Abstract: Beta-gallium oxide （β-Ga₂O₃） has emerged as a highly promising ultra-wide band gap （~4.9 eV） semiconductor for next-generation power electronics and solar-blind ultraviolet photodetectors， owing to its exceptional breakdown electric field strength and high Baliga figure of merit. However， the intrinsically low intrinsic carrier concentration of β-Ga₂O₃ significantly limits its electrical conductivity and practical device performance. While doping engineering， particularly n-type doping with group-IV elements like Sn， has been extensively employed to modulate the electronic and optical properties， the inevitable incorporation of intrinsic point defect during crystal growth can profoundly influence doping efficiency through complex defect-dopant interactions. Despite previous investigations on isolated Sn doping， the synergistic effects between Sn dopants and intrinsic vacancy defects， as well as their combined impact on the optoelectronic properties of β-Ga₂O₃， remains insufficiently understood at the atomic scale. This work presented a comprehensive first-principles investigation based on density functional theory （DFT） to systematically elucidate the structural stability， electronic structure， and optical properties of Sn-doped β-Ga₂O₃ and its defect complexes with intrinsic vacancies （Sn_GaII-V_Gaiand Sn_GaII-V_Oi）. Calculations were performed using the Viennaab initio simulation package （VASP） with the projector augmented wave （PAW） method and Perdew-Burke-Ernzerhof （PBE） exchange-correlation functional. A 1×2×2 supercell containing 80 atoms was employed， with a plane-wave cutoff energy of 520 eV and a 3×5×3 Monkhorst-Packk-point grid. Defect formation energies were evaluated under both oxygen-rich and gallium-rich growth conditions to assess the thermodynamic stability of various configurations. The results demonstrate that Sn dopants exhibit a distinct site-selective preference in the β-Ga₂O₃ lattice， energetically favoring octahedrally coordinated Ga_II sites over tetrahedral Ga_I sites. The Sn_GaII configuration exhibits a significantly lower formation energy of -2.30 eV and minimal lattice distortion （x axis contraction of merely 0.24%， withy andz axes expanding by 0.10% and 0.12%， respectively）， compared to the Sn_GaI configuration. This preference is attributed to the larger ionic radius of Sn⁴⁺ （about 0.069 nm） relative to Ga³⁺ （about 0.047 nm） and the more flexible coordination environment of the octahedral site. Importantly， thermodynamic analysis reveals that Sn-doped β-Ga₂O₃ tends to form Sn_GaII-V_GaII defect complexes under oxygen-rich growth conditions， whereas such dopant-vacancy associations are suppressed under gallium-rich growth conditions， providing critical insights for defect engineering through growth atmosphere control. The electronic structure analysis indicates that isolated Sn doping introduces donor levels dominated by Sn-5s orbitals near the conduction band minimum， resulting in n-type conductivity with the Fermi level shifting into the conduction band. However， the introduction of gallium vacancies （V_Ga）—which act as triple acceptors—induces a pronounced self-compensation effect. In Sn_GaII-V_Gaicomplexes， the formation of V_Ga captures electrons from Sn donors， shifting the Fermi level downward and restoring the system to a high-resistance semi-insulating state. Conversely， oxygen vacancies （V_O） serve as deep donors， further increasing free electron concentration and enhancing conductivity when combined with Sn doping. Optical absorption calculations reveal that while Sn doping and vacancy complexes maintain the intrinsic deep-ultraviolet absorption edge suitable for solar-blind detection， the introduction of V_Ga vacancies creates a pronounced absorption band in the infrared-to-visible range （400~800 nm）. This arises from electronic transitions from occupied defect levels to the conduction band， significantly extending the photoresponse spectrum of β-Ga₂O₃ beyond the ultraviolet regime. These findings provide fundamental understanding of the formation mechanisms of defect complexes in Sn-doped β-Ga₂O₃ and their synergistic modulation of electronic and optical properties. By establishing the correlation between growth conditions， defect thermodynamics， and material performance， this study offers valuable theoretical guidance for optimizing doping strategies and designing high-performance β-Ga₂O₃-based optoelectronic devices and power electronics with tailored electrical and spectral characteristics.

Key words: β-Ga₂O₃; first-principle; defect; doping; optical property; electrical property; defect formation energy