\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}
\end{figure}
-The 3C-SiC unit cell is shown in Fig.~\ref{fig:sic:unit_cell}.
+Its unit cell is shown in Fig.~\ref{fig:sic:unit_cell}.
3C-SiC grows in zincblende structure, i.e. it is composed of two fcc lattices, which are displaced by one quarter of the volume diagonal as in Si.
However, in 3C-SiC, one of the fcc lattices is occupied by Si atoms while the other one is occupied by C atoms.
-Its lattice constant of \unit[0.436]{nm} compared to \unit[0.543]{nm} from that of Si results in a lattice mismatch of almost \unit[20]{\%}, i.e. four lattice constants of Si match five SiC lattice constants.
-Thus, the Si density of SiC is only slightly lower, i.e. \unit[97]{\%}, than that of Si.
+Its lattice constant of \unit[0.436]{nm} compared to \unit[0.543]{nm} from that of Si results in a lattice mismatch of almost \unit[20]{\%}, i.e. four lattice constants of Si approximately match five SiC lattice constants.
+Thus, the Si density of SiC is only slightly lower, i.e. \unit[97]{\%} of plain Si.
\section{Fabrication of silicon carbide}
-SiC usually manmade.
-The unique properties driving its applications in the same time harden the fabrication of SiC ...
+Although the constituents of SiC are abundant and the compound is chemically and thermally stable, large deposits of SiC have never been found.
+Due to the rarity, SiC is typically man-made.
+The development of several methods was necessary to synthetically produce SiC crystals matching the needs of a respective application.
+The fact that natural SiC is almost only observed as individual presolar SiC stardust grains near craters of primitive meteorite impacts, already indicates the complexity involved in the synthesis process.
+
+The attractive properties and wide range of applications, however, have triggered extensive efforts to grow this material as a bulk crystal and as an epitaxial surface thin film.
+In the following, the principal difficulties involved in the formation of crystalline SiC and the most recent achievements will be summarized.
+
+Though possible, melt growth processes \cite{nelson69} are complicated due to the small C solubility in Si at temperatures below \unit[2000]{$^{\circ}$C} and its small change with temperature \cite{scace59}.
+High process temperatures are necessary and the evaporation of Si must be suppressed by a high-pressure inert atmosphere.
+Crystals grown by this method are not adequate for practical applications with respect to their size as well as quality and purity.
+The presented methods, thus, focus on vapor transport growth processes such as chemical vapor deposition (CVD) or molecular beam epitaxy (MBE) and the sublimation technique.
+
+\subsection{SiC bulk crystal growth}
+
+The industrial Acheson process \cite{knippenberg63} is utilized to produce SiC on a large scale by thermal reaction of silicon dioxide (silica sand) and carbon (coal).
+The heating is accomplished by a core of graphite centrally placed in the furnace, which is heated up to a maximum temperature of \unit[2700]{$^{\circ}$C}, after which the temperature is gradually lowered.
+Due to the insufficient and uncontrollable purity, material produced by this method, originally termed carborundum by Acheson, can hardly be used for device applications.
+However, it is often used as an abrasive material and as seed crystals for subsequent vapor phase growth and sublimation processes.
+
+In the van Arkel apparatus \cite{arkel25}, Si and C containing gases like methylchlorosilanes \cite{moers31} and silicon tetrachloride \cite{kendall53} are pyrolitically decomposed and SiC is deposited on heated carbon rods in a vapor growth process.
+Typical deposition temperatures are in the range between \unit[1400]{$^{\circ}$C} and \unit[1600]{$^{\circ}$C} while studies up to \unit[2500]{$^{\circ}$C} have been performed.
+The obtained polycrystalline material consists of small crystal grains with a size of several hunderd microns stated to be mainly of the cubic polytype.
+
+A significant breakthrough was made in 1955 by Lely, who proposed a sublimation process for growing higher purity bulk SiC single crystals \cite{lely55}.
+In the so called Lely process, a tube of porous graphite is surrounded by polycrystalline SiC as gained by previously described processes.
+Heating the hollow carbon cylinder to \unit[2500]{$^{\circ}$C} leads to sublimation of the material at the hot outer wall and diffusion through the porous graphite tube followed by an uncontrolled crystallization on the slightly cooler parts of the inner graphite cavity resulting in the formation of randomly sized, hexagonally shaped platelets, which exibit a layered structure of various alpha polytypes with equal \hkl{0001} orientation.
+
+Subsequent research \cite{tairov78,tairov81} resulted in the implementation of a seeded growth sublimation process wherein only one large crystal of a single polytype is grown.
+In the so called modified Lely or modified sublimation process nucleation occurs on a SiC seed crystal located at the top or bottom of a cylindrical growth cavity.
