a Development target for self-powered photodetectors. Existing photodetectors are invariably constrained by a speed-responsivity trade-off (blue solid line), manifesting as either rapid response with limited responsivity, high responsivity with sluggish response, or intermediate performance in both metrics. The ultimate target (red five-pointed star) of self-powered photodetector is the concurrent realization of enhanced responsivity and accelerated response speed. b Schematic diagram of the vertical WSe₂ p-i-n photodiode. Niobium (Nb) doped WSe₂ (Nb-WSe₂, blue dash line region), pristine WSe₂ (i-WSe₂) and Argon (Ar) plasma treated WSe₂ (Ar-WSe₂, red dash line region) are used as p type/intrinsic/n type layer, respectively. P-type doping is achieved through niobium substitutional doping, while n-type doping is realized by generating selenium vacancies via Ar plasma bombardment of the WSe? surface. c Band diagrams of metal contact with lightly p-doped (upper) and degenerately p-doped (bottom) semiconductor, respectively. Light doping creates a wide and high potential barrier, resulting in large contact resistance and consequently increased RC time (t_RC). In contrast, degenerate doping produces a narrow barrier and direct tunneling transport of carriers, yielding lower contact resistance and reduced RC time. d Band diagrams of the p-i-n photodiode with lightly doped (upper) and degenerately doped (bottom) p-type layer under light illumination, respectively. Light doping creates a narrow depletion region in the intrinsic layer with relatively weak electric field, resulting in low drift velocity of photo-generated carriers under illumination. In contrast, degenerate doping enables complete depletion of the intrinsic layer, where the strong electric field facilitates high-speed carrier drift. e Schematic diagram of the photodiode response time with lightly doped (upper) and degenerately doped (bottom) p-type layer, respectively. Light doping results in a high RC time and slow carrier drift, leading to a sluggish detector response speed, as evidenced by the gradual transition in the current-time (I-t) curve. In contrast, degenerate doping reduces the RC time and accelerates carrier drift, enabling fast detector response with sharp transitions in the I-t curve.

Two-dimensional (2D) materials with the strong light-matter interaction^8,9,10, are currently the subject of intense investigation as the optoelectronic responsive layer prompted by the need for superior-performance photodiodes in terms of sensitivity, detection speed, as well as flexibility and self-powered ability. Owing to the high optical absorption coefficient (e.g., 3.38 × 10⁵cm⁻¹ at 532 nm for WSe₂, 40 times higher than Si)¹¹, 2D materials allow for significantly reduced thickness of intrinsic layer, which can greatly decrease the drift/diffusion length and amplify the built-in electric field. Until now, the design of 2D materials-based self-powered photodiodes has largely relied on a lateral metal–2D materials–metal phototransistor or a lateral p-n junction^12,13,14. However, the long transport length leads to the small built-in electric field, the low carrier drift speed, and the long diffusion length, resulting in a slow response speed in self-powered mode, which is not ideal for efficient photon harvesting and photon-current conversion. In contrast, the vertical structure with a short transport length greatly enhances the built-in electric field and reaches the saturation drift velocity, achieving high-speed carrier drift and the fast response speed. Therefore, it is essential to fabricate 2D materials based vertical p-i-n photodiodes, exploring the photocarrier generation/transfer dynamics to solve responsivity-speed dilemma. The major challenges include the achievement of high-quality contact (degenerate doping) and the optimization of p-type/intrinsic/n-type layer thickness, leading to the maximized optical absorption in intrinsic layer (high responsivity), the efficient photocarrier separation (high built-in electric field and self-powered ability), and the saturation drift velocity (fast speed).

