Reverse dark current in organic photodetectors and the major role of traps as source of noise

Organic photodetectors have promising applications in low-cost imaging, health monitoring and near-infrared sensing. Recent research on organic photodetectors based on donor–acceptor systems has resulted in narrow-band, flexible and biocompatible devices, of which the best reach external photovoltaic quantum efficiencies approaching 100%. However, the high noise spectral density of these devices limits their specific detectivity to around 1013 Jones in the visible and several orders of magnitude lower in the near-infrared, severely reducing performance. Here, we show that the shot noise, proportional to the dark current, dominates the noise spectral density, demanding a comprehensive understanding of the dark current. We demonstrate that, in addition to the intrinsic saturation current generated via charge-transfer states, dark current contains a major contribution from trap-assisted generated charges and decreases systematically with decreasing concentration of traps. By modeling the dark current of several donor–acceptor systems, we reveal the interplay between traps and charge-transfer states as source of dark current and show that traps dominate the generation processes, thus being the main limiting factor of organic photodetectors detectivity.

In this section, we discuss a series of optimizations that have been performed to disclose the dependence of J D on E CT . As discussed in the main text, many effects can hide this dependence, since different effects increase the leakage current. The device structure used in each section is depicted in Supplementary Table 1. The final device structure of each of the following results corresponds to a glass substrate coated with structured ITO(Thin Film Devices Inc., 90 nm)/p-layer/i-layer/C 60 (20 nm, buffer layer)/n-layer/Al (100 nm). After optimization, the final structure used within the main text is OPD 7, highlighted in green.
Supplementary Table 1: Structures used to study different aspects of J D in the following sections | The devices were produced by thermal evaporation on a glass substrate coated with structured ITO/p-i-n (as described in the table)/C 60 (20 nm, buffer layer)/Al (100 nm).

Contact Selectivity and Blocking Layers
When biasing the device in reverse direction, the selectivity of the contacts is very important. Selectivity means how efficiently the injection of the wrong charge carriers (electrons into p-type contact and holes into n-type contact) is blocked. Generally, this property should be controlled by the energy levels of the materials. However, in some cases, different effects can also play a role. In Supplementary Figure 1a and Supplementary Figure 1b, we show JV characteristics comprising ZnPc and TPDP as donors, respectively. Using p-HATNA-Cl 6 in ZnPc:C 60 bulk heterojunction (BHJ) reduces J D considerably. This effect is caused by a better selectivity of the p-doped layer, in comparison to BPhen. Interestingly, the same is not true for the TPDP BHJ. This indicates that, in the case of TPDP, another mechanism dominates J D and the minor effect of selectivity is no longer observed. Moreover, because it has a very low ionization potential (IP), which should express a better selectivity, HAT(CN) 6 was also employed as n-doped layer, as further comparison. Once more, no improvements are observed reinforcing the secondary character of the selectivity for this material system.
Comparing IPs of HATNA-Cl 6 and BPhen, -7.20 eV 1 and -6.46 eV 2 , respectively, one can already conclude that the selectivity should be better for HATNA-Cl 6 . In addition, BPhen should cause an extraction barrier in forwards bias, when used with C 60 , as its electron affinity (EA) is shallower in energy. However, this is not observed for thin layers (≤ 8 nm). Therefore, it is reasonable to assume that a thin BPhen layer gets doped by the metal 3 or that trap states are formed within its gap, allowing not only electron extraction in forward direction, but also hole injection in reverse bias, explaining the bad selectivity observed in Supplementary Figure 1a.
Similarly to the selectivity property, another commonly used strategy to reduce J D is the use of blocking layers. For blocking electron (holes) injection in reverse direction, the material should have as low (high) as possible EA (IP) level. This relies once more in the energy levels of these materials. By itself, the energy levels of n-HATNA-Cl 6 and p-MeO-TPD should comply this role. Besides, we have inserted a further layer of neat HATNA-Cl 6 and MeO-TPD as hole blocking layer (HBL) and electron blocking layer (EBL), respectively. HATNA-Cl 6 is employed as HBL using different thicknesses. J D is reduced for both cases but due to the lower conductivity of these undoped layers, the forward region is also affected.
The results shown in Supplementary Figure 2 indicate that the insertion of a further blocking layer slightly improves the dark current, in both sides of the device. These layers, however, can also affect the behavior in forward bias, as can be seen for thicker layers of neat HATNA-Cl 6 and MeO-TPD. Note that the curves indicated as "0 nm" still contain the doped layers, which also presents blocking properties, as discussed above.

