c in si

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 616e722..d2f1727 100644 (file)
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -197,7 +197,15 @@ Todo: Plot the electron density for these types of defect to derive conclusions
 
 \section{Carbon related point defects}
 
+Carbon is a common and technologically important impurity in silicon.
+Concentrations as high as $10^{18}\text{ cm}^{-3}$ occur in Czochralski-grown silicon samples.
+It is well established that carbon and other isovalent impurities prefer to dissolve substitutionally in silicon.
+However, radiation damage can generate carbon interstitials \cite{watkins76} which enough mobility at room temeprature to migrate and form defect complexes.
+
 Formation energies of the most common carbon point defects in crystalline silicon are summarized in table \ref{tab:defects:c_ints}.
+The type of reservoir of the carbon impurity to determine the formation energy of the defect was chosen to be SiC.
+This is consistent with the methods used in the articles \cite{tersoff90,dal_pino93} which the results are compared to in the following.
+Hence, the chemical potential of silicon and carbon is determined by the cohesive energy of silicon and silicon carbide.
 \begin{table}[h]
 \begin{center}
 \begin{tabular}{l c c c c c c}
@@ -205,8 +213,9 @@ Formation energies of the most common carbon point defects in crystalline silico
 \hline
  & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B \\
 \hline
- Erhard/Albe MD & 5.41 & 8.37$^*$ & 3.21 & 4.50 & 0.07 & 4.91$^*$ \\
- VASP & unstable & unstable & 3.15 & 3.60 & 1.39 & 4.10 \\
+ Erhard/Albe MD & 6.09 & 9.05$^*$ & 3.88 & 5.18 & 0.75 & 5.59$^*$ \\
+ VASP (C [dia] reservoir) & unstable & unstable & 3.15 & 3.60 & 1.39 & 4.10 \\
+ VASP (SiC reservoir) & unstable & unstable & 3.72 & 4.16 & 1.95 & 4.66 \\
  Tersoff \cite{tersoff90} & 3.8 & 6.7 & 4.6 & 5.9 & 1.6 & 5.3 \\
  ab initio & - & - & x & - & 1.89 \cite{dal_pino93} & x+2.1 \cite{capaz94} \\
 \hline
@@ -216,10 +225,22 @@ Formation energies of the most common carbon point defects in crystalline silico
 \caption[Formation energies of carbon point defects in crystalline silicon determined by classical potential molecular dynamics and density functional calculations.]{Formation energies of carbon point defects in crystalline silicon determined by classical potential molecular dynamics and density functional calculations. The formation energies are given in eV. T denotes the tetrahedral, H the hexagonal, B the bond-centered and S the substitutional interstitial configuration. The dumbbell configurations are abbreviated by DB.  Formation energies for unstable configurations are marked by an asterisk and determined by using the low kinetic energy configuration shortly before the relaxation into the more favorable configuration starts.}
 \label{tab:defects:c_ints}
 \end{table}
-Except for Tersoff's tedrahedral configuration results the \hkl<1 0 0> dumbbell is the energetically most favorable configuration for all types of interaction models.
-The low energy of formation for the tetrahedral interstitial in the case of the Tersoff potential is believed to be an artifact of the short cutoff (see Ref. 13 in \cite{tersoff90}) and the real formation energy is supposed to be located between 3 and 10 eV.
 
+Substitutional carbon in silicon is found to be the lowest configuration in energy for all potential models.
+
+
+
+Except for Tersoff's tedrahedral configuration results the \hkl<1 0 0> dumbbell is the energetically most favorable interstital configuration.
+The low energy of formation for the tetrahedral interstitial in the case of the Tersoff potential is believed to be an artifact of the short cutoff (see ref. 13 in \cite{tersoff90}) and the real formation energy is supposed to be located between 3 and 10 eV.
+The formation energy for substitutional carbon is about 3 eV lower than the \hkl<1 0 0> dumbbell for both classical potentials.
+
+The highest energy is observed for the hexagonal interstitial configuration using classical potentials.
+Quantum-mechanical calculations reveal this configuration to be unstable, which is also reproduced by the Erhard/Albe potential.
+In both cases a relaxation towards the \hkl<1 0 0> dumbbell configuration is observed.
+
+\subsection[\hkl<1 0 0> dumbbell interstitial configuration]{\boldmath\hkl<1 0 0> dumbbell interstitial configuration}
 
+\subsection{Bond-centered interstitial configuration}
 
 \section[Migration of the carbon \hkl<1 0 0> interstitial]{\boldmath Migration of the carbon \hkl<1 0 0> interstitial}