In this work, we utilize WSe₂ thin layers to construct high-performance vertical p-i-n photodiode by optimizing the photocarrier generation and transfer dynamics. The Nb-doped WSe₂ with high hole concentration of 2.65 × 10²¹ cm⁻³ as the degenerate p-doped layer effectively reduces the contact resistance and boosts the built-in electric field, leading to the efficient photocarrier separation/collection, the high-field drift velocity, and short intrinsic response time. The ultimate thickness downscaling of the 2D Nb-doped WSe₂ p-type layer results in the maximized photocarrier generation in the intrinsic WSe₂ layer, contributing to high responsivity and the nearly ideal external quantum efficiency (EQE). The fabricated vertical WSe₂ p-i-n photodiode exhibits a current rectification ratio of 6 × 10⁶. Under self-powered condition (zero voltage bias), the device displays a high responsivity of 0.388 A W⁻¹ (corresponding to EQE of 90.5%), a high specific detectivity of 1 × 10¹² Jones, a short intrinsic response time down to sub-10 picoseconds, and a fast switching response time of 23 ns. Furthermore, the photodiode achieves a high fill factor of 0.629 and a power conversion efficiency of 6.5%. Our strategy resolves the dilemma between high responsivity and fast speed via the construction of van der Waals vertical p-i-n photodiodes.

a Transfer curve, output curve and structure schematic of WSe₂ FET with Ar-WSe₂ (red dash line region) contact. b Transfer curve, output curve and structure schematic of WSe₂ FET with Nb-WSe₂ (blue dash line region) contact. c Transmission electron microscope (TEM) image of vertical WSe₂ p-i-n junction. Pristine WSe? exhibits a distinct layered crystalline structure, while Ar plasma-treated WSe? demonstrates a clearly amorphous phase (denoted as WSe??_y) with a thickness of 4 nm. d Current density ( J_ds) – V_ds curves of WSe₂ p-i-n photodiode under 532 nm laser illumination with different power density (P_in). e Power dependent open-circuit voltage (V_oc) and short-circuit current density ( J_sc). The maximum V_oc is 0.7 V, and J_sc exhibits linear correlation with P_in ( J_sc ∝ P^0.98). f Short-circuit SPCM image of the p-i-n photodiode using a 488 nm focused laser with power of 1.73 μW. The photocurrent originates from the overlapping area of Ar-WSe₂ (orange dash line), i-WSe₂ (orange dash line) and Nb-WSe₂ (blue dash line). The gray dash lines are Ag metal electrodes.

Nb doped WSe₂ (Nb-WSe₂) works as the degenerate p-type doping layer, where the atomic ratio of Nb is 5%. Hall effect measurements using van der Pauw sample configuration demonstrate that the carrier concentration of Nb-WSe₂ is 2.65 × 10²¹cm⁻³ (Supplementary Figs. 6 and 7). This high hole concentration can contribute to the low contact resistance and the high built-in electric field in WSe₂ p-i-n photodiode. We further fabricated a WSe₂ FET with Nb-WSe₂ as contact electrodes (optical image in Supplementary Fig. 8). The transfer and output curves in Fig. 2b demonstrate a significant hole transport behavior over a wide range of back gate voltage (V_bg). The FET exhibits an extremely high I_on/I_off exceeding 10⁸. The maximum I_ds is 4.17 μA·μm⁻¹ at drain voltage V_ds = 1 V and V_bg = −60 V. Moreover, I_ds shows a linear relationship with V_ds, indicating that p-type Ohmic contact is achieved. Improved ohmic contact between the electrode and the doped layer indicates that doping can indeed enhance contact quality, and this effect is also effective in vertical structures.

