## Introduction

As Johan Stark first observed in hydrogen atoms1, applying an electric field on Coulomb-bound particles shifts their energy levels and eventually leads to their dissociation (Fig. 1a). In condensed matter physics, Wannier–Mott excitons display features analogous to those of hydrogen2, but with the crucial difference that they recombine if they are not dissociated. Thermal energy is usually sufficient to ionize excitons in 3D semiconductors owing to their small binding energy EB (typically a few meV). In contrast, quantum confinement effects and reduced Coulomb screening in low-dimensional materials give rise to large exciton binding energy (EB > 100 meV), which prevents thermal or spontaneous dissociation even at elevated temperatures and exciton densities.

In particular, monolayer transition metal dichalcogenides (TMDs) have aroused tremendous interest due to their unique optical properties governed by prominent excitonic features3,4,5,6 and spin- and valley dependent effects7,8,9,10,11. These 2D semiconductors provide an exciting testbed for probing the physics arising from many-body Coulomb interactions6,12. Recently, all-optical experiments have revealed a wealth of physical phenomena such as exciton13,14, trion15,16, and biexciton17 formation, bandgap renormalization18, exciton–exciton annihilation19,20,21,22,23,24,25, and optical Stark effect7,11. Exciton dissociation, on the other hand, can in principle be assessed through photocurrent measurements since photocurrent directly stems from the conversion of excitons into free carriers. A large number of studies have investigated photodetection performances of 2D TMDs26,27,28,29 and demonstrated their potential as photodetectors and solar cells. However, it is still unclear which dissociation process can overcome the large exciton binding energy and lead to efficient photocurrent generation in these devices. Theoretical studies suggest that strong electric fields may provide the energy required to dissociate the excitons30,31,32, but the precise mechanism governing exciton dissociation in 2D TMDs remains to be experimentally investigated.

Here, we address this important issue by monitoring the exciton dissociation and subsequent transport of free carriers in a monolayer TMD pn junction through spectrally and temporally resolved photocurrent measurements. Combining these two approaches allow us to assess and correlate two essential excitonic properties under static electric field, namely the Stark shift and the dissociation time. Further, we make use of the extreme thinness of 2D materials and their contamination-free assembly into heterostructures to reliably control the potential landscape experienced by the excitons. By placing the monolayer TMD in close proximity to metallic split gates, we can generate high in-plane electric fields and drive a photocurrent (PC). We find that at low field the photoresponse time of our device is limited by the rate at which excitons tunnel into the continuum through the potential barrier created by their binding energy, a process known as tunnel ionization (Fig. 1a). Tuning the electric field inside the pn junction further allows us to disentangle various dynamical processes of excitons and free carriers and to identify the kinetic bottlenecks that govern the performance of TMD-based optoelectronic devices.

## Results

### Device structure and characterization

Figure 1b, c presents a schematic and optical micrograph of our lateral pn junction device made by assembling exfoliated flakes on metallic split gates (VG1 and VG2) separated by 200 nm (see “Methods”). Few-layer graphite flakes placed on both ends of a monolayer WSe2 flake serve as ambipolar electrical contacts33 that we use to apply a bias voltage VB and collect the photogenerated charges. The lateral graphite-WSe2-graphite assembly is fully encapsulated in hexagonal boron nitride, typically 20 nm thick, which provides a clean and flat substrate. Three devices were measured (see Supplementary Note 1 and Supplementary Figs. 13), but unless otherwise specified, all measurements presented in the main text are obtained at room temperature from the device shown in Fig. 1c.

Tuning of bias and gate voltages allows us to finely control the in-plane electric field F. Finite-element and analytical calculations of the electric field distribution in our device (see Supplementary Note 2 and Supplementary Figs. 47) provide us with a precise estimate of F and the electrostatic doping inside the WSe2 (Fig. 1d). Applying gate voltages of opposite polarity (Vasym = VG1 = −VG2 = −10 V) leads to the formation of a sharp pn junction (Fig. 1e) with an in-plane electric field reaching 21 V µm−1 (Fig. 1d). The photoresponse that we observed at the junction (Fig. 1c) follows a photodiode-like behavior: PC is only generated in the pn or np configuration (see Supplementary Fig. 1c) and can be increased by applying a reverse bias voltage (Fig. 1f).

