Results of atomistic simulations aimed at understanding precipitation of the highly attractive wide band gap semiconductor material silicon carbide in silicon are presented.
The study involves a systematic investigation of intrinsic and carbon-related defects as well as defect combinations and defect migration by both, quantum-mechanical first-principles as well as empirical potential methods.
Comparing formation and activation energies, ground-state structures of defects and defect combinations as well as energetically favorable agglomeration of defects are predicted.
-Moreover, the highly accurate {\em ab initio} calculations unveil limitations of the analytical method based on a Tersoff-like bond order potential.
+Moreover, accurate {\em ab initio} calculations unveil limitations of the analytical method based on a Tersoff-like bond order potential.
A work-around is proposed in order to subsequently apply the highly efficient technique on large structures not accessible by first-principles methods.
The outcome of both types of simulation provides a basic microscopic understanding of defect formation and structural evolution particularly at non-equilibrium conditions strongly deviated from the ground state as commonly found in SiC growth processes.
-A possible precipitation mechanism, which conforms well to experimental findings clarifying contradictory views present in the literature is outlined.
+A possible precipitation mechanism, which conforms well to experimental findings and clarifies contradictory views present in the literature is outlined.
}
\maketitle
The plane-wave based Vienna {\em ab initio} simulation package (VASP) \cite{kresse96} is used for the first-principles calculations based on density functional theory (DFT).
Exchange and correlation is taken into account by the generalized-gradient approximation \cite{perdew86,perdew92}.
-Norm-conserving ultra-soft pseudopotentials \cite{hamann79} as implemented in VASP \cite{vanderbilt90} are used to describe the electron-ion interaction.
+Norm-con\-ser\-ving ultra-soft pseudopotentials \cite{hamann79} as implemented in VASP \cite{vanderbilt90} are used to describe the electron-ion interaction.
A kinetic energy cut-off of \unit[300]{eV} is employed.
Defect structures and migration paths were modelled in cubic supercells with a side length of \unit[1.6]{nm} containing $216$ Si atoms.
These structures are large enough to restrict sampling of the Brillouin zone to the $\Gamma$-point and formation energies and structures are reasonably converged.
\section{Mobility of the carbon defect}
-The migration barriers of the ground-state C defect are investigated by both, first-principles as well as the empirical method, their migration pathways shown in Fig.~\ref{fig:mig}.
+The migration barriers of the ground-state C defect are investigated by both, first-principles as well as the empirical method.
+The migration pathways are shown in Fig.~\ref{fig:mig}.
\begin{figure}
\subfloat[Transition path obtained by first-principles methods.]{%
In contrast, the empirical approach does not reproduce the same path.
Related to the above mentioned instability of the BC configuration, a pathway involving the C$_{\text{i}}$ \hkl<1 1 0> DB as an intermediate configuration must be considered most plausible \cite{zirkelbach11}.
Considering a two step diffusion process and assuming equal preexponential factors, a total effective migration barrier 3.5 times higher than the one obtained by first-principles methods is obtained.
-A more detailed description can be found in previous studies \cite{zirkelbach10,zirkelbach11}.
+A more detailed description can be found in previous studies \cite{zirkelbach11,zirkelbach10}.
\section{Defect combinations}
The C atom moves towards the vacant site forming a stable C$_{\text{s}}$ configuration resulting in the release of a huge amount of energy.
The second most favorable configuration is accomplished for a V located right next to the Si atom of the DB structure.
This is due to the reduction of compressive strain of the Si DB atom and its two upper Si neighbors present in the isolated C$_{\text{i}}$ DB configuration.
-This configuration is followed by the structure, in which the V is created at one of the neighbored lattice site below one of the Si atoms that are bound to the C atom of the initial DB.
+This configuration is followed by the structure, in which the V is created at one of the neighbored lattice sites below one of the Si atoms that are bound to the C atom of the initial DB.
Relaxed structures of the latter two defect combinations are shown in the bottom left of Fig.~\ref{fig:314-539} and \ref{fig:059-539} respectively together with their energetics during transition into the ground state.
\begin{figure}
\subfloat[V created right next to the Si atom of the initial DB. Activation energy: {\unit[0.1]{eV}}.]{%
Considering the small activation energies, a high probability for the formation of stable C$_{\text{s}}$ must be concluded.
