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+\documentclass[prb,twocolumn,superscriptaddress,a4paper,showkeys,showpacs]{revtex4}\r
+\usepackage{graphicx}\r
+\usepackage{subfigure}\r
+\usepackage{dcolumn}\r
+\usepackage{booktabs}\r
+\usepackage{units}\r
+\usepackage{amsmath}\r
+\usepackage{amsfonts}\r
+\usepackage{amssymb}\r
+\r
+\r
+\begin{document}\r
+\r
+\title{Description of Defects in Carbon implanted Silicon -- a comparison of classical potentials and first principles methods}\r
+\author{F. Zirkelbach} \author{B. Stritzker}\r
+\affiliation{Experimentalphysik IV, Universit\"at Augsburg, D-86153 Augsburg, Germany}\r
+\author{K. Nordlund}\r
+\affiliation{Accelerator Laboratory, University of Helsinki, 00014 Helsinki, Finland}\r
+\author{J. K. N. Lindner}\r
+\affiliation{Experimentelle Physik, Universit\"at Paderborn, 33095 Paderborn, Germany}\r
+\author{W. G. Schmidt} \author{E. Rauls}\r
+\affiliation{Theoretische Physik, Universit\"at Paderborn, 33095 Paderborn, Germany}\r
+\r
+\begin{abstract}\r
+We present a comparative theoretical investigation of carbon interstitials in silicon.\r
+Calculations using classical potentials are put aside first principles density functional theory calculations of the geometries, formation and activation energies of the carbon dumbbell interstitial, showing the importance of a quantum mechanical description of this system.\r
+\end{abstract}\r
+\r
+\keywords{point defects, migration, interstitials, first principles calculations, classical potentials }\r
+\pacs{ find out later... }\r
+\maketitle\r
+\r
+% --------------------------------------------------------------------------------\r
+\section{Introduction}\r
+\r
+%Frank: Idea: description of 3C-SiC-precipitation in C-implanted silicon.\\ \r
+% cite and describe briefly experimental work - why is this material important/better than other SiC). \\ \r
+% Describe the precipitation process in brief.\\ \r
+% Sum up literature where classical potentials have been used (a) successful, and (b) failed. Also add citations of Nordlunds papers. Not only on silicon or SiC!\\\r
+\r
+% there should be a short motivation for the material system!\r
+Silicon carbide (SiC) has a number of remarkable physical and chemical properties.\r
+The wide band gap semiconductor (2.3 eV - 3.3 eV) exhibiting a high breakdown field, saturated electron drift velocity and thermal conductivity in conjunction with its unique thermal and mechanical stability as well as radiation hardness is a suitable material for high-temperature, high-frequency and high-power devices\cite{wesch96}, which are moreover deployable in harsh environments\cite{capano97}.\r
+% there are different polytpes with different properties and 3c-sic in special\r
+SiC, which forms fourfold coordinated covalent bonds, tends to crystallize into many different modifications, which solely differ in the one-dimensional stacking sequence of identical, close-packed SiC bilayers\cite{fischer90}.\r
+Different polytypes exhibit different properties, where the only cubic phase (3C-SiC) shows increased values for the thermal conductivity and breakdown field compared to other polytypes\cite{wesch96}, which is of special interest for highly efficient and high-power electronic device applications.\r
+\r
+% (thin films of) 3c-sic can be produced by ibs\r
+Next to epitaxial layer growth by chemical vapor deposition\cite{powell90} and molecular beam epitaxy\cite{mbe}, ion beam synthesis (IBS) constitutes a promising method to produce 3C-SiC epitaxial layers of high quality in silicon\cite{ibs}.\r
+\r
+\r
+ \r
+\r
+The relevant structures are with $\approx$ 20000 atoms/nanocrystal way too large to be completely be described with high accuracy \r
+quantum mechanical methods. Modelling the processes described above require the use of less accurate methods, like e.g. classical \r
+potentials (Erhard/Albe\cite{albe},Stillinger-Weber\cite{stillinger},...). Whether such potentials are appropriate for the description of the \r
+physical problem has, however, to be verified first by applying both methods to relevant processes that can be treated by both methods. \r
+In this work, we have implemented and compared the applicability of several (?) classical potentials to ab initio results for one \r
