2.1 Photodetector Performance of AgBiS₂ PDs in the NIR Region

The AgBiS₂ NCs used in this work were synthesized through a modified hot-injection process^[22] (see the Experimental Section for details), and they had a mean size of 4 ±1 nm (Figure S1a, Supporting Information). These AgBiS₂ NCs have a rocksalt crystal structure, with both Ag⁺ and Bi³⁺ randomly occupying the same crystallographic lattice site. Drop-cast AgBiS₂ NCs could retain their phase and visual appearance in ambient air with relative humidity ranging from 60–70% for over a month (Figure S2, Supporting Information), suggesting their high air stability.

Herein, AgBiS₂ PDs were fabricated using an established n-i-p photodiode architecture^{[22, 24]} (Figure 1a), where ZnO and PTB7/MoO_x were adopted as the electron (ETL) and hole transport layers (HTL), respectively. The energy levels of the ETL and HTL were acquired from Kelvin probe (KP) and photoelectron yield spectroscopy (PYS) measurements^[28] (Figure S12, Supporting Information). As displayed in Figure S12c (Supporting Information), although photo-excited holes could be extracted effectively, a small barrier might be present between AgBiS₂ and the ETL, which will be discussed in Section 2.4. Ligand exchange treatment with tetramethylammonium iodide (TMAI) in methanol solution enabled the use of the LBL method to fabricate PDs with controlled photoactive layer thickness (see details in the Experimental Section). A representative secondary electron microscopy (SEM) image of the cross-section of a complete PD is shown in Figure S3 (Supporting Information), where we can see the well-defined ETL, photoactive layer, and Ag electrode, verifying the uniformity of each layer over a large length scale. Our TMAI-treated AgBiS₂ films showed a bandgap of 1.2 eV (Figure S4b, Supporting Information) along with high absorption coefficients from the UV to NIR region, which exceeded 10⁴ cm⁻¹ for wavelengths below 1200 nm, and exceeded 10⁵ cm⁻¹ for wavelengths below 775 nm (Figure S4, Supporting Information), making them suitable for NIR photodetection.

To achieve high-performing PDs, the number of photoactive layers (i.e., TMAI-treated AgBiS₂ NC films) was tuned from 2 to 9 to reduce the dark current density J_D. Herein, J_D was only monitored at reverse biases smaller than 0.5 V (i.e., –V_A ≤ 0.5 V). Although a larger reverse bias (−1–−10 V) is commonly used in commercial silicon PDs in order to extract charge-carriers out of their thick photoactive layers (hundreds of micrometers), it is not necessary for AgBiS₂ PDs because ultrathin photoactive layers (<120 nm) are sufficient for absorbing >65% of visible and near-infrared light (wavelengths <800 nm). Being able to operate these devices under smaller applied biases is advantageous for applications in wireless sensors as part of the Internet of Things, where reducing external power requirements is critical for these autonomous devices. The J_D–V curves of AgBiS₂ PDs with 2–9 photoactive layers deposited (denoted as 2L–9L) are shown in Figure S5a (Supporting Information), where we can see that there is an overall decrease in J_D with an increase in the number of the photoactive layers deposited. At the same time, AgBiS₂ PDs with different photoactive layers exhibited distinct external quantum efficiency (EQE) spectra (Figure S5b, Supporting Information), possibly caused by different optical interference effects. To compare the capability of these AgBiS₂ PDs in terms of NIR photodetection, the EQE values at 940 nm wavelength, and the J_D values at −0.5 V, are simultaneously shown in Figure S5c (Supporting Information), where we can clearly see that the highest EQE and the lowest J_D value, which are both desired for ideal NIR PDs, were not obtained from the same thickness of photoactive layer. Therefore, to investigate how the photoactive layer thickness affects PD performance, AgBiS₂ PDs with 3, 5, and 9 photoactive layers (denoted as the 3L, 5L, and 9L AgBiS₂ PD) were characterized in detail, as will be discussed below. We note that in order to make direct comparisons between these devices, the operational conditions used (i.e., light sources and applied biases) were all the same for these different measurements. Herein, 5L and 9L AgBiS₂ PDs account for the devices showing the highest EQE values in the NIR region and the lowest J_D, respectively, while 3L AgBiS₂ PDs account for the thinnest devices among the three types as a reference.

