Investigation of Ga interstitial and vacancy diffusion in β-Ga₂O₃ via split defects: a direct approach via master diffusion equations

The low symmetry of monoclinic β-Ga₂O₃ leads to elaborate intrinsic defects, such as Ga vacancies split amongst multiple lattice sites. These defects contribute to fast, anisotropic Ga diffusion, yet their complexity makes it challenging to understand dominant diffusion mechanisms. Here, we predict the 3D diffusivity tensors for Ga interstitials (Gaᵢ³⁺) and vacancies (VGa³⁻) via first principles and direct solution of the master diffusion equations. We first explore the maximum extent of configurationally complex ''N-split'' Ga interstitials and vacancies. With dominant low-energy defects identified, we enumerate all possible elementary hops connecting defect configurations to each other, including interstitialcy hops. Hopping barriers are obtained from nudged elastic band simulations. Finally, the comprehensive sets of (i) defect configurations and their energies and (ii) the hopping barriers that connect them are used to construct the master diffusion equations for both Gaᵢ³⁺ and VGa³⁻. The solution to these equations yields the Onsager transport coefficients, i.e. the components of the 3D diffusivity tensors D_Gaᵢ and D_VGa for Gaᵢ³⁺ and VGa³⁻, respectively. It further reveals the active diffusion paths along all crystallographic directions. We find that both Gaᵢ³⁺ and V_Ga³⁻ diffusion are fastest along the c-axis, due to 3-split defects that bridge neighboring unit cells along the c-axis and divert diffusing species around high-energy bottlenecks. Although isolated Gaᵢ³⁺ diffuse faster than isolated VGa³⁻, self-diffusion of Ga is predominantly mediated by VGa³⁻ due to the higher VGa³⁻ defect concentration under most thermodynamic environments.