■ INTRODUCTION

The two-dimensional (2D) monolayer semiconductors of formula MX 2 (M = Mo, W; X = S, Se) have direct optical band gaps. 1,2 Nevertheless, when pristine exfoliated monolayers are photoexcited, nonradiative recombination usually dominates. 3,4 This is in part a consequence of Auger processes, 5 whose rates are enhanced relative to those in 3D semiconductors because of stronger Coulomb interactions. 6 Among these processes is exciton-exciton annihilation, which dominates at high excitation density, [7][8][9] and results in either an excited electron in the conduction band or a hole in the valence band. At lower densities, however, opinions vary on the significance of different Auger contributions. One possibility is thermal activation of trapped photocarriers and subsequent increase in the number of delocalized carriers conducive to Auger scattering. 10 This process has been argued to become more important at elevated temperatures, 11,12 although the lack of temperature dependence in some measurements argues against the significance of such processes. 13,14 In addition, in the tungsten-based materials, there are dark exciton ground states which may provide a phonon-assisted Auger channel at low excitation powers, 15 though the significance of this too is unclear. 16 The ambiguous situation is a consequence of the fact that, despite their ubiquity, Auger processes are hard to probe because they are both ultrafast and nonradiative.

In this work, we employ an unconventional photocurrent technique to reveal exciton/trion-hole Auger scattering in monolayer WSe 2 . From the dependence of the photocurrent on electrode voltage and excitation energy, we can extract spectral information and band offsets. Figure 1a is a schematic and Figure 1b an optical micrograph of the device which we will focus on in the main text. We obtained consistent results with other similar devices (Supporting Information §6). A WSe 2 monolayer flake is sandwiched between thin hexagonal boron nitride (hBN) dielectric layers, in this case with thicknesses of 8 nm (top) and 10 nm (bottom). Few-layer graphene (FLG) is used for electrical contacts CT1 and CT2 to the WSe 2 monolayer. Their separation of about 5 μm defines the WSe 2 channel length. Another FLG piece on top serves both as a gate for electrostatically doping the WSe 2 and as an optically transparent electrode for collecting carriers that cross the hBN barrier. A further pair of split FLG bottom gates, labeled BG1 and BG2, is included for doping the WSe 2 at the respective contacts to reduce the contact resistance. (See the Methods and Supporting Information §1 for fabrication details.)

■ RESULTS

Device Operating Condition in Auger Photocurrent Mode. Figure 1c shows the conductance between CT1 and CT2 as a function of back-gate voltage V BG , applied equally to BG1 and BG2, measured in the dark with a bias of 50 mV on CT2. We obtain ambipolar operation at low temperature (here 5 K), implying suitably conducting contacts for either electrons or holes, by setting the top electrode voltage V T to -3 V when V BG < 0 and to +3 V when VBG > 0. This dopes the channel with the same carrier type as the contact regions (see Supporting Information §2). In a similar manner, whenever we vary V T , we set V BG to either +3 or -3 V as appropriate to keep the contacts conducting.

This device structure permits multiple photocurrent spectroscopy modes (see Supporting Information §3). In Auger photocurrent mode, we measure the current I C that flows from the top electrode through the thin hBN to contact CT1, keeping CT2 disconnected. Similar measurement results were obtained using contact CT2 instead. The I C -V T characteristic in the dark (black trace in Figure 1d) is typical for an hBN tunneling barrier of thickness 8 nm with low defect density: 17 the current is negligible at biases smaller than about 4 V and rises rapidly at larger biases due to Fowler-Nordheim tunneling. To have negligible dark current and to avoid degrading the hBN, we keep the magnitude of V T smaller than 4 V in the following measurements.

Exciton-and Trion-Induced Auger Photocurrent. When a laser of frequency ω is focused to a spot (∼1 μm in diameter) between the contacts, appreciable photocurrent can be generated, depending on V T and ℏω. For example, at ℏω = 1.71 eV (red trace in Figure 1d), photocurrent appears when V T is more negative than -2 V, rises to a peak at V T ≈ -2.7 V, and then exhibits negative differential photoconductance 18 (NDPC), decreasing to a minimum at -4 V. The dependence of I C jointly on V T and ℏω in the hole-doped regime (V BG = -3 V and V T ranging negative) is shown as an intensity plot in Figure 2a. A corresponding plot of the optical absorption (see Supporting Information §4) is shown in Figure 2b, where the peaks due to the neutral A and B excitons (X A 0 and X B 0 ) and the positive trion (X A + ) of monolayer WSe 2 are labeled. Evidently, I C shows features associated with these absorption resonances (labeled accordingly). In the cases of X A 0 and X A + , I C exhibits a peak as a function both of ℏω and of V T . Figure 2c shows traces of I C versus V T for selected photon energies close to the trion absorption resonance. Multiple peaks can be seen, each with an associated region of NDPC.

