Mid-gap trap state-mediated dark current in organic photodiodes

Photodiodes are ubiquitous in industry and consumer electronics. Constantly emerging new applications for photodiodes demand different mechanical and optoelectronic properties from those provided by conventional inorganic-based semiconductor devices. This has stimulated considerable interest in the use of organic semiconductors, which provide a vast palette of available optoelectronic properties, can be incorporated into flexible form factor geometries, and promise low-cost, low-embodied energy manufacturing from earth-abundant materials. The sensitivity of a photodiode depends critically on the dark current. Organic photodiodes (OPDs), however, are characterized by a much higher dark current than expected for thermally excited radiative transitions. Here we show that the dark saturation current in OPDs is fundamentally limited by mid-gap trap states. This new insight is generated by the universal trend observed for the dark saturation current of a large set of OPDs and further substantiated by sensitive external-quantum-efficiency- and temperature-dependent current measurements. Based on this insight, an upper limit for the specific detectivity is established. A detailed understanding of the origins of noise in any detector is fundamental to defining performance limitations and thus is critical to materials and device selection, and design and optimization for all applications. Our work establishes these important principles for OPDs. Researchers demonstrate that the dark saturation current in organic photodiodes is fundamentally limited by mid-gap trap states. This leads to an upper limit for specific detectivity.

Photodiodes are ubiquitous in industry and consumer electronics. Constantly emerging new applications for photodiodes demand different mechanical and optoelectronic properties from those provided by conventional inorganic-based semiconductor devices. This has stimulated considerable interest in the use of organic semiconductors, which provide a vast palette of available optoelectronic properties, can be incorporated into flexible form factor geometries, and promise low-cost, low-embodied energy manufacturing from earth-abundant materials. The sensitivity of a photodiode depends critically on the dark current. Organic photodiodes (OPDs), however, are characterized by a much higher dark current than expected for thermally excited radiative transitions. Here we show that the dark saturation current in OPDs is fundamentally limited by mid-gap trap states. This new insight is generated by the universal trend observed for the dark saturation current of a large set of OPDs and further substantiated by sensitive external-quantum-efficiency-and temperature-dependent current measurements. Based on this insight, an upper limit for the specific detectivity is established. A detailed understanding of the origins of noise in any detector is fundamental to defining performance limitations and thus is critical to materials and device selection, and design and optimization for all applications. Our work establishes these important principles for OPDs.
Organic semiconductors present promising complementary alternatives to inorganic semiconductors for photodetection, in particular in the wavelength (λ) range between 1 and 2 μm (ref. 1 ). This spectral window is interesting for bioimaging 2 , optical telecommunication 3 and machine vision 4 . The advantages of organic semiconductors include monolithic integrability with silicon readout circuitry 5,6 , reduced material and manufacturing costs from earth-abundant feedstocks, and inherent material properties like flexibility, bandgap tunability and light weight 7 . Combining these properties with state-of-the-art device performance and operational lifetimes is expected to result in disruptive innovations, particularly in the field of consumer electronics 8 , such as previously demonstrated with organic light-emitting diodes.
In the past decade, advances in absorber materials and device architectures used in organic photodiodes (OPDs) based on donor (D):acceptor (A) bulk heterojunction (BHJ) semiconductor blends have delivered substantial performance improvements. The key quality metric of a photodetector is the specific detectivity:

