\subsection[C \hkl<1 0 0> dumbbell interstitial configuration]{\boldmath C \hkl<1 0 0> dumbbell interstitial configuration}
\label{subsection:100db}
-As the \ci{} \hkl<1 0 0> DB constitutes the ground-state configuration of a C atom incorporated into otherwise perfect c-Si it is the most probable and, hence, one of the most important interstitial configurations of C in Si.
+As the \ci{} \hkl<1 0 0> DB constitutes the ground-state configuration of a C atom incorporated into otherwise perfect c-Si, it is the most probable and, hence, one of the most important interstitial configurations of C in Si.
The structure was initially suspected by IR local vibrational mode absorption~\cite{bean70} and finally verified by electron paramagnetic resonance (EPR)~\cite{watkins76} studies on irradiated Si substrates at low temperatures.
Fig.~\ref{fig:defects:100db_cmp} schematically shows the \ci{} \hkl<1 0 0> DB structure and Table~\ref{tab:defects:100db_cmp} lists the details of the atomic displacements, distances and bond angles obtained by classical potential and quantum-mechanical calculations.
Present results suggest this configuration to correspond to a real local minimum.
In fact, an additional barrier has to be passed to reach this configuration starting from the \ci{} \hkl<1 0 0> interstitial configuration, which is investigated in section~\ref{subsection:100mig}.
After slightly displacing the C atom along the \hkl[1 0 0] (equivalent to a displacement along \hkl[0 1 0]), \hkl[0 0 1], \hkl[0 0 -1] and \hkl[1 -1 0] direction the distorted structures relax back into the BC configuration.
-As will be shown in subsequent migration simulations the same would happen to structures where the C atom is displaced along the migration direction, which approximately is the \hkl[1 1 0] direction.
+As will be shown in subsequent migration simulations, the same would happen to structures where the C atom is displaced along the migration direction, which approximately is the \hkl[1 1 0] direction.
These relaxations indicate that the BC configuration is a real local minimum instead of an assumed saddle point configuration.
Fig.~\ref{img:defects:bc_conf} shows the structure, charge density isosurface and Kohn-Sham levels of the BC configuration.
In fact, the net magnetization of two electrons is already suggested by simple molecular orbital theory considerations with respect to the bonding of the C atom.
Fig.~\ref{fig:defects:cp_bc_00-1_mig} shows the evolution of structure and energy along the \ci{} BC to \hkl[0 0 -1] DB transition.
Since the \ci{} BC configuration is unstable relaxing into the \hkl[1 1 0] DB configuration within this potential, the low kinetic energy state is used as a starting configuration.
Two different pathways are obtained for different time constants of the Berendsen thermostat.
-With a time constant of \unit[1]{fs} the C atom resides in the \hkl(1 1 0) plane
+With a time constant of \unit[1]{fs}, the C atom resides in the \hkl(1 1 0) plane
resulting in a migration barrier of \unit[2.4]{eV}.
However, weaker coupling to the heat bath realized by an increase of the time constant to \unit[100]{fs} enables the C atom to move out of the \hkl(1 1 0) plane already at the beginning, which is accompanied by a reduction in energy, approaching the final configuration on a curved path.
The energy barrier of this path is \unit[0.2]{eV} lower in energy than the direct migration within the \hkl(1 1 0) plane.
\label{fig:defects:110_mig}
\end{figure}
Fig.~\ref{fig:defects:110_mig} shows migration barriers of the \ci{} \hkl[1 1 0] DB to \hkl[0 0 -1], \hkl[0 -1 0] (in place) and BC configuration.
-As expected there is no maximum for the transition into the BC configuration.
+As expected, there is no maximum for the transition into the BC configuration.
As mentioned earlier, the BC configuration itself constitutes a saddle point configuration relaxing into the energetically more favorable \hkl[1 1 0] DB configuration.
An activation energy of \unit[2.2]{eV} is necessary to reorientate the \hkl[0 0 -1] into the \hkl[1 1 0] DB configuration, which is \unit[1.3]{eV} higher in energy.
Residing in this state another \unit[0.90]{eV} is enough to make the C atom form a \hkl[0 0 -1] DB configuration with the Si atom of the neighbored lattice site.
\end{table}
Obviously the EA potential properly describes the relative energies of formation.
Combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ T are energetically less favorable than the ground state C$_{\text{i}}$ \hkl<1 0 0> DB configuration.
-With increasing separation distance the energies of formation decrease.
+With increasing separation distance, the energies of formation decrease.
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 a C$_{\text{s}}$ and Si$_{\text{i}}$ DB according to quantum-mechanical calculations, 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.
However, it turns out that the BC configuration is not a saddle point configuration as proposed by Capaz et~al.~\cite{capaz94} but constitutes a real local minimum if the electron spin is properly accounted for.
A net magnetization of two electrons, which is already clear by simple molecular orbital theory considerations on the bonding of the $sp$ hybridized C atom, is settled.
By investigating the charge density isosurface it turns out that the two resulting spin up electrons are localized in a torus around the C atom.
-With an activation energy of \unit[0.9]{eV} the C$_{\text{i}}$ carbon interstitial can be expected to be highly mobile at prevailing temperatures in the process under investigation, i.e.\ IBS.
+With an activation energy of \unit[0.9]{eV}, the C$_{\text{i}}$ carbon interstitial can be expected to be highly mobile at prevailing temperatures in the process under investigation, i.e.\ IBS.
Since the \ci{} \hkl<1 0 0> DB is the ground-state configuration and highly mobile, possible migration of these DBs to form defect agglomerates, as demanded by the model introduced in section~\ref{section:assumed_prec}, is considered possible.
Unfortunately the description of the same processes fails if classical potential methods are used.
projects / lectures / latex.git / blobdiff