Just as for the Si self-interstitial a carbon \hkl<1 1 0> dumbbell configuration exists.
For the Erhard/Albe potential the formation energy is situated in the same order as found by quantum-mechanical results.
-Similar structures arise in both types of simulations with the silicon and carbon atom sharing a silicon lattice site aligned along \hkl[1 1 0] where the carbon atom is localized slightly closer to the next nearest silicon atom located in the opposite direction to the site-sharing silicon atom even forming a bond to the next but one silicon atom in this direction.
+Similar structures arise in both types of simulations with the silicon and carbon atom sharing a silicon lattice site aligned along \hkl<1 1 0> where the carbon atom is localized slightly closer to the next nearest silicon atom located in the opposite direction to the site-sharing silicon atom even forming a bond to the next but one silicon atom in this direction.
The bond-centered configuration is unstable for the Erhard/Albe potential.
The system moves into the \hkl<1 1 0> interstitial configuration.
However, this fact could not be reproduced by spin polarized VASP calculations performed in this work.
Present results suggest this configuration to be a real local minimum.
In fact, an additional barrier has to be passed to reach this configuration starting from the \hkl<1 0 0> interstitital configuration, which is investigated in section \ref{subsection:100mig}.
-The carbon atom has been displaced along the axes ... relaxation back ... indicating a real local minimum.
+After slightly displacing the carbon 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 resulting structures relax back into the bond-centered configuration.
+As we will see in later migration simulations the same would happen to structures where the carbon atom is displaced along the migration direction, which approximately is the \hkl<1 1 0> direction.
+These relaxations indicate that the bond-cenetered configuration is a real local minimum instead of an assumed saddle point configuration.
Figure \ref{img:defects:bc_conf} shows the structure, the charge density isosurface and the Kohn-Sham levels of the bond-centered configuration.
The linear bonds of the carbon atom to the two silicon atoms indicate the $sp$ hybridization of the carbon atom.
Two electrons participate to the linear $\sigma$ bonds with the silicon neighbours.
The other two electrons constitute the $2p^2$ orbitals resulting in a net magnetization.
This is supported by the charge density isosurface and the Kohn-Sham levels in figure \ref{img:defects:bc_conf}.
-The blue torus, reinforcing the assumption of the p orbital, illsutrates the resulting spin up electron density.
+The blue torus, reinforcing the assumption of the p orbital, illustrates the resulting spin up electron density.
In addition, the energy level diagram shows a net amount of two spin up electrons.
\section[Migration of the carbon \hkl<1 0 0> interstitial]{\boldmath Migration of the carbon \hkl<1 0 0> interstitial}
\label{subsection:100mig}
In the following the problem of interstitial carbon migration in silicon is considered.
+Since the carbon \hkl<1 0 0> dumbbell interstitial is the most probable hence most important configuration the migration simulations focus on this defect.
+
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}{15cm}
+\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/bc_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/100_next_2333.eps}
+\end{minipage}
+\end{minipage}\\
+\begin{minipage}{15cm}
+\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/00-1-0-10_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/0-10_2333.eps}
+\end{minipage}
+\end{minipage}\\
+\begin{minipage}{15cm}
+\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/0-10_ip_2333.eps}
+\end{minipage}
+\end{minipage}
+\end{center}
+\caption{Migration pathways of the carbon \hkl<1 0 0> interstitial dumbbell in silicon.}
+\label{img:defects:c_mig_path}
+\end{figure}
+Three different migration paths are accounted in this work, which are shown in figure \ref{img:defects:c_mig_path}.
+The first migration investigated is a transition of a \hkl<0 0 -1> into a \hkl<0 0 1> dumbbell interstitial configuration.
+During this migration the carbon atom is changing its silicon dumbbell partner.
+The new partner is the one located at $\frac{a}{4}\hkl<1 1 -1>$ relative to the initial one.
+Two of the three bonds to the next neighboured silicon atoms are preserved while the breaking of the other bond and the formation of a new bond is observed.
+The carbon atom resides in the \hkl(1 1 0) plane.
+This transition involves the bond-centerd configuration.
+Due to symmetry it is enough to consider the transition from the bond-centered to the \hkl<1 0 0> configuration.
+In the second path, the carbon atom is changing its silicon partner atom as in path one.
+In addition, the dumbbell configuration is changing
+
+As a last migration path, the \hkl<0 0 -1>
+
+Since the starting and final structure, which are both local minima of the potential energy surface are known, the aim is to find the minimum energy path from one local minimum to the other one.
+One method is to move the diffusing atom stepwise from the starting to the final position and only allow relaxation in the plane perpendicular to the direction of the vector connecting its starting and final position.
+No constraints are applied to the remaining atoms.
+
+Different approaches were used to compute migration paths and energies.
+CRT erklaeren
+Nur C atom constrainted
+Problem, 1) relaxation of host matrix 2) abrubt changes in energy and configuration
+as can be seen in ...
+Thus, 'all atom CRT' but! relaxation perpendicular to delta step ...
+
+Results and comparison with diffusion experiments.
\section{Combination of point defects}
projects / lectures / latex.git / blobdiff