Thickness and strain effects on electronic structures of transition metal dichalcogenides: 2H-$M{X}_2$ semiconductors ($M$ $=$ Mo, W; $X$ $=$ S, Se, Te)

Using the first-principles calculations, we explore the electronic structures of 2H-$M{X}_2$ ($M$ $=$ Mo, W; $X$ $=$ S, Se, Te). When the number of layers reduces to a single layer, the indirect gap of bulk becomes a direct gap with larger gap and the band curvatures are found to lead to the drastic changes of effective masses. On the other hand, when the strain is applied on the single layer, the direct gap becomes an indirect gap and the effective masses vary. Especially, the tensile strain reduces the gap energy and effective masses while the compressive strain enhances them. Furthermore, the much larger tensile stress leads to become metallic.

Figure 1

Band structures of (a) MoS${}_2$, (b) MoSe${}_2$, (c) MoTe${}_2$, (d) WS${}_2$, and (e) WSe${}_2$ from the bulk (upper panels) to double-layer (2L, middle panels) and single-layer (1L, bottom panels). The horizontal solid lines in each panel indicate the VBM and the dotted lines indicate the CBM. The solid blue arrows indicate the lowest energy transitions.

Figure 2

Thickness dependence of band gap energies of 2H-$M{X}_2$ ($M$ $=$ Mo, W; $X$ $=$ S, Se, Te). Right axis corresponds to the wavelengths.

Figure 3

(a) Strain dependence of band gap energies of 1L-MoS${}_2$ ($a$ $=$ 3.160 Å). The representative band structures for the (b) compressive and (c), (d) tensile stresses are displayed, respectively. Inset indicates the hexagonal structure consisting of Mo (red/gray balls) and S (yellow/light gray balls) from the top views.