Evidence for carrier compensation by gallium vacancies during annealing of highly Si-doped β-Ga₂O₃

Net carrier densities in highly Si-doped β-Ga₂O₃ decrease during thermal annealing as a function of temperature, time, and P_O2 for both in situ and implant-doped films. The mechanism for this loss has been attributed to the formation of gallium vacancies (V_Ga³⁻), which act as compensating acceptors and form passivating defect complexes. Samples doped above 3 × 10¹⁹ cm⁻³, annealed at the same temperature and P_O2, ultimately approach a similar net carrier density of 1-3 × 10¹⁹ cm⁻³ (for 950 °C and P_O2 < 2 × 10⁻⁷ bar) independent of the starting dopant concentration or doping method. These highly doped samples, metastable under these conditions, generate V_Ga³⁻ to reach the steady state |N_D − N_A|, determined by the Fermi level. An activation energy of 1.6 ± 0.2 eV was observed for the rate of net carrier loss in high concentration in situ doped films. Scanning transmission electron microscopy and electrical results for implanted samples show that dopant activation, lattice recovery, and compensation are all active within the first minutes of annealing. Understanding the metastability of higher doping levels and V_Ga³⁻ formation allows for the development of mitigation strategies to achieve highly Si-doped β-Ga₂O₃ by implant (8 × 10¹⁹ cm⁻³ with >70 cm²/V s mobility), including using the minimum required anneal time to achieve lattice recovery and dopant activation, reducing vacancy formation. Compensation initially limited full activation of deeper implants to 1 × 10²⁰ cm⁻³; by protecting the free surface with a SiO₂ cap during annealing, the activation efficiency doubled, and the mobility increased by 30%, highlighting the importance of controlling V_Ga³⁻ formation and compensation.