Coulomb engineering of the bandgap and excitons in two-dimensional materials

Abstract

The ability to control the size of the electronic bandgap is an integral part of solid-state technology. Atomically thin two-dimensional crystals offer a new approach for tuning the energies of the electronic states based on the unusual strength of the Coulomb interaction in these materials and its environmental sensitivity. Here, we show that by engineering the surrounding dielectric environment, one can tune the electronic bandgap and the exciton binding energy in monolayers of WS₂ and WSe₂ by hundreds of meV. We exploit this behaviour to present an in-plane dielectric heterostructure with a spatially dependent bandgap, as an initial step towards the creation of diverse lateral junctions with nanoscale resolution.

Figure 1. Engineering Coulomb interactions through environmental screening.

(a) Schematic illustration of a semiconducting 2D TMDC material, partially covered with an ultra-thin dielectric layer. The strong Coulomb interaction between charged particles in low-dimensional systems affects both the exciton binding energy and the quasiparticle bandgap. The interaction can be strongly modified by modulating the environmental dielectric screening on atomic length scales. (b) An optical micrograph of the heterostructure under study: monolayer WS₂ covered with a bilayer of graphene. Dotted circles indicate positions for the optical measurements. (c) Illustration of the optical response of an ideal 2D semiconductor, including exciton ground and excited state resonances and the onset of the (quasiparticle) bandgap. (d) Reflectance contrast spectra of the bare bilayer graphene, monolayer WS₂ and the resulting WS₂/graphene heterostructure at a temperature of 70 K. (e) First derivatives of the reflectance contrast spectra in d (after averaging over a 20 meV interval), offset for clarity. Peak positions of the exciton ground state (n=1) and the first excited state (n=2) resonances, roughly corresponding to the points of inflection, are indicated by dashed lines; Δ₁₂ denotes the respective energy separations. The observed decrease of Δ₁₂ across the in-plane boundary of the heterostructure is indicative of a reduction of the exciton binding energy and bandgap by more than 100 meV due to the presence of the adjacent graphene bilayer.

Figure 2. Out-of-plane spatial sensitivity of environmental screening.

(a) Experimentally and theoretically obtained energy separation Δ₁₂ between the n=1 and n=2 exciton states as a function of the number of layers of capping graphene. Dashed lines indicate Δ₁₂ values from the solution of the electrostatic model for uncapped WS₂ supported by fused silica substrate (grey) and covered with bulk graphite (red), representing two ideal limiting cases. (b) Absolute energies of the experimentally measured exciton ground state (n=1) and the first excited state (n=2) resonances, as well as the estimated positions of the bandgap obtained by adding the exciton binding energy to the energy of the n=1 state. The binding energy scales with Δ₁₂, where the limiting cases are an experimentally determined non-hydrogenic scaling for WS₂ on SiO₂ substrate from ref. and the 2D-hydrogen model in a homogeneous dielectric . These are compared to the bandgap energies deduced from the calculated exciton binding energies using the QEH model. The solid lines are guides to the eye.

Figure 3. Influence of the choice and configuration of materials on the dielectric tuning of the bandgap.

(a) Experimentally measured exciton ground state (n=1) and the first excited state (n=2) transition energies, as well as the estimated shifts of the bandgap for a variety of heterostructures. Their respective stacking configurations are indicated along the horizontal axis. The bandgap is obtained by adding the exciton binding energy to the measured transition energy of the n=1 state. To estimate the binding energy from the energy separation of the exciton states Δ₁₂, we considered the limiting cases of a non-hydrogenic scaling from ref. and the 2D-hydrogen model . (b) An overview of predicted changes in the exciton binding energy in 1L WS₂, encapsulated between two thick layers of dielectrics. The binding energy E_B is calculated by using the electrostatic approach in the effective mass approximation and presented in a 2D false-colour plot as a function of the top and bottom dielectric constants. The changes in the magnitude of E_B are roughly equal to the corresponding shifts of the bandgap and can reach 500 meV.

Figure 4. In-plane heterostructure via Coulomb engineering of monolayer WS₂.

(a) First-order derivatives of the reflectance contrast of a 1L WS₂ sample for varying spatial positions across the lateral 1L WS₂/2L graphene boundary. The data are shown in the spectral range of the exciton ground state (n=1) resonance and vertically offset for clarity. (b) For the spectral range of the excited state (n=2) of the exciton with the vertical axis scaled by factor of 100 for direct comparison. Full circles in a,b indicate peak energies of the resonances, corresponding to the points of inflection of the derivatives. (c) Spatially dependent bandgap energy extracted from the exciton peak positions along the profile of the lateral WS₂/graphene heterostructure, as illustrated in the schematic representation and marked by the dashed line in the optical micrograph. The shaded areas indicate the diffraction limit corresponding to the spatial resolution of our measurement and the solid line is a guide to the eye.