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 mainly 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, mostly covalent $\sigma$ bonds of equal length and strength for each atom with its neighbors.
24 Although the local order of Si and C next neighbor 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[height=5.5cm]{polytypes_own.eps}\\[0.1cm]
30 \begin{minipage}{0.45\textwidth}
32 \hspace*{0.05cm} a \hspace*{0.09cm} b \hspace*{0.09cm} c \hspace*{0.44cm} a \hspace*{0.09cm} b \hspace*{0.44cm} a \hspace*{0.09cm} b \hspace*{0.09cm} c \hspace*{0.44cm} a \hspace*{0.09cm} b \hspace*{0.09cm} c \hspace*{0.09cm} a\\
33 \hspace*{0.5cm} 3C \hspace*{0.9cm} 2H \hspace*{1.0cm} 4H \hspace*{1.3cm} 6H
36 %\includegraphics[width=10cm]{polytypes.eps}
38 \caption[Stacking sequence of SiC bilayers of the most common polytypes of SiC.]{Stacking sequence of SiC bilayers of the most common polytypes of SiC (from left to right): 3C, 2H, 4H and 6H.}
39 \label{fig:sic:polytypes}
41 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.
43 \bibpunct{}{}{,}{n}{}{}
46 \begin{tabular}{l c c c c c c}
49 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
51 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
52 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
53 Break down field$^{\text{A}}$ [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
54 Saturation drift velocity$^{\text{A}}$ [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
55 Electron mobility$^{\text{B}}$ [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
56 Hole mobility$^{\text{B}}$ [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
57 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
62 \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}.}
63 \label{table:sic:properties}
65 \bibpunct{[}{]}{,}{n}{}{}
66 % todo add more refs + check all values!
67 Different polytypes of SiC exhibit different properties.
68 Some of the key properties are listed in Table~\ref{table:sic:properties} and compared to other technologically relevant semiconductor materials.
69 Despite the lower charge carrier mobilities for low electric fields, SiC outperforms Si concerning all other properties.
70 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}.
71 In addition, the high thermal conductivity enables the implementation of small-sized electronic devices enduring increased power densities.
72 Its formidable mechanical stability, heat resistance, radiation hardness and low neutron capture cross section allow operation in harsh and radiation-hard environments~\cite{capano97}.
74 In addition to high-temperature operations, the wide band gap also allows the use of SiC in optoelectronic devices.
75 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}.
76 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.
77 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.
78 And indeed, the first significant blue LEDs reinvented at the start of the 1990s were based on SiC.
79 Due to the indirect band gap and, thus, low light emitting efficiency, however, it is nowadays replaced by GaN and InGaN based diodes.
80 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}.
81 As such, SiC will continue to play a major role in the production of future super-bright visible emitters.
82 Especially substrates of the 3C polytype promise good quality, single crystalline GaN films~\cite{takeuchi91,yamamoto04,ito04,haeberlen10}.
84 The focus of SiC based applications, however, is in the area of solid state electronics experiencing revolutionary performance improvements enabled by its capabilities~\cite{wesch96,morkoc94,casady96,capano97,pensl93,park98,edgar92}.
85 These devices include ultraviolet (UV) detectors~\cite{brown93,yan04}, high power radio frequency (RF) amplifiers, rectifiers and switching transistors~\cite{pribble02,baliga96,weitzel96,zhu08,bhatnagar92,bhatnagar93,ryu01} as well as microelectromechanical system (MEMS) applications~\cite{sarro00}.
86 For UV detectors the wide band gap is useful for realizing low photodiode dark currents as well as sensors that are blind to undesired near-infrared wavelengths produced by heat and solar radiation.
87 These photodiodes serve as excellent sensors applicable in the monitoring and control of turbine engine combustion.
88 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.
89 The low neutron capture cross section and radiation hardness favors its use in detector applications.
90 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.
91 Smaller transistor sizes and less cooling requirements lead to a reduced overall size and cost of these systems.
92 For instance, SiC based solid state transmitters hold great promise for High Definition Television (HDTV) broadcast stations~\cite{temcamani01,pribble02} abandoning the reliance on tube-based technology for high-power transmitters significantly reducing the size of such transmitters and long-term maintenance costs.
93 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.
94 Thus, rectifier diodes and switching transistors with higher switching frequencies and much greater efficiencies can be realized and exploited in highly efficient power converters.
95 Therefore, SiC constitutes a promising candidate to become the key technology towards an extensive development and use of regenerative energies and electromobility.
96 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.
98 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~\cite{neudeck95,wesch96}.
99 In contrast to its hexagonal counterparts, 3C-SiC exhibits isotropic mechanical and electronic properties.
100 Additionally, the smaller band gap is expected to be favorable concerning the interface state density in MOSFET devices fabricated on 3C-SiC~\cite{pensl00}.
