In this paper, we calculated the defect formation energy of oxygen vacancies with different charge states (0, +1, +2) in beryllium oxide crystal by using density functional theory (DFT). Based on defect formation energy, the positions of charge transition levels are obtained. However, there is a well-known problem that DFT will underestimate the band gap, which leads to the positions of charge transition levels are arguable. To obtain more accurate charge transition levels, we employ the hybrid functionals (HSE) to relieve the band edge problem, as well as use the finite-size corrections (FNV) to correct the defect formation energy. After obtaining the location of the charge transition level, we obtain a reliable description of the optical line shape of the F/F+ center containing electron–phonon coupling. The absorption spectra of the F center and F+ center peak at 7.1 eV and 6.3 eV, respectively. The luminescence band of the F center peaks at 4.7 eV. Furthermore, we speculate that the luminescence band near 3.7 eV is assigned to the F+ center.

中文翻译：

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BeO晶体中F型色心的第一性原理研究

在本文中，我们利用密度泛函理论（DFT）计算了氧化铍晶体中不同电荷态（0、+1、+2）氧空位的缺陷形成能。基于缺陷形成能，获得电荷跃迁能级的位置。但是，有一个众所周知的问题是 DFT 会低估带隙，这导致电荷跃迁能级的位置存在争议。为了获得更准确的电荷跃迁水平，我们采用混合泛函（HSE）来缓解带边问题，并使用有限尺寸校正（FNV）来校正缺陷形成能量。得到电荷跃迁能级的位置后，我们就得到了 F/F 光线形状的可靠描述+中心包含电子 - 声子耦合。F中心和F的吸收光谱+中心峰值分别为 7.1 eV 和 6.3 eV。F中心的发光带在4.7 eV处达到峰值。此外，我们推测 3.7 eV 附近的发光带分配给 F+中央。