In Figure 2d, we plot the positions of the peaks in both I C (blue) and absorption (red) for X A 0 and X A + as a function of ℏω and V T , derived from the data in the red boxes in Figure 2a and b, respectively. The absorption peaks blue-shift substantially with increasingly negative V T . This implies a reduction of the exciton/trion binding energy that exceeds the bandgap renormalization, as seen previously. 19 The observation that the X B 0 peak does not blue-shift with V T is consistent with this understanding, because the initial electron state for X B 0 generation is in the lower spin-split valence band far below the Fermi level. The close correspondence between the features in the photocurrent and the absorption strongly implies that the photocurrent is related to the rate of exciton generation. The NDPC occurs when the absorption resonances blue-shift above the excitation energy as V T increases, thereby reducing the exciton generation rate.

We also plot in Figure 2d, in black, the positions of the X A 0 and X A + photoluminescence (PL) peaks measured in the same device. At small V T , they match the absorption peak positions, but as V T increases, the PL peaks red-shift and so diverge from the blue-shifting absorption peaks. This can be understood as a consequence of the fact that PL is not sensitive to the occupancy of valence band states, combined with free-carrier screening that renormalizes the band gap downward. 20 Mechanism of Auger Hole Detection. The sign of photocurrent here implies that illumination causes holes to flow from the WSe 2 through the hBN to the top electrode. One possible mechanism for this is direct photoexcitation of holes to states in the WSe 2 valence bands near or below the hBN valence band edge, from which they can simply pass over the barrier. This is energetically possible, since the photon energy is much larger than the WSe 2 -hBN valence band offset, E VBO ∼ 0.8 eV, deduced from recent measurements of WSe 2graphene 21 and graphene-hBN 22 band offsets. However, direct one-photon absorption is parity forbidden, 23 and moreover, its rate should be independent of excitonic effects. Similar arguments also rule out direct photoactivation of midgap charged defects in hBN. Instead, the fact that the photocurrent has peaks near the exciton absorption resonances implies that it depends on the exciton population, and therefore that the passage of holes through the barrier is assisted by excitons.

In the simplest case, a hole is excited to below the hBN valence band edge by the Auger recombination of a single exciton. This process is energetically possible, since the exciton energy is much greater than E VBO , and unlike for one-photon absorption, the process is not parity forbidden and the rate should be proportional to the exciton population, which is greatest near the absorption resonances. The hole is injected far from the Fermi energy in the graphite, where, as in any metallic electrode, the quasi-particle lifetime is very short and in-plane momentum is not a good quantum number; hence, momentum conservation places no constraint. Since I C is simply proportional to the laser power (see Figure 2a, inset), this must be the dominant process, because Auger processes involving more than one exciton would produce a superlinear power dependence. With this understanding, using rate equations (see Supporting Information §7), we can estimate a lower bound for the exciton-hole Auger rate of 10 10 s -1 . This is surprisingly large compared with Auger rates in highly doped bulk semiconductors 24 of between 10 6 and 10 8 s -1 .

Figure 3a and b show measurements corresponding to those in Figure 2a andb, respectively, but here in the electron-doped regime (V BG = +3 V and V T ranging positive). Unlike in the hole-doped regime, no photocurrent at all is seen for ℏω < 2.2 eV, even though a negative trion (X A -) resonance is visible at ℏω ≈ 1.7 eV in the absorption. This is explained by the WSe 2 -hBN conduction band offset, E CBO , being much larger than the energy a conduction-band electron can gain by either onephoton absorption or Auger recombination of X A -. Using E VBOE = 0.8 eV together with WSe 2 and hBN band gaps of 2.1 25 and 6.0 eV, 26 respectively, gives E CBO ∼ 3.0 eV. Photocurrent does however flow at higher ℏω, above a bias threshold which is indicated by the white dashed line in Figure 3a. This can be explained by direct one-photon absorption by electrons at the WSe 2 conduction band edge, 23 which is parity-allowed, immediately followed by tunneling though the hBN barrier, whose transparency increases with increasing electric field. The linear decrease of the bias threshold with ℏω can be reproduced well using the WKB approximation assuming a step height of 3.0 eV that matches E CBO (see Supporting Information §9).