The vertical Nb-WSe₂/WSe₂/Ar-WSe₂ p-i-n photodiode has been fabricated via dry transfer technique and the detailed fabrication process has been described in Methods section and Supplementary Fig. 9. We used transmission electron microscopy (TEM) to characterize the interface quality of the p-i-n diode. The cross-sectional TEM image (Fig. 2c) shows a distinct layered structure and high-quality van der Waals interfaces, with the thickness of monolayer i-WSe₂ and Nb-WSe₂ being approximately 0.7 nm. The region treated with Ar plasma exhibits a clear amorphous structure (WSe_2-y), which is non-conductive (Supplementary Fig. 10), and the thickness is about 4 nm. Under dark, the diode displays a unidirectional conductivity with a low reverse saturation current density of 1.29 × 10⁻³mA cm⁻² and a high rectification ratio of 5.9 × 10⁶ (V_ds = ±2 V), as shown in Fig. 2d. The photoresponse characteristics of the vertical WSe₂ p-i-n photodiode have been tested under 532 nm laser with different power density (P_in). When the optical power density is over 29730 mW·cm⁻², the maximum open-circuit voltage (V_oc) of 0.7 V is achieved. The current-power relationship of the photodiode can be described as power-law: I ∝ P^α. Within the range of P_in from 0.0016 to 29730 mW cm⁻², the short-circuit current density ( J_sc) exhibits excellent linear correlation with P_in, with exponent α close to 1 (α = 0.98), indicating that the photovoltaic effect is dominant (Fig. 2e). The contact resistance (series resistance) in the vertical Nb-WSe₂/WSe₂/Ar-WSe₂ p-i-n photodiode, estimated from the dark I-V curve, is 9 kΩ, and can even reach as low as 1 kΩ (Supplementary Note 1 and Supplementary Fig. 11). Therefore, we ascribe this excellent V_oc to the large Fermi energy gradient across p-i-n junction and the low voltage drop at the contact regions, which stem from the high concentration in Nb-WSe₂ and Ar-WSe₂, minimizing contact resistance. Supplementary Fig. 12 illustrates the band alignment diagram of the vertical p-i-n photodiode. Due to the high carrier concentration in Nb-WSe₂ (three orders of magnitude higher than that in Ar-WSe₂), the depletion region is entirely concentrated in i-WSe₂ and Ar-WSe₂. When the device is forward biased, the depletion region narrows, the potential barrier for carriers decreases, and the current starts to increase. Conversely, when the device is reverse biased, the depletion region begins to extend into Ar-WSe₂. When the reverse bias is much greater than 0 V, Ar-WSe₂ becomes fully depleted, significantly increasing the reverse tunneling current. When the device is under light and no bias, the depleted i-WSe₂ fully absorbs photons and converts them into photogenerated electron-hole pairs, which are quickly separated under the large built-in electric field. Since the thickness of WSe_2-y is relatively thin (~4 nm), the carriers can easily tunnel through the WSe_2-y layer and reach the electrode to generate photocurrent. To further verify the mechanism of our device, scanning photocurrent mapping (SPCM) is used to obtain the photocurrent distribution in Fig. 2f. Under zero bias condition, the photosensitive region corresponds to the overlapping area of Ar-WSe₂, i-WSe₂ and Nb-WSe₂. It confirms that the photocurrent originates from the generation of photoexcited charge carriers in the i-WSe₂ layer, followed by the transfer of these charges to the Ar-WSe₂ and Nb-WSe₂, rather than the contact region around the electrode/WSe₂ interface in lateral photovoltaic devices. Furthermore, Fig. 2f shows negligible response at the Ar-WSe₂ and i-WSe₂ interface, indicating that the depletion region is contributed by the junction between Nb-WSe₂ and i-WSe₂. The primary function of Ar-WSe₂ is to improve contact and enhance carrier collection efficiency. Therefore, the thickness of Ar-WSe₂ does not affect the response speed and responsivity of the p-i-n device.

To obtain the intrinsic response time of the vertical WSe₂ p-i-n photodiode and exclude the impact of RC delay time, we performed the time-resolved photocurrent (TRPC) measurement by exciting the device with a pair of ultrashort optical pulses (80 fs, 780 nm) separated by a variable time delay (Fig. 3a). TRPC technique exploits the photocurrent dynamics of the vertical WSe₂ p-i-n photodiode under the nonlinear power dependence of the photocurrent. Figure 3b shows that when average laser pulse intensities exceed 882 W cm^–2, our device exhibits the significant nonlinear power dependence (?J_sc ∝ P^0.68). The observed sub-linearity probably originates from saturable absorption. With the presence of the pump beam, the photocurrent has been suppressed at zero delay time, further indicating the saturation of the photocurrent. We plotted the normalized photocurrent as a function of the delay time with different WSe₂ thickness (L) at V_ds = 0 V (Fig. 3c). The photoresponse characteristics of the samples are shown in Supplementary Fig. 13. Assuming that the photogenerated V_oc is equal to the built-in potential V_bi (in fact, V_oc is usually smaller than V_bi), the estimated built-in electric field strengths from 9 nm sample to 284 nm sample are 333 kV cm⁻¹, 115 kV cm⁻¹, 93.1 kV cm⁻¹, 37.3 kV cm⁻¹ and 23.9 kV cm⁻¹, respectively. The intrinsic response time τ can be extracted from the photocurrent-delay time curve by the following equation²¹:

