Tuning of exciton type by environmental screening

TL;DR

The paper addresses tuning of exciton type at planar type-II MoS2/WS2 heterostructures by environmental screening and interface width. It develops an effective-mass variational framework with a smooth interfacial WχMo1-χS2 alloy and a Rytova–Keldysh electron–hole interaction, solving the resulting two-body problem via a separable Ansatz and finite-difference diagonalization. The study shows that interface excitons are favored only for small interface width and/or strong dielectric screening, with the exciton type (interface vs. direct) and the electron–hole overlap tunable by $w$ and the surrounding dielectric ε2. These results guide experimental efforts to observe interface excitons in 2D van der Waals heterostructures and inform design principles for devices with long-lived excitons, such as photodetectors and solar cells.

Abstract

We theoretically investigate the binding energy and electron-hole (e-h) overlap of excitonic states confined at the interface between two-dimensional materials with type-II band alignment, i.e., with lowest conduction and highest valence band edges placed in different materials, arranged in a side-by-side planar heterostructure. We propose a variational procedure within the effective mass approximation to calculate the exciton ground state and apply our model to a monolayer MoS$_2$/WS$_2$ heterostructure. The role of nonabrupt interfaces between the materials is accounted for in our model by assuming a W$_x$Mo$_{1-x}$S$_2$ alloy around the interfacial region. Our results demonstrate that (i) interface-bound excitons are energetically favorable only for small interface thickness and/or for systems under high dielectric screening by the materials surrounding the monolayer, and that (ii) the interface exciton binding energy and its e-h overlap are controllable by the interface width and dielectric environment.

Figures (9)

• Figure 1: (color online) (a) Sketch of the side-by-side monolayer heterostructure investigated here. From the left to the right side, a W$_{\chi}$Mo$_{1-\chi}$S$_2$ alloy goes from pristine WS$_2$ to pristine MoS$_2$, with a smoothly increasing (decreasing) Mo (W) concentration along the interface region. (b) Sketch of the tungsten concentration function $\chi(x)$ (red dashed), along with the complementary Mo concentration function $1-\chi(x)$ (blue solid) along the interface, with width $w$. (c) Sketch of the interaction mechanisms in an interface exciton, where the electron is in the left side and the hole is in the right side. The heterostructure potential produces a force $\vec{F_{ht}}$ strong enough to keep the electron and the whole separated, while the e-h interaction force ($\vec{F_{in}}$) keeps them close enough to form a bound exciton at the interface. (d) Sketch of the interaction mechanisms in an system in which the e-h attraction force ($\vec{F_{in}}$) is stronger than the heterostructure forces, thus being able to push the whole exciton to the pure MoS$_2$ region.
• Figure 2: (color online) Sketch of (a) the potential and (b) the effective mass profiles for the electron (red dashed) and hole (blue solid) across the interface between WS$_2$ and MoS$_2$ within the side-by-side monolayer heterostructure.
• Figure 3: (color online) (a) Effective potential of the system, including both the e-h interaction, which is responsible for the dip along the $x_e = x_h$ line observed in the figure, and the heterostructure potential, which originates the steps observed in the potential. An interface width $w = 20$Å and a dielectric constant $\epsilon_2 = 9.0\epsilon_0$ are assumed. (b) Color map of the effective potential shown in (a).
• Figure 4: (Color online) Color maps of the probability density distribution assuming an environment with dielectric constant $\epsilon_2 = 1.0\epsilon_0$ and interface widths (a) $w = 10$ Å , (b) $25$ Å , (c) $40$ Å , and (d) $60$ Å .
• Figure 5: (Color online) Same as in Fig. \ref{['fig:WF_1']}, but assuming $\epsilon_2$ = 4.5 $\epsilon_0$.