A lot of theoretical work has been done on intrinsic point defects in Si\cite{bar-yam84,bar-yam84_2,car84,batra87,bloechl93,tang97,leung99,colombo02,goedecker02,al-mushadani03,posselt08,ma10}, threshold displacement energies in Si\cite{mazzarolo01,holmstroem08} important in ion implantation, C defects and defect reactions in Si\cite{tersoff90,dal_pino93,capaz94,burnard93,leary97,capaz98,zhu98,mattoni2002,park02,jones04}, the SiC/Si interface\cite{chirita97,kitabatake93,cicero02,pizzagalli03} and defects in SiC\cite{bockstedte03,rauls03a,gao04,posselt06,gao07}.\r
However, none of the mentioned studies consistently investigates entirely the relevant defect structures and reactions concentrated on the specific problem of 3C-SiC formation in C implanted Si.\r
% but mattoni2002 actually did a lot. maybe this should be mentioned!\r
+In fact, in a combined analytical potential molecular dynamics and ab initio study\cite{mattoni2002} the interaction of substitutional C with Si self-interstitials and C interstitials is evaluated.\r
+However, investigations are, first of all, restricted to interaction chains along the $\langle 1 1 0 \rangle$ and $\langle -1 1 0 \rangle$ direction, secondly lacking combinations of C interstitials and, finally, not considering migration barriers giving further information about the probability of defect agglomeration.\r
\r
By first principles atomistic simulations this work aims to shed light on basic processes involved in the precipitation mechanism of SiC in Si.\r
During implantation defects such as vacancies (V), substitutional C (C$_{\text{s}}$), interstitial C (C$_{\text{i}}$) and Si self-interstitials (Si$_{\text{i}}$) are created, which play a decisive role in the precipitation process.\r
% we need both: Si self-int & C int ground state configuration (for combos)\r
\r
Several geometries have been calculated to be stable for individual intrinsic and C related defects in Si.\r
-Fig.~\ref{fig:sep_def} shows the obtained structures while the corresponding energies of formation are summarized and compared to values from literature in table~\ref{table:sep_eof}.\r
+Fig.~\ref{fig:sep_def} shows the obtained structures while the corresponding energies of formation are summarized and compared to values from literature in Table~\ref{table:sep_eof}.\r
\begin{figure}\r
\begin{minipage}[t]{0.32\columnwidth}\r
\underline{Si$_{\text{i}}$ $\langle 1 1 0 \rangle$ DB}\\\r
However, the present study indicates a local minimum state for the BC defect if spin polarized calculations are performed resulting in a net magnetization of two electrons localized in a torus around the C atom.\r
Another DFT calculation without fully accounting for the electron spin results in the smearing of a single electron over two non-degenerate Kohn-Sham states and an increase of the total energy by \unit[0.3]{eV} for the BC configuration.\r
Regardless of the rather small correction due to the spin, the difference we found is much smaller (\unit[0.9]{eV}), which would nicely compare to experimental findings $(\unit[0.73-0.87]{eV})$\cite{tipping87,song90} for the migration barrier.\r
-However, since the BC configuration constitutes a real local minimum another barrier exists which is about \unit[1.2]{eV} (\unit[0.9+0.3]{eV}) in height.\r
+However, since the BC configuration constitutes a real local minimum another barrier exists which is about \unit[1.2]{eV} ($\unit[0.9]{eV}+\unit[0.3]{eV}$) in height.\r
Indeed Capaz et al. propose another path and find it to be the lowest in energy\cite{capaz94}, in which a C$_{\text{i}}$ $\langle 0 0 -1\rangle$ DB migrates into a C$_{\text{i}}$ $\langle 0 -1 0\rangle$ DB located at the next neighboured Si lattice site in $[1 1 -1]$ direction.\r
Calculations in this work reinforce this path by an additional improvement of the quantitative conformance of the barrier height (\unit[0.9]{eV}) to experimental values.\r
A more detailed description can be found in a previous study\cite{zirkelbach10a}.\r
\r
Next to the C BC configuration the vacancy and Si$_{\text{i}}$ $\langle 1 0 0\rangle$ DB have to be treated by taking into account the spin of the electrons.\r
-For the latter two the net spin up electron density is located in caps at the four surrounding Si atoms oriented towards the vacant site and in two caps at each of the two DB atoms perpendicular aligned to the bonds to the other two Si atoms respectively.\r
+For the latter two the net spin up electron density is localized in caps at the four surrounding Si atoms directed towards the vacant site and in two caps at each of the two DB atoms perpendicularly aligned to the bonds to the other two Si atoms respectively.\r
