Plasmon Excited Ultrahot Carriers and Negative Differential

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Plasmon Excited Ultrahot Carriers and Negative Differential Photoresponse in a Vertical Graphene van der Waals Heterostructure Lingfei Li,†,‡ Wei Liu,†,‡ Anyuan Gao,†,§ Yaolong Zhao,† Qin Lu,† Li Yu,† Junzhuan Wang,† Linwei Yu,† Lei Shao,*,∥ Feng Miao,†,§ Yi Shi,† Yang Xu,*,‡ and Xiaomu Wang*,† Nano Lett. Downloaded from pubs.acs.org by UNIV AUTONOMA DE COAHUILA on 04/26/19. For personal use only.

†

National Laboratory of Solid State Microstructures, School of Electronic Science and Engineering, Collaborative Innovation Center of Advanced Microstructure and §School of Physics, Nanjing University, Nanjing 210093, China ‡ Department of Information Science & Electronic Engineering, Zhejiang University, Hangzhou 310058, China ∥ Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR China S Supporting Information *

ABSTRACT: Photogenerated nonequilibrium hot carriers play a key role in graphene’s intriguing optoelectronic properties. Compared to conventional photoexcitation, plasmon excitation can be engineered to enhance and control the generation and dynamics of hot carriers. Here, we report an unusual negative differential photoresponse of plasmoninduced “ultrahot” electrons in a graphene−boron nitride− graphene tunneling junction. We demonstrate nanocrescent gold plasmonic nanostructures that substantially enhance the absorption of long-wavelength photons whose energy is greatly below the tunneling barrier and significantly boost the electron thermalization in graphene. We further analyze the generation and transfer of ultrahot electrons under different bias and power conditions. We find that the competition among thermionic emission, the carrier-cooling effect, and the field effect results in a hitherto unusual negative differential photoresponse in the photocurrent−bias plot. Our results not only exemplify a promising platform for detecting low-energy photons, enhancing the photoresponse, and reducing the dark current but also reveal the critically coupled pathways for harvesting ultrahot carriers. KEYWORDS: Hot carriers, plasmonic nanostructures, negative differential photoresponse, vdW heterostructure

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he photoelectric effect,1 which fundamentally determines the performance of a plethora of photodetectors, solar cells, and photocatalysis, intrinsically possesses a threshold frequency (e.g., barriers in the p−n junction or Schottky junction) for incident light. Under thermal equilibrium, photons only with energy higher than the threshold can be used. Namely, carriers excited by photons with energy higher than the threshold can be ejected, which results in photocurrent, whereas those excited by photons with lower energy mostly convert their energy to heat. Utilizing the excess thermal energy of nonequilibrium photoexcited carriers (also referred to as “hot” carriers,2 which are not in equilibrium with phonons and have an equivalent temperature higher than that of the lattice) provides an opportunity to extend the photoresponse to low-energy photons. Graphene, with strong electron−electron interaction and weak electron−phonon coupling,3−6 can realize ultrafast thermalization within an electron system4,7 (∼50 fs) before transferring its energy to the lattice (several picoseconds). Combined with a long lifetime (∼100 ps),8 photon-excited hot carriers in graphene and graphene-based heterostructures have © XXXX American Chemical Society

been demonstrated for detecting and harvesting photons with energy slightly lower than that of the Schottky barrier.9,10 However, traditional hot carriers have two major challenges in applications. First, the ejection of hot carriers competes with very fast carrier relaxation processes, resulting in insufficient carrier collection before their energy is converted to heat. In addition, the excess thermal energy (corresponds to the increment of electron temperature) excited by photons with energy greatly below the threshold is very limited, dropping the harvesting efficiency of low-energy excitations. To alleviate these difficulties, it is crucial to achieve hot electrons with a much higher equivalent temperature. Surface plasmon resonances (SPRs)11−13 induced by plasmonic nanostructures (such as metallic nanostructures14−18) can effectively transfer their energy to the electron bath through nonradiative decay,19,20 thus providing a new channel to excite Received: March 4, 2019 Revised: April 6, 2019

