Defect Engineering in β-Ga2O3: Hybrid functional study on the formation and stability of copper substitutional and complex defects

The formation of single substitutional copper (Cu) at the gallium (Ga) site and Cu complex defects in monoclinic gallium oxide (β-Ga₂O₃) has been studied using an optimized hybrid functional approach. Our calculations show that substitutional Cu is more favorable at the octahedral Ga (Cu_Ga2) site compared to the tetrahedral Ga (Cu_Ga1) site. Furthermore, substitutional of Cu at gallium site (Cu_Ga) tends to form complex defects with oxygen vacancies (Cu_Ga-V_O) when both defects are present in the sample. The relative concentrations of single substitutional Cu_Ga and Cu_Ga-V_O complexes in β-Ga₂O₃ depend significantly on the crystal growth conditions. This study highlights the favorability of the Cu_Ga2 complex defect with oxygen 1 vacancy (V_O1) over other possible Cu_Ga-V_O configurations. Based on our results, we assign the Cu_Ga2 in the −1 charge state and Cu_Ga2+V_O1 in the +1 charge state to the Cu²⁺(A) and Cu²⁺(B) defect centers, respectively. Importantly, the study demonstrates that oxygen vacancies not only compensate acceptor dopants but also can form complex defects with Cu, acting as donor defects. These findings underscore the importance of carefully controlling oxygen vacancies and crystal growth methods when doping β-Ga₂O₃ with metals to achieve p-type conductivity, which is essential for optoelectronic applications.