In addition, it is instructive to investigate combinations of C$_{\text{s}}$ and Si$_{\text{i}}$, which can be created in IBS by highly energetic C atoms that kick out a Si atom from its lattice site, resulting in a Si self-interstitial accompanied by a vacant site, which might get occupied by another C atom that lost almost all of its kinetic energy.
-Provided that the first C atom has enough kinetic energy to escape the affected region, the remaining C$_{\text{s}}$-Si$_{\text{i}}$ pair can be described as a separated defect complex.
-Considering the energetically most favorable Si$_{\text{i}}$ defect, i.e. the Si$_{\text{i}}$ \hkl<1 1 0> DB, the most favorable combination is found for C$_{\text{s}}$ located right next to that DB enabling the largest possible reduction of strain.
-The configuration and the transition into the ground-state configuration, i.e. the C$_{\text{i}}$ hkl<1 0 0> DB is displayed in Fig.~\ref{fig:162-097}
+The most favorable configuration, which is C$_{\text{s}}$ located right next to the ground-state Si$_{\text{i}}$ defect, i.e.\ the Si$_{\text{i}}$ \hkl<1 1 0> DB, and the transition of this structure into the ground-state configuration, i.e. the C$_{\text{i}}$ \hkl<1 0 0> DB is displayed in Fig.~\ref{fig:162-097}
\begin{figure}
\includegraphics[width=\columnwidth]{162-097.ps}
\caption{Transition of a \hkl[1 1 0] Si$_{\text{i}}$ DB next to C$_{\text{s}}$ (right) into the C$_{\text{i}}$ \hkl[0 0 -1] DB configuration (left).}
\label{fig:162-097}
\end{figure}
Due to the low barrier of \unit[0.12]{eV}, the C$_{\text{i}}$ \hkl<1 0 0> DB configuration is very likely to occur.
-However, the barrier of only \unit[0.77]{eV} for the reverse process indicates a high probability for the the formation of C$_{\text{s}}$ and a Si$_{\text{i}}$ DB out of the ground state, which must be considered to be activated without much effort either thermally or by introduced energy of the implantation process.
+However, the barrier of only \unit[0.77]{eV} for the reverse process indicates the possibility to form a C$_{\text{s}}$ and Si$_{\text{i}}$ DB out of the ground state activated without much effort either thermally or by introduced energy of the implantation process.
\begin{figure}
\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. 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}
-Furthermore, the interaction strength, i.e. the absolute value of the binding energy, quickly drops to zero with increasing separation distance as can be seen in Fig.~\ref{fig:dc_si-s}.
-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.
+Furthermore, the interaction strength quickly drops to zero with increasing separation distance as can be seen in Fig.~\ref{fig:dc_si-s}.
+The interaction of the defects is well approximated by a Lennard-Jones (LJ) 6-12 potential.
+Unable to model possible positive values of the binding energy, i.e. unfavorable configurations, 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 LJ fit estimates almost zero interaction already at \unit[0.5-0.6]{nm}, indicating a low interaction capture radius of the defect pair.
In IBS separations exceeding this capture radius are easily produced.
For these reasons, it must be concluded that configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ instead of the thermodynamically stable C$_{\text{i}}$ \hkl<1 0 0> DB play a decisive role in IBS, a process far from equilibrium.
Results of the MD simulations at \unit[450]{$^{\circ}$C}, an operative and efficient temperature in IBS \cite{lindner01}, indicate the formation of C$_{\text{i}}$ \hkl<1 0 0> DBs if C is inserted into the total simulation volume.
However, no agglomeration is observed within the simulated time, which was increased up to several nanoseconds.
-To overcome the drastically overestimated migration barriers of the C defect, which hamper C agglomeration, the simulation temperature is successively increased up to \unit[2050]{$^{\circ}$C}.
-Fig.~\ref{fig:tot} shows the resulting radial distribution function of Si-C bonds for various elevated temperatures.
+This is attributed to the drastically overestimated migration barrier of the C defect, which hampers C agglomeration.
+To overcome this obstacle, the simulation temperature is successively increased up to \unit[2050]{$^{\circ}$C}.