in which A and τ are the fitting parameters. When thickness is 284 nm, τ = 7.87 ps is obtained. And when L is 9 nm, τ reaches as short as 0.89 ps, which is the shortest intrinsic response time in TMDs based vertical photodetectors as far as we know^22,23,24,25, indicating the potential application of our device in high-speed and high-responsivity detectors.

Fig. 3: Intrinsic response time and switching response time of the vertical WSe₂ p-i-n photodiode.

a Schematic illustration of time-resolved photocurrent measurement (TRPC) by 780 nm pulsed laser (80 fs) at V_ds = 0 V. The Δt represents the delay time between pump and probe beams. Under pulsed laser excitation and built-in electric field, photogenerated electron-hole pairs are created, separated, and transported to the metal electrodes. b Short-circuit photocurrent density (?J_sc) as a function of probe beam power without pump beam. The red dash and solid lines are the power-law fits with J_ph ∝ P¹ and J_ph ∝ P^0.68, respectively. The linear-to-sublinear transition occurs at P = 882 W cm⁻². c TRPC measurements of the p-i-n devices with different WSe₂ thicknesses. d Normalized transient photoresponse under 266 nm pulsed laser with different thicknesses of pristine WSe₂. Response time extracted from the full width at half maximum of the response curve. e Photoswitching behaviors of the WSe₂ p-i-n photodiodes under 532 nm laser at V_ds = 0 V and laser on/off switching frequency of 400 kHz. The switching response time is the time that photocurrent rises from 10% to 90% or falls from 90 to 10% of the peak. f Broadband frequency response of the vertical WSe₂ p-i-n photodiode. The gray dash lines show the bandwidth when the amplitude of the normalized photoresponse drops by −3 dB (the frequency that photocurrent reduces to 0.707 of the maximum value).

The intrinsic response time from TRPC technology is composed of drift time τ_drift, recombination time τ_r, exciton dissociation time and interface transfer time τ_s, and there is the specific relationship^22,26:

By varying the i-WSe₂ thicknesses in vertical p-i-n photodiodes, we plot ? with E/L (Supplementary Fig. 14) and extract τ_s of 0.884 ps, τ_r of 11.1 ps, the mobility of 16.2 cm²V⁻¹s⁻¹, and the carriers drift velocity of >10⁶cm/s, approaching the saturation drift velocity of WSe?²⁷. Overall, our results show that the degenerate doping and the vertical structure with short channels contribute to the high-field velocity transport and the short intrinsic response time.

Different from the intrinsic response measurement, which provides the upper speed limit of photoresponse, the extrinsic switching response time is actual response time of photodiode, indicating the ability of a photodetector to process high frequency signals. To test the switching response time, the devices are manually soldered and bonded to a homemade PCB board, and the response time is obtained by connecting the transimpedance amplifier and the oscilloscope. We conducted photocurrent - time (I-t) tests using 266 nm pulsed laser (Fig. 3d) and 532 nm continuous laser (Fig. 3e). The switching response time decreases with the increasing WSe₂ thickness. When the thickness is 118 nm, the switching response time is 36 ns, which is quite fast in TMDs based photodetectors^{28,29,30,31,32,33}. The full cycles of the two samples under 532 nm laser illumination are shown in Supplementary Fig. 15. In addition, we tested the broadband frequency response of vertical p-i-n devices from 1 kHz to 25 MHz. The 3 dB cutoff frequency of 9 MHz is obtained in 78-nm-thick devices. And the 3 dB cutoff frequency increases to 13 MHz in 118-nm-thick devices (Fig. 3f). Based on the results from three different characterization methods, we concluded that as the thickness increases (or junction capacitance decreases), the device response time decreases. The relation between junction capacitance (C) and switching response time (t_ex) follows the function of t_ex ∝ C^1.04 (Supplementary Fig. 16). In addition, it has been demonstrated that the test board and the transimpedance amplifier (TIA) seriously affect the response time of the device (Supplementary Fig. 17)³⁴. Therefore, the obtained response time is limited by the test setup and the actual response time of p-i-n device should be faster.