101 Thus, the cubic phase is most effective for highly efficient high-performance electronic devices.
104 \includegraphics[width=0.35\columnwidth]{sic_unit_cell.eps}
106 \caption[3C-SiC unit cell.]{3C-SiC unit cell. Yellow and gray spheres correspond to Si and C atoms respectively. Covalent bonds are illustrated by blue lines.}
107 \label{fig:sic:unit_cell}
109 Its unit cell is shown in Fig.~\ref{fig:sic:unit_cell}.
110 3C-SiC grows in zincblende structure, i.e.\ it is composed of two face-centered cubic (fcc) lattices, which are displaced by one quarter of the volume diagonal as in Si.
111 However, in 3C-SiC, one of the fcc lattices is occupied by Si atoms while the other one is occupied by C atoms.
112 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.
113 Thus, the Si density of SiC is only slightly lower, i.e.\ \unit[97]{\%} of plain Si.
115 \section{Fabrication of silicon carbide}
117 Although the constituents of SiC are abundant and the compound is chemically and thermally stable, large deposits of SiC have never been found.
118 Due to the rarity, SiC is typically man-made.
119 The development of several methods was necessary to synthetically produce SiC crystals matching the needs of a respective application.
120 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.
122 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.
123 In the following, the principal difficulties involved in the formation of crystalline SiC and the most recent achievements will be summarized.
125 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}.
126 High process temperatures are necessary and the evaporation of Si must be suppressed by a high-pressure inert atmosphere.
127 Crystals grown by this method are not adequate for practical applications with respect to their size as well as quality and purity.
128 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.
129 Excellent reviews of the different SiC growth methods have been published by Wesch~\cite{wesch96} and Davis~et~al.~\cite{davis91}.
131 \subsection{SiC bulk crystal growth}
133 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).
134 The heating is accomplished by a core of graphite centrally placed in a furnace, which is heated up to a maximum temperature of \unit[2700]{$^{\circ}$C}, after which the temperature is gradually lowered.
135 Due to the insufficient and uncontrollable purity, material produced by this method, originally termed carborundum by Acheson, can hardly be used for device applications.
136 However, it is often used as an abrasive material and as seed crystals for subsequent vapor phase growth and sublimation processes.
138 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.
139 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.
140 The obtained polycrystalline material consists of small crystal grains with a size of several hundred microns stated to be mainly of the cubic polytype.
142 A significant breakthrough was made in 1955 by Lely, who proposed a sublimation process for growing higher purity bulk SiC single crystals~\cite{lely55}.
143 In the so called Lely process, a tube of porous graphite is surrounded by polycrystalline SiC as gained by previously described processes.
144 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 exhibit a layered structure of various alpha (non-cubic) polytypes with equal \hkl{0001} orientation.
146 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.
147 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.
148 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.
149 Controlled nucleation occurs on the SiC seed, which is held at approximately \unit[2200]{$^{\circ}$C}.
150 The growth process is commonly done in a high-purity argon atmosphere.
151 The method was successfully applied to grow 6H and 4H boules with diameters up to \unit[60]{mm}~\cite{tairov81,barrett91,barrett93,stein93}.
152 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}.
154 Although significant advances have been achieved in the field of SiC bulk crystal growth, a variety of problems remain.
155 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.
156 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.
157 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.
158 Additionally, to preserve epitaxial growth conditions, graphitization of the seed crystal has to be avoided.
159 Avoiding defects constitutes a major difficulty.
160 These defects include growth spirals (stepped screw dislocations), subgrain boundaries and twins as well as micropipes (micron sized voids extending along the
161 %c axis of the crystal)
162 core of screw dislocations)~\cite{frank51,heindl97}
163 and 3C inclusions at the seed crystal in hexagonal growth systems.
164 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}.
165 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.
167 \subsection{SiC epitaxial thin film growth}
169 Crystalline SiC layers have been grown by a large number of techniques on the surfaces of different substrates.
170 Most of the crystal growth processes are based on CVD, solid-source MBE (SSMBE) and gas-source MBE (GSMBE) on Si as well as SiC substrates.
171 In CVD as well as GSMBE, 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.
172 In the case of SSMBE, atoms are provided by electron beam evaporation of graphite and solid Si or thermal evaporation of fullerenes.
173 The following review will exclusively focus on CVD and MBE techniques.
175 The availability and reproducibility of Si substrates of controlled purity made it the first choice for SiC epitaxy.
176 The heteroepitaxial growth of SiC on Si substrates has been stimulated for a long time due to a lack of suitable large substrates that could be adopted for homoepitaxial growth.
177 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.
178 The main difficulties in SiC heteroepitaxy on Si arise due to the lattice mismatch of Si and SiC by \unit[20]{\%} and the difference in the thermal expansion coefficient of \unit[8]{\%}.
179 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}.
180 Cleaning of the substrate surface with HCl is required prior to carbonization.
181 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 of about \unit[1400]{$^{\circ}$C}.
182 In a next step, the epitaxial deposition of SiC is realized by an additional supply of Si atoms at similar temperatures.
183 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 to the SiC/Si interface~\cite{shibahara86}.
184 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}.
185 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}.
186 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}.
187 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}.
189 A reduction of the SF in addition to the APB defects was recently achieved by growing 3C-SiC on undulant Si~\cite{nagasawa06}, i.e.\ a Si \hkl(0 0 1) substrate covered with continuous slopes oriented in the \hkl[1 1 0] and \hkl[-1 -1 0] directions.