Results and discussion
To clarify the dominant dark current mechanism in OPDs, we first quantify the radiative current components, which are generally dominated by energy-gap edge and sub-gap features in the EQE. To this end, we conducted ultra-sensitive EQE measurements on a wide range of D:A BHJ systems with different D-A energy gaps ( Supplementary  Fig. 1). Figure 1a presents the EQE spectra of three exemplary D:A systems, PBTQ(OD):PC 71 BM, PBDB-T:PC 71 BM and PBDB-T:EH-IDTBR. The corresponding energy-level diagrams are depicted in Fig. 1b. The full names of the chemicals used are provided in the Methods. The EQE spectra, measured over a dynamic range of 90 dB, are shown on a logarithmic scale, illustrating the energy gap edges and the sub-gap spectral range. The measured EQE spectra of the BHJs are generally found to display two distinct features in the sub-gap region: a CT state feature below the gap and an additional low-energy sub-gap feature, which is assigned to radiative transitions via mid-gap states. A schematic energy diagram with the respective radiative processes is shown in Fig. 1c. The CT state contribution is expected to follow a Gaussian function from which E CT can be obtained. For narrow-gap BHJs, however, the E CT is expected to be very close to the singlet exciton energy of the donor polymer, with the CT absorption shoulder correspondingly overshadowed by the donor singlet exciton absorption in these systems. As such, E CT was instead estimated from the intercept between the measured EQE and the associated electroluminescence expected from detailed balance (see ref. 16 for details). We further note that the EQE tails directly below the gap approximately follow a ln (EQE) ∝ E/kT type behaviour 30 , suggesting that exponential tail states, if present, will have a negligible impact.
Based on the measured EQE, the corresponding dark current density induced by radiative transitions (J RAD ) can be estimated 31 . In general, J RAD can be written as a sum of the CT state contribution and the trap state contribution. In forward bias, at voltages comparable to the open-circuit voltage of solar cells, J RAD in BHJs has been observed to be dominated by the CT state recombination 19 . In reverse bias, at voltages relevant for OPDs, however, the contribution from trap states is expected to play a decisive role. In accordance with detailed balance, the radiative current at small reverse bias is given by is the blackbody spectrum (E is the photon energy) 17 . Figure 1d shows the estimated J RAD (at small reverse bias) as a function of E CT for the BHJ systems considered (Supplementary Table 1). In (low offset) systems where CT states cannot be distinguished from singlet excitons, we used the optical gap as a proxy for E CT instead. For comparison, we include the radiative J 0 (based on measured EQE) of six inorganic photodiodes with different bandgaps (E g ), showing an activation energy of E a = E g , consistent with band-to-band transitions dominating the radiative current in these systems. Conversely, for organic BHJs, J RAD is found to scale with E a = E CT /2. This can be traced back to the dominant contribution from the low-energy EQE features (Fig. 1a), reflecting their Gaussian distributions characterized by energy gaps around E CT /2, as expected for mid-gap states. These observations imply that J RAD in BHJs is dominated by radiative transitions via mid-gap states at voltages relevant for OPDs.
To clarify the origin of the dominant NR process, we next conducted T-dependent J D -V measurements on three different where i noise is the noise current, q the elementary charge, h is the Planck constant, c the speed of light, the device area, Δf the frequency bandwidth, and EQE is the photovoltaic external quantum efficiency. Although the operational spectral window of OPDs has been expanded from the visible range up to λ = 1,700 nm, the highest D* values above 1,500 nm have only reached modest levels of 10 9 cm Hz 1/2 W −1 (refs. 9,10 ). The longer λ range has remained unattainable 11 , despite the implementation of optical and electrical amplification 12 , which can boost the EQE to as high as 2,000% (ref. 13 ). The main obstacle for achieving higher D* has proven to be the large dark current density J D or, more precisely, the electrical shot noise produced by it (equation (1)) at the operational bias voltage V (typically −0.5 to −2 V).
In general, the dark current of an OPD operating in reverse bias is composed of two distinctly different components: a deviceintrinsic diode component, represented by the dark saturation current density J 0 , and an ohmic leakage current component (J shunt ). J shunt is believed to originate from imperfections related to device fabrication and non-optimized device layouts that induce alternative conducting pathways, so called shunts (for example, pinholes in the active layer and lateral currents 14 ). Conversely, J 0 is an inherent device parameter, determined by thermally activated radiative and non-radiative (NR) processes in the active layer and/or at the contacts, and being of the form J 0 ∝ exp (−E a /kT), where E a is the associated activation energy of the dominant process and kT is the thermal energy. As such, the specific detectivity of OPDs is fundamentally limited by J 0 , being the dominant source of noise for narrow-gap systems in particular. In BHJs, J 0 has been found to be dominated by non-radiative processes, resulting in J 0 levels substantially above those expected from radiative transitions alone 15 . However, the origin of the large non-radiative current, limiting the detectivities in OPDs, is currently hotly debated.
Three different mechanisms that contribute to J 0 in reverse bias have been suggested: (1) NR transitions via charge transfer (CT) states 16 , (2) charge injection of (minority) carriers at the contacts 15 and (3) trap-mediated transitions 17,18 . These processes, however, are expected to display distinctly different E a . For transitions taking place between the ground state and the CT states, we generally expect E a = E CT , where E CT is the CT state energy, reflecting the effective D-A energy gap in BHJs. It has been shown that NR transitions via CT states limit the open-circuit voltage (V OC ) in organic solar cells, and thus are also expected to play a role in OPDs 19,20 . For minority carrier injection, in turn, J 0 is limited by the associated injection barrier at the electrode 21 . This barrier is effectively lowered by both energetic disorder and image-charge effects, resulting in a Poole-Frenkel-like current with a voltage-dependent E a (refs. 22,23 ). Although this process is important in the case of misaligned energy levels at the electrodes, it is commonly negligible for optimized ohmic contacts 21 . Finally, for trap-mediated transitions, E a generally depends on the related trap energy and distribution; for mid-gap traps, E a = E CT /2 is typically expected. The presence of trap states has been suggested in a broad range of BHJ solar cells [24][25][26][27][28][29] , but their shape and role in OPDs have remained elusive.
