First-principles investigation of defect formation energies and charge transition levels in Mg-C co-doped GaN

Achieving efficient p-type doping in GaN remains a major challenge because of the high activation energy of conventional Mg acceptors. Although C codoping has been proposed as a potential strategy for enhancing acceptor activation in other semiconductor systems, its underlying mechanism and the effect of local C coordination remain unclear. In this work, first-principles calculations based on the HSE06 hybrid functional were performed to systematically investigate the thermodynamic stability, charge-transition levels, and electronic structures of Mg-doped (Mg Ga ), C-doped (C N ), and Mg-C co-doped (Mg Ga -C N and Mg Ga -2C N ) GaN systems under both Ga-rich and N-rich conditions. Thermodynamic analysis indicates that Mg Ga remains the most stable acceptor defect, whereas the Mg-C co-doping complexes, particularly Mg Ga -2C N , are thermodynamically less favorable to form. The Mg Ga -C N configuration exhibits a relatively deep acceptor level, whereas the Mg Ga -2C N configuration exhibits a substantially reduced calculated acceptor ionization energy from 0.45 eV to approximately 0.03 eV, indicating shallow-acceptor characteristics within the present supercell model. Electronic-structure analyses indicate that the introduction of a second C atom enhances the interaction between the C-derived defect states and the host valence-band states, accompanied by an increased C-p contribution near the valence-band edge. Consequently, the acceptor level shifts toward the valence-band maximum, leading to a substantially reduced acceptor ionization energy. These findings elucidate the microscopic mechanism by which local C coordination modulates Mg acceptor states and highlight the theoretical potential of defect engineering for tuning acceptor levels in GaN, while also emphasizing the thermodynamic limitations associated with highly C-coordinated configurations.