+As in the Lely process, SiC sublimes at a temperature of \unit[2400]{$^{\circ}$C} from a polycrystalline source diffusing through a porous graphite retainer along carefully adjusted thermal and pressure gradients.
+Controlled nucleation occurs on the SiC seed, which is held at approximately \unit[2200]{$^{\circ}$C}.
+The growth process is commonly done in a high-purity argon atmosphere.
+The method was successfully applied to grow 6H and 4H boules with diameters up to \unit[60]{mm} \cite{tairov81,barrett91,barrett93,stein93}.
+This refined versions of the physical vapor transport (PVT) technique enabled the reproducible boule growth of device quality SiC crystals, which were for instance used to fabricate blue light emitting diodes with increased quantum efficiencies \cite{hoffmann82}.
+
+Although significant advances have been achieved in the field of SiC bulk crystal growth, a variety of problems remain.
+The high temperatures required in PVT growth processes limit the range of materials used in the hot zones of the reactors, for which mainly graphite is used.
+The porous material constitutes a severe source of contamination, e.g. with the dopants N, B and Al, which is particularly effective at low temperatures due to the low growth rate.
+Since the vapor pressure of Si is much higher than that of C, a careful manipulation of the Si vapor content above the seed crystal is required.
+Additionally, to preserve epitaxial growth conditions, graphitization of the seed crystal has to be avoided.
+Avoiding defects constitutes a mojor difficulty.
+These defects include growth spirals (stepped screw dislocations), subgrain boundaries and twins as well as micropipes (micron sized voids extending along the c axis of the crystal) and 3C inclusions at the seed crystal in hexagonal growth systems.
+Micropipe-free growth of 6H-SiC has been realized by a reduction of the temperature gradient in the sublimation furnace resulting in near-equilibrium growth conditions in order to avoid stresses, which is, however, accompanied by a reduction of the growth rate \cite{schulze98}.
+Further efforts have to be expended to find relations between the growth parameters, the kind of polytype and the occurrence and concentration of defects, which are of fundamental interest and might help to improve the purity of the bulk materials.
+
+\subsection{SiC epitaxial thin film growth}
+
+Crystalline SiC layers have been grown by a large number of techniques on the surfaces of different substrates.
+Most of the crystal growth processes are based on chemical vapor deposition (CVD), solid-source molecular beam epitaxy (MBE) and gas-source MBE on Si as well as SiC substrates.
+In CVD as well as gas-source MBE, C and Si atoms are supplied by C containing gases like CH$_4$, C$_3$H$_8$, C$_2$H$_2$ or C$_2$H$_4$ and Si containing gases like SiH$_4$, Si$_2$H$_6$, SiH$_2$Cl$_2$, SiHCl$_3$ or SiCl$_4$ respectively.
+In the case of solid-source MBE atoms are provided by electron beam evaporation of graphite and solid Si or thermal evaporation of fullerenes.
+The following review will exclusively focus on CVD and MBE techniques.
+
+The availability and reproducibility of Si substrates of controlled purity made it the first choice for SiC epitaxy.
+The heteroepitaxial growth of SiC on Si substrates has been stimulated for a long time due to the lack of suitable large substrates that could be adopted for homoepitaxial growth.
+Furthermore, heteroepitaxy on Si substrates enables the fabrication of the advantageous 3C polytype, which constitutes a metastable phase and, thus, can be grown as a bulk crystal only with small sizes of a few mm.
+The main difficulties in SiC heteroepitaxy on Si is due to the lattice mismatch of Si and SiC and the difference in the thermal expansion coefficient of \unit[8]{\%}.
+Thus, in most of the applied CVD and MBE processes, the SiC layer formation process is split into two steps, the surface carbonization and the growth step, as proposed by Nishino~et~al. \cite{nishino83}.
+Cleaning of the substrate surface with HCl is required prior to carbonization.
+During carbonization the Si surface is chemically converted into a SiC film with a thickness of a few nm by exposing it to a flux of C atoms and concurrent heating up to temperatures about \unit[1400]{$^{\circ}$C}.
+In a next step, the epitaxial deposition of SiC is realized by an additional supply of Si atoms at similar temperatures.
+Low defect densities in the buffer layer are a prerequisite for obtaining good quality SiC layers during growth, although defect densities decrease with increasing distance of the SiC/Si interface \cite{shibahara86}.
+Next to surface morphology defects such as pits and islands, the main defects in 3C-SiC heteroepitaxial layers are twins, stacking faults (SF) and antiphase boundaries (APB) \cite{shibahara86,pirouz87}.