In this Article we provide evidence that the dark saturation current in OPDs is universally limited by transitions mediated by mid-gap states. From sensitive EQE measurements of a considerable number of D:A BHJ systems, the presence of radiative mid-gap states is observed. The active role of the mid-gap states in determining J 0 is further demonstrated by temperature-dependent measurements on narrow-gap BHJs, where the shunt effects are minimal, from which we find the E a of J D to be half the D-A energy gap. Additionally, the observed voltage dependence of J D is consistently explained by mid-gap state-mediated transitions. Finally, the determined J 0 for the OPD systems considered in this work, along with a large set of literature-known narrow-gap systems, are observed to follow the general trend expected for mid-gap states. These results have several important implications Article https://doi.org/10.1038/s41566-023-01173-5 narrow-gap D:PC 71 BM systems with PBTQ(OD), PTTBAI or PTTQ(HD) as the donor. The advantage of using narrow-gap BHJs is that the measured J D directly reflects the J 0 of these devices, owing to their high J 0 (relative to the shunt). In Fig. 2a, the corresponding J D measured at −0.1 V at room temperature (r.t.) is compared to the respective J RAD . A voltage of −0.1 V was chosen to further minimize the effects of shunts (present at high reverse bias) and noise (at voltages near zero). We find that J RAD is about six orders of magnitude below the experimental J D (at low reverse bias), suggesting that J 0 is strongly dominated by NR transitions. Figure 2b shows J D (−0.1 V) as a function of 1/kT for the different narrow-gap blends. We find that ln |J D | depends linearly on 1/kT for temperatures above 260 K. For temperatures below 260 K, deviations from linearity are seen, caused by the inability to measure currents below 10 −12 A or the dominance of other current channels with weaker temperature dependences. Figure 2c shows the obtained E a as a function of the D-A energy-level gap E g (obtained from cyclic voltammetry 32,33 ) and the estimated E CT . Similar values are obtained for reverse bias voltages up to −1 V ( Supplementary Fig. 2), suggesting that the contribution from shunts remains minimal at these voltages. Despite the uncertainties 34,35 of the energy gap, we generally observe E a ≈ E CT /2 for the three narrow-gap BHJs. This is compared with the results from T-dependent measurements of three commercial NIR photodetectors composed of germanium (Ge) and strained and unstrained indium gallium arsenide (InGaAs) in Fig. 2c, where E a equals the bandgap energy, as expected (Supplementary Figs. 3 and 4).
The observation that E a is insensitive to the reverse-bias voltage and equals half of the related D-A gap energy suggests that J D in narrow-gap OPDs are limited by mid-gap states. To substantiate this, we further clarified the corresponding voltage dependence of J D . In general, the diode current component of J D can be expressed as (Supplementary Note 1) where m is the diode ideality factor, J 0, m is the corresponding dark saturation current density, and η 0, m (V) is a voltage-dependent prefactor accounting for the effect of nonuniform generation and recombination rates inside the active layer. For direct transitions m = 1, and η 0, 1 = 1 is typically expected. For trap-mediated transitions, generally described by Shockley-Read-Hall (SRH) statistics, however, m typically ranges between 1 and 2 depending on the energetic distribution of traps involved. In the case of mid-gap trap states 36 m = 2, (ii) (i)  Fig. 2d and compared to the analytical model (equation (2)) with m = 2. At small forward bias and reverse bias, a good agreement is obtained between the experiments (symbols) and the analytical model with m = 2 (solid lines), using the associated J 0 as the only fitting parameter. We note that deviations between analytical and experimental currents at high reverse bias are eventually expected as the contribution of J shunt increases. To validate that the dark current in the relevant forward-bias voltage regime is not limited by poor charge transport (for example, caused by low mobilities), we also included corresponding intensity-dependent short-circuit current density (J SC ) versus V OC measurements, which are known to not be affected by limitations related to transport and series resistance 37 . These results corroborate the assertion that J 0 is dominated by thermal transitions via mid-gap trap states, simultaneously explaining the experimentally observed V-dependence of J D in reverse and forward bias.
To assess the generality of these findings, we plot in  Fig. 3b. The presence and dominant role of mid-gap states in narrow-gap BHJ systems in general is further corroborated by corresponding J SC -V OC data at 1 sun ( Supplementary Fig. 5).
As J 0 decreases exponentially with increasing E CT , however, J D (−0.1 V) for BHJs with wider D-A gaps in Fig. 3a inevitably becomes dominated by J shunt , overshadowing the true J 0 . Although J shunt dominates in the reverse bias of these systems, the diode current eventually becomes prevalent in the forward bias. This is demonstrated in the inset of Fig. 3a for PBDB-T:EH-IDTBR, showcasing the superposition between the symmetric shunt current density, typically of the form J shunt = V/ (R shunt ) (R shunt is the shunt resistance), and the exponential diode current density (J diode ) contribution. Subsequently, the dark current in the forward bias can be used to extract J 0 for systems with wider D-A gaps. Indeed, we generally find that the dark current density at small forward bias, above the J shunt level, is well-approximated by equation (2) with m = 2 (Fig. 3a, inset and Supplementary Fig. 6). Figure 3b shows the corresponding J 0 obtained for the wider-gap BHJs considered in this work. These systems are seen to follow the same trend as the narrow-gap systems, strongly suggesting that J 0 in OPDs is universally and fundamentally limited by mid-gap state-mediated transitions. Based on these findings, a universal efficiency limit for D* of OPDs can be obtained. In accordance with equation (1) Figure 4 shows the estimated upper limits of D*, based on the extracted J 0 for the BHJs from Fig. 3b. The corresponding trend expected for transitions mediated by mid-gap trap states is indicated by the red line, reproducing the general behaviour of the experimentally estimated upper limits of D*. For comparison, the blue solid line in Fig. 4 indicates the background-limited infrared photodetector (BLIP) limit, corresponding to the upper theoretical limit of a perfectly radiative photodiode (that is, J D = J RAD , with EQE = 1 for E ≥ E CT and EQE = 0 otherwise).
When calculating the expected noise current or analysing experimental noise measurements, it is important to emphasize that i 2 noise , and hence D*, generally also depends on the applied voltage. As discussed in Supplementary Note 3, the voltage dependence of i 2 noise in reverse bias depends on the dominant current channel. If J D is dominated by band-to-band transitions, a voltageindependent i 2 noise is expected for V ≪ −kT/q in the dark. On the other hand, if the dark current is dominated by transitions via mid-gap states, with J D given by equation (2) in reverse bias, a sublinear voltage dependence of i 2 noise is expected. Finally, we emphasize that an understanding of the exact nature of the mid-gap trap states in OPDs has remained elusive. The trap states may have different origins and broad energetic distributions within the gap. However, as stipulated by SRH statistics 36 , and further demonstrated experimentally in Supplementary Note 4, transitions mediated by trap states in the centre of the gap are most l ikely to occur. As a result, the J 0 in BHJ-based OPDs is also predo minantly dominated by these mid-gap states. We note that these states are also observed in neat-material devices based on polymer, fullerene and non-fullerene small molecules, while being insensitive to the contacts used, suggesting an organic semiconductor material-