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DOI: 10.1021/acs.nanolett.9b00908 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. Plasmonic nanostructure-decorated Gr-hBN-Gr heterostructure. (a) Schematic of the Gr-hBN-Gr vdW heterostructures with a gold nanostructure array on top under optical excitation. The purple (blue) flake in the middle (bottom) represents a thin hBN tunneling barrier (thick hBN substrate). (b) Optical image of a typical device (device A). The top (bottom) Gr layer and hBN barrier are outlined by white (black) and blue dashed lines, respectively. (c) Scanning electron microscope (SEM) image of the same device shown in panel b. (d) Close-up SEM image of the area outlined by the dashed box in panel c, which shows an aligned array of the asymmetric “nanocrescent”-shaped gold nanostructures. (Scale bars are 20 μm, 10 μm, and 200 nm in panels b−d, respectively.) (e) Simplified band diagram of the traditional hot carrier (electron) generation process under infrared laser optical excitation. The photoexcited electrons and thermalized hot electrons are colored blue and orange, respectively. (f) Simplified band diagram of the ultrahot carrier (electron) generation process under infrared laser optical excitation. The plasmon-excited hot electrons and thermalized ultrahot electrons are colored red and orange, respectively. The energetic electrons in the high-energy regime of the thermal tail can cross the barrier and produce photocurrent (represented by gradient arrow). Here, T0, Te1, and Te2 represent the temperature of the phonon system, hot electrons, and ultrahot electrons, respectively. For all measurements in the text, we applied bias to the bottom graphene with top graphene grounded unless otherwise mentioned.

and control hot carriers.15,21 Fulfilling SPR’s great potential in photocatalytic,20 photovoltaic,22,23 and photodetection24 applications requires a comprehensive understanding of the electron and energy-transfer pathways as well as the effects of external interactions. Here we demonstrate a nanocrescent gold plasmonic nanostructure-decorated graphene (Gr)−hexagonal boron nitride (hBN)−graphene vertical heterostructure. By associating the advantages of ultrafast electron thermalization in graphene with SPRs of gold nanostructures, we realize plasmon-excited ultrahot electrons in graphene under the

illumination of an infrared laser (1550 nm). The ultrahot carriers have a much higher temperature than the lattice and longer thermal tail compared to conventional hot carriers under the identical excitation power condition; therefore, they acquire sufficient energy to overcome the large energy barrier at the Gr−hBN interface and produce a prominent current. We find that the electron-transfer pathway in the sandwiched heterostructures can be tuned from thermalized hot electrondominated thermionic emission to nonthermalized/cooled photoexcited electron-dominated tunneling by using a bias voltage.9,25 We experimentally demonstrate the hitherto B

DOI: 10.1021/acs.nanolett.9b00908 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 2. Intrinsic hot carrier generation in vdW heterostructures. (a) Photocurrent mapping of a typical device (device C) at power density P = 0.33 MW/cm2 and bias Vb = 0.9 V; top and bottom graphene are outlined by white and gray dashed lines, respectively (scale bar is 4 μm). (b) Current as a function of bias Vb under different excitation power density. (Inset) Current−bias plot on the logarithm scale. (c) Photocurrent as a function of excitation power density P at different Vb values. The data are fitted with power law I ∼ Pγ. The dashed lines are fitting results corresponding to each set of data of the same color. (d) Current noise spectra of the Gr−hBN−Gr heterostructure under different Vb conditions.

