\begin{document}\r
\r
%\title{Mobility of Carbon in Silicon -- a first principles study}\r
-\title{Extensive first principles study of carbon defects in silicon}\r
+\title{First principles study of defects in carbon implanted silicon}\r
\author{F. Zirkelbach}\r
\author{B. Stritzker}\r
\affiliation{Experimentalphysik IV, Universit\"at Augsburg, 86135 Augsburg, Germany}\r
\affiliation{Department Physik, Universit\"at Paderborn, 33095 Paderborn, Germany}\r
\r
\begin{abstract}\r
-A first principles investigation of the mobility of carbon interstitials in silicon is presented.\r
-The migration mechanism of a carbon \hkl<1 0 0> interstitial and a silicon \hkl<1 1 0> self-interstitial in otherwise defect-free silicon has been investigated using density functional theory calculations.\r
-Furthermore, the influence of nearby vacancies, another carbon interstitial and substitutional defects as well as silicon self-interstitials has been investigated systematically.\r
+A first principles investigation of the mobility of carbon and silicon interstitials in silicon is presented.\r
+The migration mechanism of a carbon \hkl<1 0 0> interstitial in otherwise defect-free silicon has been investigated using density functional theory calculations.\r
+Furthermore, the influence of a nearby vacancy, another carbon interstitial and a substitutional defect as well as a silicon self-interstitial has been investigated systematically.\r
Interactions of various combinations of defects have been characterized including a couple of selected migration pathways within these configurations.\r
Almost all of the investigated pairs of defects tend to agglomerate allowing for a reduction in strain.\r
The formation of structures involving strong carbon-carbon bonds was found to occur very unlikely.\r
Based on these results conclusions regarding the precipitation mechanism of silicon carbide in bulk silicon are derived and its conformability to experimental findings is discussed.\r
\end{abstract}\r
\r
-\keywords{point defects, migration, interstitials, first principles calculations }\r
-\pacs{ find out later... }\r
+\keywords{point defects, defect clusters, migration, interstitials, ion implantation, first principles calculations}\r
+\pacs{61.72.J-,61.72.Yx,61.72.uj,66.30.J-,79.20.Rf,31.15.A-}\r
\maketitle\r
\r
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However, the process of the formation of SiC precipitates in Si during C implantation is not yet fully understood.\r
Based on experimental high resolution transmission electron microscopy (HREM) studies\cite{werner96,werner97,eichhorn99,lindner99_2,koegler03} it is assumed that incorporated C atoms form C-Si dimers (dumbbells) on regular Si lattice sites.\r
The highly mobile C interstitials agglomerate into large clusters followed by the formation of incoherent 3C-SiC nanocrystallites once a critical size of the cluster is reached.\r
-In contrast, investigations of the precipitation in strained Si$_{1-y}$C$_y$/Si heterostructures formed by molecular beam epitaxy (MBE)\cite{strane94,guedj98} suggest an initial coherent clustering of substitutional instead of interstitial C followed by a loss of coherency once the increasing strain energy surpasses the interfacial energy of an incoherent 3C-SiC precipitate in c-Si.\r
+In contrast, investigations of the precipitation in strained Si$_{1-y}$C$_y$/Si heterostructures formed by molecular beam epitaxy (MBE)\cite{strane94,guedj98} suggest an initial coherent precipitation by an agglomeration of substitutional instead of interstitial C followed by a loss of coherency once the increasing strain energy surpasses the interfacial energy of the incoherent 3C-SiC precipitate and c-Si.\r
These two different mechanisms of precipitation might be attributed to the respective method of fabrication, i.e. whether it occurs inside the Si bulk or on a Si surface.\r
-However, in another IBS study Nejim et al. propose a topotactic transformation remaining structure and orientation likewise based on the formation of substitutional C and a concurrent reaction of the excess Si self-interstitials with further implanted C atoms in the initial state\cite{nejim95}.\r
+However, in another IBS study Nejim et al. propose a topotactic transformation remaining structure and orientation that is likewise based on the formation of substitutional C and a concurrent reaction of the excess Si self-interstitials with further implanted C atoms in the initial state\cite{nejim95}.\r