Shunt Paths in OPDs
The presence of shunt paths in thin-film devices is well-known in the literature 4,5 . Shunt usually refers to ohmic metallic paths formed between the top and bottom contact, but it may also be understood as an easier path that might be followed by charge carriers than the rectifying diode path 6 . Since the active layer is sandwiched between buffer and/or blocking layers in our device, the latter is assumed to be very unlikely. Moreover, p-i-n devices, using doped layers, should also contribute in this sense, due to the good selectivity of the contacts achieved by doping 7 . Hence, we mainly investigate the presence of metallic paths, which could lead to high dark currents, especially in reverse bias.
In Supplementary Figure 3 we show JV characteristics for four different active layer thicknesses using the same optimized structure and TPDP:C 60 as BHJ. The thickness of the active layer is varied from 50 nm to 200 nm. If shunts would be present in the device, it is likely that J D would decrease upon thickness increase. As can be seen, J D does not show any trend within this range and the lowest value is achieved for 50 nm. Supplementary Figure 3 supports the fact that shunts are not responsible for high J D observed in these devices.

Device Structuring
The last topic investigated within this optimization is the influence of the lateral leakage current, as discussed by Zheng et al. 8 . The doped layers, namely n-HATNA-Cl 6 and p-MeO-TPD, were structured following the same approach discussed by the authors. The devices discussed in this work are formed by organic materials sandwiched between two crossed-like electrodes: a pre-structured ITO layer as anode and a metal layer cathode. The organic materials are deposited over a larger area than that of the actual device area. Due to the high conductivity of doped layers, lateral leakage current might flow from the surroundings and be collected as dark current. This means that in fact the real device area could be larger than 6.44 mm 2 and undefined.
By structuring the doped layers using shadow masks, Zheng et al. were able to reduce the dark current of OLEDs by at least two orders of magnitude. More details about the structuring procedure can be found elsewhere 8 . Our results employing this approach are shown in Supplementary Figure 4. Interestingly, the effect of structuring can be clearly observed for TAPC:C 60 devices, however, for TPDP:C 60 this is not the case, where J D remain unaffected. This result shows that lateral current becomes important when the intrinsic J D is low (high E CT ). In the scope of Zheng et al.'s work, the authors have used mostly high gap materials, so that this effect was clearly observed. For low E CT BHJs, the intrinsic J D is much higher than the lateral contribution, such that its effect becomes irrelevant.
Summarizing the optimizations that have been performed, J D is affected by selectivity of the contacts, blocking layers usage and device structuring. However, the low E CT BHJ TPDP:C 60 seems to be unaffected by any of these optimization proceedings, including thickness variation. Thus, we have strong indications that further effects, than a matter of device optimization, are causing high J D .
Considering that the BHJ results, discussed in Figure 1 in the main text, are acquired by means of the afore-discussed optimization and, more importantly, rely on the same device structure and material combination, except for the donor blended with C 60 , it is reasonable to assume that the high J D is an intrinsic property of each material combination. As argued in the main text, experimental J D cannot be explained solely by thermal excitation through CT states.

Density of States via Impedance Spectroscopy
The trap distribution is determined using the method proposed by Walter et al. 9 . In this method, the trap concentration is reconstructed based on its contribution to the device capacitance, when the trap states are filled by an AC signal. The thermal emission of charges from traps states happens with a specific time constant, τ t . Therefore, the maximum frequency f t at which trapped charges can respond to the applied signal can be determined as 1/τ t . We can write f t in terms of the angular frequency of the AC modulation 10 : where E t is the trap energy with respect to the transport energy and ν 0 is the attempt-to-scape frequency 11 . Equation (S2.1) relates the trap energy to the modulation frequency of the signal. Different trap energies can be probed as each trap energy corresponds to a transition in the C-f spectrum. The attempt-to-scape frequency is also related to the thermal velocity, v th , and capture cross-section (σ n,p ), via 10 : which serves an approximation for the recombination rate β SRH . An exact agreement (β SRH is not expected here, as N n,p is unknown. The trap contribution to the capacitance has been derived based on the Boltzmann occupation of trap states with respect to the Fermi level (E F ) and can be written as: where ũ n,p and ũ ext are the local shift in the quasi-fermi level and the external perturbation, respectively. According to equation (S2.3), when the frequency of the external perturbation is low enough, traps states crossed by the Fermi-level contribute more strongly to the capacitance.
As the distance of trap states from E F increases, their contribution decreases exponentially.
Considering ũ n,p and ũ ext constant and assuming that the trap distribution is constant in the interval E F ± 2k B T , equation (S2.3) can be integrated in the depletion region, from which an analytic expression for N t can be derived: where V bi is the built-in voltage and W is the space charge width region.

