Silicon carbide (SiC) has a number of remarkable physical and chemical properties that make it a promising new material in various fields of applications.
The high electron mobility and saturation drift velocity as well as the high band gap and breakdown field in conjunction with its unique thermal stability and conductivity unveil SiC as the ideal candidate for high-power, high-frequency and high-temperature electronic and optoelectronic devices exceeding conventional silicon based solutions \cite{wesch96,morkoc94,casady96,capano97,pensl93}.
-Due to the large Si--C bonding energy SiC is a hard and chemical inert material suitable for applications under extreme conditions and capable for \aclp{MEMS} (\acs{MEMS}), both as structural material and as a coating layer \cite{sarro00,park98}.
+Due to the large Si--C bonding energy SiC is a hard and chemical inert material suitable for applications under extreme conditions and capable for microelectromechanical systemis, both as structural material and as a coating layer \cite{sarro00,park98}.
Its radiation hardness allows the operation as a first wall material in nuclear reactors \cite{giancarli98} and as electronic devices in space \cite{capano97}.
The realization of silicon carbide based applications demands for reasonable sized wafers of high crystalline quality.
A two-temperature implantation technique was proposed to achieve single crytalline SiC layers and a sharp SiC/Si interface \cite{lindner99,lindner99_2,lindner01,lindner02}.
Although high-quality SiC can be achieved by means of IBS the precipitation mechanism is not yet fully understood.
-High resolution transmisson electron microscopy (HRTEM) studies indicate the formation of C-Si interstitial complexes sharing conventional silicon lattice sites (C-Si dumbbells) during the implantation of carbon in silicon.
+High resolution transmisson electron microscopy studies indicate the formation of C-Si interstitial complexes sharing conventional silicon lattice sites (C-Si dumbbells) during the implantation of carbon in silicon.
These C-Si dumbbells agglomerate and once a critical radius is reached, the topotactic transformation into a SiC precipitate occurs \cite{werner97,lindner01}.
A better understanding of the supposed SiC conversion mechanism and related carbon-mediated effects in silicon will enable significant technological progress in SiC thin film formation on the one hand and likewise offer perspectives for processes which rely upon prevention of precipitation events for improved silicon based devices on the other hand.
-Implanted carbon is known to suppress transient enhanced diffusion (TED) of dopant species like boron or phosphorus in the annealing step \cite{cowern96} which can be exploited to create shallow p-n junctions in submicron technologies.
+Implanted carbon is known to suppress transient enhanced diffusion of dopant species like boron or phosphorus in the annealing step \cite{cowern96} which can be exploited to create shallow p-n junctions in submicron technologies.
Si self-interstitials (Si$_{\text{i}}$), known as the transport vehicles for dopants \cite{fahey89,stolk95}, get trapped by reacting with the carbon atoms \cite{stolk97}.
Furthermore, carbon incorporated in silicon is being used to fabricate strained silicon \cite{strane94,strane96,osten99} utilized in semiconductor industry for increased charge carrier mobilities in silicon \cite{chang05,osten97} as well as to adjust its band gap \cite{soref91,kasper91}.
The intention of this work is to contribute to the understanding of C in Si by means of atomistic simulations targeted on the task to elucidate the SiC conversion mechanism in silicon.
The outline of this work is as follows:
-In chapter ...
-
+In chapter \ref{chapter:sic_rev} a review of the Si/C compound is given including the very central discussion on two controversial precipitation mechanisms present in literature in section \ref{section:assumed_prec}.
+Chapter \ref{chapter:basics} introduces some basics and internals of the utilized atomistic simulations as well as special methods of application.
+Details of the simulation and associated test calculations are presented in chapter \ref{chapter:simulation}.
+In chapter \ref{chapter:defects} results of investigations of single defect configurations, structures of comnbinations of two individual defects as well as some selected diffusion pathways in silicon are shown.
+More complex systems aiming to model the transformation of C incorporated in bulk Si into a SiC nucleus are examined in chapter \ref{chapter:md}.