1e,f) cannot directly cross the high barrier ϕB at the Gr−BN interface, they contribute their energy to the electron bath through the ultrafast thermalization process.4,5 The thermalized electrons are called hot electrons,2 which obey the Fermi− Dirac distribution as

unusual negative differential photoresponse (NDPR) characterized by a nonmonotonic increase in photocurrent with increasing voltage, which is caused by the complex competition among the thermionic emission, cooling, and field effect at different biases. We further demonstrate the tuning of NDPR by both the gate voltage and excitation power. Figure 1a shows a schematic of the Gr-hBN-Gr vertical van der Waals (vdW) heterostructure. A thin hBN flake (∼5 nm) is sandwiched between two graphene layers. The insulating hBN provides a large tunneling barrier for electrons (Δe ≈ 3.5 eV25,26) at the Gr−hBN interface,27,28 reducing dark current noise for photonic applications. Another thick hBN layer (∼20 nm) placed below the heterostructure serves as a substrate, isolating our device from the SiO2 substrate.29 Gold plasmonic nanostructures are then transferred to the top of the asfabricated vdW stack. Figure 1b shows the optical image of a typical device (device A). The top (bottom) graphene layer and hBN are outlined by white (black) and blue dashed lines, respectively. Figure 1c shows the scanning electron microscope (SEM) image of the whole device. Figure 1d shows a close-up SEM image of the asymmetric “nanocrescent”-shaped gold nanostructure array.30 All measurements presented in the main text are obtained from four devices and performed at room temperature under ambient conditions by using a scanning photocurrent microscopy setup. (Supplementary Table 1 provides detailed information on these four devices for clarity.) The photoresponse mechanisms of traditional hot electrons and ultrahot electrons are depicted in Figure 1e,f respectively, for comparison. Incident photons are absorbed by graphene and generate electron−hole pairs (0.4 and 1.16 eV with respect to Dirac point for 1550 and 532 nm laser, respectively). Although the photoexcited electrons (blue spheres in Figure

f (E ) =

1

(

exp

E−E − kT F e

)+1

(1)

The energy distribution can be solely characterized by the electron temperature Te (for hot electrons Te > lattice temperature Tph ≈ environment temperature T0). The hot electrons (shown in Figure 1e) will not reach thermal equilibrium with phonons even with continuous wave excitation (i.e., the elevated Te will give rise to a prolonged thermal tail in f(E) with excess energy higher than the Fermi level. (Supporting Information Figure 1 demonstrates the calculation and comparison of the carrier distributions at different Te values.) On the one hand, high excess thermal energy enables electrons to emit over the barrier, resulting in photocurrent based on thermionic emission. On the other hand, by applying an interlayer bias Vb to narrow the effective barrier height, photocurrent can also be produced through direct tunneling or Fowler−Nordheim (FN) tunneling. In this process, the small light absorption of graphene (around 2.3%31) limited the ΔTe of hot electrons (which is proportional to the light absorption10) for a given incident power. Thus, elevating Te requires much higher light absorption. Here, we utilize SPRs to tightly confine light and excite ultrahot electrons by breaking the intrinsic absorption limit of graphene. The term “ultrahot electrons” refers to hot electrons that possess much higher electron temperature and a C

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Figure 3. Plasmon-excited ultrahot electrons in a vdW heterostructure. (a, b) Photocurrent mapping of a typical device (device B) without (a) and with (b) nanostructures at interlayer bias Vb = 2.1 V and average power P = 4.2 mW. The top (bottom) graphene flake is outlined by a white (gray) dashed line (scale bar 4 μm). (c) Photocurrent as a function of Vb with (red squares) and without (blue triangles) nanostructures. (d) Photocurrent as a function of average power density P with (red squares) and without (blue triangles) nanostructures. Dashed lines are fitting results (replotted in Supporting Information Figure 4 as a function of maximum power density Pmax). (e) Experimental extinction spectrum of gold plasmonic nanostructures (red curve, left axis) and the calculated local electric (E) field (blue curve, right axis). (f) FDTD simulation result of the enhancement in the electric field of a single nanocrescent Au nanostructure. The electric field enhancement is demonstrated on a log scale [log(|E/ E0|), where E0 represents the incident field and E represents the enhanced field]. The outer-side diameter of the simulated Au nanostructure is 168 nm, the thicker lobe is 80 nm wide and 26 nm thick, and the thinner lobe is 16 nm wide and 5 nm thick (scale bars 20 nm).