Conclusion
To conclude, we have undertaken a detailed study on the origin of the dark saturation current in organic photodetectors based on next-generation organic semiconductors. Specifically, we have utilized temperature-dependent current measurements on narrowgap organic semiconductor blend photodiodes to show that the thermal activation of the dark current at small reverse bias is consistent with mid-gap state-mediated transitions. Furthermore, we show that dark saturation current densities for a large set of OPDs universally follow a trend expected for transitions via mid-gap trap states. The presence of mid-gap states is further supported by sensitive EQE measurements. These results imply that J 0 in the reverse bias is fundamentally dominated by the mid-gap statemediated transitions, setting an upper limit of D* for OPDs. Therefore, to enhance the performance of OPDs it is important to suppress and identify the origin of mid-gap states. These findings are highly relevant for other organic semiconductor-based photonic diode applications as well.

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PCDTBT PTB7-Th:PC 71 BM was dissolved in a CB solution (14 mg ml −1 with 3 vol% DIO) with a D:A ratio of 1:1.5, and spin-coated (600 r.p.m.) on ZnO to form a 100-nm film. The as-cast films were rinsed with 80 μl of methanol at 4,000 r.p.m. for 20 s to remove the residual DIO. All top electrodes were deposited by thermal evaporation under a vacuum of 10 −6 torr with an appropriate mask (from Ossila) to define a 0.04-cm 2 cell area for each pixel.

