Migration mechanisms and diffusion barriers of vacancies in Ga2O3

We employ the nudged elastic band and the dimer methods within the standard density functional theory (DFT) formalism to study the migration of the oxygen and gallium vacancies in the monoclinic structure of $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. We identify all the first nearest neighbor paths and calculate the migration barriers for the diffusion of the oxygen and gallium vacancies. We also identify the metastable sites of the gallium vacancies which are critical for the diffusion of the gallium atoms. The migration barriers for the diffusion of the gallium vacancies are lower than the migration barriers for oxygen vacancies by 1 eV on average, suggesting that the gallium vacancies are mobile at lower temperatures. Using the calculated migration barriers we estimate the annealing temperature of these defects within the harmonic transition state theory formalism, finding excellent agreement with the observed experimental annealing temperatures. Finally, we suggest the existence of percolation paths which enable the migration of the species without utilizing all the migration paths of the crystal.