Data-driven feasibility study of VGF β-Ga2O3 growth under traveling magnetic fields

Numerical simulations were conducted to examine the impact of a traveling magnetic field on the vertical gradient freeze growth of β-Ga₂O₃ crystals within a coated sapphire crucible under an argon-oxygen atmosphere. The research aimed to enhance β-Ga₂O₃ crystal growth by achieving a flatter solid–liquid interface through the application of Lorentz forces generated by KRIST $\stackrel{\sim }{\mathrm{MAG}}$® heaters. Furthermore, the study sought to identify a coating material that is chemically resistant and has a minimal effect on the magnitude of the Lorentz force.

To derive an equation that relates the Lorentz force with key growth parameters, we utilized SISSO, a machine learning technique combining symbolic regression and compressed sensing. The numerical results indicated that an upward traveling magnetic field significantly modifies the solid–liquid interface shape by counteracting buoyancy, enhancing vortex strength, and flattening the previously convex interface. The Pt-Rh alloy coating demonstrated minimal impact on the Lorentz force magnitude. Lorentz force exhibited a quadratic dependence on AC, periodic with a phase shift, and an asymmetric Gaussian profile with frequency.

Compressed sensing, along with numerical data, produced a broadly applicable and interpretable equation for predicting Lorentz force values in the VGF growth setup, identifying phase shift as a crucial variable.