1 \chapter{Review of the silicon carbon compound}
2 \label{chapter:sic_rev}
4 \section{Structure, properties and applications of silicon carbide}
6 The phase diagram of the C/Si system is shown in Fig.~\ref{fig:sic:si-c_phase}.
7 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}.
10 \includegraphics[width=12cm]{si-c_phase.eps}
12 \caption[Phase diagram of the C/Si system.]{Phase diagram of the C/Si system \cite{scace59}.}
13 \label{fig:sic:si-c_phase}
15 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.
16 He mistakenly identified these crystals as diamond.
17 Although they might have been considered \glqq diamonds from space\grqq{} Moissan identified them as SiC in 1904 \cite{moissan04}.
18 In mineralogy SiC is still referred to as moissanite in honor of its discoverer.
19 It is extremely rare and almost impossible to find in nature.
21 SiC is a covalent material in which both, Si and C atoms are sp$^3$ hybridized.
22 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.
23 This results in fourfold coordinated covalent $\sigma$ bonds of equal length and strength for each atom with its neighbours.
24 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}.
25 The polytypes differ in the one-dimensional stacking sequence of identical, close-packed SiC bilayers.
26 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.
29 \includegraphics[width=12cm]{polytypes.eps}
31 \caption{Stacking sequence of SiC bilayers of the most common polytypes of SiC (from left to right): 3C, 2H, 4H and 6H.}
32 \label{fig:sic:polytypes}
34 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.
38 \begin{tabular}{l c c c c c c}
41 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
43 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
44 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
45 Break down field$^{\text{A}}$ [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
46 Saturation drift velocity$^{\text{A}}$ [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
47 Electron mobility$^{\text{B}}$ [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
48 Hole mobility$^{\text{B}}$ [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
49 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
54 \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!}}
55 \label{table:sic:properties}
57 Different polytypes of SiC exhibit different properties.
58 Some of the key properties are listed in Table~\ref{table:sic:properties} and compared to other technologically relevant semiconductor materials.
59 Despite the lower charge carrier mobilities for low electric fields SiC outperforms Si concerning all other properties.
60 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}.
61 In addition the high thermal conductivity enables the implementation of small-sized electronic devices enduring increased power densites.
62 Its formidable mechanical stability, heat resistant, radiation hardness and low neutron capture cross section allow operation in harsh and radiation-hard environments~\cite{capano97}.
64 Despite high-temperature operations the wide band gap also allows the use of SiC in optoelectronic devices.
65 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}.
66 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.
67 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.
68 And indeed, the first significant blue LEDs reinvented at the start of the 1990s were based on SiC.
69 Due to the indirect band gap and, thus, low light emitting efficiency, however, it is nowadays replaced by GaN and InGaN based diodes.
70 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}.
71 As such, SiC will continue to play a major role in the production of future super-bright visible emitters.
72 Especially substrates of the 3C polytype promise good quality, single crystalline GaN films~\cite{takeuchi91,yamamoto04,ito04}.
74 The focus of SiC based applications, however, is in the area of solid state electronics experiencing revolutionary performance improvements enabled by its capabilities.
75 These devices include ultraviolet (UV) detectors, high power radio frequency (RF) amplifiers, rectifiers and switching transistors as well as MEMS applications.
76 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.
77 These photodiodes serve as excellent sensors applicable in the monitoring and control of turbine engine combustion.
78 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.
79 The low neutron capture cross section and radiation hardness favors its use in detector applications.
80 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.
81 Smaller transistor sizes and less cooling requirements lead to a reduced overall size and cost of these systems.
82 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.
83 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.
84 Thus, rectifier diodes and switching transistors with higher switching frequencies and much greater efficiencies can be realized and exploited in highly efficient power converters.
85 Therefor, SiC constitutes a promising candidate to become the key technology towards an extensive development and use of regenerative energies and elctromobility.
86 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.
88 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.
89 In contrast to its hexagonal counterparts 3C-SiC exhibits isotropic mechanical and electronic properties.
90 Additionally the smaller band gap is expected to be favorable concerning the interface state density in MOSFET devices fabricated on 3C-SiC.
91 Thus the cubic phase is most effective for highly efficient high-performance electronic devices.
94 \includegraphics[width=7cm]{sic_unit_cell.eps}
96 \caption{3C-SiC unit cell. Yellow and grey spheres correpsond to Si and C atoms respectively. Covalent bonds are illustrated by blue lines.}
97 \label{fig:sic:unit_cell}
99 Its unit cell is shown in Fig.~\ref{fig:sic:unit_cell}.
100 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.
