Electrical control of interlayer exciton dynamics in atomically thin heterostructures

Long-lived excitons can be potentially used for the realization of coherent quantum many-body systems (1–3) or as quantum information carriers (4, 5). In conventional semiconductors, the exciton lifetime can be increased by constructing double–quantum well (DQW) heterostructures, in which spatially separated electrons and holes form interlayer excitons (IEs) across the quantum wells (6–12). Strongly bound IEs can also be formed by stacking two single atomic unit cells of transition metal dichalcogenides (TMDs) into a van der Waals (vdW) heterostructure. TMD heterostructures, such as MoSe₂/WSe₂, MoS₂/WS₂, and MoS₂/WSe₂, have shown ultrafast charge transfer (13), the formation of IEs with a large binding energy of ~150 meV (14), and diffusion over long distances (15). Moreover, the tight binding and small exciton Bohr radius potentially allow for quantum degeneracy of these composite bosons, which may lead to exciton condensation at substantially elevated temperatures compared to those of, e.g., conventional Bose-Einstein condensates of cold atoms (2).

In this work, we fabricate individually electrically contacted optoelectronic devices using hexagonal boron nitride (h-BN)–encapsulated vdW heterostructures of MoSe₂ and WSe₂ (16, 17). Optically transparent electrical gates and ohmic electrical contacts realized for the individual atomic layers allow us to have complete control of the carrier densities in each TMD of the DQW while maintaining full optical access. The top and bottom insets of Fig. 1A show an optical image of a representative device with false-colored top gates and a schematic cross section, respectively [a detailed device scheme is illustrated in fig. S1 (18)]. The green and red false-colored gates depict the contact gates for doping the MoSe₂ and WSe₂ regions, respectively. These contact gates, together with the prefabricated Pt electrodes, provide ohmic contacts in the WSe₂ p-channel (19).

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The presence of the top (optically transparent) and bottom electrical gates, in addition to the separately contacted TMD layers, allows us to control the carrier density in the individual TMD layers as well as the electric field across the TMD heterostructure, E_hs, using the voltage V_tg (or V_bg) applied to the top (or bottom) gate. For intrinsic TMD layers (i.e., no free carriers and the chemical potential located within the semiconducting gap), where the heterostructure can be approximated by a thin dielectric slab, E_hs is controlled by a gate operation scheme in which we apply opposite gate polarity [supplementary text section 1 in (18)]. Figure 1A shows the photoluminescence (PL) spectrum measured at temperature T = 4 K as a function of E_hs, keeping both TMD layers intrinsic. We observe a linear shift of PL peak energy with E_hs, suggesting a first-order Stark shift caused by the static electric dipole moment across the vdW heterostructure. By fitting the linear PL peak shift with the linear Stark shift formula −edEhs, where ed is the dipole moment (e, electron charge; d, electron–hole separation), we estimate d ≈ 0.6 nm, in good agreement with the expected vdW separation between WSe₂ and MoSe₂. This analysis strongly suggests that the observed PL peak indeed corresponds to the IE emission of the WSe₂/MoSe₂ heterostructure with out-of-plane–oriented electric dipoles. There is a ~10% nonlinearity in the energy shift dependence versus E_hs, which, combined with weak variations of the absorption intensity (as shown in Fig. 1B), might be attributed to the charging effect caused by uncompensated gating. Similar to a previous study (14), our findings indicate that the PL from the intralayer excitons is strongly suppressed compared with that of IEs in the WSe₂/MoSe₂ heterostructure region [fig. S2 in (18)], suggesting a fast dissociation of intralayer excitons and an efficient conversion to IEs in this system. We further confirm from the constant normalized reflection ΔR/R at the intralayer exciton resonances (20–22) that our gate operation scheme only varies E_hs while keeping the layers intrinsic (Fig. 1B).

The IEs in the vdW heterostructure can live longer than intralayer excitons, owing to the spatial separation of electrons and holes in the heterostructure. Figure 1C shows the IE lifetime τ as a function of E_hs, measured by time-dependent PL after pulsed laser illumination. The lifetime τ increases as E_hs increases, reaching ≈600 ns for E_hs > 0.1 V/nm, an order of magnitude larger than in previous studies (14, 23). The observed dependence of τ on E_hs can be explained by changes in the overlap between the electron and hole wave functions [section 3 of (18)]. The recombination rate of an exciton is proportional to the probability that the electron and the hole occupy the same location. An electric field antiparallel to the IE dipole moment is therefore expected to reduce the recombination rate as it pulls the two carriers apart, consistent with our measurements. Considering the PL intensity modulation shown in Fig. 1A together with the measured τ, we also demonstrate that the emission efficiency (η) can be tuned with E_hs, reaching η ~ 80% when E_hs is aligned against the IE dipole moment, promoting the recombination process [section 4 of (18)].