heterostructure using a 532 nm laser. Figure 2a shows the photocurrent mapping of a typical device (device C) in which top and bottom graphene are outlined by white and gray dashed lines, respectively. Despite the lower energy of the photon-excited electrons compared to the barrier (about 0.34 eV below the barrier ϕB), significant photocurrent is observed as a result of hot electron generation. One approach to validating this intrinsic hot carrier generation in graphene is by analyzing the photocurrent dependency on the incident power.9,10 Figure 2b shows the photocurrent as a function of interlayer bias Vb under different power conditions. Photocurrent as a function of excitation laser power density P at different Vb values is summarized and fitted with power law Ipc ∼ Pγ in Figure 2c. The clear superlinear power dependence at low bias is a hallmark of the

longer thermal tail (as presented in Figure 1f and further quantitatively discussed below) compared to equilibrium electrons and traditional hot electrons under the same incident power condition. We realized these ultrahot electrons through a strongly coupled electromagnetic field, which distinguishes them from the commonly known hot electrons9,10,28 generated from normal far-field light excitation. We emphasize that although SPR can enhance light absorption to produce ultrahot carriers, the slow cooling rate of the material is another essential factor. In other words, electron−phonon coupling must be slow enough to allow further heating in the electron system. Prior to transferring plasmonic nanostructures, we first characterized the traditional hot carrier generation in the photoresponse of a plain graphene−boron nitride−graphene D

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Figure 4. NDPR in vdW heterostructure. (a) (Top) Calculated electron temperature as a function of the bias voltage. Corresponding band diagrams show the dynamics in the transport mechanism with interlayer bias Vb. TE and FE represent thermionic emission and field emission, respectively. (Bottom) Photocurrent as a function of bias voltage. Red, yellow, and blue colors in the background represent the thermionic region, NDPR transition region, and FN tunneling region, respectively. (b) Photocurrent as a function of average laser power density P at different interlayer bias Vb. The data are fitted with a power law I ∼ Pγ. The colored dashed lines are fitted results corresponding to each set of data presented in the same color. (c) Calculated increase in electron temperature (ΔTe = Te − Tph) as a function of maximum power density Pmax.

power density P = 0.42 MW/cm2, with the positive Vb applied to the bottom graphene with the top graphene grounded to facilitate electron transfer. A detailed discussion on dominant carrier type is in Supporting Information section 3.) An obvious enhancement in the photoresponse is achieved after the deposition of the plasmonic nanostructures (Figure 3c,d). Noticing that our devices are generally stable under laser illumination during one test circle, the devices may slightly degrade after long-time illumination and frequent test circles. We also perform a finite-difference time-domain (FDTD) simulation (Figure 3f) to demonstrate the field enhancement. We averaged the integrated field enhancement according to the measured nanostructure density and obtained a field enhancement factor of ∼25. It should be noted that the experimental data shows a smaller increment in photoresponse (maximum at around 8). The reasons for this discrepancy are as follows. First, the distribution of plasmonic nanoparticles is nonuniform. The existence of off-resonance particles (characterized by the wider resonance peak of the extinction spectrum) reduces the efficiency of light confinement. Second, the calculation is based on an ideal lossless case. Third, the interface between gold nanoparticles and graphene may be not clean enough and thus hampers the charge/energy transfer. The responsivity and external quantum efficiency (EQE) of our devices are around 70 pA/mW and 5 × 10−8, respectively, at a wavelength of 1550 nm (those parameters for 532 nm are 13 nA/mW and 3 × 10−5, respectively), which are not high compared to those of other graphene-based detectors.34,35 However, this is reasonable considering the large barriers at the Gr−BN interface. Nonetheless, plasmon significantly elevates the hot carrier temperature. We calculate the increment of electron temper-