Supplementary Note 3. Impedance spectroscopy in Organic Blends
Using the method introduced by Walter et al. 9 to characterize trap states organic devices is debated in literature, especially when dealing with low mobility materials or devices where energy barriers are present. As both conditions apply for our devices, we exemplary compare different devices and analyze the effects on the trap characterization to ensure that the results discussed within this chapter can be accurately estimated. In order to do that, we analyze devices comprising different thicknesses and under different biasing conditions.
In Supplementary Figure 5 data for devices with different active layer thicknesses is shown. The trap density is not expected to depend/vary with thickness. Indeed, from 50 to 150 nm, N t remains constant. As indicated in the main text, the attempt-to-scape frequency (ν 0 ) is obtained by overlapping N t measured at different temperatures. For 150 nm, in order to achieve that, ν 0 has to be set to a lower value. As pointed out by different research groups, thicker devices 10        and low mobility materials 12 lead to a wrong estimation of ν 0 . This further explains why using equation (S2.2) as a direct estimation of the recombination rate is not possible as ν 0 can be underestimated. Therefore, the values of ν 0 must be taken only a first approximation in our study, representing a limitation of the method. Also E t can be slightly affected, depending on the mobility of the blend. The results shown in Supplementary Figure 5 were measured in devices fabricated in the same batch, but in a different batch than that of the samples presented in the main text, explaining the small deviations in the absolute amount of traps.
Another important aspect when applying this method in devices is the presence of energy barriers, as they can produce the same signature in the capacitance spectra as those produced by traps. As argued by Siebentritt et al., the occupancy of trap states is governed by the crossing of the Fermi level with the trap level, therefore, any trap signature should disappear at high enough forward bias, since the Fermi level will no longer cross the trap level 13 . Following the same reasoning, a minority carrier trap signature should also disappear at high enough reverse bias. Indeed, measuring our device at different biases we can clearly observe this effect: the step in the capacitance spectra, observed at zero bias in the range from 10 Hz to 10 kHz, disappears when both forward and reverse bias are used. From this measurement, shown in Supplementary Figure 6, we can infer that the step in the capacitance arises from traps and, more importantly, that these states are minority carrier traps 13 .  Figure 6: Capacitance spectra at different biases for a device based on TPDP:C 60 (13.3 mol%) | Note that the reconstruction of the trap density uses the derivative of the capacitance spectra. This implies that all spectra at bias below -0.3 V, as well as above 0.3 V, lead to the same trap density, which tends to zero, given their rather constant shape.

Supplementary Note 4. Generation-Recombination
Statistics Due to a Distribution of Traps and

Drift-Diffusion Modeling
When recombination centers, such as the ones measured in the previous section, are found within the energy gap of semiconductors, they contribute to the generation and recombination processes. This is a consequence of the static of occupation of these states, which happens through the excitation of charges carriers. SRH theory was firstly derived for a single trap level and is based on four rates of capture (energy absorption) and release (energy emission) of charges 14 , as schematically represented in Supplementary Figure 7. In order to obtain the rates shown in Supplementary Figure 7, one assumes a Fermi-Dirac occupation function f (E, T ) for the probability that a trap at energy E t is occupied. The rates can then be written as 15 : Electron capture In equation (S4.5), n and p are the electron and hole concentration, respectively. σ n,p and e n,p are the capture cross-section and emission coefficients, respectively, for holes (p) and electrons (e). v n,p is the thermal velocity. The product σ n,p v n,p can be estimated from the trap analyses via equation (S2.2). Because N n,p are unknown, a direct input via equation (S2.2) was not considered and the value was adjusted to achieve a good agreement with the experimental curve.
In thermal equilibrium, the capture and emission rates for electrons and holes must be equal (r 1 = r 2 , r 3 = r 4 ). With this assumption, using the set of equations above, e n and e n can be found. We define the net generation/recombination efficiency as: Once more using the set of equation above and equation (S4.6), we can derive the occupation function (solving equation (S4.6) for f (E, T )) and generation/recombination rate, which can be written as: By multiplying equation (S4.7) by the number of trap states (N t ) we can obtain the rate of generation (G) and recombination (R), which are related as G = −R. We are interested in the reverse region of the JV curve, because photodetectors are mainly operated at negative bias. Considering that, we can make some approximations to understand the behavior of equation (S4.7). Firstly, under reverse conditions, the concentration of free charges in the device is very small, because they are easily extracted by the drift-applied field. Moreover, the capture rates are proportional to the number of free charges, making these processes irrelevant for the device. This also allows considering σ n = σ p = σ 0 .
In reverse bias, the important processes are the emission of electron and holes assisted by the trap states. These electrons (holes) are then emitted to the EA (IP), increasing the dark current value. Applying the aforementioned considerations/assumptions and expressing e n and e n in terms of appropriated variables, equation (S4.7) can be written as Equation (4) in the main text: Equation (4) has its maximum value when E t = E i . This means that trap states close to mid gap are the most relevant for generation.
Recalling the experimental results presented in the main text, in the trap distribution, E t values cross or are very close to mid gap, explaining the high values of J D as well as its increase with the number of traps. Since the devices measured presented a distribution of traps that could be approximated by a Gaussian distribution, we model the SRH generation in the drift-diffusion simulation by integrating the product of equation (S4.7) by the measured distribution over the entire band gap:

