Investigation of O interstitial diffusion in β-Ga₂O₃: a direct approach via master diffusion equations

Monoclinic beta gallium oxide (β-Ga₂O₃) is an anisotropic ultra-wide-bandgap semiconductor that has gained significant attention due to its large bandgap of 4.8 eV, high breakdown electric field, and notable thermal stability. These properties make it ideal for specialized electronic devices, such as power electronics and UV-photo detectors. Due to its anisotropic nature, native defects in β-Ga₂O₃ play a critical role in determining direction-dependent electrical and optical behaviors, which are strongly influenced by defect diffusion. A complete understanding of the diffusion network, which encompasses the pathways and mechanisms of atomic migration, is vital for controlling doping processes and enhancing material stability at various operating conditions. In this work, the 3D diffusion tensor for oxygen interstitials in β-Ga₂O₃ was predicted using first principles calculations and direct solution of the master diffusion equations. First, we exhaustively explore the configuration space of in the two dominant charge states (0 and 2-) and obtained their formation energies. Second, by connecting each low-energy configuration, we enumerate all possible hopping paths, accounting for both interstitial or interstitialcy hops, to describe the migration of within the highly anisotropic lattice. Using the nudged elastic band method, we find the hopping barriers identified hops. Lastly, combining the complete collection of (i) defect configurations and their formation energies and (ii) hopping barriers between them, we construct the master diffusion equations for each charge state separately using the Onsager method. This yields the 3D diffusion tensors and , which include the Onsager transport coefficients (diffusivity) for each crystallographic direction. Both and were found to diffuse significantly faster along the b-axis compared to the a^*- and c-axes, exhibiting strong anisotropy. Self-diffusivities reported herein along the (100) and (-201) directions correspond well with those obtained from isotopically labeled oxygen tracer experiments. These findings enhance the current understanding of intrinsic defect diffusion in β-Ga₂O₃, which is crucial to addressing defect-related challenges that can compromise device efficiency and stability.