### Spectral response

We probe the absorption spectrum in the photoactive region by measuring the PC as a function of photon energy at a constant laser power P and in-plane electric field F. Figure 2a shows the responsivity (PC/P) spectra of a device similar to the one presented in Fig. 1c, measured at various VB and at low temperature (T = 30 K) in order to reduce thermal broadening. We observe a pronounced peak at a photon energy  = 1.73 eV, corresponding to the A exciton, and a step-like increase around 1.87 eV. For increasing electric field, this step-like feature broadens and an additional shoulder appears at 1.83 eV.

To identify the various spectral features, we compare the experimental spectra with first-principles calculations for a monolayer WSe2 embedded in hBN (see Supplementary Note 3 and Supplementary Fig. 8). By including the electronic screening from the hBN layers in the many-body G0W0 and Bethe–Salpeter Equation (BSE) frameworks34 we obtain a bandgap of 1.85 eV and a lowest bound exciton at 1.67 eV in good agreement with the experimental spectra. To account for the effect of a constant in-plane electric field we use a model based on the 2D Wannier equation (see Supplementary Note 4 and Supplementary Fig. 9). In these model calculations, screening by the TMD itself as well as the surrounding dielectric materials is described via the Keldysh potential for the electron–hole interaction. Figure 2b shows calculated absorption spectra for different in-plane fields F. Excellent agreement between experiment and calculations is found assuming a bandgap of 1.9 eV, which yields a binding energy of EB = 170 meV for the A excitons consistent with the first-principles calculations. The unbroadened spectrum calculated at zero field (Fig. 2b, solid black line) confirms the presence of multiple overlapping excited excitonic peaks below the bandgap. The calculated spectra for higher field reproduce remarkably well the field-induced increase of the sub-bandgap absorption observed experimentally. This is a manifestation of the Franz–Keldysh effect, which results from the leakage of the free electron and hole wave functions into the bandgap (inset of Fig. 2b). We note that our experimental value of EB agrees well with the one estimated from the diamagnetic shift of a monolayer WSe2 encapsulated between silica and hBN35. Larger EB has been observed in SiO2-supported WSe2 samples36,37,38, underlining the role of the dielectric environment on the excitonic properties39.

### Excitonic Stark effect

Turning our attention to the A exciton photocurrent peak, we observe a pronounced red-shift as VB (Fig. 2c) and Vasym increase. We attribute this to the DC Stark effect. In first approximation, the Stark shift of a 1s exciton (without dipole moment) is given by $${\mathrm{\Delta }}E = - \frac{1}{2}\alpha F^2$$, where $$\alpha$$ is the in-plane polarizability. As shown in Fig. 2d, the A exciton energy shows a quadratic dependence with the maximum in-plane electric field FM calculated for different values of Vasym and VB (Fig. 2e), yielding a polarizability of $$\alpha = \left( {1 \pm 0.2} \right) \times 10^{ - 6}$$ Dm/V. This shift matches well with the predicted polarizability of $$\alpha = 9.4 \times 10^{ - 7}$$ Dm/V for EB = 170 meV, thus supporting our previous spectral analysis. Interestingly, we note that the measured in-plane polarizability is two order of magnitude larger than the out-of-plane value recently obtained in PL experiments40. This strong anisotropy confirms the 2D nature of the A exciton and demonstrates the advantage of using in-plane electric fields for controlling the optical properties of TMDs31.

### Photoresponse dynamics

Along with the Stark shift, the application of a large in-plane electric field shortens the lifetime of excitons, which eventually decay into free electrons and holes (Fig. 1a). We probe these decay dynamics by assessing the photoresponse time $$\tau$$ of the device with time-resolved photocurrent measurements (TRPC), banking on the nonlinear photoresponse of the WSe2. Figure 3a, b shows the strong sublinear power dependence of the photocurrent (and the corresponding responsivity) under resonant pulsed optical excitation ( = 1.65 eV, see “Methods”). Many physical processes may be responsible for or contribute to the observed sublinearity, including phase space filling41 and dynamic screening effects (e.g., bandgap renormalization18). These many-body effects become intricate as the exciton gas approaches the Mott transition42. However, recent time-resolved spectroscopy19,22 and photoluminescence20,23 experiments indicate that in this exciton density regime (1011 $$\lesssim$$ N $$\lesssim$$ 1013 cm−2), exciton–exciton annihilation (EEA, or exciton Auger recombination) is the dominant decay process for excitons in TMDs24. To account for EEA in the rate equation governing the photocurrent we add a loss term that scales quadratically with the exciton density ($$\gamma N^2$$, where $$\gamma$$ is the EEA rate). Assuming that each pulse generates an initial exciton population $$N_0$$, this model yields $${\rm{PC}} \propto {\mathrm{ln}}\left( {1 + \gamma \tau N_0} \right)$$, which reproduces well the observed sublinear photoresponse (black lines in Fig. 3a, b, see Supplementary Note 5). Moreover, the fits capture adequately the variation of the sublinear photoresponse with bias (Fig. 3a, b) and gate (Supplementary Fig. 10a) voltages, from which we extract the values of $$1/\gamma \tau$$ (Fig. 3c). Hence, these nonlinear measurements already offer an indirect way to probe the photoresponse time.

