\chapter{Review of the silicon carbon compound}
+\label{chapter:sic_rev}
-\section{Properties and applications of silicon carbide}
+\section{Structure, properties and applications of silicon carbide}
-The stoichiometric composition of silicon and carbon termed silicon carbide (SiC) is the only chemical stable compound in the C/Si system \cite{}.
+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{center}
+\includegraphics[width=12cm]{si-c_phase.eps}
+\end{center}
+\caption[Phase diagram of the C/Si system.]{Phase diagram of the C/Si system \cite{scace59}.}
+\label{fig:sic:si-c_phase}
+\end{figure}
SiC was first discovered by Henri Moissan in 1893 when he observed brilliant sparkling crystals while examining rock samples from a meteor crater in Arizona.
He mistakenly identified these crystals as diamond.
Although they might have been considered \glqq diamonds from space\grqq{} Moissan identified them as SiC in 1904 \cite{moissan04}.
In mineralogy SiC is still referred to as moissanite in honor of its discoverer.
It is extremely rare and almost impossible to find in nature.
-\subsection{SiC polytypes}
+SiC is a covalent material in which both, Si and C atoms are sp$^3$ hybridized.
+Each of the four sp$^3$ hybridized orbitals of a Si atom overlaps with one of the four sp$^3$ hybridized orbitals of the four surrounding C atoms and vice versa.
+This results in fourfold coordinated covalent $\sigma$ bonds of equal length and strength for each atom with its neighbours.
+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{center}
+\includegraphics[width=12cm]{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.
-Each of the four sp$^3$ hybridized orbitals of the Si atom overlaps with one of the four sp$^3$ hybridized orbitals of the four surrounding C atoms and vice versa.
-This results in fourfold coordinated covalent $\sigma$ bond of equal length and strength for each atom with its neighbours.
+\begin{table}[ht]
+\begin{center}
+\begin{tabular}{l c c c c c c}
+\hline
+\hline
+ & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
+\hline
+Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
+Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
+Break down field$^{\text{A}}$ [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
+Saturation drift velocity$^{\text{A}}$ [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
+Electron mobility$^{\text{B}}$ [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
+Hole mobility$^{\text{B}}$ [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
+Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption[Properties of SiC polytypes and other semiconductor materials.]{Properties of SiC polytypes and other semiconductor materials. Doping concentrations are $10^{16}\text{ cm}^{-3}$ (A) and $10^{17}\text{ cm}^{-3}$ (B) respectively. References: \cite{wesch96,casady96,park98}. {\color{red}Todo: add more refs + check all values!}}
+\label{table:sic:properties}
+\end{table}
+Different polytypes of SiC exhibit different properties.
+Some of the key properties are listed in Table~\ref{table:sic:properties} and compared to other technologically relevant semiconductor materials.
+Despite the lower charge carrier mobilities for low electric fields SiC outperforms Si concerning all other properties.
+The wide band gap, large breakdown field and high saturation drift velocity make SiC an ideal candidate for high-temperature, high-power and high-frequency electronic devices exhibiting high efficiency~\cite{wesch96,morkoc94,casady96,capano97,pensl93,park98,edgar92}.
+In addition the high thermal conductivity enables the implementation of small-sized electronic devices enduring increased power densites.
+Its formidable mechanical stability, heat resistant, radiation hardness and low neutron capture cross section allow operation in harsh and radiation-hard environments~\cite{capano97}.
-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, closed-packed SiC bilayers.
+Despite high-temperature operations the wide band gap also allows the use of SiC in optoelectronic devices.
+Indeed, a forgotten figure, Oleg V. Losev discovered what we know as the light emitting diode (LED) today in the mid 1920s by observing light emission from SiC crystal rectifier diodes used in radio receivers when a current was passed through them~\cite{losev27}.
+Apparently not known to Losev, Henry J. Round published a small note~\cite{round07} reporting a bright glow from a SiC diode already in 1907.
+However, it was Losev who continued his studies providing comprehensive knowledge on light emission of SiC (entitled luminous carborundum) and its relation to diode action~\cite{losev28,losev29,losev31,losev33} constituting the birth of solid-state optoelectronics.
+And indeed, the first significant blue LEDs reinvented at the start of the 1990s were based on SiC.
+Due to the indirect band gap and, thus, low light emitting efficiency, however, it is nowadays replaced by GaN and InGaN based diodes.
+However, even for GaN based diodes SiC turns out to be of great importance since it constitutes an ideal substrate material for GaN epitaxial layer growth~\cite{liu_l02}.
+As such, SiC will continue to play a major role in the production of future super-bright visible emitters.
+Especially substrates of the 3C polytype promise good quality, single crystalline GaN films~\cite{takeuchi91,yamamoto04,ito04}.
+
+The focus of SiC based applications, however, is in the area of solid state electronics experiencing revolutionary performance improvements enabled by its capabilities.
+These devices include ultraviolet (UV) detectors, high power radio frequency (RF) amplifiers, rectifiers and switching transistors as well as MEMS applications.
+For UV dtectors the wide band gap is useful for realizing low photodiode dark currents as well as sensors that are blind to undesired near-infrared wavelenghts produced by heat and solar radiation.
+These photodiodes serve as excellent sensors applicable in the monitoring and control of turbine engine combustion.
+The low dark currents enable the use in X-ray, heavy ion and neutron detection in nuclear reactor monitoring and enhanced scientific studies of high-energy particle collisions as well as cosmic radiation.
+The low neutron capture cross section and radiation hardness favors its use in detector applications.
+The high breakdown field and carrier saturation velocity coupled with the high thermal conductivity allow SiC RF transistors to handle much higher power densities and frequencies in stable operation at high temperatures.
+Smaller transistor sizes and less cooling requirements lead to a reduced overall size and cost of these systems.
+For instance, SiC based solid state transmitters hold great promise for High Definition Television (HDTV) broadcast stations abandoning the reliance on tube-based technology for high-power transmitters significantly reducing the size of such transmitters and long-term maintenance costs.
+The high breakdown field of SiC compared to Si allows the blocking voltage region of a device to be designed roughly 10 times thinner and 10 times heavier doped, resulting in a decrease of the blocking region resistance by a factor of 100 and a much faster switching behavior.
+Thus, rectifier diodes and switching transistors with higher switching frequencies and much greater efficiencies can be realized and exploited in highly efficient power converters.
+Therefor, SiC constitutes a promising candidate to become the key technology towards an extensive development and use of regenerative energies and elctromobility.
+Beside the mentioned electrical capabilities the mechanical stability, which is almost as hard as diamond, and chemical inertness almost suggest SiC to be used in MEMS designs.
+
+Among the different polytypes of SiC, the cubic phase shows a high electron mobility and the highest break down field as well as saturation drift velocity.
+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{center}
+\includegraphics[width=7cm]{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}
+\end{figure}
+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 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}
-\section{Ion beam synthesis of cubic silicon carbide}
+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.
-\section{Assumed precipitation mechanism of cubic silicon carbide in silicon}
+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 \cite{}, lower process temperatures than these typically employed in CVD have been realized, 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 not yet statisfactory.
+
+SiC on SiC epitaxy ...
+
+\section{Ion beam synthesis of cubic silicon carbide}
\section{Substoichiometric concentrations of carbon in crystalline 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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