+Fig.~\ref{fig:tot} shows the resulting radial distribution functions of Si-C bonds for various elevated temperatures.
\begin{figure}
\includegraphics[width=\columnwidth]{tot_pc_thesis.ps}
\caption{Radial distribution function for Si-C pairs for C insertion at various elevated temperatures. Si-C distances of a single C$_{\text{s}}$ defect configuration are plotted.}
\label{fig:tot}
\end{figure}
-A transformation from a structure dominated by C$_{\text{i}}$ into a C$_{\text{s}}$ dominated structure with increasing temperature can clearly be observed if compared with the radial distribution of C$_{\text{s}}$ in c-Si.
-Thus, the C$_{\text{s}}$ defect and, thus, stretched coherent structures of SiC, must be considered to play an important role in the IBS at elevated temperatures.
-This, in fact, is in agreement with experimental findings of annealing experiments \cite{strane94,nejim95,serre95} and also with the previous DFT results, which suggest C$_{\text{s}}$ to be involved at higher temperatures and in conditions out of thermodynamic equilibrium.
+Although not intended, a transformation from a structure dominated by C$_{\text{i}}$ into a structure consisting of C$_{\text{s}}$ with increasing temperature can clearly be observed if compared with the radial distribution of C$_{\text{s}}$ in c-Si.
+
+Thus, the C$_{\text{s}}$ defect and resulting stretched coherent structures of SiC must be considered to play an important role in the IBS at elevated temperatures.
+This, in fact, satisfies experimental findings of annealing experiments \cite{strane94,nejim95,serre95} as well as previous DFT results, which suggest C$_{\text{s}}$ to be involved at higher temperatures and in conditions that deviate the system out of the thermodynamic ground state.
\section{Summary and discussion}
Although investigations of defect combinations show the agglomeration of C$_{\text{i}}$ DBs to be energetically most favorable, configurations that may arise during IBS were presented, their dynamics indicating C$_{\text{s}}$ to play an important role particularly at high temperatures.
-This is supported by the empirical MD results, which show an increased participation of C$_{\text{s}}$ at increased temperatures that allow the system to deviate from the ground state.
+This is supported by the classical MD results, which show an increased participation of C$_{\text{s}}$ at increased temperatures that allow the system to deviate from the ground state.
Based on these findings, it is concluded that in IBS at elevated temperatures, SiC conversion takes place by an initial agglomeration of C$_{\text{s}}$ into coherent, tensily strained structures of SiC followed by precipitation into incoherent SiC once a critical size is reached and the increasing strain energy of the coherent structure surpasses the interfacial energy of the incoherent precipitate.
Rearrangement of stable C$_{\text{s}}$ is enabled by excess Si$_{\text{i}}$, which not only acts as a vehicle for C but also as a supply of Si atoms needed elsewhere to form the SiC structure and to reduce possible strain at the interface of coherent SiC precipitates and the Si host.
We gratefully acknowledge financial support by the Bayerische Forschungsstiftung (Grant No. DPA-61/05) and the Deutsche Forschungsgemeinschaft (Grant No. DFG SCHM 1361/11).
\end{acknowledgement}
-\bibliography{../../bibdb/bibdb}{}
-\bibliographystyle{pss.bst}
+%\bibliography{../../bibdb/bibdb}{}
+%\bibliographystyle{pss.bst}
+
+
+\providecommand{\WileyBibTextsc}{}
+\let\textsc\WileyBibTextsc
+\providecommand{\othercit}{}
+\providecommand{\jr}[1]{#1}
+\providecommand{\etal}{~et~al.}
+
+
+\begin{thebibliography}{[10]}
+
+\bibitem{edgar92}% article
+ \textsc{J.\,H. Edgar}\iffalse Prospects for device implementation of wide band
+ gap semiconductors\fi,
+ \jr{J. Mater. Res.} \textbf{7}(January), 235 (1992).
+
+
+\bibitem{capano97}% article
+ \textsc{M.\,A. Capano} and \textsc{R.\,J. Trew}\iffalse Silicon carbide
+ electronic materials and devices\fi,
+ \jr{MRS Bull.} \textbf{22}(3), 19--22 (1997).
