Optical Properties of Mo S 2 , Mo Se 2 , WS 2 , and W Se 2 under External Electric Field

The combination of finite semiconductor band gap and ultrasmall thickness makes few-layer transition-metal dichalcogenides (TMDCs) promising materials for use in optoelectronics devices. Here, we use density-functional theory to investigate the photon-energy-dependent optical properties of two-layer (2L), three-layer, four-layer, and five-layer ${\mathrm{Mo}\mathrm{S}}_{2}$, ${\mathrm{Mo}\mathrm{Se}}_{2}$, ${\mathrm{WS}}_{2}$, and ${\mathrm{W}\mathrm{Se}}_{2}$ TMDCs. We find that the values of the dielectric constant and the refractive index always increase with the number of layers as well as with external electric field in the static region. However, in the visible region (400--600 nm), the values of the dielectric constant and the refractive index decrease with increasing external electric field. Among these TMDCs, ${\mathrm{Mo}\mathrm{Se}}_{2}$ shows the strongest response under electric field. We find that in contrast to a small electro-optic response in the weak-field limit, a large change in the refractive index is applied under large applied fields, with the increasing response obtained for thinner TMDC films. The magnitude and even the sign of the electro-optic response changes with the photon frequency and reaches the peak values in the 1.5--2.5 eV range. The position of the peak electro-optic response can be tuned by both changing the number of layers and the TMDC composition. 2L ${\mathrm{Mo}\mathrm{Se}}_{2}$ exhibits the highest response of 8.8 pm/V at 2.3 eV that is comparable to the response of typical oxide electro-optic ${\mathrm{Li}\mathrm{Nb}\mathrm{O}}_{3}$. Analysis of the sensitivity trends of these TMDC systems shows that compared to the changes in the band gap, the changes of the onset of strong absorption under electric field and change in the number of layers show better correlation with the changes in the electro-optic response. Our results provide guidance for the possible use of these materials in optical micro- or nanocavities for devices such as tunable optical filters and fast optical switches.