Anisotropic thermal expansion tensor of β-Ga₂O₃ and its critical role in casting-grown crystal cracking

Thermal expansion tensor represents a key parameter for the numerical modeling of the crystal growth process. However, the modeling of β-Ga₂O₃ commonly utilizes one single thermal expansion constant that misses its anisotropic nature and temperature-dependent characteristics. Herein, we addressed this limitation by calibrating an anisotropic, temperature-dependent thermal expansion tensor using the experimental lattice parameters of β-Ga₂O₃ up to 1200 K. We found that COMSOL Multiphysics simulations employing the calibrated tensor yield stress distribution remarkably distinct from those relying on the commonly assumed constants. Specifically, our simulations predict a von Mises stress concentration near the crystal bottom, which explains the experimentally observed crack formation at corresponding locations. This contrasts with the simulations using the single-value thermal expansion constant, which fails to predict such stress concentration. The physical origin of crystal cracking is found to be rooted in the compressive force exerted by the iridium crucible during the cooling process. Our findings suggest that the physical anisotropy of β-Ga₂O₃ should be carefully considered in modeling and simulation. With the calibrated thermal expansion tensor, we provide a validated set of thermomechanical parameters for reliable β-Ga₂O₃ crystal growth simulations.