\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}
-\section{Assumed precipitation mechanism of cubic silicon carbide in silicon}
+The industrial Acheson process \cite{acheson} is utilized to produce SiC on a large scale by thermal reaction of silicon dioxide (silica sand) and carbon.
+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.
+
+van Arkel (CVD)
+
+Lely (sublimation)
+
+modified Lely or modified sublimation
+
+though significant advances have been achieved a bunch of defects ...
+
+\subsection{SiC epitaxial thin film growth}
+
+\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}
+\label{section:assumed_prec}
+
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