EQE
For the EQE measurements, a homebuilt set-up was used that included a Perkin Elmer UV/Vis/NIR spectrophotometer (LAMBDA 950) as a source of monochromatic light 40 . The light was chopped at 273 Hz and directed onto the device under test (DUT). The resulting photocurrent was amplified by a low-noise current amplifier (FEMTO DLPCA-200) and measured with a Stanford SR860 lock-in amplifier. To decrease the noise floor of the set-up, the DUT was mounted in an electrically shielded Linkam sample holder (Linkam, LTS420E-P) and an integration time of 30 s on the lock-in amplifier was used for detecting wavelengths above 1,500 nm. NIST-calibrated Si and Ge photodiodes (Newport) were used as calibration references.

Dark current density-voltage and temperature-dependent current measurements
The J D -V characteristics were measured with a Keithley 2450 source measure unit scanning from the reverse to forward bias regime.
The DUT was mounted in a temperature-controlled and electromagnetically shielded sample stage (Linkam, LTS420E-P), which was connected to a temperature controller (Linkam, T96) and a liquid-nitrogen pump (Linkam, LNP96), allowing for the temperature to be changed. In addition, T-dependent current measurements were conducted, where the current was measured continuously under a constant applied bias for a given temperature. This ensures that trapped charge carriers have sufficient time to be released and reach the electrodes, while minimizing the impact of both the voltage-sweep direction and the input impedance of the source measure unit (especially at low current levels near to zero applied bias voltage) when determining the activation energy.

Short-circuit current density versus open-circuit voltage
A custom-built continuous-wave laser operating at 520 nm was used for J SC -V OC measurements. The incident light intensity was stepwise increased by a motorized two-wheel attenuator from Standa (10MCWA168-1) containing different optical density filters. A Keithley 2450 source measure unit was used to record J SC and V OC of the DUT at each incident light intensity.

Gaussian fits to the EQE
The expected EQEs and energy gaps (E j ) of CT states (j = CT) and trap states (j = trap) were obtained by fitting the associated sub-gap absorption features in the experimental EQE data with a Gaussian function of the form in accordance with the Marcus theory. Here, λ j is the corresponding reorganization energy, and f j is a prefactor reflecting the oscillator strength and magnitude of light absorption.

Data availability
The experimental data in the main figures are provided in a tabulated excel file format as Supplementary Data. Additional supporting data are available from the corresponding authors upon reasonable request.

Code availability
The drift-diffusion simulator used in this study has been described in detail elsewhere 29,41 . Further information is available from the corresponding authors upon reasonable request.