190 In this way, APB defects are eliminated by a mechanism similar to that in the off-axis growth process while, at the same time, SFs are aligned in the \hkl(1 1 1) or \hkl(-1 -1 1) planes and, thus, terminate as they connect with each other during the growth process.
192 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.
193 In summary, the almost universal use of Si has allowed significant progress in the understanding of heteroepitaxial growth of SiC on Si.
194 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 satisfactory.
196 The alternative attempt to grow SiC on SiC substrates has shown to drastically reduce the concentration of defects in deposited layers.
197 By CVD, both, the 3C~\cite{kong88,powell90} as well as the 6H~\cite{kong88_2,powell90_2} polytype could be successfully grown.
198 In order to obtain the homoepitaxially grown 6H polytype, off-axis 6H-SiC wafers are required as a substrate~\cite{kimoto93}.
199 %In the so called step-controlled epitaxy, lateral growth proceeds from atomic steps without the necessity of preceding nucleation events.
200 Investigations indicate that in the so-called step-controlled epitaxy, crystal growth proceeds through the adsorption of Si species at atomic steps and their carbonization by hydrocarbon molecules.
201 This growth mechanism does not require two-dimensional nucleation.
202 Instead, crystal growth is governed by mass transport, i.e.\ the diffusion of reactants in a stagnant layer.
203 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.
204 These films show a high density of double positioning boundary (DPB) defects, which is a special type of twin boundary arising at the interface of regions that occupy one of the two possible orientations of the hexagonal stacking sequence, which are rotated by \unit[60]{$^{\circ}$} relative to each other.
205 However, lateral 3C-SiC growth was also observed on low tilt angle off-axis substrates originating from intentionally induced dislocations~\cite{powell91}.
206 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.
207 Thus, 3C nucleation is assumed as a result of migrating Si and C containing molecules interacting with surface disturbances, in contrast to a model~\cite{ueda90}, in which the competing 6H versus 3C growth depends on the density of surface steps.
208 Combining the fact of a well defined 3C lateral growth direction, i.e.\ the tilt direction, and an intentionally induced dislocation, enables the controlled growth of a 3C-SiC film mostly free of DPBs~\cite{powell91}.
210 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.
211 Using alternating supply of the gas beams Si$_2$H$_6$ and C$_2$H$_2$ in GSMBE, 3C-SiC epilayers were obtained on 6H-SiC substrates at temperatures between \unit[850]{$^{\circ}$C} and \unit[1000]{$^{\circ}$C}~\cite{yoshinobu92}.
212 On \hkl(000-1) substrates twinned \hkl(-1-1-1) oriented 3C-SiC domains are observed, which suggest a nucleation driven rather than step-flow growth mechanism.
213 On \hkl(0-11-4) substrates, however, single crystalline \hkl(001) oriented 3C-SiC grows with the c axes of substrate and film being equal.
214 The beneficial epitaxial relation of substrate and film limits the structural difference between the two polytypes in two out of six layers with respect to the stacking sequence along the c axis.
215 Homoepitaxial growth of 3C-SiC by GSMBE was realized for the first time by atomic layer epitaxy (ALE) utilizing the periodical change in the surface superstructure by the alternating supply of the source gases, which determines the growth rate giving atomic level control in the growth process~\cite{fuyuki89}.
216 The cleaned substrate surface shows a C terminated $(2\times 2)$ pattern at \unit[1000]{$^{\circ}$C}, which turns into a $(3\times 2)$ pattern when Si$_2$H$_6$ is introduced and it is maintained after the supply is stopped.
217 A more detailed investigation showed the formation of a preceding $(2\times 1)$ and $(5\times 2)$ pattern within the exposure to the Si containing gas~\cite{yoshinobu90,fuyuki93}.
218 The $(3\times 2)$ superstructure contains approximately 1.7 monolayers of Si atoms, crystallizing into 3C-SiC with a smooth and mirror-like surface after C$_2$H$_6$ is inserted accompanied by a reconstruction of the surface into the initial C terminated $(2\times 2)$ pattern.
219 A minimal growth rate of 2.3 monolayers per cycle exceeding the value of 1.7 is due to physically adsorbed Si atoms not contributing to the superstructure.
220 To realize single monolayer growth, precise control of the gas supply to form the $(2\times 1)$ structure is required.
221 However, accurate layer-by-layer growth is achieved under certain conditions, which facilitate the spontaneous desorption of an additional layer of one atom species by supply of the other species~\cite{hara93}.
222 Homoepitaxial growth of the 6H polytype has been realized on off-oriented substrates utilizing simultaneous supply of the source gases~\cite{tanaka94}.
223 Depending on the gas flow ratio either 3C island formation or step flow growth of the 6H polytype occurs, which is explained by a model including aspects of enhanced surface mobilities of adatoms on a $(3\times 3)$ reconstructed surface.
224 Due to the strong adsorption of atomic hydrogen~\cite{allendorf91} decomposed of the gas phase reactants at low temperatures, however, there seems to be no benefit of GSMBE compared to CVD.