thermionic emission of the hot electrons. In addition, much weaker superlinear dependence in the high-bias regime indicates FN tunneling of nonthermalized photoexcited electrons. We also observed a linear dependence in the higher power region, which is caused by the saturation in absorption (Supporting Information Figure 2). The vdW junction provides a favorable noise figure for photonic applications. Figure 2d shows the low-frequency noise density spectra. The vdW junction possesses standard flicker noise (nearly perfect 1/f spectrum) and fairly low noise power densities. The flicker noise eventually approaches the instrument noise floor under low bias. For example, operating at Vb = 2.5 V, the specific detectivity reads 5 × 1014 Jones. The excellent low-noise property of the vdW heterostructure is promising for improving the sensitivity in photodetection applications. The photothermionic effect10 has been demonstrated in Figure 2, which validates the intrinsic hot carrier generation in graphene. Although this effect allows the detection of photons with energy slightly lower than the barrier, the efficiency of hot carrier generation rapidly drops with decreasing photon energy. Plasmonic nanostructures enable harvesting photons32,33 at the resonance frequency (which may be much below the barrier). Figure 3e is the experimental extinction spectrum (red curve) of the gold nanostructures array and theoretically calculated local electric field (blue curve) of a single gold nanostructure at different wavelengths, both showing a resonance peak at around 1550 nm.30 We compare the photocurrent mappings from a device (device B) without (Figure 3a) and with (Figure 3b) plasmonic nanostructures under the same conditions. (Vb = 1.6 V and average laser E

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Figure 5. Schematic of the generation, thermalization, emission, and cooling processes of ultrahot electrons. The green (blue) gradient color in n(E) − E and corresponding green (blue) spheres in the conduction band of graphene represent plasmon-excited electrons (photoexcited electrons). The gradient colors in the n(E) − E plot from blue to red represent the energy level of electrons. Paths 1 and 3 represent thermalization and the resulting thermionic emission for traditional hot electrons. Paths 2 and 4 represent ultrahot electrons, which have a much higher temperature than hot electrons (Te2 > Te1). Path 5 represents the cooling pathway which competes with thermionic emission. This competition results in NDPR and can be tuned by applied bias, Vb. At the same time, direct FN tunneling competes with the thermalized process in both the traditional hot electron and ultrahot electron cases (paths 6 and 7, respectively) in the high bias region. Notice that if the incident power is too low (path (2′)) then the increase in electron temperature will be small and thus the NDPR disappears.

ature ΔTe for a particular device (device D) before and after transferring plasmonic nanostructures (by a method adapted from ref 10; see also Supporting Information Section 4 for details). The calculated ΔTe (Figure 4c) is increased by nearly 1 order of magnitude under the identical power condition. We emphasize that the gold plasmonic structure-assisted injection of hot electron into graphene is the kernel working mechanism of our device. To identify the mechanism, we tested a control sample (MoS2 FET, which cannot produce photocurrent at 1550 nm light even after enhancing the absorption) to verify the origin of photocurrent enhancement in our plasmonic structure/2D material hybrid system (Supporting Information Figure 5). Electron transfer pathways of ultrahot electrons exhibit an unusual NDPR in the plasmon-enhanced vdW junction as shown in Figure 4a. For conventional hot carrier-based vdW heterostructures, photocurrent monotonically increases with increases in bias voltage, suggesting a smooth transition from the thermionic emission regime (paths 1 and 3 in Figure 5) to the tunneling regime (path 6 in Figure 5).9 Power-dependent photoresponses in Figure 4b validate the transition in the transport mechanism. (See the discussion in Supporting Information section 6.) However, a nonmonotonic increase in photocurrent is observed in the transition region for ultrahot electrons, which we attribute to a complex competition among field-induced barrier lowering in thermionic emission (path 4 in Figure 5), field-effect tunneling (path 7 in Figure 5), and the hot-carrier cooling effect (path 5 in Figure 5).25 In the low bias

region (Vb < 2.8 V), the field effect thins the effective barrier by shifting the Fermi level in graphene. The thermionic emission current thus increases with increasing bias due to the reduction of the effective barrier height caused by the field effect as ij −ϕB(Vb) yz zz Ipc(Vb , Te) ∝ Te(Vb , P)2 expjjj j kTe(Vb , P) zz k {

