Beyond the Anderson rule: importance of interfacial dipole and hybridization in van der Waals heterostructures

Abstract

Vertical stacking of two-dimensional materials with weak van der Waals (vdW) interactions has laid the ground for breakthroughs in physics as well as in technological applications. Although vdW interactions dominate interlayer binding, interlayer electronic coupling may not be negligible and can lead to properties beyond the superposition of constituent monolayers. Here, studying heterobilayers of transition-metal dichalcogenides (MQ 2; M = Mo, Ni, Pt; Q = S, Se) by means of density functional theory calculations, we show two mechanisms that influence the band gaps of vdW heterostructures beyond the Anderson rule: (1) interfacial hybridization (mainly involving out-of-plane states, such as chalcogen p z -states), which leads to an upshift in the valence band maxima and accordingly a decrease in the band gap. (2) Formation of an interfacial electric dipole, resulting in an effective gap increase in type-II junctions. While the former is material specific, depending on the proximity of p z -states to each other and the valence band maxima, the latter can be generally described using a model based on the charge density decay outside the monolayers and the pristine band edge positions with respect to the vacuum level, irrespective of junction type.

Ab initio study of structural, energetic, and electronic properties of two-dimensional transition metal dichalcogenides

“…The results were obtained from calculations with PBE+D3. 144 the role of strain energy in the equilibrium lattice parameters of heterobilayers, the relative energies of the monolayers unit cells were calculated with strain ranging from −1.0 % to 1.0 %. In this range, the energy as a function of the lattice parameter can be well fitted by a quadratic relation ∆E = α i (a − a 0i ) 2 , where a 0i is the equilibrium lattice parameter, as displayed in Figure 18(a).…”

“…The band edge positions of the monolayers with respect to the vacuum level, displayed in Table 5, can be employed to predict the band alignments of heterobilayers, according to Anderson's rule, as discussed in Chapter 1. However, to better describe the Source: Adapted from BESSE et al 144 heterobilayers configurations, the strain on the monolayers should also be considered. Therefore, Figure 19 shows the VBM and CBM with respect to vacuum level of the monolayers pairs with the same strain of the equilibrium configuration of the respective heterobilayers.…”

“…Source: Adapted from BESSE et al 144 structures of monolayers correspond to the same supercell of the heterobilayer, to enable a direct comparison between them. From the top of the valence band, it is clear that the heterobilayer band structure differs from a superposition of the monolayers band structures.…”

“…Thus, this effect does not account entirely for ∆E g in all systems and other effects can play an important role, as evident by the cases in which ∆E g > 0, particularly the heterobilayers with ∆E g > 0.10 eV, namely MoSe 2 /NiS 2 and MoSe 2 /PtS 2 , as shown in Figure 20(b). Source: Adapted from BESSE et al 144…”

“…151 The results are displayed in Figure 23, which show that the expected relation has good validity, except for PtS 2 /PtSe 2 , due to the hybridization effect on the CBM, as previously discussed. Although the band offsets of Figure Source: Adapted from BESSE et al 144 indicate that MoS 2 /PtSe 2 and NiS 2 /PtSe 2 form type-II junctions, they have small offsets of conduction bands and valence bands, respectively, with differences of 0.02 eV. Because of that, with the shift introduced by the interfacial dipole, they adopt type-I band alignment, and their ∆E g < 0 comes entirely from the VBM upshift caused by hybridization.…”