No other configuration, within the ones that are mentioned, is affected.\r
\r
Concerning the mobility of the ground state Si$_{\text{i}}$, an activation energy shortly below \unit[0.7]{eV} was found for the migration of a Si$_{\text{i}}$ $\langle 0 1 -1\rangle$ into a $\langle 1 1 0\rangle$ DB configuration located at the next neighboured Si lattice site in $[1 1 -1]$ direction.\r
+% look for values in literature for neutraly charged Si_i diffusion\r
\r
\subsection{Pairs of C$_{\text{i}}$}\r
\r
C$_{\text{i}}$ pairs of the $\langle 1 0 0\rangle$-type have been considered in the first part.\r
-Table~\ref{table:dc_c-c} summarizes the binding energies obtained for configurations, in which an initial C$_{\text{i}}$ $\langle 0 0 -1\rangle$ DB located at position Si$_{\text{i}}$/C$_{\text{i}}$ is combined with a defect of the same type occupying various orientations at positions 1 to 5 (see Fig.~ref{fig:combos}).\r
+Table~\ref{table:dc_c-c} summarizes the binding energies obtained for configurations, in which an initial C$_{\text{i}}$ $\langle 0 0 -1\rangle$ DB located at position Si$_{\text{i}}$/C$_{\text{i}}$ is combined with a defect of the same type occupying various orientations at positions 1 to 5 (see Fig.~\ref{fig:combos}).\r
\begin{table}\r
\begin{ruledtabular}\r
\begin{tabular}{l c c c c c c }\r
Antiparallel orientations of the second defect ($\langle 0 0 1\rangle$) at positions located below the (001) plane with respect to the initial one (positions 1, 2 and 4) show the energetically most unfavorable configurations.\r
In contrast, the parallel and particularly the twisted orientations constitute energetically favorable configurations, in which a vast reduction of strain is enabled by combination of these defects.\r
\r
-In the energetically most favorable configuration, in which differently oriented next neighboured DBs with the two C atoms facing each other, a strong C-C bond has formed.\r
-Migration C-C ...\r
+Mattoni et al.\cite{mattoni2002} predict the ground state configuration for a $\langle 1 0 0\rangle$ or equivalently a $\langle 0 1 0\rangle$ defect created at position 1 with both defects basically maintaining the DB structure, resulting in a binding energy of \unit[-2.1]{eV}.\r
+% in mattoni db structures are basically amintained. there is further relaxation in our case and a lower binding energy\r
+In this work we found a further relaxation of this defect structure.\r
+The C atom of the second and the Si atom of the initial DB move towards each other forming a bond, which results in a somewhat lower binding energy of \unit[-2.25]{eV}.\r
+Furthermore a more favorable configuration was found for the combination with a $\langle 0 -1 0\rangle$ and $\langle -1 0 0\rangle$ DB respectively, which is assumed to constitute the actual ground state configuration of two C$_{\text{i}}$ DBs in Si.\r
+The two C atoms form a strong C-C bond, which is responsible for the large gain in energy resulting in a binding energy of \unit[-2.39]{eV}.\r
+\r
+Investigating migration barriers enables to predict the probability of formation of the thermodynamic ground state defect complex by thermally activated diffusion processes.\r
+High activation energies are necessary for the migration of low energy configurations, in which the C atom of the second DB is located in the vicinity of the initial DB.\r
+The transition of the configuration, in which the second DB is of the $\langle 0 1 0\rangle$ type at position 2 (\unit[-1.90]{eV}) into a $\langle 0 1 0\rangle$-type DB at position 1 (\unit[-2.39]{eV}) for instance, revealed a barrier height of more than \unit[4]{eV}.\r
+Low barriers are only expected from energetically less favorable configurations, e.g. the configuration of the $\langle -1 0 0\rangle$ DB located at position 2.\r
+A migration barrier of \unit[?.?]{eV} \r
% strange mig from -190 -> -2.39 (barrier > 4 eV)\r
% C-C migration -> idea:\r
% mig from low energy confs has extremely high barrier!\r
% low barrier only from energetically less/unfavorable confs (?)! <- prove!\r
% => low probability of C-C clustering ?!?\r
+Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, mass C clustering is not expected.\r
+\r
+% look for precapture mechnism (local minimum in energy curve)\r
+\r
+% mattoni2002: c_i c_i attraction basin not explored, too wide paramter range\r
\r
Energetically most favorable orientations along $[1 1 0]$ direction ...\r
\r
\subsection{C$_I$ next to C$_{\text{s}}$}\r
\r
+% c_i and c_s, capaz98, mattoni2002 (restricted to 110 -110 bond chain)\r
+\r
+\r
\subsection{C$_I$ next to vacancies}\r
\r
\subsection{C$_{\text{s}}$ next to Si self interstitials}\r
projects / lectures / latex.git / commitdiff