The rediscovery of black phosphorus (BP) has attracted remarkable interest for its potential applications in optoelectronics because of its excellent optical and electrical properties [1–4]. In contrast to other 2D layered materials, including graphene and transition metal dichalcogenides (TMDCs), BP has a direct bandgap in the range of 0.3–1.8 eV, depending on the number of layers [4–7]. This sizable and tunable bandgap makes BP more suitable than graphene, which is gapless, for photodetection because it suppresses dark current when the photodetector is operated with an applied bias [8–12]. The bandgap of BP also allows absorption of infrared photons, whereas TMDCs are only photosensitive in the visible spectral range. Additionally, BP has a remarkably high hole mobility, reaching up to 5200 cm2 V−1 s−1 at room temperature and 45,000 cm2 V−1 s−1 at cryogenic temperature [13, 14]. Therefore, among the existing 2D materials, BP is most promising for infrared photodetection with the prospect of achieving high efficiency, high speed, and low noise. Particularly noteworthy is that multi-layer BP’s bandgap is ~0.33 eV, making it suitable for applications in the mid-infrared, up to 3.75 µm. The mid-infrared has become more accessible recently because of the fast development of light sources, such as quantum cascade lasers and frequency combs [15–17], and has many important applications including spectroscopic chemical analysis, remote sensing, and free-space communication [18]. Mid-infrared photodetectors have largely been based on narrowband compound semiconductors including mercury cadmium telluride (MCT), indium arsenide antimonide (InAsSb), and their heterostructures, which are relatively expensive and difficult to integrate with other photonic materials [19]. The characteristics of BP discussed above make it very promising as an alternative material to replace compound semiconductors for many mid-infrared applications [20, 21].

Previous studies on BP photodetectors have only focused on the visible and near-infrared spectral ranges [10–12]. Only very recently, the mid-infrared characteristics and photodetection using BP have been reported. A BP photodetector operating at 3.39 µm wavelength emitted by the He–Ne laser has recently been demonstrated [22], while two other works have provided systematic studies of BP’s infrared absorption [23, 24]. However, a comprehensive characterization and understanding of BP photodetection in the mid-infrared is still lacking. In this work, utilizing a tunable mid-infrared laser, we investigate BP photodetectors operating in a broad wavelength range spanning from 2.5 to 3.7 µm.

The devices we measured were fabricated by mechanical exfoliation of BP flakes from a crystal onto a highly doped Si substrate with 300 nm SiO2 on the top. Electron beam lithography and metal deposition were used to pattern the contact electrodes (5 nm Ti/60 nm Au). A layer of 20 nm Al2O3 was deposited using atomic layer deposition (ALD) to encapsulate the BP, protecting it from degradation. Between measurements, precaution was taken to store the devices in a dark, nitrogen purged box to preserve the devices and prevent degradation of the BP.

Figure 1a shows an optical microscope image of a representative device. The photodetector has multiple interdigital metal fingers with a spacing of 0.5 µm to collect photocarriers efficiently. The atomic force microscope (AFM) image in Fig. 1b reveals that the thickness of the BP is 15 nm. Characterization of the device’s photoresponse was performed at ambient conditions. A pulsed, optical parametric oscillator (OPO) laser source (Firefly-IR, MSqaured Lasers) with a tunable output in the mid-infrared ranging from 2.5 to 3.7 µm was used as the light source in the experiment. For DC measurements, a source measurement unit (SMU) was employed. For AC measurements, the incident light on the photodetector was modulated at 1 kHz with a mechanical chopper, and a transimpedance amplifier connected to a lock-in amplifier was used to measure the modulated photocurrent. The photocurrent was obtained from the difference between the source–drain current when the device is under illumination at different received optical powers P rec and the dark current: \(I_{{{\text{ph}}}} \left( {P_{{{\text{rec}}}} } \right) = I_{{{\text{light}}}} \left( {P_{{{\text{rec}}}} } \right) - I_{{{\text{dark}}}}\). Because the photoresponsivity R = I ph/P does not take into account the different photon energy at different wavelengths λ, we also evaluate the devices’ spectral response over a broadband with the external quantum efficiency η e =R·(hc/eλ), where h is Planck’s constant, c is the speed of light in vacuum, and e is the electron charge.

Fig. 1
figure 1

Optical microscope image (a) and atomic force microscopy image (b) of the BP mid-infrared photodetector with interdigitated electrical fingers investigated in the paper. The inset in b shows the height profile along the dashed line, indicating the BP has a thickness of 15 nm

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The laser beam is focused on to the device using a reflective objective, which forms a non-ideal, elliptical spot shape and was measured with the knife-edge method to be w a =54.1-μm long along the semi-major axis and w b =19.9-μm wide along semi-minor axis. This spot is much larger than the active area of the BP flake between the electrode fingers. Therefore, the power received by the active area of the device P rec is estimated from the total incident power P inc by assuming a Gaussian intensity distribution in the beam spot and the device being positioned at the center. The calculation shows P rec/Pinc~11%. Figure 2a shows the measured DC responsivity R and external quantum efficiency η e of the device at different wavelengths and fixed P inc of 40 µW. We note that the minor peak observed around 2.7 µm is likely due to uncertainty in laser power rather than a band-to-band resonance in the absorption of the BP as observed in Ref [24]. We observed photoresponse from the BP photodetectors over the entire range of mid-infrared wavelengths from 2.5 to 3.7 µm. The responsivity varies from 47 to 21 mA/W, with a corresponding η e in the range of 1–2%. The low external quantum efficiency is attributed to the low absorption in the thin BP layer for normally incident light. It is possible to enhance optical absorption by critically coupling the device to an optical cavity, but this limits the usable optical bandwidth to the cavity resonances [25]. Additionally, the use of an electrostatic gate could also lead to improved efficiency [26]. We used the transfer matrix method [27], incorporating the theoretical values and the recent experimental measurement of the optical conductivity of BP [6, 23, 28], to calculate the portion of incident power absorbed in the 20 nm BP layer on top of the silicon dioxide and silicon substrate. The result plotted in Fig. 2c shows that due to the interference effect, the absorption in BP reduces from 11% to less than 2% as the incident light waveguides increases from 2.5 to 3.7 µm. Taking the absorption α into account, the intrinsic quantum efficiency η i= η e/α is plotted in Fig. 2d. It shows that the η i is in the range of 16–31%. The large variation of η i with wavelength will need further investigation to be understood.