In order to directly extract $$\tau ,$$we resonantly excite A excitons in the pn junction with a pair of 200 fs-long laser pulses separated by a variable time delay Δt, for various values of Vasym (Fig. 3d, e). Due to the sublinear power dependence, the photocurrent displays a symmetric dip when the two pulses coincide in time (Δt = 0). By extending our nonlinear photocurrent model to the case of two time-delayed pulses (see Supplementary Note 5 and Supplementary Fig. 10), we can show that the time dependence of this dip is dominated by an exponential time constant corresponding to the intrinsic photoresponse time τ of the device. The photoresponse rate $$\Gamma = \frac{1}{\tau }$$ is extracted from TRPC measurements at various values of Vasym (Fig. 3d, e) and VB (see Supplementary Fig. 10d) and presented in Fig. 3c. We observe that Γ increases markedly with gate and bias voltages, and remarkably follows the same trend as the values of $$1/\gamma \tau$$ obtained from the power dependence measurements. Comparing these two results, we obtain an EEA rate of $$\gamma$$ = 0.05 cm2/s, which is similar to those found in WSe219,23, MoS221,22, and WS220,25. We also note that the shortest response time we measure, $$\tau$$ = 10.3 ± 0.4 ps, translates into a bandwidth of f = 0.55/$$\tau$$ ~ 50 GHz, which compares with the fastest responses measured in TMD-based photodetectors43,44.

## Discussion

To directly address the exciton dissociation caused by the in-plane electric field FM, we examine the dependence of the photoresponse rate Γ on FM at the pn junction (Fig. 4a). Clearly, two regimes can be distinguished. The rapid increase of Γ with FM is attributed to dissociation by tunnel ionization. We verify this by comparing the measured Γ to the calculated tunnel ionization rate $${\mathrm{\Gamma }}_{{\mathrm{diss}}}$$, obtained by introducing the complex scaling formalism in the 2D Wannier–Mott exciton model (see Supplementary Note 4 and Supplementary Table 1). According to this model, $${\mathrm{\Gamma }}_{{\mathrm{diss}}}$$ can be evaluated in first approximation by the product of the “attempt frequency”45, which scales with $$E_{\mathrm{B}}/h$$, and the exponential tunneling term $${\mathrm{exp}}( - E_{\mathrm{B}}/e_0dF_{\mathrm{M}})$$, where $$e_0$$ is the elementary charge, d is the exciton diameter, and $$h$$ is the Plank constant. We find that the dependence of Γ at low field (FM < 15 V µm−1) coincides well with the calculated dissociation rate of excitons with EB = 170 meV, in agreement with our photocurrent spectroscopy analysis. More importantly, this shows that in the low-field regime the exciton dissociation process is the rate-limiting step governing the generation of photocurrent. We note that in multilayer TMDs, where EB ~ 50 meV, the ionization rate is two orders of magnitude larger than in the monolayer case46, and hence this process was not found to limit the photoresponse rate of multilayer devices44.

At high electric field (FM > 20 V µm−1), the photoresponse rate deviates from the dissociation rate-limited model and enters a new regime characterized by a more moderate increase of Γ with FM. The observed linear scaling of Γ(FM) suggests that, in this regime, the photoresponse rate is limited by the drift-diffusive transport of free carriers out of the pn junction. By considering a carrier drift velocity $$v_{{\mathrm{drift}}} = \mu F$$, we estimate that carriers generated in the center of the junction of length L = 200 nm escape the junction at a rate $${\mathrm{\Gamma }}_{{\mathrm{drift}}} = 2\mu F/L$$. Comparing this simple expression (dotted line in Fig. 4a) to the measured Γ at high field, we find $$\mu = 4 \pm 1$$ cm2 V−1 s–1, which is very similar to the room temperature field-effect mobility that we measure in our sample (μFE ~ 3 cm2 V−1 s–1, see Supplementary Note 1).