+
+
+\othercit
+\bibitem{park98}% book
+ \textsc{Y.\,S. Park},
+Si{C} Materials and Devices (Academic Press, San Diego, 1998).
+
+
+\bibitem{borders71}% article
+ \textsc{J.\,A. Borders}, \textsc{S.\,T. Picraux}, and
+ \textsc{W.~Beezhold}\iffalse {FORMATION} {OF} si{C} {IN} {SILICON} {BY} {ION}
+ {IMPLANTATION}\fi,
+ \jr{Appl. Phys. Lett.} \textbf{18}(11), 509--511 (1971).
+
+
+\bibitem{lindner01}% article
+ \textsc{J.\,K.\,N. Lindner}\iffalse Ion beam synthesis of buried si{C} layers
+ in silicon: Basic physical processes\fi,
+ \jr{Nucl. Instrum. Methods Phys. Res. B} \textbf{178}(1-4), 44--54 (2001).
+
+
+\othercit
+\bibitem{werner96}% inproceedings
+ \textsc{P.~Werner}, \textsc{R.~K{\"{o}}gler}, \textsc{W.~Skorupa}, and
+ \textsc{D.~Eichler},
+{TEM} investigation of {C}-si defects in carbon implanted silicon,
+ in: Proceedings of the 11th International Conference on Ion Implantation
+ Technology., (June 1996), pp.\,675--678.
+
+
+\bibitem{lindner99_2}% article
+ \textsc{J.\,K.\,N. Lindner} and \textsc{B.~Stritzker}\iffalse Mechanisms in
+ the ion beam synthesis of si{C} layers in silicon\fi,
+ \jr{Nucl. Instrum. Methods Phys. Res. B} \textbf{148}(1-4), 528--533 (1999).
+
+
+\bibitem{koegler03}% article
+ \textsc{R.~K{\"{o}}gler}, \textsc{F.~Eichhorn}, \textsc{J.\,R. Kaschny},
+ \textsc{A.~M{\"{u}}cklich}, \textsc{H.~Reuther}, \textsc{W.~Skorupa},
+ \textsc{C.~Serre}, and \textsc{A.~Perez-Rodriguez}\iffalse Synthesis of
+ nano-sized si{C} precipitates in si by simultaneous dual-beam implantation of
+ {C}+ and si+ ions\fi,
+ \jr{Appl. Phys. A} \textbf{76}(March), 827--835 (2003).
+
+
+\bibitem{strane94}% article
+ \textsc{J.\,W. Strane}, \textsc{H.\,J. Stein}, \textsc{S.\,R. Lee},
+ \textsc{S.\,T. Picraux}, \textsc{J.\,K. Watanabe}, and \textsc{J.\,W.
+ Mayer}\iffalse Precipitation and relaxation in strained si[sub 1 - y]{C}[sub
+ y]/si heterostructures\fi,
+ \jr{J. Appl. Phys.} \textbf{76}(6), 3656--3668 (1994).
+
+
+\bibitem{nejim95}% article
+ \textsc{A.~Nejim}, \textsc{P.\,L.\,F. Hemment}, and
+ \textsc{J.~Stoemenos}\iffalse Si{C} buried layer formation by ion beam
+ synthesis at 950 [degree]{C}\fi,
+ \jr{Appl. Phys. Lett.} \textbf{66}(20), 2646--2648 (1995).
+
+
+\bibitem{serre95}% article
+ \textsc{C.~Serre}, \textsc{A.~P\'{e}rez-Rodr\'{\i}guez},
+ \textsc{A.~Romano-Rodr\'{\i}guez}, \textsc{J.\,R. Morante},
+ \textsc{R.~K{\"{o}}gler}, and \textsc{W.~Skorupa}\iffalse Spectroscopic
+ characterization of phases formed by high-dose carbon ion implantation in
+ silicon\fi,
+ \jr{J. Appl. Phys.} \textbf{77}(7), 2978--2984 (1995).
+
+
+\bibitem{bar-yam84}% article
+ \textsc{Y.~Bar-Yam} and \textsc{J.\,D. Joannopoulos}\iffalse Barrier to
+ migration of the silicon self-interstitial\fi,
+ \jr{Phys. Rev. Lett.} \textbf{52}(13), 1129--1132 (1984).
