favor of Moir\'e patterns (Fig.~\ref{fig:hrem:sic}) due to the lattice mismatch of \unit[20]{\%} of the 3C-SiC precipitate and c-Si.
The insignificantly lower Si density of SiC ($\approx \unit[4]{\%}$) compared to c-Si results in the emission of only a few excess Si atoms.
In contrast, investigations of strained Si$_{1-y}$C$_y$/Si heterostructures formed by MBE\cite{strane94,guedj98}, which incidentally involve the formation of SiC nanocrystallites, suggest an initial coherent precipitation by agglomeration of substitutional instead of interstitial C.
Coherency is lost once the increasing strain energy of the stretched SiC structure surpasses the interfacial energy of the incoherent 3C-SiC precipitate and the Si substrate.
However, even for non-interacting defects, the energy of formation, which is then given by the sum of the formation energies of the separated defects (\unit[4.15]{eV}) is still higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB.
Unexpectedly, the structure of a Si$_{\text{i}}$ \hkl<1 1 0> DB and a neighbored C$_{\text{s}}$, which is the most favored configuration of C$_{\text{s}}$ and Si$_{\text{i}}$ according to quantum-mechanical calculations\cite{zirkelbach10b}, likewise constitutes an energetically favorable configuration within the EA description, which is even preferred over the two least separated configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ T.
This is attributed to an effective reduction in strain enabled by the respective combination.
-Quantum-mechanical results reveal a more favorable energy of fomation for configuration a of C$_{\text{s}}$ and Si$_{\text{i}}$ T.
-However, this involves a structural transition into the C$_{\text{i}}$ \hkl<1 1 0> interstitial, thus, not maintaining the tetrahedral Si nor the substitutional C defect.
-%qm results show smaller energies for the a type of si tet + c sub, however this involves structural change towards the 110 DB not maintaining tetrahedral nor the substitutional defect.
-% in anyways, no configurations more favorable than c-si DB arise.
+Quantum-mechanical results reveal a more favorable energy of fomation for the C$_{\text{s}}$ and Si$_{\text{i}}$ T (a) configuration.
+However, this configuration is unstable involving a structural transition into the C$_{\text{i}}$ \hkl<1 1 0> interstitial, thus, not maintaining the tetrahedral Si nor the substitutional C defect.
+In either case, no configuration more favorable than the C$_{\text{i}}$ \hkl<1 0 0> DB has been found.
Thus, a proper description with respect to the relative energies of formation is assumed for the EA potential.
\subsection{Carbon mobility}
By considering a two step process and assuming equal preexponential factors for both diffusion steps, the probability of the total diffusion event is given by $\exp(\frac{\unit[2.24]{eV}+\unit[0.90]{eV}}{k_{\text{B}}T})$, which corresponds to a single diffusion barrier that is 3.5 times higher than the barrier obtained by ab initio calculations.
Accordingly, the effective barrier of migration of C$_{\text{i}}$ is overestimated by a factor of 2.4 to 3.5 compared to the highly accurate quantum-mechanical methods.
-This constitutes a serious limitation that has to be taken into account for modeling the C-Si system using the EA potential.
+This constitutes a serious limitation that has to be taken into account for modeling the C-Si system using the otherwise quite promising EA potential.
\subsection{Molecular dynamics simulations}
In the low C concentration simulation the number of C-C bonds is small, as can be seen in the upper part of Fig.~\ref{fig:450:a}.
On average, there are only 0.2 C atoms per Si unit cell.
By comparing the Si-C peaks of the low concentration simulation with the resulting Si-C distances of a C$_{\text{i}}$ \hkl<1 0 0> DB in Fig.~\ref{fig:450:b} it becomes evident that the structure is clearly dominated by this kind of defect.
-One exceptional peak at \unit[0.26]{nm} exists, which is due to the Si-C cut-off, at which the interaction is pushed to zero.
+One exceptional peak at \unit[0.26]{nm} (marked with an arrow in Fig.~\ref{fig:450:b}) exists, which is due to the Si-C cut-off, at which the interaction is pushed to zero.
Investigating the C-C peak at \unit[0.31]{nm}, which is also available for low C concentrations as can be seen in the upper inset of Fig.~\ref{fig:450:a}, reveals a structure of two concatenated, differently oriented C$_{\text{i}}$ \hkl<1 0 0> DBs to be responsible for this distance.
Additionally, in the inset of the bottom part of Fig.\ref{fig:450:a} the Si-Si radial distribution shows non-zero values at distances around \unit[0.3]{nm}, which, again, is due to the DB structure stretching two neighbored Si atoms.
This is accompanied by a reduction of the number of bonds at regular Si distances of c-Si.
\end{figure}
\begin{figure}
\begin{center}
-\includegraphics[width=\columnwidth]{../img/plot.eps}
+\includegraphics[width=\columnwidth]{../img/2050.eps}
\end{center}
\caption{Cross section along the \hkl(1 -1 0) plane of the atomic structure of the high concentration simulation for a C insertion temperature of \unit[2050]{$^{\circ}$C}.}
\label{fig:v2as}
projects / lectures / latex.git / commitdiff