Effects of Cu, Ag, and Au Elements Doping on the Electronic and Optical Properties of β-Ga₂O₃ via First-Principles Calculations

β-Ga₂O₃, as a semiconductor material with an ultrawide band gap (<i>E</i>_g > 4.8 eV), emerges as a promising candidate for ultraviolet (UV)-transparent semiconductors. Its distinctive property of high transparency from visible light to the ultraviolet region gives it broad application prospects in the fields of deep UV light-emitting diodes (LEDs), UV lasers, and electronic devices. This study employed first-principles calculations utilizing the generalized gradient approximation+ <i>U</i> (GGA+<i>U</i>) method to investigate the impact of doping β-Ga₂O₃ with transition metals including copper (Cu), silver (Ag), and gold (Au) on its electronic structure and optical properties. The findings reveal that under oxygen (O)-rich conditions, the formation energy of the doped system is lower compared to gallium (Ga)-rich conditions. And the Cu-doped β-Ga₂O₃ is demonstrated to possess the lowest formation energy, indicating an enhanced stability of the β-Ga₂O₃. Additionally, the intrinsic band gap of β-Ga₂O₃ is calculated to be 4.853 eV, whereas the band gaps of transition metal (TM)-doped β-Ga₂O₃ are significantly reduced. Specifically, the band gaps of Cu-doped, Ag-doped, and Au-doped β-Ga₂O₃ are 1.228, 0.982, and 1.648 eV, respectively. This reduction can be attributed to the introduction of impurity levels by the transition metals, which modify the electron distribution of gallium and oxygen atoms in the vicinity of the Fermi level. Remarkably, β-Ga₂O₃ exhibits superior ultraviolet light absorption performance, and the incorporation of transition metals such as Cu, Ag, and Au facilitates the expansion of the absorption region from the ultraviolet to the visible light range. This transformation not only enhances the material's light-harvesting capability but also improves the electron transition capability of the intrinsic β-Ga₂O₃, providing a crucial theoretical foundation for the development of novel β-Ga₂O₃-based optoelectronic devices.