The representative current density–voltage (J–V) curves of the AgBiS₂ PDs in the dark and under 1-sun illumination are displayed in Figure 1b, where we can see a J_D value of 4.1  ×  10⁻⁵, 1.8  ×  10⁻⁵, and 0.37  ×  10⁻⁵ A cm⁻² at −0.5 V for the 3L, 5L, and 9L PD, respectively. This decrease in J_D with increasing AgBiS₂ NC film thickness was possibly caused by a decrease in shunt pathways. We therefore estimated the shunt resistance R_shunt of the devices from the reciprocals of the first derivative of the J_D–V curves at 0 V (Figure S6a, Supporting Information). Despite the large variation between devices, we could still observe an overall enhanced R_shunt in thicker PDs. As shown in Figure S6b (Supporting Information), the average R_shunt value of the 3L, 5L, and 9L PD is 0.22 ± 0.08, 0.61 ± 0.17, and 0.76 ± 0.17 MΩ cm², respectively. While we cannot make a like-for-like comparison in the J_D values with other reports due to the different measurement conditions used by different groups, the J_D values achieved with AgBiS₂ PDs at 0.5 V applied bias are within the range of strongly-performing NIR organic,^{[10, 29]} lead-halide perovskite^{[30, 31]} and PbS QD PDs^{[32, 33]} (see Table S1, Supporting Information). Figure 1c shows the responsivity (R) spectra of these devices. Since R is proportional to the EQE value, it is not surprising that the 5L PD would display higher R values in the NIR region (750–1080 nm) with a peak value of 0.28 A W⁻¹ at 770 nm.

In Equation 1, q is the elementary charge, i_D the static dark current, k the Boltzmann constant, T the temperature, and R_shunt the shunt resistance. In practice, other sources of noise could contribute to i_n as well. Therefore, using Equation 1, or even $$\sqrt {2q{i}_D} $$ only, which is also widely used in the literature,^{[32, 36]} would overestimate D* values, as depicted in Figure S8 (Supporting Information). To avoid such an overestimation, we determined the i_n spectra of the devices by performing a Fast Fourier Transform (FFT) on the time evolution of the dark current (details in the Experimental Section). As shown in Figure S7a (Supporting Information), thicker devices tended to show lower i_n values, mainly due to their lower dark currents. The i_n spectra for all of the devices were invariant with frequency, indicating that flicker noise, which is usually ascribed to the random trapping and de-trapping processes,^[37] does not play a significant role in these devices. The calculated i_n values based on Equation 1 for all devices are displayed as horizontal lines in Figure S7a (Supporting Information), and it can be seen that all of the measured i_n were at least an order of magnitude higher than the values calculated from Equation 1. This result again verifies the importance of direct noise current measurements for precise D* determination. The tendency of the wider field working on solution-processed PDs to assume that the noise current only comes from shot noise, or a combination of shot and thermal noise, rather than directly measuring the noise current makes a comparison of D* values between different reports difficult, with many previous reported values being over-estimated (see footnote to Table S1, Supporting Information).

The D* spectra of AgBiS₂ PDs were determined by their R spectra and the directly-measured i_n values, as shown in Figure 1d. Herein, the i_n value was extracted from the high-frequency region (>1 kHz) of the i_n spectrum for each device biased at −0.5 V (Figure S7a, Supporting Information), which is estimated to be 8.9 × 10⁻¹¹, 1.3 × 10⁻¹¹, and 9.5 × 10⁻¹²A Hz^−1/2 for the 3, 5, and 9L PD, respectively. The 9L PD showed the highest D*, with values over 10⁹ Jones in the region below 780 nm wavelength due to its lowest i_n value, which is consistent with the lowest J_D value occurring in the 9L PD. However, the higher R values in the NIR region of the 5L PD enabled it to exhibit the highest D* values (between 7 × 10⁸ and 4 × 10⁹ Jones) for wavelengths > 780 nm. Additionally, the peak D* values of each PD (at 710, 770, and 620 nm wavelength for the 3L, 5L, and 9L PD, respectively) calculated based on the i_n values at different frequencies are also displayed in Figure S7b (Supporting Information), where we can see that the D* values are almost frequency-independent. This frequency independence further verifies the validity of the D* values reported in our work.

The linear dynamic range (LDR) and film morphology were also characterized for our AgBiS₂ PDs. Under 940 nm wavelength illumination, the 3L, 5L, and 9L PDs biased at −0.2 V could reach LDR values of 52, 68, and 65 dB, respectively (Figure S9a, Supporting Information). The slight decrease in the LDR value for the 3L device mainly resulted from the increased J_D values, which determined the lower limit of LDR. On the other hand, the AgBiS₂ PDs biased at −0.5 V showed a slightly sub-linear variation in photocurrent with light intensity (Figure S9b, Supporting Information), making the acquired LDR values less reliable. Such sub-linearity is possibly affected by ion migration taking place in AgBiS₂, which will be discussed in Section 2.4.

