Internal Radiation During β -Ga2O3 Crystal Growth Process by Vertical Bridgman Method

doi:10.16553/j.cnki.issn1000-985x.2025.0222

Abstract

Abstract: β-phase gallium oxide （β-Ga₂O₃） crystals have become a key material for high-power devices due to their ultra-wide bandgap characteristics. The vertical Bridgman （VB） method is currently the most promising approach for commercial-scale growth of gallium oxide single crystals. However， the semi-transparent nature of gallium oxide crystals and melts can cause significant internal radiation， which affects the temperature and flow fields during crystal growth process， and thus the crystal quality. Therefore， in this paper， a heat transfer numerical model for the growth process of gallium oxide crystals by VB method was established using the finite element software Comsol Multiphysics. The influence of internal radiation on the temperature field， melt flow field， melt-crystal interface， and crystal thermal stress was systematically investigated. The numerical simulation results show that the internal radiation in the crystal significantly enhances the thermal transport of the crystal. The radiation heat from the melt-crystal interface can directly penetrate the semi-transparent crystal to the crucible wall， reducing the temperature gradient and thermal stress inside the crystal. This radiation directly cools the melt-crystal interface， causing a downward trend in the temperature at the interface. To maintain the melting point temperature， the melt-crystal interface must move towards the upper high-temperature melt， increasing the convexity of the interface. The internal radiation in the melt also affects the heat transfer in the melt region. The radiation from the hot zone can penetrate the melt to the melt-crystal interface， radiatively heating the interface. Therefore， the melt-crystal interface moves towards the crystal side， and the convexity of the interface shape decreases， presenting a W-shaped distribution. However， since the isothermal lines and thermal stress of the crystal mainly accumulate at the bottom of the crystal， the effect on the temperature gradient and thermal stress inside the crystal is small. In addition， the sensitivity of internal radiation to the absorption coefficients of the crystal and melt was systematically analyzed. It was found that as the absorption coefficient of the crystal decreases， the internal radiation in the crystal increases， the temperature gradients in the melt and crystal decrease， the thermal stress of the crystal decreases， and the convexity of the melt-crystal interface increases， leading to an uneven radial distribution of solutes. As the absorption coefficient of the melt decreases， the internal radiation in the melt increases， the temperature gradient and thermal stress at the bottom of the crystal slightly decrease， the convexity of the melt-crystal interface at the center decreases， the W-shaped distribution becomes more obvious， and the edges are more prone to polycrystalline nucleation， thereby affecting the crystal quality.

Key words: gallium oxide crystal; vertical Bridgman method; internal radiation; thermal stress; numerical simulation

CLC Number:

O782

ZHAO Qi, LIU Yihao, QI Xiaofang, MA Wencheng, XU Yongkuan, HU Zhanggui. Internal Radiation During β -Ga₂O₃ Crystal Growth Process by Vertical Bridgman Method[J]. Journal of Synthetic Crystals, 2026, 55(3): 439-451.

Figures/Tables 13

Fig.1 Schematic diagram of VB method for β-Ga2O3 crystal growth device

Table 1 Thermophysical parameters of main materials［17，19，21?22］

Material	Variable	Value
Ga₂O₃ melt	Density/（kg·m^-3）	6 000
	Thermal conductivity（W·m^-1·K^-1）	3.5
	Heat capacity/（J·kg^-1·K^-1）	800
	Latent heat/（kJ·kg^-1）	535.5
	Dynamic viscosity/（kg·m^-1·s^-1）	0.1
	Surface emissivity	0.5
	Thermal expansion/K^-1	1.8×10^-5
	Refractive index	1.9
Ga₂O₃ crystal	Density/（kg·m^-3）	5 950
	Thermal conductivity（W·m^-1·K^-1）	1.07
	Heat capacity/（J·kg^-1·K^-1）	720
	Melting point/K	2 068
	Surface emissivity	0.3
	Thermal expansion/K^-1	3.4×10^-6
	Elastic modulus/GPa	200
	Poisson ratio	0.26
Al₂O₃	Density/（kg·m^-3）	3 965
	Thermal conductivity/（W·m^-1·K^-1）	35
	Heat capacity/（J·kg^-1·K^-1）	730
	Surface emissivity	0.75
Pt-20%Rh	Density/（kg·m^-3）	20 500
	Thermal conductivity/（W·m^-1·K^-1）	70.05
	Heat capacity/（J·kg^-1·K^-1）	133
	Surface emissivity	0.75
Felt	Density/（kg·m^-3）	120
	Thermal conductivity/（W·m^-1·K^-1）	1.2
	Heat capacity/（J·kg^-1·K^-1）	1 890
	Surface emissivity	0.8

Fig.2 Temperature fields， flow fields， and von Mises stress diagrams at different growth stages when both the crystal and the melt are opaque

Fig.3 Temperature fields， flow fields， and von Mises stress diagrams at different growth stages when the crystal is semi-transparent

Fig.4 Temperature fields， flow fields， and von Mises stress diagrams at different growth stages when the melt is semi-transparent

Fig.5 Temperature fields， flow fields， and von Mises stress diagrams at different growth stages when both the crystal and the melt are semi-transparent

Fig.6 Comparison of melt-crystal interface shapes under different internal radiation conditions at early stage （a）， middle stage （b）， and late stage （c）

Fig.7 Temperature fields， flow fields， and von Mises stress diagrams under different crystal absorption coefficients

Fig.8 Comparison of melt-crystal interface shapes with different crystal absorption coefficients

Fig.9 Influence of internal radiation on the temperature gradient （a） and von Mises stress （b） along the centerline at the bottom of the crystal

Fig.10 Influence of crystal absorption coefficient on the temperature gradient （a） and von Mises stress distribution （b） along the periphery of the crystal

Fig.11 Temperature fields， flow fields， and von Mises stress diagrams under different melt absorption coefficients

Fig.12 Comparison of melt-crystal interface shapes under different melt absorption coefficients

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Internal Radiation During β -Ga₂O₃ Crystal Growth Process by Vertical Bridgman Method

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