+of the most important processes of our original question. \r
+\r
+In the following we will present a comparative investigation of density functional theory (DFT) studies and \r
+classical potential calculations of the structure, energetics and mobility of carbon defects in silicon. \r
+\r
+% --------------------------------------------------------------------------------\r
+\section{Methodology}\r
+% ----- DFT ------\r
+The first-principles DFT calculations were performed with the plane-wave based \r
+Vienna Ab-initio Simulation Package (VASP)\cite{kresse96}. The Kohn-Sham equations were solved \r
+using the generalized-gradient XC-functional approximation proposed by Perdew and \r
+Wang (GGA-PW91)\cite{perdew92}. \r
+The electron-ion interaction was described by the projector-augmented wave (PAW) method\cite{bloechel94,kresse99}. \r
+In the PAW data scalar relativistic corrections are contained. Throughout this work an \r
+energy cut-off of \unit[300]{eV} was used to expand the wave functions into the plane-wave basis. \r
+For the sampling of the Brillouin zone, only the $\Gamma$-point was used. \r
+The defect structures and the migration paths were modelled in cubic supercells containing 216 Si-atoms. Spin polarization has been \r
+fully accounted for. \r
+\r
+% ------ Albe potential ---------\r
+%% Frank: Setup/short description of the potential ?\r
+For the calculations with the classical potentials... \r
+\r
+\r
+\section{Results}\r
+\r
+After ion implantation, carbon interstitials are the most common defects in the silicon sample. Their mobility is the \r
+crucial quantity to be investigated. We thus started our comparative investigations by comparing the stability and the \r
+mobility of an isolated carbon interstitial in silicon bulk in the various possible geometries it can take. \r
+\r
+\subsection{Carbon interstitials in various geometries}\r
+\r
+Several geometries have been calculated to be stable for the carbon interstitial. Fig.\ref{fig:interstitials} shows all these \r
+structures. However, there are some discrepancies between the results from classical potential calculations and those obtained \r
+from first principles. \r
+Table \ref{table:formation} summarizes the formation energies of the interstitial geometries for both methods used in this work \r
+and compares the results to literature values. (...check references for more data, ..) \r
+\r
+% Tables: like in the talk, but add further literature data and give the references/citations (also to bibliography \r
+% at the end!) \r
+%\begin{figure}\r
+%\includegraphics[width=1.0\columnwidth]{models.eps}\r
+%\caption{\label{fig:interstitials} Molecular model of the possible carbon interstitials. }\r
+%\end{figure} \r
+\r
+While the Albe potential predicts ... as stable, DFT does not. ...(further comparisons, trend "too high/low" E-formation,...)... \r
+ Nevertheless, both methods predict the (110) dumb bell configuration to be the most stable... (?) \r
+\r
+\r
+\subsection{Mobility}\r
+A measure for the mobility of the interstitial carbon is the activation energy for the migration path from one stable \r
+position to another. The stable defect geometries have been discussed in the previous subsection. We now investigate \r
+the migration from the most stable structure (...should be named somehow...) on one site of the silicon host lattice to \r
+a neighbored site. \r
+On the lowest energy path (first principles), the carbon atom starts to move along (110)..(check that!)... The center of the line connecting \r
+initial and final structure has been found to be a local minimum and not a saddle point as could be expected. The two \r
+saddle points shortly before and behind this local minimum are slightly displaced out of the (110) plane by ... {\AA}. ..(check that!)..\r
+This path is not surprising -- a similar behavior was e.g. found earlier for the carbon split interstitial \cite{rauls03a} and the phosphorus \r
+interstitial \cite{rauls03b,gerstmann03} in SiC. However, an interesting effect is the change of the spin state from zero at the (110) dumb bell \r
+configuration to one at the local minimum. By this, the energy of the local minimum is lowered by 0.3 eV (... check it!!..). \r