101 However, in 3C-SiC, one of the fcc lattices is occupied by Si atoms while the other one is occupied by C atoms.
102 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.
103 Thus, the Si density of SiC is only slightly lower, i.e. \unit[97]{\%} of plain Si.
105 \section{Fabrication of silicon carbide}
107 Although the constituents of SiC are abundant and the compound is chemically and thermally stable, large deposits of SiC have never been found.
108 Due to the rarity, SiC is typically man-made.
109 The development of several methods was necessary to synthetically produce SiC crystals matching the needs of a respective application.
110 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.
112 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.
113 In the following, the principal difficulties involved in the formation of crystalline SiC and the most recent achievements will be summarized.
115 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}.
116 High process temperatures are necessary and the evaporation of Si must be suppressed by a high-pressure inert atmosphere.
117 Crystals grown by this method are not adequate for practical applications with respect to their size as well as quality and purity.
118 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.
120 \subsection{SiC bulk crystal growth}
122 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).
123 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.
124 Due to the insufficient and uncontrollable purity, material produced by this method, originally termed carborundum by Acheson, can hardly be used for device applications.
125 However, it is often used as an abrasive material and as seed crystals for subsequent vapor phase growth and sublimation processes.
127 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.
128 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.
129 The obtained polycrystalline material consists of small crystal grains with a size of several hunderd microns stated to be mainly of the cubic polytype.
131 A significant breakthrough was made in 1955 by Lely, who proposed a sublimation process for growing higher purity bulk SiC single crystals \cite{lely55}.
132 In the so called Lely process, a tube of porous graphite is surrounded by polycrystalline SiC as gained by previously described processes.
133 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.
135 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.
136 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.
137 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.
138 Controlled nucleation occurs on the SiC seed, which is held at approximately \unit[2200]{$^{\circ}$C}.
139 The growth process is commonly done in a high-purity argon atmosphere.
140 The method was successfully applied to grow 6H and 4H boules with diameters up to \unit[60]{mm} \cite{tairov81,barrett91,barrett93,stein93}.
141 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}.
143 Although significant advances have been achieved in the field of SiC bulk crystal growth, a variety of problems remain.
144 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.
145 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.
146 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.
147 Additionally, to preserve epitaxial growth conditions, graphitization of the seed crystal has to be avoided.
148 Avoiding defects constitutes a mojor difficulty.
149 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.
150 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}.
151 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.
153 \subsection{SiC epitaxial thin film growth}
155 Crystalline SiC layers have been grown by a large number of techniques on the surfaces of different substrates.
156 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.
157 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.
158 In the case of solid-source MBE atoms are provided by electron beam evaporation of graphite and solid Si or thermal evaporation of fullerenes.
159 The following review will exclusively focus on CVD and MBE techniques.
161 The availability and reproducibility of Si substrates of controlled purity made it the first choice for SiC epitaxy.
162 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.
163 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.
164 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]{\%}.
165 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}.
166 Cleaning of the substrate surface with HCl is required prior to carbonization.
167 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}.
168 In a next step, the epitaxial deposition of SiC is realized by an additional supply of Si atoms at similar temperatures.
169 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}.
170 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}.
171 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}.
172 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}.
173 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}.
174 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.
175 In summary, the almost universal use of Si has allowed significant progress in the understanding of heteroepitaxial growth of SiC on Si.
176 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.
178 The alternative attempt to grow SiC on SiC substrates has shown to drastically reduce the concentration of defects in deposited layers.
179 By CVD, both, the 3C \cite{kong88,powell90,powell91} as well as the 6H \cite{kong88_2,powell90_2} polytype could be successfully grown.
180 In order to obtain the homoepitactically grown 6H polytype, off-axis 6H-SiC wafers are required as a substrate \cite{kimoto93}.
181 %In the so called step-controlled epitaxy, lateral growth proceeds from atomic steps without the necessity of preceding nucleation events.
182 Investigations indicate that in so-called step-controlled epitaxy, crystal growth proceeds through the adsorbtion of Si species at atomic steps and their carbonization by hydrocarbon molecules.
183 A model is suggested ...
185 ... diffusion of reactants in a stagnant layer.
188 \section{Ion beam synthesis of cubic silicon carbide}
190 \section{Substoichiometric concentrations of carbon in crystalline silicon}
192 \section{Assumed cubic silicon carbide conversion mechanisms}
193 \label{section:assumed_prec}
195 on surface ... md contraction along 110 ... kitabatake ... and ref in lindner ... rheed from si to sic ...
197 in ibs ... lindner and skorupa ...
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