Ga vacancy-mediated diffusion of Sn donors in β-Ga₂O₃

Diffusion of the n-type dopant Sn in β-Ga₂O₃ is studied using secondary-ion mass spectrometry combined with first-principles calculations. Diffusion of Sn from a Sn-doped bulk substrate with surface orientation (001) into an epitaxial layer is observed after heat treatments under O₂ gas flow in the temperature range 1000-1250°C. Calculated formation energies of Sn-related and intrinsic defects suggest that the migration of Sn is primarily mediated by Ga vacancies (V_Ga), through the formation and dissociation of intermediate mobile V_GaSn_Ga complexes. The Sn concentration-depth profiles reveal diffusion starting at 1050°C, and all profiles exhibit a plateau and a sharp drop in Sn concentration at the diffusion front. The evolution of the Sn diffusion profiles is well-described by a reaction-diffusion (RD) model, yielding diffusion parameters for the V_GaSn_Ga complex. The effect of lattice anisotropy is studied by calculating migration barriers for the V_GaSn_Ga complex, using the nudged elastic band method. Good agreement is found between the RD modelling results and the first-principles calculations. Notably, the energetics of the complex correlate with the favored coordination environment of Sn, and this trend is further explored by comparing with calculations for Si and Ge donors.