+Finally a summary and some concluding remarks are given in chapter \ref{chapter:summary}.
The phase diagram of the C/Si system is shown in Fig.~\ref{fig:sic:si-c_phase}.
In the solid state the stoichiometric composition of silicon and carbon termed silicon carbide (SiC) is the only chemical stable compound in the C/Si system \cite{scace59}.
-\begin{figure}[ht]
+\begin{figure}[t]
\begin{center}
\includegraphics[width=12cm]{si-c_phase.eps}
\end{center}
Although the local order of Si and C next neighbour atoms characterized by the tetrahedral bonding is the same, more than 250 different types of structures called polytypes of SiC exist \cite{fischer90}.
The polytypes differ in the one-dimensional stacking sequence of identical, close-packed SiC bilayers.
Each SiC bilayer can be situated in one of three possible positions (abbreviated a, b or c) with respect to the lattice while maintaining the tetrahedral bonding scheme of the crystal.
-\begin{figure}[ht]
+\begin{figure}[t]
\begin{center}
-\includegraphics[width=12cm]{polytypes.eps}
+\includegraphics[width=10cm]{polytypes.eps}
\end{center}
\caption{Stacking sequence of SiC bilayers of the most common polytypes of SiC (from left to right): 3C, 2H, 4H and 6H.}
\label{fig:sic:polytypes}
\end{figure}
Fig.~\ref{fig:sic:polytypes} shows the stacking sequence of the most common and technologically most important SiC polytypes, which are the cubic (3C) and hexagonal (2H, 4H and 6H) polytypes.
-\begin{table}[ht]
+\begin{table}[t]
\begin{center}
\begin{tabular}{l c c c c c c}
\hline
In contrast to its hexagonal counterparts 3C-SiC exhibits isotropic mechanical and electronic properties.
Additionally the smaller band gap is expected to be favorable concerning the interface state density in MOSFET devices fabricated on 3C-SiC.
Thus the cubic phase is most effective for highly efficient high-performance electronic devices.
-\begin{figure}[ht]
+\begin{figure}[t]
\begin{center}
-\includegraphics[width=7cm]{sic_unit_cell.eps}
+\includegraphics[width=0.35\columnwidth]{sic_unit_cell.eps}
\end{center}
\caption{3C-SiC unit cell. Yellow and grey spheres correpsond to Si and C atoms respectively. Covalent bonds are illustrated by blue lines.}
\label{fig:sic:unit_cell}
To form a narrow, box-like density profile of oriented SiC nanocrystals \unit[93]{\%} of the total dose of \unit[$8.5\cdot 10^{17}$]{cm$^{-2}$} is implanted at \unit[500]{$^{\circ}$C}.
The remaining dose is implanted at \unit[250]{$^{\circ}$C}, which leads to the formation of amorphous zones above and below the SiC precipitate layer and the desctruction of SiC nanocrystals within these zones.
After annealing for \unit[10]{h} at \unit[1250]{$^{\circ}$C} a homogeneous, stoichiometric SiC layer with sharp interfaces is formed.
+Fig. \ref{fig:sic:hrem_sharp} shows the respective \ac{HREM} micrographs.
+\begin{figure}[t]
+\begin{center}
+\includegraphics[width=0.6\columnwidth]{ibs_3c-sic.eps}
+\end{center}
+\caption{Bright field (a) and \hkl(1 1 1) SiC dark field (b) cross-sectional TEM micrographs of the buried SiC layer in Si created by the two-temperature implantation technique and subsequent annealing as explained in the text \cite{lindner99_2}. The inset shows a selected area diffraction pattern of the buried layer.}
+\label{fig:sic:hrem_sharp}
+\end{figure}
To summarize, by understanding some basic processes, \ac{IBS} nowadays has become a promising method to form thin SiC layers of high quality exclusively of the 3C polytype embedded in and epitaxially aligned to the Si host featuring a sharp interface.
Due to the high areal homogeneity achieved in \ac{IBS}, the size of the layers is only limited by the width of the beam-scanning equipment used in the implantation system as opposed to deposition techniques, which have to deal with severe wafer bending.
