Opto-electronic properties of Sn-C Co-doped β-Ga<sub>2</sub>O<sub>3</sub> at different concentrations: a GGA + U study.

Abstract

<h4>Content</h4>This study investigates the electronic structure and optical properties of Sn-C co-doped β-Ga₂O₃ at different concentrations using the generalized gradient approximation (GGA + U) method within density functional theory (DFT). The results show that, compared to intrinsic β-Ga₂O₃, all doped systems induce lattice distortion. Among them, the Sn-C system exhibits higher stability in both oxygen-rich and gallium-rich environments. Additionally, doping significantly reduces the band gap, with the Sn-2C doped system having the smallest band gap (0.98 eV), while both the 5 at% system and Sn-3C system display weak metallic characteristics. The static dielectric constant of the co-doped system increases with concentration, enhancing its polarization ability. The absorption spectrum shows clear redshift, with significantly improved absorption in the 150-400 nm wavelength range and a trend toward extension into the visible light region. These results suggest that Sn-C co-doping is an effective strategy for optimizing the optoelectronic properties of β-Ga₂O₃, potentially enhancing its application in optoelectronic devices.<h4>Methods</h4>In the first-principles calculations, density functional theory (DFT) was employed, using the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA). The calculations were performed using the Cambridge Sequential Total Energy Package (CASTEP) program, where the interaction between valence electrons and ionic cores was treated with on-the-fly generated (OTFG) ultrasoft pseudopotentials. A plane-wave basis set was constructed with a cutoff energy of 450 eV. The Brillouin zone was sampled using a 1 × 4 × 2 k-point mesh generated by the Monkhorst-Pack method, and structural optimization was carried out using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. During optimization, the following energy convergence criteria were set: a total energy convergence threshold of 10^-5 eV/atom, a maximum internal stress of 0.05 GPa, an interatomic force less than 0.03 eV/nm, and a maximum atomic displacement limited to 10^-3 Å. The valence electron configurations used in the calculations were Ga (3d¹⁰ 4s² 4p¹), O (2s² 2p⁴), Sn (5s² 5p²), and C (2s² 2p²). It should be noted that the standard GGA method neglects the strong correlation effects of Ga 3d electrons, which leads to an underestimated band gap compared to experimental values, thereby affecting the accurate assessment of material properties. To address this issue, the GGA + U approach was adopted in this work, introducing Hubbard U corrections to more accurately describe the electronic structure of β-Ga₂O₃. Specifically, a U value of 6.5 eV was applied to the O 2p electrons, and a U value of 10.5 eV was applied to the Ga 3d electrons.