Interlayer excitons in van der Waals heterostructures: Binding energy, Stark shift, and field-induced dissociation

Abstract

Photoexcited intralayer excitons in van der Waals heterostructures (vdWHs) with type-II band alignment have been observed to tunnel into interlayer excitons on ultrafast timescales. Such interlayer excitons have sufficiently long lifetimes that inducing dissociation with external in-plane electric fields becomes an attractive option of improving efficiency of photocurrent devices. In the present paper, we calculate interlayer exciton binding energies, Stark shifts, and dissociation rates for six different transition metal dichalcogenide (TMD) vdWHs using a numerical procedure based on exterior complex scaling (ECS). We utilize an analytical bilayer Keldysh potential describing the interaction between the electron-hole pair, and validate its accuracy by comparing to the full multilayer Poisson equation. Based on this model, we obtain an analytical weak-field expression for the exciton dissociation rate. The heterostructures analysed are MoS 2 /MoSe 2 , MoS 2 /WS 2 , MoS 2 /WSe 2 , MoSe 2 /WSe 2 , WS 2 /MoSe 2 , and WS 2 /WSe 2 in various dielectric environments. For weak electric fields, we find that WS 2 /WSe 2 supports the fastest dissociation rates among the six structures. We, furthermore, observe that exciton dissociation rates in vdWHs are significantly larger than in their monolayer counterparts.Naturally occurring layered materials held together by van-der-Waals-like forces have been intensely studied in recent years. Peeling graphite layer-by-layer and forming graphene 1 , a task thought impossible, turned researchers on to two-dimensional materials. Realizing that these layers may be used as building blocks of artificially layered materials, so-called van der Waals heterostructures, provides an endless array of possible combinations 2, 3 . The extraordinary electronic and optical properties of TMDs 4-11 have made them one of the most interesting classes of building blocks for vdWHs. Potential electro-optical applications of TMDs include photodetectors 12-14 , light-emitting diodes 15-17 , and solar cells 16,18,19 . It is well known that the optical properties of TMD monolayers are dominated by excitons 2,3,6,8,20 , as such two-dimensional excitons can have giant binding energies 6,8,[21][22][23] . Strongly bound excitons, in turn, make generation of photocurrents difficult, as excitons must first be dissociated into free electrons and holes. This is one of the challenges facing the use of monolayer TMDs in efficient photocurrent devices. A further complication is the fast recombination rates of excitons in these monolayers [24][25][26] . Without inducing dissociation in some way, excitons will typically recombine before they are dissociated. Applying an in-plane electric field to the excitons, however, enhances generation of photocurrents for two reasons: (i) the electric field counteracts recombination by pulling electrons and holes in opposite directions, and (ii) the electric field assists dissociation of excitons [27][28][29][30] .When two TMD monolayers are brought together with a type-II band align...

Interlayer exciton formation, relaxation, and transport in TMD van der Waals heterostructures

“…Since electrons and holes are confined in opposite layers of a type-II vdW heterostructure, interlayer excitons have a static electric dipole along the out-of-plane direction ( p = e · d , where e is the charge quantity and d is the charge separation distance), which allows their energy to be tuned (Δ ε ) by an external electric field ( E ) along the dipole axis (i.e., the Stark effect, Δ ε = − p · E ) 22 , 95 , 117 . Strong and linear tuning of the interlayer exciton PL energy with an applied electric field was indeed observed in several studies with a tuning range of ~80–138 meV 22 , 26 , 30 , 86 , 95 , 117 , reflecting that the linear Stark effect mainly contributed to the energy shift (Fig. 3d ).…”

“…As stated above, immediately after rapid interlayer charge transfer, a strong Coulomb interaction of the electrons and holes in opposite layers could exist due to the layer separation (~0.7 nm) comparable to the intralayer exciton Bohr radius (~1-3 nm) 73,78,79 , which facilitates the formation of interlayer excitons that have been both theoretically 80 and experimentally evidenced [20][21][22]42 . The binding energy of the interlayer exciton, with a reported value of~100-350 meV from both theoretical [81][82][83][84][85][86] and experimental 17,21,42,55,[87][88][89] results, is a further indication of the strong Coulomb interaction strength between the layer-separated electrons and holes, of which the value depends sensitively on the interlayer distance 83,85 .…”

“…In traditional semiconductor CQWs, the resulting indirect excitons usually have a small E b of several to tens of meV (<k B T in most cases), resulting in excitonic devices generally operating at cryogenic temperatures 172,187,188 . However, the interlayer excitons formed in TMD vdW heterostructures have a much larger E b , with reported values exceeding 100 meV 17,21,42,55,87,[81][82][83][84][85][86]88,89 , leading to a much higher predicted temperature (>1000 K), which facilitates the realization of excitonic devices that operate at room temperature. In fact, excitonic devices based on an hBN-encapsulated MoS 2 /WSe 2 heterobilayer with electrically controlled transistor actions at room temperature were realized recently 29 .…”

Excitonic Emission in Atomically Thin Electroluminescent Devices

“…Formation of IX usually requires heterobilayers with type II band alignments, where free carriers generated in higher energy bands would transfer to lower energy bands in adjacent layers to form IXs within an ultrashort time interval ≈50 ps. [ 118 ] Binding energies of IXs are ≈150 meV [ 119 ] for heavily screened TMDC heterobilayers and ≈250 meV [ 119 ] for suspended ones, strong enough against dissociation resulted from heat fluctuation or external electric field. As shown in Figure a, prominent IX signal can be observed in type II band aligned MoS 2 /WSe 2 heterobilayers, [ 34 ] of which emission energy is well below intralayer signals.…”

Plasmonic Modulation of Valleytronic Emission in Two‐Dimensional Transition Metal Dichalcogenides

“…Delightfully, the novel phenomena of semiconducting TMDs (MX 2 , M = Mo, W; X = S, Se, and Te) [ 14 ] such as valley physics, [ 15 ] exciton super‐fluidity, [ 16 ] and interlayer tunneling [ 17 ] are found by degrees and make classical valleytronics exceedingly prosper in recent years. TMDs as a kind of hexagonal 2D materials is a van der Waals layered‐semiconductor with direct bandgap energy.…”