A complete photocurrent model is achieved by introducing competing loss mechanisms caused by the radiative and non-radiative recombination of excitons (see Supplementary Note 6). Good agreement with the experimental data is obtained by considering the finite lifetime of excitons ($$\tau _{{\mathrm{r}},N} = 1/{\mathrm{\Gamma }}_{{\mathrm{r}},N}$$ ~ 1 ns20,23, see Supplementary Note 1) and free carriers ($$\tau _{{\mathrm{r}},n} = 1/{\mathrm{\Gamma }}_{{\mathrm{r}},n}$$~ 30 ps41) at zero electric field. This comprehensive picture of the dynamical processes (Fig. 4b) offers valuable insights into the internal quantum efficiency (IQE) of the photocurrent generation mechanism in this device. Indeed, the efficiency $$\eta$$ of each photocurrent step depends on the competition between the PC-generating ($$\tau _{{\mathrm{drift}}}$$, $$\tau _{{\mathrm{diss}}}$$) and the loss ($$\tau _{{\mathrm{r}},N/n}$$) pathways, such that $$\eta _{{\mathrm{diss}}/{\mathrm{drift}}} = {\mathrm{\tau }}_{{\mathrm{r}},N/n}/({\mathrm{\tau }}_{{\mathrm{r}},N/n} + {\mathrm{\tau }}_{{\mathrm{diss}}/{\mathrm{drift}}})$$. In the inset of Fig. 4a, we compare the IQE measured at low power as a function of VB with the total extraction efficiency $$\eta _{{\mathrm{extract}}} = \eta _{{\mathrm{drift}}}\,\eta _{{\mathrm{diss}}}$$ derived from the kinetic model shown in Fig. 4b. We find that $$\eta _{\rm{extract}}$$ captures very well the bias dependence of the IQE, indicating that we correctly identified the relevant PC-generating processes. The field-independent discrepancy of 30% is attributed to the collection efficiency $$\eta _{{\mathrm{coll}}}$$, which we define as the ratio between the number of excitons reaching the pn junction and the number of absorbed photons. This value coincides with our analysis of the measured photocurrent profile and with the prediction of our exciton diffusion model (see Supplementary Note 7 and Supplementary Fig. 11).

In summary, our study offers a global understanding of the fundamental mechanisms governing the exciton dynamics and associated photoresponse in monolayer TMDs under in-plane electric field. We demonstrate that despite their large binding energy, photogenerated excitons can rapidly dissociate into free carriers via tunnel ionization, thereby outcompeting recombination processes. Importantly, this knowledge allows us to identify the main material properties that limit photocurrent generation in TMDs such as carrier mobility, exciton binding energy, and lifetime. This provides guidelines in terms of device design, material quality improvement, and Coulomb engineering of the van der Waals heterostructure to further improve the performances of TMD-based optoelectronics devices and develop their applications in valleytronics. We finally note that the observed Stark and Franz–Keldysh effects open up exciting opportunities for modulating light with 2D materials47.

## Methods

### Device fabrication

Exfoliated layers are assembled in a van der Waals heterostructure using the same technique as described in ref. 48. The monolayer of WSe2 is identified by photoluminescence measurement (see Supplementary Note 1). The heterostructure is deposited onto metallic split gates (15 nm palladium) defined by electron-beam lithography on a degenerately doped silicon substrate covered with a 285-nm-thick SiO2 layer. The two graphite flakes are electrically connected by one-dimensional contacts48 made of Ti/Au (2/100 nm).

### Photocurrent measurements

Photocurrent measurements are performed using a photocurrent scanning microscope setup, where a laser beam is focused by a microscope objective (Olympus LUCPlanFLN × 40) onto the device placed on a piezoelectric stage (Attocube ANC300). Photocurrent is measured with a preamplifier and a lock-in amplifier synchronized with a mechanical chopper. A supercontinuum laser (NKT Photonics SuperK Extreme), with a pulse duration of 40 ps, repetition rate of 40 MHz and tunable wavelength (from 500 to 1500 nm) is employed to characterize the devices, perform photocurrent spectroscopy, and measure the photocurrent power dependence. Time-resolved photocurrent measurements are performed using a Ti:sapphire laser (Thorlabs Octavius) with 200 fs pulses (at the sample), with a repetition rate of 85 MHz, and centered at  = 1.65 eV (FWHM = 0.07 eV), which corresponds to the A exciton absorption peak. The laser beam is split into two arms and recombined using 50/50 beamsplitters. A mechanical chopper modulates the laser beam in one arm (pump), while the other arm (probe) has a motorized translation stage that allows for the generation of a computer-controlled time delay Δt between the two pulses.

### Data availability

The data that support the findings of this study are available from the corresponding author on request.