Supplementary Note 5. Noise Measurements
The setup is shown in Supplementary Figure 8a. The circuit consists of an input stage transimpedance amplifier that converts the current through the OPD into the voltage v o1 , followed by two stages of high-pass filter (HPF) and two stages of signal amplification (gain) plus low-pass filter (LPF). The output signal v out is then sampled at 4 to 12 million points in real-time using an oscilloscope with 16-bit of resolution. The spectrum of v out is calculated using the Welch's method for estimating the power spectral density (S n ) in MATLAB 16 . The LPFs and HPFs significantly attenuate the signal power content outside of the target frequency bandwidth. This prevents any mistranslation of non-target signal power into the target measurement bandwidth.
Since the transfer function of each stage and the noise of intermediate components are known, S n of v o1 can be calculated back from v out . Then the total noise current (i total ) would be v o1 divided by R 1 ||C 1 impedance. i total has several known sub-components that can be removed by subtracting their power to extract the net OPD noise. The noise voltage and noise current of the amplifiers 1 are known from the datasheet or separate measurements. These sub-components could dominate the OPD noise at very low or very high frequencies and therefore limit the frequency range that the OPD noise can be accurately extracted.

Bias Generator
Battery   Tables   Supplementary Table 2: Donors used to fabricate different photodiodes | E CT varies from 0.85 to 1.58 eV when blended to C 60 at 6 mol%. The CT absorption tails in Supplementary Figure 9 were fitted as described elsewhere 17 . From fitting the EQE spectra, values of E CT , λ CT and f CT were extracted, as listed here. The statistical error of the fitting procedure is estimated by systematically changing the start and end value of the fit, resulting to 25 different fits.

Short Name
Chemical structure         Table 6: Parameters used in the drift-diffusion simulation showed in Figure  4a,b and Figure 5b in the main text.
ZnPc:C 60 TPDP:C 60 Unit Trap As measured 50 + 50 + 50 50 + 50 + 50 nm µ n,p 9 × 10 −9 2 × 10 −9 a See discussion about the accuracy of this approximation in section 3. b EBL + active layer + HBL. The simulation is performed for a single-layer device with ohmic contacts and an effective thickness, which accounts for the field drop along undoped EBL, active layer and HBL. The generation is limited within the active layer. As suggested by the experimental data, traps are found only in this region supporting this approach.             18 . In organic devices, the voltage drops along the organic intrinsic layers. Therefore, the depletion region width (W ) is assumed to be 90 nm, which corresponds to the device thickness minus the doped layer thicknesses. According to equation (S2.4), variations in V bi and W lead to minor errors in N t , which does not affect the main discussion of this work. As discussed in the main text, the trap density is studied in the region from 10 Hz to 10 kHz, where the device resistance does not play a major role and series resistance can also be neglected. For guidance, the frequency at 323.15 K is also plotted. Note that this frequency corresponds only to one temperature. The fitting range is further adjusted, depending on the material system and the effect of the blend resistance of that specific material system. For Spiro-MeO-TPD and P4-Ph4-DIP, for example, it seems that another type of distribution starts to appear at higher energy. We, however, neglect it as within the frequency range where a reliable result can be obtained and the temperature range we studied, these features could not be properly resolved.           22 showing a dependence on the square root of the applied field. This is a further indication that Poole-Frenkel effect is present in these systems.  Figure 20: Ideality factor, n id , for TPDP devices | (a) for 24.1 mol% at different temperatures. A common value of n id is found for all temperatures, namely around 1.8, in agreement with trap assisted recombination process. At room temperature, n id can be analyzed at around 10 −1 mA cm 2 . This is done for all concentration in (b). For these devices, however, we could not observe any trend with the amount of traps and nid, which, as discussed in the main text, can still be a consequence of energetic barriers in these devices. The curve 60 meV away from midgap represents E t at -4.51 eV, as measured for this system. As E t is moved away from midgap, the contribution of traps to the dark current decreases, as predicted by by Eq. 4 of the main text. (b) Simulated for different widths of the trap density of states. Within the studied range, this width plays a minor role, and no strong trend can be observed when varying this parameter.