In addition, the morphology of the TMAI-treated AgBiS₂ films with different thicknesses deposited on top of the ZnO layer was characterized by atomic force microscopy (AFM). As displayed in Figure S10 (Supporting Information), all of the AgBiS₂ films showed a compact surface with a small root-mean-square (RMS) roughness (3.7, 3.5, and 3.3 nm for the 3, 5, and 9L AgBiS₂ films, respectively). Although smaller roughness values might be observed in thicker films, we emphasize that the present roughness values achieved in all of the samples are comparable to or even smaller than those reported in PbS QD (≈0.5–5 nm),^{[38, 39]} organic (≈0.5–10 nm),^{[10, 40]} and lead-halide perovskite films (≈10–50 nm),^[41-43] suggesting that film morphology is not limiting the performance of these devices.

2.2 Fast Photo-Response of AgBiS₂ PDs

In Equation 2, I₀ is the photocurrent measured under continuous-wave (CW) light illumination. As the damping of the photocurrent drops to −3 dB, the associated frequency is f_−3dB. Figure 2a displays the damping measurements for AgBiS₂ PDs excited by a 940 nm LED driven by sinusoidal voltages at different frequencies, where we can see the high f_−3dB values of 244, 496, and 399 kHz for the 3L, 5L, and 9L PDs, respectively. We note that when PDs are illuminated by visible or UV light, they usually display higher f_−3dB values,^{[25, 30, 31]} which might be due to higher diffusion currents as higher excess charge-carrier densities are created near the surface or increased filling of traps due to the higher power densities achieved in the shorter wavelength range. Indeed, this was also the case for the AgBiS₂ PDs under white light (400–800 nm wavelength) illumination, where f_−3dB values could reach 1.20, 1.44, and 1.35 MHz for the 3L, 5L, and 9L devices, respectively. These cut-off frequencies are not only the highest values for AgBiS₂ PDs, but they also exceed most solution-processed NIR PDs, as can be seen in Table S1 (Supporting Information).

2.3 Rationalizing the Fast Response of AgBiS₂ PDs

In Equation 3, V is the applied voltage across the two electrodes of the photodiode, d the thickness of the photoactive layer, and µ_e and µ_h the electron and hole mobilities, respectively. In most solution-processed NIR PDs, d is at least a few hundreds of nanometers in order to achieve sufficient light absorption,^{[7, 15, 36]} and their f_−3dB values would thus be limited by the long transit distances required. In addition, organic PDs suffer from low or unbalanced charge-carrier mobilities,^{[29, 44]} which could further lower their f_−3dB values, since charge-carrier transport will be limited by the smallest charge-carrier mobility. By contrast, the high absorption coefficients of AgBiS₂ NCs enable the fabrication of ultrathin devices here. As determined from AFM measurements, the AgBiS₂ film thicknesses in the 3L, 5L, and 9L PDs were only 19 ± 3, 38 ± 4, and 115 ± 9 nm, respectively. Furthermore, calculations also predicted the comparable effective masses of electrons and holes (the hole effective mass m_h* is approximately only double the electron effective mass m_e*)^{[45, 46]} in AgBiS₂, which could also be beneficial for achieving higher f_−3dB values by having relatively balanced electron and hole transport.

In Equation 4, v_drift is the drift velocity. From time-resolved microwave conductivity (TRMC) measurements,^[47] the electron and hole diffusion lengths of TMAI-treated AgBiS₂ NC films have been reported to be ≈60 and 150 nm, respectively.^[47] Considering the AgBiS₂ PDs with different photoactive layers biased at −0.5 V, and assuming no screening of this field within the device, a L_drift value of at least 3516, 1758, and 611 nm (for holes) could be estimated for the 3L, 5L, and 9L devices, respectively. We can see that all of the L_drift values obtained from Equation 4 are substantially larger than the corresponding photoactive layer thicknesses in each device. Therefore, most photo-generated charge-carriers would be quickly swept across the photoactive layers under bias even in the thickest 9L AgBiS₂ PD. It has been reported in a PbS QD/metal Schottky diode, the response speed of the diode could be significantly improved when photo-generated charge-carriers were transported mainly by drift.^[20] We note that a similar condition could be met in our AgBiS₂ PDs, where the thin photoactive layers were all included in the depletion regions so that drift transport would dominate and lead to a fast response.