+
+
+\bibitem{car84}% article
+ \textsc{R.~Car}, \textsc{P.\,J. Kelly}, \textsc{A.~Oshiyama}, and
+ \textsc{S.\,T. Pantelides}\iffalse Microscopic theory of atomic diffusion
+ mechanisms in silicon\fi,
+ \jr{Phys. Rev. Lett.} \textbf{52}(20), 1814--1817 (1984).
+
+
+\bibitem{bloechl93}% article
+ \textsc{P.\,E. Bl{\"o}chl}, \textsc{E.~Smargiassi}, \textsc{R.~Car},
+ \textsc{D.\,B. Laks}, \textsc{W.~Andreoni}, and \textsc{S.\,T.
+ Pantelides}\iffalse First-principles calculations of self-diffusion constants
+ in silicon\fi,
+ \jr{Phys. Rev. Lett.} \textbf{70}(16), 2435--2438 (1993).
+
+
+\bibitem{tang97}% article
+ \textsc{M.~Tang}, \textsc{L.~Colombo}, \textsc{J.~Zhu}, and \textsc{T.\,D.
+ de\,la Rubia}\iffalse Intrinsic point defects in crystalline silicon:
+ Tight-binding molecular dynamics studies of self-diffusion,
+ interstitial-vacancy recombination, and formation volumes\fi,
+ \jr{Phys. Rev. B} \textbf{55}(21), 14279--14289 (1997).
+
+
+\bibitem{leung99}% article
+ \textsc{W.\,K. Leung}, \textsc{R.\,J. Needs}, \textsc{G.~Rajagopal},
+ \textsc{S.~Itoh}, and \textsc{S.~Ihara}\iffalse Calculations of silicon
+ self-interstitial defects\fi,
+ \jr{Phys. Rev. Lett.} \textbf{83}(12), 2351--2354 (1999).
+
+
+\bibitem{al-mushadani03}% article
+ \textsc{O.\,K. Al-Mushadani} and \textsc{R.\,J. Needs}\iffalse Free-energy
+ calculations of intrinsic point defects in silicon\fi,
+ \jr{Phys. Rev. B} \textbf{68}(23), 235205 (2003).
+
+
+\bibitem{hobler05}% article
+ \textsc{G.~Hobler} and \textsc{G.~Kresse}\iffalse Ab initio calculations of
+ the interaction between native point defects in silicon\fi,
+ \jr{Mater. Sci. Eng., B} \textbf{124-125}, 368--371 (2005),
+EMRS 2005, Symposium D - Materials Science and Device Issues for Future
+ Technologies.
+
+
+\bibitem{sahli05}% article
+ \textsc{B.~Sahli} and \textsc{W.~Fichtner}\iffalse Ab initio molecular
+ dynamics simulation of self-interstitial diffusion in silicon\fi,
+ \jr{Phys. Rev. B} \textbf{72}(24), 245210 (2005).
+
+
+\bibitem{posselt08}% article
+ \textsc{M.~Posselt}, \textsc{F.~Gao}, and \textsc{H.~Bracht}\iffalse
+ Correlation between self-diffusion in si and the migration mechanisms of
+ vacancies and self-interstitials: An atomistic study\fi,
+ \jr{Phys. Rev. B} \textbf{78}(3), 035208 (2008).
+
+
+\bibitem{ma10}% article
+ \textsc{S.~Ma} and \textsc{S.~Wang}\iffalse Ab initio study of self-diffusion
+ in silicon over a wide temperature range: Point defect states and migration
+ mechanisms\fi,
+ \jr{Phys. Rev. B} \textbf{81}(19), 193203 (2010).
-\end{document}
+\bibitem{tersoff90}% article
+ \textsc{J.~Tersoff}\iffalse Carbon defects and defect reactions in silicon\fi,
+ \jr{Phys. Rev. Lett.} \textbf{64}(15), 1757--1760 (1990).
+
+
+\bibitem{dal_pino93}% article
+ \textsc{A.~{Dal Pino}}, \textsc{A.\,M. Rappe}, and \textsc{J.\,D.
+ Joannopoulos}\iffalse Ab initio investigation of carbon-related defects in
+ silicon\fi,
+ \jr{Phys. Rev. B} \textbf{47}(19), 12554--12557 (1993).