(2)

where ϕB is the effective barrier, k is the Boltzmann constant, and P is the absorption power density. However, with higher bias (2.8 V < Vb < 3.3 V), the Fermi level becomes difficult to shift because of graphene’s high density of states at high energy and the effective barrier height stops decreasing with bias. Simultaneously, an enlarged carrier density accelerates the electron−phonon interactions25,36 and opens up an extra cooling pathway for hot electrons. Consequently, if the bias-induced cooling effect surpasses the saturated barrier lowering effect, then the photocurrent decreases with increasing bias voltage as (see details in Supporting Information section 7) dIpc/dVb =

dIpc dTe dIpc dϕB dIpc dTe + ≈ 3.3 V), FN tunneling of nonthermalized photoexcited electrons dominates (path 6 and F

DOI: 10.1021/acs.nanolett.9b00908 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 6. Tuning NDPR by the excitation power density and gate voltage. (a) Power dependence of the NDPR in the Ipc − Vb curve at average excitation power densities of 0.08, 0.33, and 0.54 MW/cm2, respectively. (b) Gate dependence of the NDPR in the Ipc − Vb curve at Vg = 60, 0, and −50 V (measured at an average power density of P = 0.46 MW/cm2 with a 1550 nm laser).

Figure 5). Figure 6a shows the Ipc as a function of Vb at different powers. The NDPR becomes pronounced with increasing laser power. It nearly disappears when the average laser power is lower than 0.7 mW (corresponding to a power density of 0.08 MW/cm2). This is because under the lowpower condition (corresponding to a relatively low Te), the bias-induced barrier lowering effect dominates the cooling effect. (This competition is also validated by calculation in Supporting Information Figure 8a−c.) In addition, NDPR can also be controlled by electrical gating.27,38−40 Under high doping, on the one hand, the tunneling current rapidly increases as the barrier becomes low. Thus, the FN tunneling dominates the total current before NDPR becomes pronounced in the thermionic emission current (calculated in Supporting Information Figure 8d−f). On the other hand, an increase in the doping level results in an increase in the cooling rate and thus a smaller NDPR. We use device D (which is “intrinsically” n-type-doped, see Supporting Information Figure 9) to measure the photocurrent under different gating conditions. As shown in Figure 6b, NDPR gradually disappears with increasing doping level (from −50 to 60 V, in which the Fermi level in graphene moves away from the Dirac point) because the tunneling current overwhelms both the thermionic current and the cooling effect before the NDPR occurs. We also measured the Ipc − Vg of another device (device B, shown in Figure 4a) which demonstrates NDPR under no gate condition due to small doping at Vg = 0 (Supporting Information Figure 10). In summary, we realized plasmon-induced ultrahot electrons in a graphene−hexagonal boron nitride−graphene tunneling junction. We also demonstrated that the nanocrescent gold plasmonic nanostructures substantially enhance the photoresponse of 1550 nm light by generating ultrahot electrons. Compared to traditional hot electron generation, the excitation of ultrahot electrons largely relies on SPR-enhanced light absorption, which results in a highly elevated electron temperature and pronounced photocurrent. We also observed

7 in Figure 5, as discussed in Supporting Information section 8), where photocurrent increases with bias again as ij (ϕ − hω/2)3/2 yz zz Ipc(Vb) ∝ Vb 2 expjjjj−κ B zz j z Vb k {

