Ab initio calculations for electronic and optical properties of Er_W defects in single-layer tungsten disulfide

Ab initio calculations for the electronic and optical properties of single-layer (SL) tungsten disulfide (SL $WS2$⁠) in the presence of substitutional Erbium defects (⁠$ErW$⁠) are presented, where the W atom is replaced by an Er atom. Although Er is much larger than W, we show that Er:SL $WS2$ is stable using density functional theory. In order to understand defect related optical transitions, odd states, which are usually neglected for pristine cases, need to be considered in addition to even states. We use group theory to derive strict selection rules for the optical transitions, which are in excellent agreement with the absorption spectrum calculated by means of the Kubo–Greenwood formula using the Kohn–Sham orbitals. Defects usually play an important role in tailoring electronic and optical properties of semiconductors. We show that neutral and negatively charged Er$W$ defects lead to localized defect states in the band structure due to the f-orbital states of Er, which in turn give rise to sharp optical transitions in in-plane and out-of-plane components of the susceptibility tensor Im$χ∥$ and Im$χ⊥$⁠, respectively. We identify the optical transitions at 5.3 $μ$m, 1.5 $μ$m, 1.2 $μ$m, 920 nm, 780 nm, 660 nm, and 550 nm to originate from $ErW$ defect states. Our results for the optical spectra are in good agreement with experimental data.