The precipitates with diamateres between \unit[2]{nm} and \unit[5]{nm} are incorporated in the Si matrix without any remarkable strain fields, which is explained by the nearly equal atomic density of C-Si agglomerates and the SiC unit cell.
Implantations at \unit[500]{$^{\circ}$C} likewise suggest an initial formation of C-Si dumbbells on regular Si lattice sites, which agglomerate into large clusters \cite{lindner99_2}.
The agglomerates of such dimers, which do not generate lattice strain but lead to a local increase of the lattice potential \cite{werner96}, are indicated by dark contrasts and otherwise undisturbed Si lattice fringes in \ac{HREM}, as can be seen in Fig.~\ref{fig:sic:hrem:c-si}.
-\begin{figure}[ht]
+\begin{figure}[t]
\begin{center}
\subfigure[]{\label{fig:sic:hrem:c-si}\includegraphics[width=0.25\columnwidth]{tem_c-si-db.eps}}
\subfigure[]{\label{fig:sic:hrem:sic}\includegraphics[width=0.25\columnwidth]{tem_3c-sic.eps}}
The same mechanism was identified by high resolution x-ray diffraction \cite{eichhorn99}.
For implantation temperatures of \unit[500]{$^{\circ}$C} C-Si dumbbells agglomerate in an initial stage followed by the additional appearance of aligned SiC precipitates in a slightly expanded Si region with increasing dose.
The precipitation mechanism based on a preceeding dumbbell agglomeration as indicated by the above-mentioned experiemnts is schematically displayed in Fig.~\ref{fig:sic:db_agglom}.
-\begin{figure}[ht]
+\begin{figure}[t]
\begin{center}
\subfigure[]{\label{fig:sic:db_agglom:seq01}\includegraphics[width=0.30\columnwidth]{sic_prec_seq_01.eps}}
%C-Si dumbbell formation
Finally, when the cluster size reaches a critical radius, the high interfacial energy due to the 3C-SiC/c-Si lattice misfit is overcome and precipitation occurs.
Due to the slightly lower silicon density of 3C-SiC excessive silicon atoms exist, which will most probably end up as self-interstitials in the c-Si matrix since there is more space than in 3C-SiC.
-In contrast, investigations of strained Si$_{1-y}$C$_y$/Si heterostructures formed by \ac{SPE} \cite{strane94} and \ac{MBE} \cite{guedj98}, which incidentally involve the formation of SiC nanocrystallites, suggest a coherent initiation of precipitation by agglomeration of substitutional instead of interstitial C.
-todo: more strane94 ...
-C incorporated as substitutional C.
-Increased temperatures enable diffusion by forming a C-Si interstitial dumbbell followed by the formation of small coherent precipitates.
+In contrast, \ac{IR} spectroscopy and \ac{HREM} investigations on the thermal stability of strained Si$_{1-y}$C$_y$/Si heterostructures formed by \ac{SPE} \cite{strane94} and \ac{MBE} \cite{guedj98}, which finally involve the incidental formation of SiC nanocrystallites, suggest a coherent initiation of precipitation by agglomeration of substitutional instead of interstitial C.
+These experiments show that the C atoms, which are initially incorporated substitutionally at regular lattice sites, form C-rich clusters maintaining coherency with the Si lattice during annealing above a critical temperature prior to the transition into incoherent 3C-SiC precipitates.
+Increased temperatures in the annealing process enable the diffusion and agglomeration of C atoms.
Coherency is lost once the increasing strain energy of the stretched SiC structure surpasses the interfacial energy of the incoherent 3C-SiC precipitate and the Si substrate.
+Estimates of the SiC/Si interfacial energy \cite{taylor93} and the consequent critical size correspond well with the experimentally observed precipitate radii within these studies.
This different mechanism of precipitation might be attributed to the respective method of fabrication.
-While in CVD and MBE surface effects need to be taken into account, SiC formation during IBS takes place in the bulk of the Si crystal.