225 Next to lattice imperfections, incorporated hydrogen effects the surface mobility of the adsorbed species~\cite{eaglesham93} setting a minimum limit for the growth temperature, which would preferably be further decreased in order to obtain sharp doping profiles.
226 Thus, growth rates must be adjusted to be lower than the desorption rate of hydrogen, which leads to very low deposition rates at low temperatures.
227 SSMBE, by supplying the atomic species to be deposited by evaporation of a solid, presumably constitutes the preferred method in order to avoid the problems mentioned above.
228 Although, in the first experiments, temperatures still above \unit[1100]{$^{\circ}$C} were necessary to epitaxially grow 3C-SiC films on 6H-SiC substrates~\cite{kaneda87}, subsequent attempts succeeded in growing mixtures of twinned 3C-SiC and 6H-SiC films on off-axis \hkl(0001) 6H-SiC wafers at temperatures between \unit[800]{$^{\circ}$C} and \unit[1000]{$^{\circ}$C}~\cite{fissel95,fissel95_apl}.
229 In the latter approach, as in GSMBE, excess Si atoms, which are controlled by the Si/C flux ratio, result in the formation of a Si adlayer and the formation of a non-stoichiometric, reconstructed surface superstructure, which influences the mobility of adatoms and, thus, has a decisive influence on the growth mode, polytype and crystallinity~\cite{fissel95,fissel96,righi03}.
230 Therefore, carefully controlling the Si/C ratio could be exploited to obtain definite heterostructures of different SiC polytypes providing the possibility for band gap engineering in SiC materials.
232 To summarize, much progress has been achieved in SiC thin film growth during the last few years.
233 However, the frequent occurrence of defects such as dislocations, twins and double positioning boundaries limit the structural and electrical quality of large SiC films.
234 Solving this issue remains a challenging problem necessary to drive SiC for potential applications in high-performance electronic device production~\cite{wesch96}.
236 \subsection{Ion beam synthesis of cubic silicon carbide}
237 \label{subsection:ibs}
239 Although tremendous progress has been achieved in the above-mentioned growth methods during the last decades, available wafer dimensions and crystal qualities are not yet satisfactory.
240 Thus, alternative approaches to fabricate SiC have been explored.
241 The ion beam synthesis (IBS) technique, i.e.\ high-dose ion implantation followed by a high-temperature annealing step, turned out to constitute a promising method to directly form compound layers of high purity and accurately controllable depth and stoichiometry.
242 A short chronological summary of the IBS of SiC and its origins is presented in the following.
244 High-dose carbon implantation into crystalline silicon (c-Si) with subsequent or in situ annealing was found to result in SiC microcrystallites in Si~\cite{borders71}.
245 Rutherford backscattering spectrometry (RBS) and infrared (IR) spectroscopy investigations indicate a \unit[10]{at.\%} C concentration peak and the occurrence of disordered C-Si bonds after implantation at room temperature (RT) followed by crystallization into SiC precipitates upon annealing.
246 This is demonstrated by a shift in the IR absorption band and the disappearance of the C profile peak in RBS.
247 Implantations at different temperatures revealed a strong influence of the implantation temperature on the compound structure~\cite{edelman76}.
248 Temperatures below \unit[500]{$^{\circ}$C} result in amorphous layers, which are transformed into polycrystalline 3C-SiC after annealing at \unit[850]{$^{\circ}$C}.
249 Otherwise, single crystalline 3C-SiC is observed for temperatures above \unit[600]{$^{\circ}$C}.
250 Annealing temperatures necessary for the onset of the amorphous to crystalline transition have been confirmed by further studies~\cite{kimura81,kimura82}.
251 Overstoichiometric doses result in the formation of clusters of C, which do not contribute to SiC formation during annealing up to \unit[1200]{$^{\circ}$C}~\cite{kimura82}.
252 The amount of formed SiC, however, increases with increasing implantation temperature.
253 The authors, thus, concluded that implantations at elevated temperatures lead to a reduction in the annealing temperatures required for the synthesis of homogeneous layers of SiC.
254 In a comparative study of O, N and C implantation into Si, the absence of the formation of a stoichiometric SiC compound layer involving the transition of a Gaussian into a box-like C depth profile with respect to the implantation depth for the superstoichiometric C implantation and an annealing temperature of \unit[1200]{$^{\circ}$C} in contrast to the O and N implantations, which successfully form homogeneous layers, has been observed~\cite{reeson86}.
255 This was attributed to the difference in the enthalpy of formation of the respective compound and the different mobility of the respective impurity in bulk Si.
256 Thus, higher annealing temperatures and longer annealing times were considered necessary for the formation of homogeneous SiC layers.
257 Indeed, for the first time, buried homogeneous and stoichiometric epitaxial 3C-SiC layers embedded in single crystalline Si were obtained by the same group consequently applying annealing temperatures of \unit[1405]{$^{\circ}$C} for \unit[90]{min} and implantation temperatures of approximately \unit[550]{$^{\circ}$C}~\cite{reeson87}.