(4)

where κ is a constant and ω is the frequency of incident light. We notice that with varying bias and power conditions the response time of the device also changes. As has been discussed in ref 9, carrier tunneling occurs faster at higher bias and smaller ω. In the tunneling-dominated region, the tunneling happens on the scale of femtoseconds to picoseconds depending on the bias. In the thermionic-dominated region, to successfully collect the nonequilibrium carriers before cooling, the response time must shorter than 1 ps.4 These ultrafast response times are highly desired in applications, although they are difficult to measure by the commonly used electrical method (limited by the RC delay in the unoptimizable electrical connection and limited bandwidth of the test circuit). We also calculate Te as a function of the bias voltage based on the Landauer transport model for tunneling junctions37 (details in Supporting Information section 9). The maximum calculated Te of ultrahot carrier is around 700 K as shown in top panel of Figure 4a (at maximum power density Pmax of 1.08 MW/cm2). This value is consistent with the calculated values shown in Figure 4c. The decrease in Te with Vb is consistent with previous NDPR analysis and has already been specifically discussed in ref 25. We emphasize that inducing ultrahot electrons is necessary for observing NDPR. The current lowering induced by the hotcarrier cooling effect is not significant if the Te is not high enough. As a result, the NDPR is inaccessible in previous reports of traditional hot electrons. On the basis of this fact, there are several methods for dynamically adjusting the NDPR as shown in Figure 6. First, the carrier temperature can be tuned through changing the excitation power (path 2′ in G

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photocurrent is collected using a preamplifier (SR570) and a lock-in amplifier (SR830) that are synchronized with an optical chopper operated at 500 Hz. For 532 nm laser measurements, photocurrent is collected by using semiconductor analyzer (PDA, FS Pro). For noise measurements, the device is set in a vibration-free probe station to ensure that the device works in the dark as well as to reduce the noise originating from the environment. Noise spectra are obtained with a noise characterization system (PDA, NC300L). All measurements are performed at room temperature under ambient conditions. Finite-Difference Time-Domain Simulations (FDTD) Simulation. The FDTD simulations were performed using FDTD Solutions 8.7 (Lumerical Inc., Canada). During the simulations, an electromagnetic pulse was launched into a box containing the gold nanostructure. A mesh size of 1 nm was used for the nanostructure and the surrounding space. The nanostructure model in the simulation was built with a homemade script, and the geometrical parameters were set according to the SEM-measured average values. The refractive index of the medium in the top and side regions was set at 1.0, and that in the bottom was set at 1.515. The dielectric function of gold was taken from Johnson and Christy’s data. The electric field enhancements were calculated at a laser wavelength of 1550 nm. The averaging of the field enhancement was performed over the area that a nanostructure occupies on average.