Solving this controversy and understanding the effective underlying processes will enable significant technological progress in 3C-SiC thin film formation driving the superior polytype for potential applications in high-performance electronic device production\cite{wesch96}.\r
\r
Atomistic simulations offer a powerful tool of investigation providing detailed insight not accessible by experiment.\r
-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,hobler05,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
+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,hobler05,sahli05,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 \hkl[1 1 0] and \hkl[-1 1 0] direction, secondly lacking combinations of C interstitials and, finally, not considering migration barriers giving further information about the probability of defect agglomeration.\r
+However, investigations are, first of all, restricted to interaction chains along the \hkl[1 1 0] and \hkl[-1 1 0] direction, secondly lacking combinations of C interstitials and, finally, not considering migration barriers providing further information on 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
Instead, Capaz et al.\cite{capaz94}, investigating migration pathways of the C$_{\text{i}}$ \hkl<1 0 0> DB, find this defect to be \unit[2.1]{eV} lower in energy than the bond-centered (BC) configuration, which is claimed to constitute a saddle point configuration in the migration path within the \hkl(1 1 0) plane and, thus, interpreted as the barrier of migration for the respective path.\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 $(\unit[0.70-0.87]{eV})$\cite{lindner06,tipping87,song90} for the migration barrier.\r
+Regardless of the rather small correction of \unit[0.3]{eV} due to the spin, the difference we found is much smaller (\unit[0.9]{eV}), which would nicely compare to experimental findings $(\unit[0.70-0.87]{eV})$\cite{lindner06,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} 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$_{\text{i}}$ \hkl[0 0 -1] DB migrates into a C$_{\text{i}}$ \hkl[0 -1 0] DB located at the next neighbored Si lattice site in \hkl[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
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$_{\text{i}}$ \hkl[0 1 -1] into a \hkl[1 1 0] DB configuration located at the next neighbored Si lattice site in \hkl[1 1 -1] direction.\r
+Concerning the mobility of the ground state Si$_{\text{i}}$, an activation energy of \unit[0.67]{eV} was found for the Si$_{\text{i}}$ \hkl[0 1 -1] to \hkl[1 1 0] DB configuration located at the next neighbored Si lattice site in \hkl[1 1 -1] direction.\r
+Further investigations revealed a barrier of \unit[0.94]{eV} for the Si$_{\text{i}}$ \hkl[1 1 0] DB to Si$_{\text{i}}$ H, \unit[0.53]{eV} for the Si$_{\text{i}}$ \hkl[1 1 0] DB to Si$_{\text{i}}$ T and \unit[0.35]{eV} for the Si$_{\text{i}}$ H to Si$_{\text{i}}$ T transition.\r
+The obtained values are within the same order of magnitude than values derived from other ab initio studies\cite{bloechl93,sahli95}.\r
% look for values in literature for neutraly charged Si_i diffusion\r
+% T seems to constitute a saddle point according to migration calculations\r
\r
\subsection{Pairs of C$_{\text{i}}$}\r
\r
\r
% add somewhere: nearly same energies of C_i -> Si_i + C_s, Si_i mig and C_i mig\r
\r
+% add somewhere: controversy c_i vs c_s agglomeration, we suggest both!\r
+\r
These findings allow to draw conclusions on the mechanisms involved in the process of SiC conversion in Si.\r
Agglomeration of C$_{\text{i}}$ is energetically favored and enabled by a low activation energy for migration.\r
Although ion implantation is a process far from thermodynamic equlibrium, which might result in phases not described by the Si/C phase diagram, i.e. a C phase in Si, high activation energies are believed to be responsible for a low probability of the formation of C clusters.\r
Based on these findings conclusions on basic processes involved in the SiC precipitation in bulk Si are drawn.\r
It is concluded that the precipitation process is governed by the formation of C$_{\text{s}}$ already in the initial stages.\r
Agglomeration and rearrangement of C$_{\text{s}}$, however, is only possible by mobile C$_{\text{i}}$, which, thus, needs to be present at the same time.\r
-It is concluded that the precipitation proceeds by a successive occupation of Si lattice sites by C$_{\text{s}}$.\r
-However, rearrangement and agglomeration of these C atoms is only possible by forming acting as a vehicle for ...\r
+Si$_{\text{i}}$ constitutes the vehicle for the rearrangement of C$_{\text{s}}$.\r
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