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A review of the simulation studies on the bulk growth of silicon carbide single crystals

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Abstract

Silicon carbide (SiC) is a wide-bandgap semiconductor material that is viable for the next generation of high-performance and high-power electrical devices. In general, bulk SiC single crystals have been grown at very high temperatures in a closed reactor; hence, the growth process is difficult to monitor using in situ techniques. Consequently, computational simulations have been utilized to understand, validate, and design crystal growth processes. In this review, we summarize the results of computational simulations of SiC bulk crystal growth using three primary methods: physical vapor transport, high-temperature chemical vapor deposition, and top-seeded solution growth. The simulations reveal the effects of physicochemical phenomena, such as temperature distribution, fluid flow, and chemical reactions, on crystal growth behaviors. Process parameters for high-quality and high-yield crystal growth have been realized with the aid of simulations. Furthermore, recent advances in machine learning techniques for accelerating the design of crystal growth parameters and enabling real-time parameter optimization are introduced. Overall, computational simulations are a crucial tool for the development of SiC bulk crystal growth and its applications.

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Abbreviations

\({\varvec{H}}\) :

Magnetic field intensity, A/m

\({\varvec{B}}\) :

Magnetic flux density, T

\({\varvec{A}}\) :

Magnetic potential vector, Vs/m

\(\omega\) :

Angular frequency, rad/s

\({\varvec{E}}\) :

Electric field intensity, V/m

\({\varvec{D}}\) :

Electric flux density, C/m2

\({\varvec{J}}\) :

Electric current density, A/m2

\(\sigma\) :

Electrical conductivity, S/m

\(i\) :

Imaginary unit

\(\mathrm{Re}\) :

Real part of a complex number

\(Q\) :

Heat, J

\(\rho\) :

Density, kg/m3

\({C}_{\mathrm{p}}\) :

Heat capacity, J/(kg·K)

\(T\) :

Temperature, K

\(k\) :

Thermal conductivity, W/(m·K)

\(G\) :

Surface irradiation, W/m2

\({G}_{\mathrm{m}}\) :

Mutual surface irradiation, W/m2

\({F}_{\mathrm{amb}}\) :

Ambient view factor

\({\varepsilon }_{\mathrm{s}}\) :

Surface emissivity

\({\sigma }_{\mathrm{sb}}\) :

Stefan–Boltzmann constant, W/(m2K4)

\({T}_{\mathrm{amb}}\) :

Ambient temperature, K

\(J\) :

Surface radiosity, W/m2

\({\varvec{n}}\) :

Radiation direction vector

\({\varvec{u}}\) :

Velocity field, m/s

\(p\) :

Pressure, Pa

\(t\) :

Time, s

\({\varvec{\tau}}\) :

Viscous stress, Pa

\({{\varvec{F}}}_{\mathbf{e}\mathbf{x}\mathbf{t}}\) :

External force density, N/m3

\(D\) :

Diffusion coefficient, m2/s

\(c\) :

Concentration, mol/m3

\({G}_{\mathrm{rate}}\) :

Growth rate, m/s

\(M\) :

Molar mass, g/mol

\({J}_{\mathrm{species}}\) :

Mass flux, mol/m2s

\(r\) :

Radius, m

\(S\) :

Area, m2

\(K\) :

Equilibrium constant

\(P\) :

Partial pressure, Pa

\(R\) :

Molar gas constant, J/molK

\({S}_{\mathrm{eff}}\) :

Effective vapor supersaturation

\(A\) :

Pre-exponential factor

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    Minh-Tan Ha & Seong-Min Jeong

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Ha, MT., Jeong, SM. A review of the simulation studies on the bulk growth of silicon carbide single crystals. J. Korean Ceram. Soc. 59, 153–179 (2022). https://doi.org/10.1007/s43207-022-00188-y

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