We fabricated a vertical graphene/WSe₂/Ar-WSe₂ p-i-n photodiode as a control device. The J–V characteristics of the photodiode under 808 nm laser illumination and the photoswitching behaviors are shown in Supplementary Fig. 18. The device exhibits a saturated open-circuit voltage V_oc of 0.24 V when the optical power density is over 757 mW·cm⁻² and a long rise/fall time of 10 μs/6.5 μs. The extracted contact (series) resistance is as large as 8 MΩ, and several control devices all exhibit high contact resistance (Supplementary Fig. 19), leading to a high RC time delay and a reduced voltage drop across the intrinsic region. From the statistical analysis of the response times (Supplementary Fig. 18), we can conclude that the difference in contact resistance causes a significant variation in the response speed. Therefore, a degenerate doping layer can reduce the contact resistance and increase the built-in electric field, which is crucial for a high-speed vertical WSe₂ p-i-n photodiode.

Downscaling p-type layer thickness to approach ideal efficiency

To resolve the dilemma in the vertical WSe₂ p-i-n photodiode in terms of speed and responsivity, we need to improve the external quantum efficiency (EQE) expressed in the number of photogenerated carriers collected per incident photon. The ideal condition is that the light is completely absorbed by the intrinsic WSe₂ layer and the photogenerated carriers are efficiently separated by the built-in electric field without recombination. However, the heavily doped layer on top can also absorb the light and the photogenerated carriers at the doped layer have to diffuse into the depletion region. In fact, most of the photogenerated carriers at the doped layer quickly recombine and result in a noticeable decrease in the EQE and responsivity, as depicted in Fig. 4a. In our work, the thickness of the p-type Nb-WSe₂ layer can be downscaled to sub-10 nanometers and even sub-1 nanometer^35,36.

Fig. 4: Downscaling of Nb-WSe₂ thickness to boost responsivity and quantum efficiency.

a Schematic of the p-type layer thickness effect in the WSe₂ p-i-n photodiode. Thick Nb-WSe? exhibits high carrier recombination, leading to reduced responsivity. In contrast, thin Nb-WSe? minimizes top-layer absorption while suppressing carrier recombination, achieving enhanced responsivity. b J_ph - V_ds curves of p-i-n photodiode under 532 nm laser illumination with different Nb-WSe₂ thicknesses. c Responsivity (R) and external quantum efficiency (EQE) as a function of Nb-WSe₂ thickness (d). The responsivity exhibits exponential decay with increasing d, following the relation: R = 398.84 × e^−d/31.13 + 11.67, responsivity is the average value under different powers. Inset is the optical power density P_in as a function of d in p-i-n photodiode, R_f is reflection at the surface, α is the light absorption coefficient of the material. The maximum optical power that i-WSe₂ can absorb is (1- R_f) P_in e^-αd. d Schematic of light absorption in the p-i-n photodiodes with thin and thick Nb-WSe₂. Thick Nb-WSe? exhibit strong optical absorption, most photogenerated carriers undergo rapid recombination, significantly reducing the photocurrent density (?J_ph) in i-WSe₂. In contrast, thin Nb-WSe? permits effective carrier diffusion into i-WSe₂ while allowing majority light absorption to occur in i-WSe₂, thereby substantially enhancing the photocurrent density.