258 The necessity of the applied extreme temperature (a few degrees below the Si melting point) and time scale is attributed to the stability of substitutional C within the Si matrix being responsible for high activation energies necessary to dissolve such precipitates and, thus, allow for redistribution of the implanted C atoms.
259 In order to avoid extreme annealing temperatures close to the melting temperature of Si, triple-energy implantations in the range from \unit[180--190]{keV} with stoichiometric doses at a constant target temperature of \unit[860]{$^{\circ}$C} achieved by external substrate heating were performed~\cite{martin90}.
260 It was shown that a thick buried layer of SiC is directly formed during implantation, which consists of small, only slightly misorientated but severely twinned 3C-SiC crystallites.
261 The authors assumed that due to the auxiliary heating rather than ion beam heating as employed in all the preceding studies, the complexity of the remaining defects in the synthesized structure is fairly reduced.
262 Even better qualities by direct synthesis were obtained for implantations at \unit[950]{$^{\circ}$C}~\cite{nejim95}.
263 Since no amorphous or polycrystalline regions have been identified, twinning is considered to constitute the main limiting factor in the IBS of SiC.
264 Layers obtained by direct synthesis are characterized by rough surfaces of the buried layer and the substrate originating from the dendritic growth of SiC crystals at these temperatures~\cite{lindner06}.
266 Further studies revealed the possibility to form buried layers of SiC by IBS at moderate substrate and anneal temperatures~\cite{lindner95,lindner96}.
267 Different doses of C ions with an energy of \unit[180]{keV} were implanted at \unit[330--440]{$^{\circ}$C} and annealed at \unit[1200]{$^{\circ}$C} or \unit[1250]{$^{\circ}$C} for \unit[5--10]{h}.
268 For a critical dose, which was found to depend on the Si substrate orientation, the formation of a stoichiometric buried layer of SiC exhibiting a well-defined interface to the Si host matrix was observed.
269 In case of overstoichiometric C concentrations, the excess C is not redistributed.
270 These investigations demonstrate the presence of an upper dose limit, which corresponds to a \unit[53]{at.\%} C concentration at the implantation peak, for the thermally induced redistribution of the C atoms from a Gaussian to a box-shaped depth profile upon annealing.
271 This is explained by the formation of strong graphitic C-C bonds for higher C concentrations~\cite{calcagno96}.
272 Increased temperatures exceeding the Si melting point are expected to be necessary for the dissociation of these C clusters.
273 Furthermore, higher implantation energies were found to result in layers of variable composition exhibiting randomly distributed SiC precipitates.
274 In another study~\cite{serre95} high dose C implantations were performed at room temperature and \unit[500]{$^{\circ}$C} respectively.
275 Implantations at room temperature lead to the formation of a buried amorphous carbide layer in addition to a thin C-rich film at the surface, which is attributed to the migration of C atoms towards the surface.
276 In contrast, implantations at elevated temperatures result in the exclusive formation of a buried layer consisting of 3C-SiC precipitates epitaxially aligned to the Si host, which obviously is more favorable than the C migration towards the surface.
277 Annealing at temperatures up to \unit[1150]{$^{\circ}$C} does not alter the C profile.
278 Instead, defect annihilation is observed and the C-rich surface layer of the room temperature implant turns into a layer consisting of SiC precipitates, which, however, are not aligned with the Si matrix indicating a mechanism different to the one of the direct formation for the high-temperature implantation.
280 Based on these findings%
281 % and extensive TEM investigations
282 , a recipe was developed to form buried layers of single-crystalline SiC featuring an improved interface and crystallinity~\cite{lindner99,lindner01,lindner02}.
283 Therefor, the dose must not exceed the stoichiometry dose, i.e.\ the dose corresponding to \unit[50]{at.\%} C concentration at the implantation peak.
284 Otherwise, clusters of C are formed, which cannot be dissolved during post-implantation annealing at moderate temperatures below the Si melting point~\cite{lindner96,calcagno96}.
285 Annealing should be performed for \unit[5--10]{h} at \unit[1250]{$^{\circ}$C} to enable the redistribution from the as-implanted Gaussian into a box-like C depth profile~\cite{lindner95}.
286 The implantation temperature constitutes the most critical parameter, which is responsible for the structure after implantation and, thus, the starting point for subsequent annealing steps.
287 Implantations at \unit[400]{$^{\circ}$C} resulted in buried layers of SiC subdivided into a polycrystalline upper and an epitaxial lower part.
288 This corresponds to the region of randomly oriented SiC crystallites and epitaxially aligned precipitates surrounded by thin amorphous layers without crystalline SiC inclusions in the as-implanted state.
289 However, an abrupt interface to the Si host is observed after annealing.
290 As expected, single-crystalline layers were achieved for an increased temperature of \unit[600]{$^{\circ}$C}.
291 However, these layers show an extremely poor interface to the Si top layer governed by a high density of SiC precipitates, which are not affected in the C redistribution during annealing and, thus, responsible for the rough interface.
292 Hence, to obtain sharp interfaces and single-crystalline SiC layers temperatures between \unit[400]{$^{\circ}$C} and \unit[600]{$^{\circ}$C} have to be used.