-However, in another IBS study Nejim et~al.\cite{nejim95} propose a topotactic transformation that is likewise based on the formation of substitutional C.
-The formation of substitutional C, however, is accompanied by Si self-interstitial atoms that previously occupied the lattice sites and a concurrent reduction of volume due to the lower lattice constant of SiC compared to Si.
-Both processes are believed to compensate one another.
-Additionally IBS studies on \cite{martin90,...} ...
-The fact that the cubic phase instead of the thermodynamically favorable $\alpha$-SiC structure is formed supports the latter mechanism ...
-
-%cites:
-
-% continue with strane94 and werner96
-
-%ibs, c-si agglom: werner96,werner97,eichhorn99,lindner99_2,koegler03
-%hetero, coherent sic by sub c: strane94,guedj98
-%ibs, c sub: nejim95
-%ibs, indicated c sub: martin90 + conclusions reeson8x, eichhorn02
-%more: taylor93, kitabatake contraction along 110, koegler03
-%taylor93: sic prec only/more_easy if self interstitials are present
-
-% -> skorupa 3.2: c sub vs sic prec
+While in \ac{CVD} and \ac{MBE} surface effects need to be taken into account, SiC formation during IBS takes place in the bulk of the Si crystal.
+However, in another \ac{IBS} study Nejim et~al. \cite{nejim95} propose a topotactic transformation that is likewise based on substitutional C, which replaces four of the eight Si atoms in the Si unit cell accompanied by the generation of four Si interstitials.
+Since the emerging strain due to the expected volume reduction of \unit[48]{\%} would result in the formation of dislocations, which, however, are not observed, the interstitial Si is assumed to react with further implanted C atoms in the released volume.
+The resulting strain due to the slightly lower Si density of SiC compared to Si of about \unit[3]{\%} is sufficiently small to legitimate the absence of dislocations.
+Furthermore, IBS studies of Reeson~et~al. \cite{reeson87}, in which implantation temperatures of \unit[500]{$^{\circ}$C} were employed, revealed the necessity of extreme annealing temperatures for C redistribution, which is assumed to result from the stability of substitutional C and consequently high activation energies required for precipitate dissolution.
+The results support a mechanism of an initial coherent precipitation based on substitutional C that is likewise valid for the \ac{IBS} of 3C-SiC by C implantation into Si at elevated temperatures.
+The fact that the metastable cubic phase instead of the thermodynamically more favorable hexagonal $\alpha$-SiC structure is formed and the alignment of these cubic precipitates within the Si matrix, which can be explained by considering a topotactic transformation by C atoms occupying substitutionally Si lattice sites of one of the two fcc lattices that make up the Si crystal, reinforce the proposed mechanism.
+
+To conclude, a controversy with respect to the precipitation of SiC in Si exists in literature.
+Next to the pure scientific interest, solving this controversy and gaining new insight in the SiC conversion mechanism might enable significant progress in the heteroepitaxial growth of thin films featuring non-coherent interfaces in the C/Si system.
+On the other hand, processes relying upon prevention of precipitation in order to produce strained heterostructures will likewise benefit.
% remember!
+
% werner96/7: rt implants followed by rta < 800: C-Si db aggloms | > 800: 3C-SiC
% taylor93: si_i reduces interfacial energy (explains metastability) of sic/si
% eichhorn02: high imp temp more efficient than postimp treatment
% eichhorn99: same as 02 + c-si agglomerates at low concentrations
+% strane94/guedj98: my model - c redist by si int (spe) and surface diff (mbe)
+
% todo
% add sharp iface image!
-
-on surface ... md contraction along 110 ... kitabatake ... and ref in lindner ... rheed from si to sic ...
-
-in ibs ... lindner and skorupa ...
-
-nejim however ...
- high temps -> good alignment with substrate
- C occupies predominantly substitutional lattice sites
- also indictaed by other direct synthesis experiments like martin90 and conclusions of reeson8X ...
-
-eichhornXX, koegler, lindner ...
-
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