+
+
+\bibitem{capaz94}% article
+ \textsc{R.\,B. Capaz}, \textsc{A.~{Dal Pino}}, and \textsc{J.\,D.
+ Joannopoulos}\iffalse Identification of the migration path of interstitial
+ carbon in silicon\fi,
+ \jr{Phys. Rev. B} \textbf{50}(11), 7439--7442 (1994).
+
+
+\bibitem{burnard93}% article
+ \textsc{M.\,J. Burnard} and \textsc{G.\,G. DeLeo}\iffalse Interstitial carbon
+ and the carbon-carbon pair in silicon: Semiempirical electronic-structure
+ calculations\fi,
+ \jr{Phys. Rev. B} \textbf{47}(16), 10217--10225 (1993).
+
+
+\bibitem{leary97}% article
+ \textsc{P.~Leary}, \textsc{R.~Jones}, \textsc{S.~{\"O}berg}, and
+ \textsc{V.\,J.\,B. Torres}\iffalse Dynamic properties of interstitial carbon
+ and carbon-carbon pair defects in silicon\fi,
+ \jr{Phys. Rev. B} \textbf{55}(4), 2188--2194 (1997).
+
+
+\bibitem{capaz98}% article
+ \textsc{R.\,B. Capaz}, \textsc{A.~{Dal Pino}}, and \textsc{J.\,D.
+ Joannopoulos}\iffalse Theory of carbon-carbon pairs in silicon\fi,
+ \jr{Phys. Rev. B} \textbf{58}(15), 9845--9850 (1998).
+
+
+\bibitem{mattoni2002}% article
+ \textsc{A.~Mattoni}, \textsc{F.~Bernardini}, and
+ \textsc{L.~Colombo}\iffalse Self-interstitial trapping by carbon complexes in
+ crystalline silicon\fi,
+ \jr{Phys. Rev. B} \textbf{66}(19), 195214 (2002).
+
+
+\bibitem{kresse96}% article
+ \textsc{G.~Kresse} and \textsc{J.~Furthm{\"{u}}ller}\iffalse Efficiency of
+ ab-initio total energy calculations for metals and semiconductors using a
+ plane-wave basis set\fi,
+ \jr{Comput. Mater. Sci.} \textbf{6}(1), 15--50 (1996).
+
+
+\bibitem{perdew86}% article
+ \textsc{J.\,P. Perdew} and \textsc{Y.~Wang}\iffalse Accurate and simple
+ density functional for the electronic exchange energy: Generalized gradient
+ approximation\fi,
+ \jr{Phys. Rev. B} \textbf{33}(12), 8800--8802 (1986).
+
+
+\bibitem{perdew92}% article
+ \textsc{J.\,P. Perdew}, \textsc{J.\,A. Chevary}, \textsc{S.\,H. Vosko},
+ \textsc{K.\,A. Jackson}, \textsc{M.\,R. Pederson}, \textsc{D.\,J. Singh},
+ and \textsc{C.~Fiolhais}\iffalse Atoms, molecules, solids, and surfaces:
+ Applications of the generalized gradient approximation for exchange and
+ correlation\fi,
+ \jr{Phys. Rev. B} \textbf{46}(11), 6671--6687 (1992).
+
+
+\bibitem{hamann79}% article
+ \textsc{D.\,R. Hamann}, \textsc{M.~Schl{\"u}ter}, and
+ \textsc{C.~Chiang}\iffalse Norm-conserving pseudopotentials\fi,
+ \jr{Phys. Rev. Lett.} \textbf{43}(20), 1494--1497 (1979).
+
+
+\bibitem{vanderbilt90}% article
+ \textsc{D.~Vanderbilt}\iffalse Soft self-consistent pseudopotentials in a
+ generalized eigenvalue formalism\fi,
+ \jr{Phys. Rev. B} \textbf{41}(11), 7892--7895 (1990).