293 Indeed, reasonable results were obtained at \unit[500]{$^{\circ}$C}~\cite{lindner98} and even better interfaces were observed for \unit[450]{$^{\circ}$C}~\cite{lindner99_2}.
294 To further improve the interface quality and crystallinity, a two-temperature implantation technique was developed~\cite{lindner99}.
295 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}.
296 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 destruction of SiC nanocrystals within these zones.
297 After annealing for \unit[10]{h} at \unit[1250]{$^{\circ}$C}, a homogeneous, stoichiometric SiC layer with sharp interfaces is formed.
298 Fig.~\ref{fig:sic:hrem_sharp} shows the respective high resolution transmission electron microscopy micrographs.
301 \includegraphics[width=0.6\columnwidth]{ibs_3c-sic.eps}
303 \caption[Bright field and \hkl(1 1 1) SiC dark field cross-sectional TEM micrographs of the buried SiC layer in Si created by the two-temperature implantation technique and subsequent annealing.]{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.}
304 \label{fig:sic:hrem_sharp}
307 To summarize, by understanding some basic processes, 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.
308 Due to the high areal homogeneity achieved in IBS, the size of the layers is only limited by the width of the beam-scanning equipment used in the implantation system.
309 % as opposed to deposition techniques, which have to deal with severe wafer bending.
310 Buried layers can be revealed at the surface by additional implantation and etching steps~\cite{attenberger03}.
311 They do not exhibit surface bending effects in contrast to these formed by the MBE or CVD technique.
312 This enables the synthesis of large area SiC films.
314 \section{Substoichiometric concentrations of carbon in crystalline silicon}
316 In the following, some basic properties of C in crystalline Si are reviewed.
317 A lot of work has been done contributing to the understanding of C in Si either as an isovalent impurity as well as at concentrations exceeding the solid solubility limit.
318 A comprehensive survey on C-mediated effects in Si has been published by Skorupa and Yankov~\cite{skorupa96}.
320 \subsection{Carbon as an impurity in silicon}
322 Below the solid solubility, C impurities mainly occupy substitutionally Si lattice sites in Si~\cite{newman65}.
323 Due to the much smaller covalent radius of C compared to Si, every incorporated C atom leads to a decrease in the lattice constant corresponding to a lattice contraction of about one atomic volume~\cite{baker68}.
324 The induced strain is assumed to be responsible for the low solid solubility of C in Si, which was determined~\cite{bean71} to be
326 c_{\text{s}}=4\times10^{24}\,\text{cm$^{-3}$}
327 \cdot\exp(-2.3\,\text{eV/$k_{\text{B}}T$})
331 The barrier of diffusion of substitutional C has been determined to be around \unit[3]{eV}~\cite{newman61}.
332 However, as suspected due to the substitutional position, the diffusion of C requires intrinsic point defects, i.e.\ Si self-interstitials and vacancies.
333 Similar to phosphorous and boron, which exclusively use self-interstitials as a diffusion vehicle, the diffusion of C atoms is expected to obey the same mechanism.
334 Indeed, enhanced C diffusion was observed in the presence of self-interstitial supersaturation~\cite{kalejs84} indicating an appreciable diffusion component involving self-interstitials and only a negligible contribution by vacancies.
335 Substitutional C and interstitial Si react into a C-Si complex forming a dumbbell structure oriented along a crystallographic \hkl<1 0 0> direction on a regular Si lattice site.
336 This structure, the so called C-Si \hkl<1 0 0> dumbbell structure, was initially suspected by local vibrational mode absorption~\cite{bean70} and finally verified by electron paramagnetic resonance~\cite{watkins76} studies on irradiated Si substrates at low temperatures.
337 Measuring the annealing rate of the defect as a function of temperature reveals barriers for migration of \unit[0.70]{eV}~\cite{lindner06}, \unit[0.73]{eV}~\cite{song90} and \unit[0.87]{eV}~\cite{tipping87}, which is highly mobile compared to substitutional C.
339 % expansion of the lattice (positive strain)
341 %\subsection{Agglomeration phenomena}
342 % c-si agglomerattion as an alternative to sic precipitation (due to strain)
343 % -> maybe this fits better in prec model in next chapter
345 \subsection{Suppression of transient enhanced diffusion of dopant species}
347 The predominant diffusion mechanism of most dopants in Si based on native self-interstitials~\cite{fahey89} has a large impact on the diffusion behavior of dopants that have been implanted in Si.
348 The excess population of Si self-interstitials created by low-energy implantations of dopants for shallow junction formation in submicron technologies may enhance the diffusion of the respective dopant during annealing by more than one order of magnitude compared to normal diffusion.
349 This kind of diffusion, labeled transient enhanced diffusion (TED), which is driven by the presence of non-equilibrium concentrations of point defects, was first discovered for implantations of boron in Si~\cite{hofker74} and is well understood today~\cite{michel87,cowern90,stolk95,stolk97}.
350 The TED of B was found to be inhibited in the presence of a sufficient amount of incorporated C~\cite{cowern96}.
351 This is due to the reduction of the excess Si self-interstitials with substitutional C atoms forming the C-Si interstitial complex~\cite{stolk97,zhu98}.