In Equation 5, A₀ is a constant typically equal to ≈3.5 and R_tC refers to the effective resistance-capacitance product of the overall experimental system. The series resistances of the AgBiS₂ PDs could be estimated from the reciprocals of the slopes of the photocurrent density–voltage curves (J_ph–V curves) at open-circuit (dashed lines in Figure 1b), and the effective resistance of the experimental system was then estimated by the summation of the series resistance of each device and the connected resistance within the oscilloscope (50 Ω). The C values were directly measured from the high-frequency range of the capacitance-frequency plots (Figure S11, Supporting Information). The R_tC values for different AgBiS₂ PDs are listed in Table 1, from which we can calculate the transit time t_tr.

As can be seen from Table 1, the calculated t_tr values were close to the t_rise/t_fall values under 940 nm light illumination, suggesting that the device response times were mainly determined by the charge-carrier transit times through the devices. On the other hand, under white light illumination, the t_rise/t_fall values tended to be slightly longer than the calculated t_tr values for each device. Indeed, smaller t_rise/t_fall values were initially expected to be reached under white light illumination (larger f_−3dB values) and also in thinner devices (larger drift velocities for charge-carriers), both of which were not the case, as can be seen from Table 1. These unusual phenomena along with the slightly sub-linear variation in photocurrent with illumination intensity when biased at −0.5 V (Figure S9b, Supporting Information) imply the influence of a hidden factor, ion migration, might occur in AgBiS₂ devices. Here, we propose that ion migration is facilitated by a stronger electric field (e.g., in thinner PDs or PDs biased at larger reverse voltages), or higher light intensity from the white light source, which could potentially induce a large charge-carrier gradient and hence drive ions migration more easily.^{[50, 51]} It is therefore important to understand the role of ion migration in AgBiS₂, which is examined in the next section.

2.4 Ion Migration in AgBiS₂

Ion migration has been observed in several perovskite and PbS QD-based devices,^{[53, 54]} where mobile cations or halide ligands could easily move when driven by the external electric field. In order to verify whether ion migration could also occur in AgBiS₂, temperature-dependent transient dark current measurements (see details in the Experimental Section) were performed here. At higher temperatures, more ions will be thermally activated^[56] and accumulated near the electrodes, which would gradually screen the electric field between the two electrodes. As a result, the transient dark currents excited by voltage pulses would decay faster when the external field was screened more by the built-in field from the accumulated ions.

To simplify the analyses of ion migration in AgBiS₂, electron-only devices (architecture: ITO/ZnO/AgBiS₂/PCBM/Ag) with 3 photoactive layers (3L) were used here. An electron-only device was used because of the n-type nature of TMAI-treated AgBiS₂ films, as verified from KP and PYS measurements (Figure S12c, Supporting Information). Figure 3a shows the dark current transients of the electron-only AgBiS₂ device excited by high-voltage (4 V) pulses from 200 to 320 K, where we could indeed see the transients decaying faster at higher rates k₁ (Table S2, Supporting Information) as temperature was increased. The corresponding Arrhenius plot (analysis details in Note S1, Supporting Information) of AgBiS₂ is then displayed in Figure 3b, and an activation energy barrier (E_a) of ≈126 ±  17 meV was extracted. This activation energy barrier is comparable to or smaller than those reported in lead-halide perovskites (typically in the range of 100–300 meV, with some reports of up to 600 meV^{[53, 54, 56, 57]}), where ion migration has been proven to strongly influence their device performance. We thus conclude here that ions could easily migrate in AgBiS₂ PDs, and possibly impact the photo-responses more significantly under a stronger electric field (e.g., in the 3L device) or higher light intensity^[59] (e.g., under white light illumination).

To examine the possible impact of ion migration on the dark current density J_D of AgBiS₂ PDs over a longer time scale, we tracked the dark current density J_D of the 3L, 5L, and 9L AgBiS₂ PDs under continuous bias for a few minutes. As shown in Figure 3c, we noticed that the initial J_D value of the 3L and 5L devices were enhanced by a factor of 24 and 7, respectively, after 13 min, while the 9L device J_D was increased by a factor of 51 after only 2 min. Such an enhancement in J_D values suggests ion migration to occur in all the AgBiS₂ PDs biased over a long timescale. The accumulated ions at the AgBiS₂/transport layer interfaces could induce charge-injection from the electrodes, therefore leading to dark current drift. Such a J_D enhancement over long-term biasing was also observed in tetrabutylammonium iodide (TBAI)-treated PbS QDs,^[60] and iodide anions have been claimed to be the main source for ion migration owing to their weaker binding energy with the PbS. Considering the similar crystal structure and iodide ligand used for AgBiS₂ films, iodide anions may also be the main source of migrating ions in AgBiS₂ PDs as well.