+
+
+\bibitem{kaukonen98}% article
+ \textsc{M.~Kaukonen}, \textsc{P.\,K. Sitch}, \textsc{G.~Jungnickel},
+ \textsc{R.\,M. Nieminen}, \textsc{S.~P{\"o}ykk{\"o}}, \textsc{D.~Porezag},
+ and \textsc{T.~Frauenheim}\iffalse Effect of {N} and {B} doping on the
+ growth of {CVD} diamond $(100):{H}(2\ifmmode\times\else\texttimes\fi{}1)$
+ surfaces\fi,
+ \jr{Phys. Rev. B} \textbf{57}(16), 9965--9970 (1998).
+
+
+\bibitem{albe_sic_pot}% article
+ \textsc{P.~Erhart} and \textsc{K.~Albe}\iffalse Analytical potential for
+ atomistic simulations of silicon, carbon, and silicon carbide\fi,
+ \jr{Phys. Rev. B} \textbf{71}(3), 035211 (2005).
+
+
+\bibitem{berendsen84}% article
+ \textsc{H.\,J.\,C. Berendsen}, \textsc{J.\,P.\,M. Postma}, \textsc{W.\,F.
+ van Gunsteren}, \textsc{A.~DiNola}, and \textsc{J.\,R. Haak}\iffalse
+ Molecular dynamics with coupling to an external bath\fi,
+ \jr{J. Chem. Phys.} \textbf{81}(8), 3684--3690 (1984).
+
+
+\bibitem{verlet67}% article
+ \textsc{L.~Verlet}\iffalse Computer {"}experiments{"} on classical fluids.
+ {I}. thermodynamical properties of lennard-jones molecules\fi,
+ \jr{Phys. Rev.} \textbf{159}(1), 98 (1967).
+
+
+\bibitem{watkins76}% article
+ \textsc{G.\,D. Watkins} and \textsc{K.\,L. Brower}\iffalse {EPR} observation
+ of the isolated interstitial carbon atom in silicon\fi,
+ \jr{Phys. Rev. Lett.} \textbf{36}(22), 1329--1332 (1976).
+
+
+\bibitem{song90}% article
+ \textsc{L.\,W. Song} and \textsc{G.\,D. Watkins}\iffalse {EPR} identification
+ of the single-acceptor state of interstitial carbon in silicon\fi,
+ \jr{Phys. Rev. B} \textbf{42}(9), 5759--5764 (1990).
+
+
+\bibitem{lindner06}% article
+ \textsc{J.\,K.\,N. Lindner}, \textsc{M.~H{\"a}berlen},
+ \textsc{G.~Thorwarth}, and \textsc{B.~Stritzker}\iffalse On the balance
+ between ion beam induced nanoparticle formation and displacive precipitate
+ resolution in the {C}-si system\fi,
+ \jr{Mater. Sci. Eng., C} \textbf{26}(5-7), 857--861 (2006),
+Current Trends in Nanoscience - from Materials to Applications.
+
+
+\bibitem{tipping87}% article
+ \textsc{A.\,K. Tipping} and \textsc{R.\,C. Newman}\iffalse The diffusion
+ coefficient of interstitial carbon in silicon\fi,
+ \jr{Semicond. Sci. Technol.} \textbf{2}(5), 315--317 (1987).
+
+
+\bibitem{zirkelbach11}% article
+ \textsc{F.~Zirkelbach}, \textsc{B.~Stritzker}, \textsc{K.~Nordlund},
+ \textsc{J.\,K.\,N. Lindner}, \textsc{W.\,G. Schmidt}, and
+ \textsc{E.~Rauls}\iffalse Combined \textit{ab initio} and classical potential
+ simulation study on silicon carbide precipitation in silicon\fi,
+ \jr{Phys. Rev. B} \textbf{84}(August), 064126 (2011).
+
+
+\bibitem{zirkelbach10}% article
+ \textsc{F.~Zirkelbach}, \textsc{B.~Stritzker}, \textsc{K.~Nordlund},
+ \textsc{J.\,K.\,N. Lindner}, \textsc{W.\,G. Schmidt}, and
+ \textsc{E.~Rauls}\iffalse Defects in carbon implanted silicon calculated by
+ classical potentials and first-principles methods\fi,
+ \jr{Phys. Rev. B} \textbf{82}(9), 094110 (2010).
+
+
+\end{thebibliography}
+
+
+\end{document}
projects / lectures / latex.git / blobdiff