The electrostatic condition in our heterostructures is greatly modified if we change the gate operation scheme such that one of the TMD layers is doped electrostatically, introducing free charge carriers. Figure 1E shows the IE PL spectrum after the gating scheme depicted in Fig. 1D. In this scheme, as shown in the normalized reflection ΔR/R at the intralayer exciton resonances (Fig. 1F), the carrier density of MoSe₂ (WSe₂), n_2D (p_2D), changes with positive V_tg (negative V_bg) while the WSe₂ (MoSe₂) layer remains intrinsic, keeping E_hs constant [section 5 of (18)]. We observe several pronounced changes in the IE emission spectrum as V_tg (V_bg) increases (decreases) and n_2D > 0 (p_2D > 0). First, the IE PL peaks exhibit a sudden red shift for n-doping (p-doping) of MoSe₂ (WSe₂). Second, the PL peaks continuously red-shift as doping increases for both n- and p-sides. In this regime, E_hs is fixed (as discussed above) and thus these shifts cannot be explained by the Stark effect. Lastly, the PL intensity diminishes rapidly as doping increases.

Our measurements in the doped regime can be explained by the formation of charged IEs (CIEs) (24). As shown in the normalized reflection measured with the same gating scheme, we can identify (i) intrinsic/p, (ii) intrinsic/intrinsic, and (iii) n/intrinsic regions by the disappearance of the absorption dips for intralayer excitons in MoSe₂ and WSe₂ (25), which are well aligned with the sudden red shift observed in IE PL (vertical dashed lines in Fig. 1, D to G). Thus, this jump in energy can be related to the CIEs. Note that charged excitons can be referred to as trions (i.e., three-body bound states) (26–29) or, alternatively, attractive polarons (i.e., excitonic states dressed by a polarized fermionic sea, similar to those in monolayer TMDs) (30, 31). The value of the observed jump ≈10 meV (15 meV) for positive (negative) CIEs is in good agreement with the calculated binding energy of CIEs (24). The lifetime of CIEs is ≈100 ns near the band edge but decreases with increased doping, presumably owing to additional decay channels enabled by scattering with free carriers (Fig. 1G).

We create high densities of IEs by increasing laser power. In particular, for neutral IEs, we observe that the PL emission is shifted to higher energy with increasing power (Fig. 2A), consistent with a mean-field shift stemming from the repulsive dipole–dipole interaction between oriented IEs. Following the analysis based on a parallel plate-capacitance model used for GaAs DQW IEs (32), we obtain a lower bound for the IE density of ~5 × 10¹¹ cm⁻² [section 6 of (18)]. The high density of long-lived IEs and the large τ observed in our heterostructures can enable transport of IEs across the samples. Figure 2, B to D, shows the spatial map of the IE PL intensity at different laser powers. The PL signal can be detected far away from the diffraction-limited focused laser spot (<1 μm in diameter). At the highest power, PL can be observed many micrometers away from the excitation spot, strongly suggesting transport of IEs across the sample. From these maps, we obtain the normalized, radially averaged PL intensity, IPLnorm(r), where r is measured from the center of the diffraction-limited steady-state laser spot. Here, the PL intensity is normalized by the value obtained at r = 0. As shown in Fig. 2E, away from the laser spot, IPLnorm(r) decreases rapidly as r increases. Note, however, that at a given r, IPLnorm(r) increases with power (P) even at a position far away from the laser spot. Similarly, an increase of IPLnorm(r) is observed when adjusting E_hs to increase τ at fixed P. The latter observation is consistent with exciton transport, as longer-lived IEs may travel farther [section 7 of (18)]. The characteristic length L_D for the decaying behavior of IPLnorm(r) can be obtained from fitting e−r/LD/r/LD to IPLnorm(r) away from the laser excitation spot (dashed lines in Fig. 2E), following the two-dimensional diffusion model with a point source [section 8 in (18)]. As shown on the left axis of Fig. 2G, we find that L_D increases as P increases, suggesting increased diffusion at high IE density, possibly due to exciton–exciton interactions.

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We also used a diffraction-limited focused pulsed laser to measure the temporal decay of the PL intensity. Figure 2F shows an estimate of the time-dependent exciton population (integrated PL signal along the heterostructure weighted by r²) after a laser pulse with peak power P. The time-dependent PL initially exhibits a faster decay process with characteristic time scale τ₁ ~ 10 ns, followed by a slower decay process occurring on the time scale τ₂ ~ 100 ns, suggesting that there are two different mechanisms for the PL intensity decay. The value of L_D estimated above can be converted to a diffusion constant according to D= LD2/τ. Two values D₁ and D₂ are obtained using the short (τ₁) and long (τ₂) decay times, respectively (Fig. 2H). Because our lifetime measurement uses a pulsed laser where the interaction-driven IE diffusion occurs just after the pulse is off when the IE density remains high, τ₁ could be more relevant than τ₂ for the IE diffusion. However, the value of L_D, measured in steady state, would be dominated by τ₂. Figure 2H shows that D₂ is in the range of 0.01 to 0.1 cm²/s, whereas D₁ changes from 0.1 to 1 cm²/s. Both D₁ and D₂ are increasing with increasing P, providing upper and lower bounds for nonlinear IE diffusion caused by dipolar repulsive interaction [section 8 in (18)], respectively.

