Role of lattice vibrations in gallium vacancy formation in monoclinic Ga₂O₃

Gallium vacancies (V_Ga) play a pivotal role in carrier compensation in n-type Ga₂O₃. Previous theoretical investigations of V_Ga formation energies and charge-state transition levels were limited to zero temperature. We investigate the effect of lattice vibrations on the defect formation energy of V_Ga, its charge-state transition levels, and band renormalization in monoclinic Ga₂O₃ at finite temperatures. Using hybrid density functional calculations, the formation energy and charge-state transition levels of four different V_Ga configurations [V_Ga(I), V_Ga(II), V_Ga^ib, V_Ga^ic] are calculated. The lattice vibrations and their contribution to the free energy are assessed using the generalized gradient approximation. Although the V_Ga^ib configuration of the split vacancy is less favorable than the V_Ga^ic configuration at zero temperature, lattice vibrations are found to stabilize V_Ga^ib over V_Ga^ic at high temperature. All studied charge-state transition levels exhibit a blue shift at elevated temperature; the impact of this shift on the electron capture process will be discussed.