352 Therefore, incorporation of C provides a promising method for suppressing TED enabling an improved shallow junction formation in future Si devices.
354 % in general: high c diffusion in areas of high damage, low diffusion for substitutional or even sic prec
356 \subsection{Strained silicon and silicon heterostructures}
358 % lattice location of implanted carbon
359 Radiation damage introduced during implantation and a high concentration of the implanted species, which results in the reduction of the topological constraint of the host lattice imposed on the implanted species, can affect the manner of impurity incorporation.
360 The probability of finding C, which will be most stable at sites for which the number of neighbors equals the natural valence, i.e.\ substitutionally on a regular Si site of a perfect lattice, is, thus, reduced at substitutional lattice sites and likewise increased at interstitial sites.
361 Indeed, x-ray rocking curves reveal a positive lattice strain, which is decreased but still remains with increasing annealing temperature, indicating the location of the majority of implanted C atoms at interstitial sites~\cite{isomae93}.
362 Due to the absence of dislocations in the implanted region, interstitial C is assumed to prevent clustering of implantation-induced Si self-interstitials by agglomeration of C-Si interstitials or the formation of SiC precipitates accompanied by a relaxation of the lattice strain.
364 % link to strain engineering
365 However, there is great interest to incorporate C onto substitutional lattice sites, which results in a contraction of the Si lattice due to the smaller covalent radius of C compared to Si~\cite{baker68}, causing tensile strain, which is applied to the Si lattice.
366 Thus, substitutional C enables strain engineering of Si and Si/Si$_{1-x}$Ge$_x$ heterostructures~\cite{yagi02,chang05,kissinger94,osten97}, which is used to increase charge carrier mobilities in Si as well as to adjust its band structure~\cite{soref91,kasper91}.
367 % increase of C at substitutional sites
368 Epitaxial layers with \unit[1.4]{at.\%} of substitutional C have been successfully synthesized in preamorphized Si$_{0.86}$Ge$_{0.14}$ layers, which were grown by CVD on Si substrates, using multiple-energy C implantation followed by solid-phase epitaxial regrowth at \unit[700]{$^{\circ}$C}~\cite{strane93}.
369 The tensile strain induced by the C atoms is found to compensate the compressive strain present due to the Ge atoms.
370 Studies on the thermal stability of Si$_{1-y}$C$_y$/Si heterostructures formed in the same way and equal C concentrations showed a loss of substitutional C accompanied by strain relaxation for temperatures ranging from \unit[810--925]{$^{\circ}$C} and the formation of spherical 3C-SiC precipitates with diameters of \unit[2--4]{nm}, which are incoherent but aligned to the Si host~\cite{strane94}.
371 During the initial stages of precipitation C-rich clusters are assumed, which maintain coherency with the Si matrix and the associated biaxial strain.
372 Using this technique, a metastable solubility limit was achieved, which corresponds to a C concentration exceeding the solid solubility limit at the Si melting point by nearly three orders of magnitude and, furthermore, a reduction of the defect density near the metastable solubility limit is assumed if the regrowth temperature is increased by rapid thermal annealing~\cite{strane96}.
373 Since high temperatures used in the solid-phase epitaxial regrowth method promotes SiC precipitation, other groups realized substitutional C incorporation for strained Si$_{1-y}$C$_y$/Si heterostructures~\cite{iyer92,fischer95,powell93,osten96,osten99,laveant2002} or partially to fully strain-compensated (even inversely distorted~\cite{osten94_2}) Si$_{1-x-y}$Ge$_x$C${_y}$ layers on Si~\cite{eberl92,powell93_2,osten94,dietrich94} by MBE.
374 Investigations reveal a strong temperature-dependence of the amount of substitutionally incorporated C, which is increased for decreasing temperature accompanied by deterioration of the crystal quality~\cite{osten96,osten99}.
375 While not being compatible to very-large-scale integration technology, C concentrations of \unit[2]{\%} and more have been realized~\cite{laveant2002}.
377 \section{Assumed silicon carbide conversion mechanisms}
378 \label{section:assumed_prec}
380 Although high-quality films of single-crystalline 3C-SiC can be produced by means of IBS, the precipitation mechanism in bulk Si is not yet fully understood.
381 Indeed, closely investigating the large amount of literature pulled up in the last two sections and a cautious combination of some of the findings reveals controversial ideas of SiC formation, which are reviewed in more detail in the following.
383 High resolution transmission electron microscopy (HREM) investigations of C-implanted Si at room temperature followed by rapid thermal annealing (RTA) indicate the formation of C-Si dumbbell agglomerates, which are stable up to annealing temperatures of about \unit[700--800]{$^{\circ}$C}, and a transformation into 3C-SiC precipitates at higher temperatures~\cite{werner96,werner97}.
384 The precipitates with diameters 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.
385 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}.
386 The agglomerates of such dimers, which do not generate lattice strain but lead to a local increase of the lattice potential~\cite{werner96,werner97}, are indicated by dark contrasts and otherwise undisturbed Si lattice fringes in HREM, as can be seen in Fig.~\ref{fig:sic:hrem:c-si}.