+APB defects, which constitute the primary residual defects in thick layers, are formed near surface terraces that differ in a single-atom-height step resulting in domains of SiC separated by a boundary, which consists of either Si-Si or C-C bonds due to missing or disturbed sublattice information \cite{desjardins96,kitabatake97}.
+However, the number of such defects can be reduced by off-axis growth on a Si \hkl(0 0 1) substrate miscut towards \hkl[1 1 0] by \unit[2]{$^{\circ}$}-\unit[4]{$^{\circ}$} \cite{shibahara86,powell87_2}.
+This results in the thermodynamically favored growth of a single phase due to the uni-directional contraction of Si-C-Si bond chains perpendicular to the terrace steps edges during carbonization and the fast growth parallel to the terrace edges during growth under Si rich conditions \cite{kitabatake97}.
+By MBE, lower process temperatures than these typically employed in CVD have been realized \cite{hatayama95,henke95,fuyuki97,takaoka98}, which is essential for limiting thermal stresses and to avoid resulting substrate bending, a key issue in obtaining large area 3C-SiC surfaces.
+In summary, the almost universal use of Si has allowed significant progress in the understanding of heteroepitaxial growth of SiC on Si.
+However, mismatches in the thermal expansion coefficient and the lattice parameter cause a considerably high concentration of various defects, which is responsible for structural and electrical qualities that are not yet statisfactory.
+
+The alternative attempt to grow SiC on SiC substrates has shown to drastically reduce the concentration of defects in deposited layers.
+By CVD, both, the 3C \cite{kong88,powell90} as well as the 6H \cite{kong88_2,powell90_2} polytype could be successfully grown.
+In order to obtain the homoepitaxially grown 6H polytype, off-axis 6H-SiC wafers are required as a substrate \cite{kimoto93}.
+%In the so called step-controlled epitaxy, lateral growth proceeds from atomic steps without the necessity of preceding nucleation events.
+Investigations indicate that in the so-called step-controlled epitaxy, crystal growth proceeds through the adsorbtion of Si species at atomic steps and their carbonization by hydrocarbon molecules.
+This growth mechanism does not require two-dimensional nucleation.
+Instead, crystal growth is governed by mass transport, i.e. the diffusion of reactants in a stagnant layer.
+In contrast, layers of the 3C polytype are formed on exactly oriented \hkl(0 0 0 1) 6H-SiC substrates by two-dimensional nucleation on terraces.
+{\color{red} Source of APB defects ...}
+However, lateral 3C-SiC growth was also observed on low tilt angle off-axis substrates originating from intentionally induced dislocations \cite{powell91}.
+Additionally, 6H-SiC was observed on clean substrates even for a tilt angle as low as \unit[0.1]{$^{\circ}$} due to low surface mobilities that facilitate arriving molecules to reach surface steps.
+Thus, 3C nucleation is assumed as a result of migrating Si and C cointaining molecules interacting with surface disturbances by a yet unknown mechanism, in contrast to a model \cite{ueda90}, in which the competing 6H versus 3C growth depends on the density of surface steps.
+{\color{red} This can be employed to create 3C layers with reduced density of APB defects.}
+
+Lower growth temperatures, a clean growth ambient, in situ control of the growth process, layer-by-layer deposition and the possibility to achieve dopant profiles within atomic dimensions due to the reduced diffusion at low growth temperatures reveal MBE as a promising technique to produce SiC epitaxial layers.
+gas source ... 3C on 6H
+3C on 3C homoepitaxy by ALE
+6H on 6H ...
+Problem of gas source ... strong adsorption and incorporation of atomic decomposited hydrogen of the gas phase reactants at low temperatures.
+Growth rate lower than desorption rate of hydrogen ...
+Solid source MBE may be the key to avoid such problems ...
+Realized on and off-axis 3C on 4H and ... \cite{fissel95,fissel95_apl} ...
+Nonstoichiometric reconstruction plays a relevenat role ... handled by Si/C flux ratio ... \cite{fissel96,righi03} ...
+change in adlayer thickness and, consequently, in the surface super structure leading to growth of another polytype \cite{fissel95} ...
+Possibility to grow heterostructures (band gap engineering) by careful control of the Si/C ratio and Si excess.
+
+To summarize ... remaining obstacles are ... APB in 3C ... and micropipes in hexagonal SiC?
\section{Ion beam synthesis of cubic silicon carbide}
\section{Substoichiometric concentrations of carbon in crystalline silicon}
-\section{Assumed precipitation mechanism of cubic silicon carbide in bulk silicon}
+\section{Assumed cubic silicon carbide conversion mechanisms}
\label{section:assumed_prec}
+on surface ... md contraction along 110 ... kitabatake ... and ref in lindner ... rheed from si to sic ...
+
+in ibs ... lindner and skorupa ...
+
+nejim however ...
+
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