Mid-gap Trap State Mediated Dark Current in Organic Photodiodes

Photodiodes are ubiquitous in industry and consumer electronics. New applications for photodiodes are constantly emerging, such as the internet of things and wearable electronics that demand different mechanical and optoelectronic properties from those provided by conventional inorganic devices. This has stimulated considerable interest in the use of next generation semiconductors, particularly the organics, which provide a vast palette of available optoelectronic properties, can be incorporated into flexible form factor geometries, and promise extremely low cost, low embodied energy manufacturing from earth abundant materials. The sensitivity of a photodiode to low light intensities (typically important in these new applications) depends critically on the dark current. Organic photodiodes, however, are characterized by a much higher dark current than expected for thermally excited band-to-band transitions. Here, we show that the lower limit of the dark current is given by recombination via mid-gap trap states. This new insight is generated from temperature dependent dark current measurements of narrow-gap photodiodes for the near-infrared. Based on Shockley-Read-Hall statistics, a diode equation is derived which can be used to determine an upper limit for the specific detectivity and to explain the general trend observed for the light to dark current ratio as a function of the experimental open-circuit voltage for a series of organic photodiodes. 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, design and optimisation for all applications. Our work establishes these important principles for organic semiconductor photodiodes for the near-infrared.


Introduction
Organic semiconductors present promising complementary absorbers to inorganic semiconductors for photodetection, in particular in the wavelength range between 1 and 2 μm. This spectral window is interesting for bioimaging 1 , optical telecommunication 2 and machine vision 3 . The advantages of organic semiconductors include monolithic integrability with silicon read-out circuitry 4,5 , reduced material and manufacturing costs from earth abundant feedstocks, and inherent material properties like flexibility, bandgap tunability and light weight. 6 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, 7 such as previously demonstrated with organic light emitting diodes.
In the past decade, advances in the absorber materials and device architectures used in organic photodetectors (OPDs) based on donor (D):acceptor (A) bulk heterojunction (BHJ) blends have delivered significant performance improvements. The operational spectral window of OPDs has been expanded from the visible range up to wavelengths of 1700 nm, however, with the best specific detectivities (D*) above 1500 nm only reaching modest levels of 10 9 cmHz 1/2 /W. 8,9 The longer wavelength range has remained unattainable 10 despite the implementation of optical and electrical 11 amplification that can boost the external quantum efficiency (EQE) to as high as 2000 %. 12 The main obstacle for achieving higher D* has proven to be the large dark current density D , or more precisely the electrical shot noise produced by it, at typical operational bias (-0.5 to -2 V). For OPDs operating at zero bias voltage, a similar problem still exists due to the thermal noise which is related to parasitic and dynamic resistance of the diode.
In efficient organic photodiodes, the main source of D in reverse bias is leakage current, or the socalled shunt current density shunt , arising from imperfections related to device fabrication and material processing. In general, D of a photodiode is given by the Shockley diode equation where 0 ( , ) is the dark saturation current density and s the series resistance, while shunt is the shunt resistance associated with shunt . s generally limits D in forward bias but is negligible at smaller voltages. In reverse bias, the dark current simplifies as D = − 0 ( , ) + shunt , being strongly affected by the shunt current shunt = / shunt . The dark saturation current density 0 ( , ) is a material dependent parameter, determined by thermally activated charge generation-recombination processes in the active layer. For an ideal diode, 0 is independent of the applied voltage. Under these conditions, band-to-band recombination dominates and the activation energy of 0 is expected to be equal to the bandgap energy. In organic BHJ photodiodes, this bandgap corresponds to the charge transfer energy ( CT ), which is closely related to the difference between the frontier molecular orbital energy levels of D and A. In the presence of additional recombination mechanisms, however, 0 is increased and generally depends on the voltage. Such a voltage dependence is commonly described in terms of a diode ideality factor ( ) deviating from unity ( 0 ( , ) exp( ⁄ ) ∝ exp( ⁄ )). For organic photodiodes, typically 0 ≪ | shunt |. However, optimizing the morphology of the BHJ blend active layer and the device stack can reduce shunt relative to 0 . Furthermore, as the bandgap energy decreases, 0 is known to increase relative to shunt . In narrow-gap organic semiconductor blends designed for near-infrared photodetection, it was observed recently that D in reverse bias shows almost ideal diode behaviour, 13 allowing for D to be fitted with eq. 1. A comparison of 0 from the fitting with the radiative dark saturation current 0,R (expected from the Shockley-Queisser limit) further led to the conclusion that non-radiative mechanisms must dominate the D generation. However, the origin of the large dark current has remained unclear. 14,15 The magnitude of D and the dark saturation current in organic photodiodes are typically explained by either non-optimized device layouts or properties of the active layer. Non-optimized device layouts result in parasitic currents such as shunt due to pinholes in the active layer, injection currents due to misaligned energy levels at the semiconductor/metal interface 15 and lateral currents 16 . In the second category, material properties such as energetic disorder and the presence of trap states are assumed to be responsible for the large D . In this regard, a possible origin is non-radiative band-to-band generationrecombination via CT states, which has been shown to increase exponentially with decreasing CT . 13,17 Another major source of D can be generation-recombination via trap states, typically described in terms of Shockley-Read-Hall (SRH) statistics. In organic semiconductors, the presence of trap states has been previously shown via sensitively measured photothermal deflection spectroscopy as well as intensity dependent photocurrent measurements for a large set of fullerene and non-fullerene blends. 18 Recently, the effect of mid-gap trap states has also been observed in the sub-gap EQE 19 directly and by impedance spectroscopy. 20 In this work, we provide evidence that the dark saturation current in organic photodiodes is dominated by recombination via mid-gap trap states. To minimize the influence of the shunt, we use narrow-gap BHJs with a relatively high 0 ( , ) such that at low reverse bias 0 > | shunt |. Based on temperature dependent current density-voltage ( -) measurements, we then find that the thermal activation energy   Figure S1 illustrating how optical interference affects the low-energy tail of the EQE. 22,23 The HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energy levels of the narrow-gap donor materials were previously obtained from cyclic voltammetry (CV) as reported in literature, 13 and are shown in Figure 1b. For comparison, the solution and thin film absorption spectra are given in Figure S2.