an unusual NDPR in the photocurrent−bias plot. By further analyzing the electron transfer pathways, the NDPR is attributed to a competition among thermionic emission, the carrier cooling effect, and the field effect under different biases. By further tuning the NDPR using the gate voltage and excitation power, we demonstrate that the NDPR is very sensitive to the change in electron temperature and doping level. Our results not only provide a practical strategy for detecting low-energy photons, enhancing the photoresponse, and reducing dark current in optoelectronic applications but also initiate a new channel for generating, harvesting, and controlling ultrahot carriers. Materials and Methods. Device Fabrication. The graphene (Gr)−hexagonal boron nitride (hBN)−graphene devices are fabricated by a vdW layer-by-layer assembly technique.41 The hBN (∼5 nm) and graphene flakes are mechanically exfoliated from bulk crystals of Kish graphite and hBN, respectively, onto a silicon wafer covered by a 285-nmthick SiO2 layer. A transparent stamp which contains watersoluble poly(vinyl acetate)42 (PVA) on the top side and elastomeric poly(dimethylsiloxane) (PDMS) placed below is used for the pick-up and release process. First, a homemade micromanipulator is used to manipulate the stamp to move to the target location and affix to the first flake (top graphene layer). Then, we heated the stamp to 75 °C using a hot plate for 2−4 min and cooled it by using an electric fan. After cooling to room temperature and lifting the stamp, the flake sticks to the PVA film. We repeated the pick-up process and stacked consecutive flakes (middle hBN layer and bottom graphene) using the same stamp. At the end, the final vdW stack is released on a thick hBN flake placed on the SiO2 (285 nm)/Si substrate by holding the stamp at 90 °C for 1 min, which softens the PVA layer. The PVA can be removed with deionized (DI) water, and the residual polymers can be removed in acetone solution. The nanocrescent gold plasmonic nanostructures fabricated on a chip (a glass or silicon wafer covered with SiO2 layer) are transferred over the as-fabricated vdW stack by using the poly(methyl methacrylate) (PMMA)-assisted transfer method.29 For this, we first spin-coat a poly(methyl methacrylate) (PMMA 950 A4) layer of thickness around 300 nm on the chip with gold plasmonic nanostructures at 2000 rpm for 1 min. Then, we immersed the chip in NaOH solution with a 0.5 mol/L concentration and heated it to 80 °C on a hot plate. After 5 min, the SiO2 will be etched partially and the PMMA with plasmonic nanostructures will be separated from the chip and float in the solution as a result of surface tension. After soaking the PMMA film in DI water for 2 min to remove NaOH residues, we transferred the PMMA film with the gold nanostructures to the vdW heterostructure. A drop of isopropyl alcohol (IPA) can help to flatten the PMMA film. PMMA can be removed with acetone after being held at 180 °C for 10 min to enhance the adhesion between the gold nanostructures and the vdW stack. The Ti/Au (5 nm Ti, 50 nm Au) contacts are formed by standard e-beam lithography, e-beam evaporation, and lift-off processes. Electrical and Optoelectronic Measurements. We use a homemade scanning photocurrent microscopy setup for the photocurrent measurement. Photocurrent is generated by a focused continuous laser with a 20× microscope objective lens on the device. The spot size of the laser on the device is ∼1 μm and 500 nm in diameter for 1550 and 532 nm lasers, respectively. In the case of 1550 nm laser measurement, the

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.9b00908.

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Calculation of carrier distribution at different electron temperatures; discussion of dominant carrier types under photon excitation; calculation of the increase in electron temperature with power using two temperature model; discussion of the mechanism of photocurrent enhancement; analysis of transport mechanism at high bias; discussion of power law dependence under the 1550 nm laser condition; discussion of bias-induced extra cooling pathway; modeling of photocurrent and analysis of the electron temperature dynamic; details of devices demonstrated in the letter; calculation of the power and doping dependence of the NDPR and gate dependence of the photocurrent (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. ORCID

Linwei Yu: 0000-0002-0801-5210 Lei Shao: 0000-0003-2161-5103 Feng Miao: 0000-0002-1910-9781 Yang Xu: 0000-0003-3148-7678 Xiaomu Wang: 0000-0001-8975-5626 Author Contributions

X.W. and Y.X. conceived the project. L.L., W.L., L.Y., and J.W. fabricated the devices and measured the photoreponse. L.S. modeled, prepared, and characterized the plasmonic nanoH

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Letter

Nano Letters

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structures. A.G., Y.Z., and Q.L. helped perform EBL and SEM. X.W., L.L., and Y.X. analyzed the data and wrote the manuscript. X.W., Y.X., F.M., and Y. S. supervised the research. All authors discussed the obtained results. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project was primarily supported by the National Key R&D Program of China (2018YFA0307200 and 2016YFA0200200), the National Natural Science Foundation of China (61775092, 61674127, and 61874094), Zhejiang Natural Science Foundation (LZ17F040001), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB30000000), and the Collaborative Innovation Center of Advanced Microstructures. L.S. acknowledges financial support from a CUHK Direct Grant (ref no. 201718, project code 4053307).

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DOI: 10.1021/acs.nanolett.9b00908 Nano Lett. XXXX, XXX, XXX−XXX