+%\begin{figure}\r
+%\includegraphics[width=1.0\columnwidth]{path-DFT.eps}\r
+%\caption{\label{fig:path-DFT} Energy of the carbon interstitial during migration from ... to ... calculated from first principles. The \r
+% activation energy of 0.9 eV (?) agrees well with experimental findings (0.7-0.9 eV?). }\r
+%\end{figure} \r
+Fig.\ref{fig:path-DFT} shows the energy along this lowest energy migration path. The activation energy of 0.9 eV (?) agrees well \r
+with experimental findings (0.7-0.9 eV?).\r
+\r
+Calculations with the Albe potential yield a different picture. \r
+%\begin{figure}\r
+%\includegraphics[width=1.0\columnwidth]{path-Albe.eps}\r
+%\caption{\label{fig:path-Albe} Energy of the carbon interstitial during migration from ... to ... calculated using the classical potential \r
+% method. Here, the activation energy is 2.2 eV (?). }\r
+%\end{figure} \r
+Fig.\ref{fig:path-Albe} shows the energy along the lowest energy migration path found by this method. The activation energy of 2.2 eV (?) \r
+is way too high to explain the experimental findings (0.7-0.9 eV?). (...further discussion...) \r
+\r
+\section{Discussion}\r
+The first principles results are in good agreement to previous work on this subject \cite{joannopoulos,xyz} (...add some references!...). With an \r
+activation energy of 0.9 eV, the carbon interstitial can be expected to be mobile at temperatures in the range of... (?). \r
+The description of the same processes obviously fails if we use the classical potential method. \r
+Already the geometry of the most stable dumb bell configuration differs considerably from that of the first principles calculated \r
+structure. (..... add description, the two main angles and bond lengths and an explanation...)\r
+Formation energies are throughout too high... (...reason?...)\r
+\r
+A reason for this failure of the classical description is most likely... (cut-off, neglect of quantum mechanical effects,...)\r
+\r
+\r
+\section{Summary}\r
+In summary, we have shown that ab initio calculations are very close to the results expected from experimental data. \r
+Furthermore, they agree well with other theoretical results. (...some results - later...) The classical potentials, however, fail to describe the \r
+selected processes. This has been shown to have two reasons, i.e. the artificial cut-off of the next nearest neighbor \r
+interaction on the one hand, on the other hand the quantum mechanical effects which are crucial in the problem under study. \r
+\r
+% ----------------------------------------------------\r
+\section*{Acknowledgment}\r
+The calculations were done using grants of computer time from the \r
+Paderborn Center for Parallel Computing (PC$^2$) and the \r
+H\"ochstleistungs-Rechenzentrum Stuttgart. The Deutsche \r
+Forschungsgemeinschaft is acknowledged for financial support.\r
+\r
+% --------------------------------- references -------------------\r
+\begin{thebibliography}{99}\r
+\bibitem{kresse96} G. Kresse and J. Furthm\"uller, \r
+ Comput. Mater. Sci. {\bf 6}, 15 (1996). \r
+\bibitem{perdew92} J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh and C. Fiolhais, \r
+ Phys. Rev. B {\bf 46}, 6671 (1992). \r
+\bibitem{ceperley80} D. M. Ceperley and B. J. Alder, \r
+ Phys. Rev. Lett. {\bf 45}, 556 (1980). \r
+\bibitem{perdew81} J. P. Perdew and A. Zunger, \r
+ Phys. Rev. B {\bf 23}, 5048 (1981). \r
+\bibitem{bloechel94} P. E. Bl\"ochl, \r
+ Phys. Rev. B {\bf 50}, 17953 (1994).\r
+\bibitem{kresse99} G. Kresse and D. Joubert, \r
+ Phys. Rev. B {\bf 59}, 1758 (1999).\r
+\bibitem{monk76} H. J. Monkhorst and J. D. Pack, \r
+ Phys. Rev. B {\bf 13}, 5188 (1976). \r
+\bibitem{albe} Albe potential\r
+\bibitem{stillinger} Stillinger-Weber potential \r
+\bibitem{joannopoulos} Joannopoulos\r
+\bibitem{xyz} who else? \r
+\bibitem{rauls03a} E. Rauls, A. Gali, P. De´ak, and Th. Frauenheim, Phys. Rev. B, 68, 155208 (2003).\r
+\bibitem{rauls03b} E. Rauls, U. Gerstmann, H. Overhof, and Th. Frauenheim, Physica B, Vols. 340-342, p. 184-189 (2003). \r
+\bibitem{gerstmann03} U. Gerstmann, E. Rauls, Th. Frauenheim, and H. Overhof, Phys. Rev. B, 67, 205202, (2003).\r
+\r
+\end{thebibliography}\r
+\r
+\r
+\end{document}\r
+\r
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