■ DISCUSSION

The interpretation of the data discussed above is summarized in Figure 4. A schematic of I C versus V T traces is plotted in Figure 4a, showing NDPC in the hole-doped regime and photoassisted tunneling in the electron-doped regime. First, consider negative V T , where the WSe 2 is hole-doped (Figure 4b). When ℏω is resonant with X A + , trions are generated (left), and when an electron and a hole in a trion recombine, the excess energy is transferred by an Auger process to the remaining hole, which then has enough energy to pass through the hBN valence band and produce photocurrent (right). Similarly, when ℏω is resonant with X A 0 or X B 0 , one of the generated neutral excitons can excite a free hole when it recombines, 24 or it can capture a free hole to form a trion and then recombine exciting the hole. Second, consider increasingly negative V T starting from one of these resonant conditions (Figure 4c). This causes the absorption resonance to blue-shift above ℏω, suppressing exciton generation and so reducing the photocurrent, resulting in NDPC. Third, consider positive V T , where the WSe 2 is electron-doped (Figure 4d). Because of the large E CBO , neither one-photon absorption nor Auger processes can excite electrons to high enough energy to pass into the hBN conduction band. However, at large enough V T and ℏω (Figure 4d), the barrier transparency for photoexcited electrons is sufficient for photoassisted tunneling to occur and give photocurrent, though without NDPC.

In conclusion, we observe excitation-frequency-dependent photoconductance peaks that result from Auger processes linked to the excitonic absorption resonances in the monolayer semiconductor WSe 2 . We find that the dominant Auger process in our WSe 2 heterostructures is excitation of holes by recombination of individual X A 0 excitons or X A + trions, and we infer a lower bound of 10 10 s -1 on the rate. While the mechanism of hot Auger carrier extraction resembles that considered in other systems, [27][28][29] our method of using van der Waals heterostructures enables the study of Auger processes at low excitation density and with gate control of the doping. 30 This opens up a window into studying the relatively inaccessible yet vitally important Auger processes. Finally, we note that similar device geometries with hBN-separated FLG gates are used widely for electrostatic gating of 2D semiconductors under optical excitation, and Auger-assisted gate photocurrent should be incorporated as an important factor in analyzing the performance of these devices.

■ METHODS Device Fabrication. A detailed description of the fabrication process can be found in Supporting Information §1 and §2. In brief, this was accomplished in three stages. In the first, individual flakes were obtained by mechanical exfoliation and identified under an optical microscope. Second, van der Waals assembly was undertaken with the aid of polycarbonate films stretched over viscoelastic stamps. For each device, a total of eight or nine nanoflakes were stacked according to the device geometry shown in Supporting Information §1. Finally, metal electrodes consisting of 10/50 nm vanadium/gold were defined by electron beam lithography and electron beam physical vapor deposition (EBPVD).

Photoluminescence, Photocurrent Spectroscopy, and Charge Modulation Spectroscopy. All measurements presented in the main text were performed in a coldfinger cryostat at a temperature of 5 K. For photoluminescence, a 660 nm beam from a pulsed supercontinuum laser was used, with the average power kept at 10 μW. V T was varied from -4 to +4 V; both CT1 and CT2 were grounded, while BG1 and BG2 were disconnected. The emission was collected in reflection geometry and spectrally resolved with a CCD-mounted spectrometer. Photocurrent and charge modulation absorption spectroscopy were performed concurrently with the setup shown in Supporting Information §4. In brief, an ac modulation voltage was added to V T and the probe laser wavelength was scanned from 500 to 760 nm. The dc component of I C is measured with a current preamplifier, and the ac component of the probe laser was detected with a Si photodiode connected to a lock-in amplifier. Both supercontinuum and tunable cw sources were used in photocurrent and optical absorption measurements, but no difference was observed in the results. Detailed postprocessing steps and analysis of the optical absorption spectra are given in Supporting Information §5.

■ ASSOCIATED CONTENT

* sı Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.0c02190.