To investigate the effect of p-type layer thickness on the optical response characteristic, we vary the p-type Nb-WSe₂ layer thickness from 9 nm to 128 nm (Supplementary Fig. 20). Figure 4b presents the photocurrent density J_ph - V_ds curves of vertical p-i-n photodiodes dependent on the Nb-WSe₂ thicknesses under a constant power density (10 mW·cm⁻²) of 532 nm laser. As the thickness of Nb-WSe₂ decreases from 128 nm to 9 nm, J_ph of the photodiode at V_ds = 0 V gradually increases from 2 × 10⁻¹²A·μm⁻² to 2.8 × 10⁻¹¹A·μm⁻². Responsivity (R) is calculated by J_ph/P_in, in which P_in is the incident laser power density. The increased photocurrent density under a constant laser power density indicates the boosted responsivity. The photoresponse curves and the responsivity as a function of incident power density for four samples are shown in Supplementary Fig. 20. It can be seen that, as the Nb-WSe₂ thickness decreases, the responsivity significantly increases. Figure 4c shows the dependence of the responsivity and EQE on the Nb-WSe₂ thicknesses. The responsivity increases from 21.36 mA W⁻¹ to 298.87 mA W⁻¹ with the decreased thickness of Nb-WSe₂. The EQE is extracted through hCJ_ph/qλP_in, where h is the Planck constant, C is speed of light, q is elementary charge, and λ is wavelength. EQE exhibits the same trend as the responsivity, which increases from 4.98 to 69.67%.

We further find that the responsivity-thickness curve fits well with an exponential decay function (Fig. 4c). Theoretically, the responsivity can be expressed as

in which R_f is the reflection at the surface, α is the light absorption coefficient of the material, η is the internal quantum efficiency, and d is the p-type layer thickness. At V_ds = 0 V, responsivity is fitted as R = 398.84 × e^-d/31.13 + 11.67. We can obtain α = 3.21 × 10⁵cm⁻¹, which is close to the WSe₂ absorption coefficient of 3.38 × 10⁵cm⁻¹ in literatures¹¹.The decreased responsivity and EQE with the increased thickness of p-type layer can be explained by the exponential increase of light absorption by the p-type layers. Before light reaches i-WSe₂, it attenuates due to the absorption by Nb-WSe₂. The maximum light intensity that pristine WSe₂ can absorb is given by (1-R_f)P_ine^-αd (inset of Fig. 4c). Moreover, only a small portion of the photogenerated carriers produced by Nb-WSe₂ near the interface will diffuse into the depletion region, while the rest will recombine quickly. Therefore, the thinner the Nb-WSe₂ layer, the smaller the recombination probability, resulting in a greater number of photo-generated carriers produced in the intrinsic region, and consequently, a higher photocurrent density, responsivity and EQE, as shown in Fig. 4d.

Due to the high carrier density of doped WSe₂ and the limited carrier density of pristine WSe₂ (6.56 × 10¹⁴cm?³), the monolayer Nb-WSe₂ can induce the depletion of 1275-nm-thick pristine WSe₂ at V_ds = 0 V (Supplementary Note 2 and 3). We can infer that the use of monolayer Nb-WSe₂ with the thickness of 0.7 nm (refs. ^37,38) can further increase responsivity and EQE to 401.6 mA W⁻¹ and 93.6%, respectively, while ensuring full depletion of the intrinsic layer and complete absorption of 532 nm laser (10 mW·cm⁻²). Therefore, to simultaneously achieve high responsivity and fast speed, it is required to use ultrathin Nb-WSe₂ and select a relatively thick intrinsic WSe₂ layer under the premise of full depletion (reduced RC time delay).

Figures of merit in vertical WSe₂ p-i-n photodiodes

After the systematic discussion of dominant limiting factors on the photodiode performance, we fabricated the optimized vertical Nb-WSe₂/WSe₂/Ar-WSe₂ p-i-n photodiode with ohmic contact and ultrathin Nb-WSe₂ top layer, which enables high efficiency and ultrafast response. The thickness of WSe₂ and Nb-WSe₂ is 307 nm and 4.5 nm, respectively (Supplementary Fig. 21). Figure 5a presents the power dependent photoresponse. Under dark, the current rectification ratio of the p-i-n photodiode is 6 × 10⁶ (V_ds = ± 2 V). As the P_in increases, both the J_sc and V_oc significantly increase (Fig. 5b). At the P_in of 612 mW·cm⁻², the ratio of J_sc to dark current density ( J_sc/J_dark) exceeds 10⁶, indicating an extremely high signal-to-noise ratio.