389 \subfigure[]{\label{fig:sic:hrem:c-si}\includegraphics[width=0.25\columnwidth]{tem_c-si-db.eps}}
390 \subfigure[]{\label{fig:sic:hrem:sic}\includegraphics[width=0.25\columnwidth]{tem_3c-sic.eps}}
392 \caption[High resolution transmission electron microscopy (HREM) micrographs of agglomerates of C-Si dimers showing dark contrasts and otherwise undisturbed Si lattice fringes and equally sized Moir\'e patterns indicating 3C-SiC precipitates.]{High resolution transmission electron microscopy (HREM) micrographs~\cite{lindner99_2} of agglomerates of C-Si dimers showing dark contrasts and otherwise undisturbed Si lattice fringes (a) and equally sized Moir\'e patterns indicating 3C-SiC precipitates (b).}
395 A topotactic transformation into a 3C-SiC precipitate occurs once a critical radius of \unit[2]{nm} to \unit[4]{nm} is reached.
396 The precipitation is manifested by the disappearance of the dark contrasts in favor of Moir\'e patterns (Fig.~\ref{fig:sic:hrem:sic}) due to the lattice mismatch of \unit[20]{\%} of the 3C-SiC precipitate and the Si host.
397 The insignificantly lower Si density of SiC of approximately \unit[3]{\%} compared to c-Si results in the emission of only a few excess Si atoms.
398 The same mechanism was identified by high resolution x-ray diffraction~\cite{eichhorn99}.
399 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.
400 The precipitation mechanism based on a preceding dumbbell agglomeration as indicated by the above-mentioned experiments is schematically displayed in Fig.~\ref{fig:sic:db_agglom}.
403 \subfigure[]{\label{fig:sic:db_agglom:seq01}\includegraphics[width=0.30\columnwidth]{sic_prec_seq_01.eps}}
404 %C-Si dumbbell formation
406 \subfigure[]{\label{fig:sic:db_agglom:seq02}\includegraphics[width=0.30\columnwidth]{sic_prec_seq_02.eps}}
407 %Dumbbell agglomeration
409 \subfigure[]{\label{fig:sic:db_agglom:seq03}\includegraphics[width=0.30\columnwidth]{sic_prec_seq_03.eps}}
410 %SiC formation and release of excess Si atoms
412 \caption[Two dimensional schematic of the assumed SiC precipitation mechanism based on an initial C-Si dumbbell agglomeration.]{Two dimensional schematic of the assumed SiC precipitation mechanism based on an initial C-Si dumbbell agglomeration. C atoms (red dots) incorporated into the Si (black dots) host form C-Si dumbbells (a), which agglomerate into clusters (b) followed by precipitation of SiC and the emission of a few excess Si atoms (black circles), which are located in the interstitial Si lattice (c). The dotted lines mark the atomic spacing of c-Si in \hkl[1 0 0] direction indicating the $4/5$ ratio of the lattice constants of c-Si and 3C-SiC.}
413 \label{fig:sic:db_agglom}
415 The incorporated C atoms form C-Si dumbbells on regular Si lattice sites.
416 With increasing dose and proceeding time, the highly mobile dumbbells agglomerate into large clusters.
417 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.
418 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.
420 In contrast, IR spectroscopy and HREM investigations on the thermal stability of strained Si$_{1-y}$C$_y$/Si heterostructures formed by solid-phase epitaxy (SPE)~\cite{strane94} and 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.
421 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.
422 Increased temperatures in the annealing process enable the diffusion and agglomeration of C atoms.
423 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.
424 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.
426 This different mechanism of precipitation might be attributed to the respective method of fabrication.
427 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.
428 However, in another IBS study Nejim et~al.~\cite{nejim95} propose a
430 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.
431 The replacement of a Si unit cell by a 3C-SiC unit cell is accompanied by a volume reduction of \unit[48]{\%} due to the \unit[20]{\%} lower lattice constant.
432 Since the emerging strain caused by the expected volume reduction 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.
433 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.
434 However, the exact atomic rearrangement involved within this topotactic transformation is not identified.
435 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.
436 The results support a mechanism of an initial coherent precipitation based on substitutional C that is likewise valid for the IBS of 3C-SiC by C implantation into Si at elevated temperatures.
437 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 straightforward 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.
439 To conclude, a controversy with respect to the precipitation model of SiC in Si exists in literature.
440 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.
441 On the other hand, processes relying upon prevention of precipitation in order to produce strained heterostructures will likewise benefit.
444 % werner96/7: rt implants followed by rta < 800: C-Si db aggloms | > 800: 3C-SiC
445 % taylor93: si_i reduces interfacial energy (explains metastability) of sic/si
446 % eichhorn02: high imp temp more efficient than postimp treatment
447 % eichhorn99: same as 02 + c-si agglomerates at low concentrations
448 % strane94/guedj98: my model - c redist by si int (spe) and surface diff (mbe)
449 % serre95: low/high t implants -> mobile c_i / non-mobile sic precipitates
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