The EQE measurements were performed down to roughly 0.5 eV (≈ 2500 nm) over a dynamic range of 90 dB. For PBTQ(OD):PC71BM and PTTQ(HD):PC71BM, the spectral range of PC71BM absorption above 1.65 eV (≈ 750 nm) can be clearly distinguished from the narrow-gap polymer absorption at lower energies. Four orders of magnitude below the above-gap EQE, organic semiconductors generally show trap state absorption, as previously reported. 24 It has been suggested that conventional D:A blends, corresponding to effective bandgaps of 1.3 eV and above, display both charge transfer and mid-gap trap state absorption at sub-gap energies 19 , which, unless overshadowed by interference effects, can be fitted with Gaussian functions to obtain the CT state energy ( CT ) and the mid-gap trap state energy ( t ). The EQE spectrum of a PBDB-T:PC71BM device in Figure 1a is an example of such a system, showing a pronounced CT state and mid-gap trap state shoulders in the sub-gap.
In the narrow-gap blends, CT is expected to be very close to the singlet exciton energy (  From the EQE spectra it is possible to calculate the thermodynamic limit of 0 , namely the radiative dark saturation current 0,R , via detailed balance: 25 where BB ( ) is the temperature dependent black body spectrum. In practice, the reliable evaluation of eq. 2 is limited by the upper and lower integration bounds set by the experimental apparatus, 19 thus providing a lower limit of 0,R . The calculated 0,R is demonstrated in Figure S3, where, for example, the narrow-gap blend PTTBAI:PC71BM is characterized by 0,R = 3.1 × 10 -16 A/cm 2 . This is to be compared to the corresponding experimental D value of D ( ─ 0.1 V) = 7.8 × 10 -9 A/cm 2 , measured at ─ 0.1 V, where shunt is expected to be minimal. Hence, even when the EQE in the spectral range of mid-gap trap states is included down to 0.6 eV, the calculated 0,R is still 6 to 7 orders of magnitude below the experimental D (at low reverse bias). This high offset between 0,R and D is commonly observed in organic photodiodes, but underlying reasons are still debated. Provided that the contribution from shunt currents is small at this voltage, the dark saturation current density is found to be strongly  To gain more insight into the dominant (non-radiative) recombination mechanism behind 0 , we conducted temperature dependentmeasurements. Assuming that D (─ 0.1 V) ≈ 0 , noting that the dark saturation current density takes the form 0 = 00 exp(− a / ), the corresponding activation energy a may be determined. Here, a equals the effective energy barrier of the dominating thermal excitation process in the dark, while 00 is a prefactor. For a CT state mediated band-to-band generationrecombination process, a = CT , while for a mid-gap state mediated generation-recombination process we expect a ≈ CT 2 ⁄ .   Table S1), where a equals the bandgap energy, as expected.
The observation that a equals half of the related bandgap energy for the organic semiconductor blends suggests that the dark saturation current in these systems is mediated by generation and recombination via mid-gap trap states in reverse bias. In general, the dark saturation current in eq. 1 can be expressed by the sum of the components related to band-to-band recombination ( 0 bb ) and mid-gap state mediated recombination ( 0 SRH ) currents: where for completeness we also include additional injection current components 0 inj related to surface recombination (and generation) at the electrodes. In organic semiconductor blends, we expect the bandto-band component to be independent of voltage, following 0 bb ∝ exp(− CT / ). The activation energy of 0 inj , on the other hand, is expected to be predominantly given by the injection barrier of minority carriers at the electrodes. 27 Given that a ≈ CT /2, our results point towards 0 ( ) ≈ 0 SRH ( ).