Fig. 5: Optoelectronic characteristics of the optimized WSe₂ p-i-n photodiode.

a J_ds-V_ds curves under 532 nm laser illumination with different power densities. b J_sc and V_oc as a function of incident power density under 532 nm and 808 nm laser illumination. The power-law fits between J_sc and power density are J_ph ∝ P^0.996 (532 nm) and J_ph ∝ P^1.008 (808 nm), respectively. c Responsivity (R), external quantum efficiency (EQE) and specific detectivity (D*) as a function of 532 nm incident light power density at V_ds = 0 V. d Photoswitching behavior of the vertical WSe₂ p-i-n photodiode at V_ds = 0 V and laser on/off switching frequency of 4 MHz. The gray dash lines represent the 10% and 90% positions of the switch. e Broadband frequency response of the vertical WSe₂ p-i-n photodiode at V_ds = 0 V. f Responsivity and response time comparison under self-powered mode with previous reports. For visible detector, the vertical WSe₂ p-i-n photodiode shows high responsivity and fast speed. (Supplementary Table 1, for more details and references).

To describe the linearity of the photodiode, the linear dynamic range (LDR) is introduced, which can be calculated by the equation³⁹

in which P_min/P_max is the lowest/highest laser power density of the linear region. It should be emphasized that when calculating LDR using optical power, 10log₁₀ should be used instead of 20log₁₀ which is widely misused. The p-i-n photodiodes show high linearity in a power range of more than five orders of magnitude under 532 nm laser illumination (Fig. 5b). To obtain the LDR limitation of our device, we test LDR under 808 nm laser with a larger power range. The LDR of p-i-n photodiodes in our study exceeding 75 dB, which is close to commercial Si photodiodes (approximately 80 dB for S1133 from Hamamatsu)⁴⁰. It is worth noting that the LDR of our device can be even higher since the power range of P_in can be further expanded. We also calculated the LDR of the control photodiodes (graphene/WSe₂/Ar-WSe₂). The average value is 24 dB, which is 10⁵ times smaller than that of the p-i-n photodiode, as shown in Supplementary Fig. 22. The LDR of the control photodiode is greatly affected by the intrinsic hot carrier dynamics of graphene and the large contact resistance³⁹. In our p-i-n photodiodes, the high doping concentration of Nb-WSe₂ and Ar-WSe₂ results in a small contact resistance, achieving a high LDR.

The responsivity and EQE of the vertical p-i-n photodiode under visible light and varied power density at V_ds of 0 V are shown in Fig. 5c and Supplementary Fig. 23. The responsivity can be as high as 388.0 mA W⁻¹ (EQE of 90.5%) at 532 nm, and 0.554 A W?¹ (EQE ~ 91.6%) at 750 nm, which is outperforming commercial silicon photodiodes⁴⁰. The responsivity and EQE of our device at zero bias are outstanding among 2D p-i-n homojunction^41,42,43, demonstrating high sensitivity and self-powered detection capabilities.

To comprehensively evaluate the detector’s ability to sense weak signals, we assess the specific detectivity (D*). D* can be given by the expression²²

where S is the effective area, k_B is the boltzmann constant, T is the temperature, R_sh is shunt resistance. Figure 5c plots D* with incident laser power density, displaying negligible dependency. At V_ds of 0 V, the D* is 1 × 10¹² Jones, close to the commercial Si photodiode. The high D* at V_ds of 0 V can be attributed to the ultralow thermal noise, which replaces shot noise as the dominant source of total noise. Supplementary Fig. 23 also shows R, NEP and D* as a function of power density and V_ds.