In addition, KP and PYS measurements indicated that the ZnO films used in this work had a lower electron affinity than the TMAI-treated AgBiS₂ film (Figure S12c, Supporting Information; i.e., negative conduction band offset). This could lead to a contact barrier (type-II heterojunction) at the ZnO/AgBiS₂ interface in these devices. Although some electrons may still tunnel through this barrier via the tail of states extending from the ZnO band edges^[60] (which are also shown to be present from the broadband photoluminescence emission of the ZnO films; Figure S13, Supporting Information), they are more likely to accumulate at this heterointerface, which could encourage hole injection from ZnO under reverse bias, and hence increase the dark current, as displayed in Figure 3d.

Given that ions are driven by the application of an external field, thinner devices were expected to exhibit more significant ion migration, with a larger increase in J_D over time under continuous reverse bias. Therefore, it is not surprising to see a larger J_D enhancement and slower photo-response in the 3L device compared to the 5L device (Figure 3). Interestingly, although the 9L device had the smallest J_D at −0.5 V (Figure 1b), its J_D enhancement is still larger than other devices, suggesting that the applied field is not the only factor facilitating ion migration. As a result, the smallest J_D enhancement factor was actually seen from the 5L device. We proposed that such a small J_D increase could have benefited from 1) a smaller electric field compared to the 3L device, and 2) a smaller number of defects introduced during the ligand-exchange process compared to the 9L device, which is further explained in Figure S14 (Supporting Information). The small J_D enhancement in the 5L device indicates the minor effect of ion migration in this device, which also contributes to its fastest photo-response (Figure 2).

Herein, we show that tuning the thickness of the photoactive layer is an effective strategy to achieve high shunt resistance while minimizing ion migration. The combination of these two factors is crucial for realizing strongly performing and fast NIR PDs. Increasing the number of layers deposited in the LBL process could lead to a larger shunt resistance, and hence lower J_D values. However, more defects are also introduced in thicker devices, which can be activated with the application of an electric field, facilitating ion migration. These mobile ions can accumulate via drift at the photoactive layer/transport layer interfaces, which could induce extra charge-carrier injection and result in dark current enhancement. As indicated above, the population of ions accumulated at these heterointerfaces is associated with both the strength of the electric field within the photoactive layer and the concentration of defects. Therefore, ion migration can be suppressed by fine-tuning the photoactive layer thickness in AgBiS₂ PDs to simultaneously reach a field strength and defect concentration as low as can be, as demonstrated in Figure S15 (Supporting Information). We note that although charge-carrier extraction is still efficient in all of our devices because of the thin photoactive layers, future efforts should focus on minimizing ion migration in order to achieve faster photo-responses. Based on the insights gained from this work, we also believe that reducing defects by using passivation agents and less polar solvents or changing the band alignment at the AgBiS₂/ZnO interface are important areas to target in future efforts.

2.5 Real-Time Heartbeat Monitoring Using AgBiS₂ PDs

To demonstrate the practical application of AgBiS₂ PDs, we performed real-time photoplethysmogram measurements using the 5L device. As shown in Figure 4a, the finger of a volunteer was placed between a 940 nm LED and a 5L AgBiS₂ PD. The pulsating bloodstream through the capillaries changed the transmission of 940 nm NIR light from an LED. In the NIR region, not only could light penetrate living tissue efficiently but also the difference in absorbance between oxygenated and deoxygenated hemoglobin will be maximized. As a result, the heartbeat rate of the volunteer could be precisely recorded as electrical signals by the 5L PD, as shown in Figure 4b. A clearer figure could be made when we differentiated the current signals with time (Figure 4c), where we could easily estimate a heartbeat rate of ≈60 beats per minute. Finally, it is worth mentioning that unlike lead-halide perovskite PDs, where J_D values might be enhanced by a factor of two after exposure to air for 10 days,^[62] the J_D value of the unencapsulated AgBiS₂ PD was not increased when stored in an ambient environment (relative humidity: 60–70%) over 34 days (Figure S16, Supporting Information). The results here therefore strongly indicate the utility of AgBiS₂ in practical applications in air, and this could inspire future studies on using these fast PDs in high-throughput applications.