We obtain further evidence for IE transport from time-dependent spatial PL maps with a pulsed laser illuminating the center of the sample. We measure the IE PL intensity IPL(r,t)as a function of distance r (referenced to the laser illumination spot) and time t (referenced to the falling edge of the laser pulse). Figure 2, I and J, shows the normalized time-dependent PL IPLnorm(r,t)=IPL(r,t)/IPL (r=0,t) at different laser peak powers. The time-dependent root mean square radius, rrms(t)=〈r2〉, computed from IPLnorm(r,t) (white lines) increases rapidly when the laser is on, reaching a steady state within ~200 ns. Notably, rrms(t) increases again rapidly within 100 ns after the laser is turned off. Although the observed two decaying time scales and the dynamics of IEs can be explained by the diffusion of IEs driven by interaction and their recombination, an alternative scenario involving the diffusion of photoexcited free carriers (33) is also possible [see section 8 of (18)]. Future experimental studies with spatially resolved resonant excitation of IEs can be potentially used to distinguish these scenarios.

Unlike the neutral IEs discussed above, CIEs can be manipulated by an in-plane electric field. Figure 3A shows the spatial map of I_PL overlaid with the device image when CIEs are optically excited at the center of the sample. Similar to neutral IEs, CIEs generated at the laser-illuminated spot can diffuse across the entire sample. Both the WSe₂ and MoSe₂ layers in our device have multiple electrical contacts away from the heterostructure edge (~10 μm away) that are used to control the lateral electric field while avoiding any local Schottky barrier effects. Figure 3B shows the spatial map of the PL intensity normalized as I_PL(V_ds)/I_PL(V_ds = 0) when applying an interlayer bias voltage of V_ds = 3 V across the WSe₂ layer. We observe that the grounded edge of the sample becomes brighter with increasing V_ds (also see Fig. 3C for the normalized average emission intensity along the heterostructure channel). This increase in PL at the boundary between the heterostructure and the highly doped monolayer region can be explained by drift of CIEs under the applied bias voltage in the channel. The applied bias V_ds creates an electric field to tilt the band structure in the direction of the WSe₂ channel, driving positive (+) CIEs along the same direction as shown in the schematic diagram in Fig. 3D. At the boundary of the heterostructure, however, the +CIE cannot be transported to the WSe₂ p-channel because current across the boundary must be preserved. Therefore, the transported +CIEs recombine to turn into a hole in the WSe₂ p-channel. In figs. S13 and S14, we further confirm this picture of CIE transport by changing the doping polarity and V_ds direction [see section 9 of (18) for details on gate configurations and alternative explanations]. We also note that, owing mainly to the limited resolution of our electrical setup, we do not observe any photocurrent >10 pA.

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Finally, we demonstrate the electrical generation of IEs by free-carrier injection using ohmic contacts in individual TMD layers. Because our heterostructure forms type II–aligned p- and n-layers, the charge transport across WSe₂ to MoSe₂ is expected to show diode-like rectifying behaviors (34, 35). Figure 4A shows interlayer current (I_ds) versus interlayer bias (V_ds) curves, whose characteristics can be modulated by V_tg and V_bg. Changing V_tg and V_bg adjusts the band offset in the type II heterojunction and the doping in each layer. The inset to Fig. 4A shows a map of the forward bias current at a fixed bias voltage. One can identify the region in which both WSe₂ and MoSe₂ layers remain intrinsic, consistent with the absorption spectrum discussed in Fig. 1. Notably, we find that this p-n device generates detectable electroluminescence (EL) at sufficiently high bias. A particularly interesting EL condition occurs when both TMD layers are intrinsic, thus allowing electrons and holes to recombine through the formation of IEs. Figure 4, B and C, shows the EL maps of the heterostructure region. The local EL intensity in the heterostructure depends on the local recombination current density, which can be controlled by V_tg and V_bg [section 10 of (18)]. We find that the EL spectrum resembles the PL spectrum in the same (V_tg, V_bg) configuration (34). Figure 4D shows EL versus E_hs. Similar to the PL shown in Fig. 1A, the EL spectrum shifts linearly with E_hs, which can be attributed to the IE Stark effect. More direct evidence that the EL process in our heterostructure is mediated through the IE formation by carrier injection is provided by the EL lifetime. Figure 4E shows the EL intensity as a function of time when we pulse V_ds at a fixed V_tg and V_bg. We measure the EL at the falling edge of the pulse. Long and short lifetimes of ≈150 and ≈25 ns are obtained for the gate voltages of V_tg = 10 and −10 V with V_bg = 16.3 V, corresponding to the neutral IE and charged IE formation regime, respectively (Fig. 4A, inset).

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The electrical generation of long-lived interlayer excitons provides an electrically driven near-infrared light source with an energy tunability that ranges over several hundreds of milli–electron volts and spatial control of the emission. Achieving high-density IEs without optical excitation could pave a way to realize quantum condensates in solid-state devices. Large valley polarization (23, 36) strongly coupled to the spin may also lead to optoelectronic devices based on electrically driven CIEs. The spin degree of freedom in such devices could be potentially used for both classical and quantum information processing.