Investigation of Ga interstitial and vacancy diffusion in β-Ga2 O3 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 DGai and DVGa for Gai3+ and VGa3-, respectively. It further reveals the active diffusion paths along all crystallographic directions. We find that both Gai3+ and VGa3- diffusion are fastest along the c axis, due to three-split defects that bridge neighboring unit cells along the c axis and enable diffusing species to circumvent pathways with high-energy migration barriers. 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.