To ascertain the response time, we monitored the temporal switching response with the incident light being alternately switched on and off at a frequency of 4 MHz. Figure 5d shows one cycle of photoswitching, operating at V_ds = 0 V. The rise and fall time are 23 ns and 28 ns, respectively. Figure 5e shows the normalized AC photoresponse in a broad frequency range from 1 kHz to 25 MHz. From the variation in the relative amplitude of the photoresponse, a 3 dB cutoff frequency of 16 MHz is obtained. As summarized in Fig. 5f and Supplementary Table 1, without voltage bias, our vertical p-i-n photodiodes achieve near-ideal external quantum efficiency while maintaining fast response speed, outperforming most self-powered photodetectors based on TMDs^44,45,46 and even commercial Si photodiodes. We can further estimate the theoretical minimum response time of the device by using RC time and TRPC test results, which is 200.4 ps (Supplementary Fig. 24).

The photovoltaic performance can also demonstrate the photocarrier generation and transfer dynamics in p-i-n photodiodes. To achieve high power conversion efficiency (PCE), it requires the strong absorption by the intrinsic layer and the effective separation of photogenerated carriers with minimized recombination^47,48. Hence, we systematically evaluate the photovoltaic performance of our optimized vertical p-i-n photodiodes. Figure 6a displays the J_ds-V_ds curves in the linear scale under dark and 532 nm laser illumination, respectively. A large V_oc of 0.62 V and a high J_sc of 125.7 mA cm⁻² are obtained under the power density of 319 mW cm⁻². We can extract the fill factor (FF) and PCE using the following equation⁴⁹

where P_el is the output electrical power defined as P_el = V_ds × I_ds. As P_el describes the power generation capability of a photovoltaic device, we need to achieve the maximum P_el at a certain voltage bias. Supplementary Fig. 25 illustrates the relationship between P_el and V_ds under 532 nm laser irradiation. Figure 6b shows that our device displays a maximum PCE of 15.37% and a maximum FF of 0.63 under P_in of 319 mW cm⁻².

Fig. 6: Photovoltaic characteristic of the optimized WSe₂ p-i-n photodiode.

a Linear J_ds - V_ds curves of the WSe₂ p-i-n photodiode under 532 nm laser illumination with varied power densities. Inset is the value of V_oc, J_sc, FF and PCE when PCE is maximum. b Fill factor (FF) and power conversion efficiency (PCE) as function of power density under 532 nm laser illumination. The maximum PCE is 15.37%, corresponding FF is 0.63. c Linear J_ds - V_ds curve of the WSe₂ p-i-n photodiode under AM 1.5 G illumination. Inset is the value of V_oc, J_sc, FF and PCE. d Spectral EQE at V_ds = 0 V and integrated short current density. The spectral response is measured under Xenon lamp.

To benchmark with other photovoltaic devices, we investigate the photovoltaic performances of vertical WSe₂ p-i-n photodiode under 1000 W m⁻² air mass 1.5 global (AM 1.5 G) illumination. We test the forward and reverse current density–voltage curve (Supplementary Fig. 26), the device exhibits negligible hysteresis. The device with an area of 1022 μm² obtains V_oc of 0.52 V, J_sc of 19.67 mA cm⁻², FF of 0.63, and PCE of 6.5% (Fig. 6c). EQE characterization under different wavelengths was further performed to confirm the measured J_SC (Fig. 6d). The integrated J_sc is 21.1 mA cm⁻², which is closed to the measured J_SC under the solar simulator. Under AM 1.5 G illumination, our vertical WSe₂ p-i-n device demonstrates excellent performance among TMDs-based photovoltaic devices (Supplementary Table 2). Compared with ultrathin silicon photovoltaics, the PCE of our device is higher than that of silicon at the same thickness⁵⁰, which is attributed to the effective separation/collection of carriers in the p-i-n structure under high built-in electric field and the high light absorption coefficient of WSe₂. Due to the narrow absorption spectrum of WSe₂ (mainly visible light), PCE of our device can be further improved by selecting other 2D layers with appropriate bandgap engineering.