From: hackbard Date: Tue, 12 Apr 2011 13:17:31 +0000 (+0200) Subject: omitted LJ + more precise ef definition X-Git-Url: https://hackdaworld.org/gitweb/?a=commitdiff_plain;h=1c0fb2a79c4743e6b4ae66d913c7050ec037f3b0;p=lectures%2Flatex.git omitted LJ + more precise ef definition --- diff --git a/posic/publications/defect_combos.tex b/posic/publications/defect_combos.tex index 7756b8d..1c8db1e 100644 --- a/posic/publications/defect_combos.tex +++ b/posic/publications/defect_combos.tex @@ -88,7 +88,8 @@ Spin polarization has been fully accounted for. Migration and recombination pathways have been investigated utilizing the constraint conjugate gradient relaxation technique (CRT)\cite{kaukonen98}. While not guaranteed to find the true minimum energy path, the method turns out to identify reasonable pathways for the investigated structures. The defect formation energy $E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\text{C}}$ is defined by choosing SiC as a particle reservoir for the C impurity, i.e. the chemical potentials are determined by the cohesive energies of a perfect Si and SiC supercell after ionic relaxation. -In the same way defect formation energies are determined in the articles used for comparison. +%In the same way defect formation energies are determined in the article\cite{dal_pino93} used for comparison. +This corresponds to the definition utilized in the article used for comparison\cite{dal_pino93}. The binding energy of a defect pair is given by the difference of the formation energy of the complex and the sum of the two separated defect configurations. %Accordingly, energetically favorable configurations show binding energies below zero while non-interacting isolated defects result in a binding energy of zero. Accordingly, energetically favorable configurations result in binding energies below zero while unfavorable configurations show positive values for the binding energy. @@ -491,15 +492,19 @@ However, only \unit[0.77]{eV} are needed for the reverse process, i.e. the forma Due to the low activation energy this process must be considered to be activated without much effort either thermally or by introduced energy of the implantation process. \begin{figure} -\includegraphics[width=\columnwidth]{c_sub_si110.ps} -\caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance. The interaction strength of the defect pairs are well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.} +%\includegraphics[width=\columnwidth]{c_sub_si110.ps} +\includegraphics[width=\columnwidth]{c_sub_si110_data.ps} +\caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance.} +%\caption{Binding energies of combinations of a C$_{\text{s}}$ and a Si$_{\text{i}}$ DB with respect to the separation distance. The interaction strength of the defect pairs are well approximated by a Lennard-Jones 6-12 potential, which is used for curve fitting.} \label{fig:dc_si-s} \end{figure} Fig.~\ref{fig:dc_si-s} shows the binding energies of pairs of C$_{\text{s}}$ and a Si$_{\text{i}}$ \hkl<1 1 0> DB with respect to the separation distance. -The interaction of the defects is well approximated by a Lennard-Jones (LJ) 6-12 potential, which is used for curve fitting. -Unable to model possible positive values of the binding energy, i.e. unfavorable configurations, located to the right of the minimum, the LJ fit should rather be thought as a guide for the eye describing the decrease of the interaction strength, i.e. the absolute value of the binding energy, with increasing separation distance. -The binding energy quickly drops to zero. -The LJ fit estimates almost zero interaction already at \unit[0.6]{nm}, indicating a low interaction capture radius of the defect pair. +%The interaction of the defects is well approximated by a Lennard-Jones (LJ) 6-12 potential, which is used for curve fitting. +%Unable to model possible positive values of the binding energy, i.e. unfavorable configurations, located to the right of the minimum, the LJ fit should rather be thought as a guide for the eye describing the decrease of the interaction strength, i.e. the absolute value of the binding energy, with increasing separation distance. +%The binding energy quickly drops to zero. +%The LJ fit estimates almost zero interaction already at \unit[0.6]{nm}, indicating a low interaction capture radius of the defect pair. +As can be seen, the interaction strength, i.e. the absolute value of the binding energy, quickly drops to zero with increasing separation distance. +Almost zero interaction may be assumed already at \unit[0.5-0.6]{nm}, indicating a low interaction capture radius of the defect pair. In IBS highly energetic collisions are assumed to easily produce configurations of defects exhibiting separation distances exceeding the capture radius. For this reason C$_{\text{s}}$ without a Si$_{\text{i}}$ DB located within the immediate proximity, which is, thus, unable to form the thermodynamically stable C$_{\text{i}}$ \hkl<1 0 0> DB, constitutes a most likely configuration to be found in IBS.