Fig. 2
figure 2

Wavelength dependence of our BP photodetector. a The external DC responsivity was measured from 2.5 to 3.7 µm. b The external quantum efficiency versus various wavelengths. c The calculated absorption ratio in the BP layer using the optical transfer matrix method for a Si substrate with 300 nm SiO2. d Intrinsic quantum efficiency as a function of wavelength calculated from data shown in b and c

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Next, we measured the device’s photoresponse at different incident optical power levels. Figure 3a shows the DC photocurrent versus bias voltage when the device was illuminated with light at a fixed wavelength of 2.5 µm and varying power levels. It can be noted that the responsivity decreases with increasing optical power, indicating a saturation effect. Figure 3b plots η e versus incident power P inc measured with both DC and AC modes. In the AC mode, the laser beam was modulated with an optical chopper at 1 kHz and the photocurrent was measured with a lock-in amplifier. The η e measured in both modes saturates with P inc albeit the value measured at AC mode is much lower than that of the DC mode. As shown with the lines in Fig. 3b, the power-dependent efficiency η e in both DC and AC modes are well fitted with a simple saturable absorption model [22, 29]:

Fig. 3
figure 3

Photocurrent generation mechanisms in BP photodetector. a DC photoresponse for various source–drain bias and incident power levels. b Power dependence of external quantum efficiency measured under DC and AC modes. c Photocurrent amplitude versus modulation frequency. d Temporal response of the photocurrent using a pulsed laser showing both the fast photovoltaic effect (pulses) and slow photogating response (DC offset). Red line represents the total time-averaged photocurrent measured in DC mode

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$$\eta _{{\text{e}}} \left( I \right) = \frac{{\eta _{0} }}{{1 + P_{{{\text{inc}}}} /P_{{{\text{sat}}}} }} + \eta _{{{\text{ns}}}}$$

P sat is the saturation power, η 0 is the linear quantum efficiency, and η ns is non-saturable efficiency. The fitting yields the saturation power P sat to be 24.4 and 13.5 µW, respectively, for the DC and AC photoresponse. In Fig. 3c, we show the photocurrent measured at different modulation frequencies from 100 Hz to 1 kHz, as well as the DC photocurrent, with constant optical power of 200 µW and 0.1 V bias voltage. It again shows a significant drop in the photocurrent from DC to AC, whereas the AC photocurrent does not change very much with the frequency. The reduced AC photoresponse and the different saturation power at DC and AC suggest that different mechanisms are contributing to the AC and DC photocurrents.

We then used an oscilloscope connected to the transimpedance amplifier (DC to 1 MHz bandwidth) to measure the real-time photocurrent generated by the laser pulses. The laser outputs pulses with a duration of ~10 ns and a repetition rate of 150 kHz. The measured time trace shown in Fig. 3d thus reflects the impulse response of the device. It clearly shows that the photocurrent consists of two mechanisms on a very different time-scale: an instantaneous pulse of current with a peak of 10 µA, generated immediately with the optical pulse but with broadened decay of ~500 ns (limited by the amplifier bandwidth), along with a persistent background current of 6 µA, which only disappears after the input light is turned off. The DC measurement mode measures the time average of the total current (the red line in 3d), whereas the AC mode measures the fast response photocurrent, and therefore does not measure the persistent background current. We attribute the fast instantaneous response to the photovoltaic effect where photogenerated free electron–hole pairs are separated by the external electric field. The slower response, on the other hand, is similar to what has been observed in MoS2 and is attributed to the photogating effect where photogenerated carriers are trapped at the material/dielectric interface and shift the threshold voltage of the device through the accumulation of excess charge [30]. These interface traps have a much longer lifetime than mid-gap traps in the BP and therefore the DC responsivity (which includes both photovoltaic and photogating effects) is greater than the AC responsivity. However, since both mechanisms depend on the number of occupied trap states, they show similar power dependence as shown in Fig. 3b. Additionally, these two effects are consistent in the photon absorption process and show a similar wavelength dependence regardless of the modulation frequency.

In summary, we have studied the photoresponse of few-layer BP under different illumination conditions. We have shown that BP photodetectors are capable of broadband photoresponse at a wide range of mid-infrared wavelengths. At wavelengths near the bandgap, the interaction of photons and BP is fundamentally different from those in the near-IR or visible range, but still can be well described by a simple interband transition model. After excluding the contribution of built-in electric field and photothermal effect, we have identified the photovoltaic and photogating effects, which can be attributed to traps in the tail states of the BP bandedge and traps at the BP/dielectric interface, respectively.