In   Table S2, allowing for the effective SRH lifetimes SRH to be calculated. Assuming a typical value of 1 × 10 20 cm -3 for 0 , we find SRH for PTTBAI, PBTQ(OD) and PTTQHD to be 0.3, 0.1 and 1 μs, respectively. We note that 0 bb from the band-to-band recombination converges to values much lower than 0 SRH ( ) and hence, can be neglected in reverse and forward bias. In contrast, shunt ( ) dominates the darkat high reverse bias. This is demonstrated, first, in the darkfits in Figure 3a and, secondly, in Figure S4, where a ( ) is shown to decrease with increasing reverse bias.  Based on the above findings, a new efficiency limit for photodiodes based on organic BHJ blends can be obtained. The performance of a photodetector is given by the specific detectivity * = √ × ( noise ) −1 , where is the responsivity, noise is the measured noise current and Δ is the frequency bandwidth. As shown in the literature, noise can be well approximated by its shot noise component shot at small bias. shot of any signal is shot = √2 . Then, assuming absorber materials that are dominated by recombination via mid-gap trap states, the lower limit of * corresponding to EQE = 1 for ≥ a and EQE = 0 for ≤ a (i.e. of an ideal photodiode) can be approximated by * = × (√2 SRH ( )) −1 .   Figure 4. Most photodiodes are generally well below this limit, consistent with previous findings by Gielen et al. 13 The theoretical behavior, expected for SRH recombination via mid-gap states dominating the dark saturation current, is indicated by the black line for the case OC → bi when 0 SRH ( OC ) → 2 0,SRH exp(− OC 2 ⁄ ) in eq. 5. Comparing with the experimental data, it can be seen that the general trend is indeed consistent with SRH recombination via mid-gap traps dominating 0 in narrow-gap systems where OC < 0.7 V. This is further corroborated by the experimentally obtained 0 ( OC ) 0 ( R ) ⁄ , estimated using eq. 6 in Figure 4b, showing that narrow-gap systems follow the trend predicted by mid-gap state mediated recombination. We note that the scatter around the black line can be partly attributed to the fact that OC ≠ bi in general, and a weak additional voltage dependence is thus expected in accordance with eq. 5. For systems with relatively wide gaps ( OC > 0.7 V), in turn, a deviation from the trend is seen. However, such a deviation is to be expected considering that the OC increases linearly with the effective bandgap CT (independent of whether band-to-band or SRH recombination dominates at open-circuit). Subsequently, high OC blends are characterized by very low 0 levels, with D ( R ) inevitably becoming dominated by parasitic shunts ( shunt ), overshadowing the true 0 in these systems.

Conclusions
To conclude, we have undertaken a detailed study on the origin of the dark current in near-infrared photodetectors based upon next generation organic semiconductors. Specifically, we utilised temperature dependent darkmeasurements on narrow-gap organic semiconductor blend photodiodes to show that the thermal activation of the dark current at small reverse bias equals half the bandgap, i.e., a ≈ 0.5 g . The dominant dark recombination mechanism is therefore mid-gap trap mediated. We derive a new expression for the dark current mediated by mid-gap trap states using SRH statistics. In this new expression, the dark saturation current 0 SRH is voltage dependent and therefore can strongly affect the reverse bias dark current and its shot noise depending on the build-in voltage. In this light, we calculate a revised upper limit of * for the studied narrow-gap blends based on 0 SRH that was obtained from a fit to the darkcharacteristics. Lastly, we show that for a large set of narrowgap organic photodiodes, the SC to D (-0.1 V) ratio as a function of voltage roughly describes a trend expected when considering SRH recombination via mid-gap trap states.          for ≤ , where and are the virtual electron and hole density at the cathode and anode contact, respectively, whereas bi is an effective built-in voltage which accounts for the energy-level bending at the anode and cathode contacts: = ln ( 2 ). Then, making use of = 2 exp ( ), the dark current for < bi can be expressed as This integral can be approximated by making use of the following regional approximation. At the anode side, the hole density dominates in the SRH recombination rate. In this region, the contribution from electrons may be neglected. On the other hand, on the cathode side the reverse is true. In this region electrons dominate and the contribution from holes to the SRH rate is negligibly small. Hence, ).

Mid-gap Trap State Mediated Dark Current in Organic Photodiodes
Based on the above regional approximation, Equation (S7), the integral 0 ( ) may be split into two simpler integrals: is the actual reverse-bias dark saturation current density in the presence of trap-assisted recombination.
Finally, we note that in the case of mid-gap trap states ( 1 ≈ 1 ≈ ), the associated dark current density at large forward bias (but well below bi ) and at high reverse bias can be approximated by