Non-Langevin bimolecular recombination in a silole-based polymer:PCBM solar cell measured by time-resolved charge extraction and resistance-dependent time-of-flight techniques

Abstract

The silole-based non-Langevin conjugated polymer KP115 has been used to demonstrate that circuit resistance is a crucial parameter in time-of-flight measurements of organic photovoltaic cells, providing a resistance-dependent bimolecular recombination coefficient. The origin of this behaviour is the biphasic decay dynamics present in KP115:PCBM devices (observed using a novel time-dependent charge extraction technique), which time-of-flight cannot accurately characterise.

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Broader context

The silole-based conjugated polymer KP115 is receiving significant attention recently due to its strongly reduced (non-Langevin) recombination behaviour. In this communication, we use KP115:PCBM organic photovoltaic devices to compare two different charge extraction techniques that provide information on the bimolecular recombination coefficient, β. A strongly resistance-dependent β was observed using the time-of-flight (TOF) technique; this was attributed to the biphasic decay dynamics measured using a novel time-resolved switch-based charge extraction technique. The conclusion that TOF cannot accurately describe the complex bimolecular recombination mechanisms involved in this system is important for the organic photovoltaics field. Due to the TOF technique rapidly gaining wider popularity, it is important to note that the resistance-dependence we observe in TOF is an important limitation of this technique. It indicates that in order to fully describe the bimolecular recombination behaviour, it is vital to utilise a variety of charge extraction techniques, such as the novel switch-based time-resolved one introduced here.

Bulk heterojunction organic photovoltaic cells have been steadily increasing in power conversion efficiencies over the past few years, with efficiencies in excess of 8–9% reported recently.^1–3 In order to further improve these devices, it is important to understand the factors that affect device performance, such as the various loss mechanisms present. Of these losses, recombination of the charges prior to collection at the electrodes has been identified as one of the most significant.^4,5 Geminate recombination most often refers to a monomolecular relaxation of the charges whilst they are still coulombically bound, although a more general definition simply requires recombination of charges generated from the same exciton. In contrast, bimolecular recombination involves recombination of fully dissociated charges created from different excitons. This latter process is known to be a significant limiting factor of the open-circuit voltage (V_oc)⁶ and also influences the fill factor.⁷

Due to the hopping transport typical of the organic materials used in solar cells and consequent low charge carrier mobilities, Langevin bimolecular recombination often dominates in these systems.^4,8,9 The Langevin recombination coefficient, β_L, is proportional to the charge carrier mobility, μ, via β_L = e(μ_p + μ_n)/εε₀. Although MDMO-PPV:PCBM solar cells exhibit behaviour consistent with Langevin recombination, annealed P3HT:PCBM cells do not.^9,10 They typically show a significant departure from this type of recombination, with a bimolecular recombination coefficient, β, several orders of magnitude lower than that expected for Langevin recombination. Recently, however, it has been reported that unannealed P3HT:PCBM possesses a β much closer to that of Langevin recombination.¹⁰ Given that the efficiencies of annealed P3HT cells are usually substantially higher than that of unannealed cells,^11–13 this result implies that this parameter has an appreciable effect on solar cell performance.

A number of techniques exist to investigate bimolecular recombination and/or mobility, including transient absorption spectroscopy (TAS), time-of-flight (TOF) and photo-induced charge extraction by linearly increasing voltage (photo-CELIV).^9,14,15TOF is one of the most widely used and allows measurement of charge transport in low mobility systems. The main concept behind this technique is that, in current mode under surface generation conditions, a sheet of photoinduced charge carriers will travel through the active layer of thickness d with a characteristic transit time, t_tr, where t_tr = d²/μU₀ (U₀ is the applied voltage). When bimolecular recombination is present, the extracted charge saturates at high light intensities. This allows the ratio between the bimolecular recombination coefficient and the Langevin recombination coefficient (β/β_L) to be directly determined, as shown by Pivrikas et al.:⁸

where C is the capacitance of the system, Q_e is the extracted charge and t_e is the extraction time. Importantly, eqn (1) is valid irrespective of the RC constant of the system.¹⁶ Once the mobility and thus the Langevin recombination coefficient β_L are known, the bimolecular recombination coefficient β can therefore also be established.

An important limitation of TOF is that eqn (1) provides only a single value for β that is valid for a particular set of conditions (charge density and extraction time, for example). However, previous reports on P3HT:PCBM devices have shown that β is dependent upon charge carrier density and/or time.^6,17 This raises the question of what β the TOF technique is really measuring; it is this topic that we will address in this communication. We therefore present recombination results obtained from TOF of a poly[(4,4′-bis(2-ethylhexyl)dithieno[3,2-b:2′,3′-d]silole)-2,6-diyl-alt-(2,5-bis(3-tetradecylthiophen-2-yl)thiazolo-5,4-d-thiazole)-2,5-diyl] (KP115) solar cell blended with PCBM (1 : 2 by weight) that show a strong dependence on the circuit resistance. Furthermore, we introduce a time-resolved charge extraction technique that reveals biphasic decay dynamics in KP115:PCBM and a time-dependent β, thereby highlighting the limitations of TOF in describing such complex recombination behaviour.

KP115 (the structure is displayed in Fig. 1a) is a new silicon-bridged push/pull polymer that produces relatively high efficiencies of ∼5%, similar to other polymers of this type.^18,19 Furthermore, this polymer is particularly promising as it is capable of producing high fill factor photovoltaic cells (>60%) with active layers greater than 200 nm thick.²⁰ This characteristic is vital for commercial viability but is rarely observed. Previous work has revealed that, similar to annealed P3HT:PCBM, KP115:PCBM solar cells possess non-Langevin recombination.²¹ This enables a long charge carrier drift length (and diffusion length), which ensures that the resultant solar cells are not limited by thickness and thicker active layers can be employed. KP115:PCBM is one of the few polymer-based systems that exhibits this highly beneficial behaviour.

Fig. 1 a) The structure of KP115. b) The normalised TOF current decays of KP115:PCBM (1 : 2) devices at high light intensity as a function of resistance. c) Analysis of the TOF results as a function of excitation density, using the three different resistances (50 Ω, 1 kΩ, and 10 kΩ) and an applied voltage of 2 V, showing the changes in Q_e/CU₀ and t_1/2 with light intensity (L/L₀), from which β/β_L is derived.

The bimolecular recombination coefficient, β, of KP115:PCBM has been measured using TOF for KP115:PCBM solar cells. As previously reported, the photo-CELIV mobility of this system is μ = 1 × 10⁻⁴ cm² V⁻¹ s⁻¹, with a corresponding Langevin recombination coefficient of β_L = 6.0 × 10⁻¹¹ cm³ s⁻¹. The subsequent TOF experiments were performed as a function of circuit resistance, R,²² with 50 Ω, 1 kΩ and 10 kΩ investigated. The effect of altering the resistance is shown in Fig. 1b: the timescale over which the signal decays clearly increases with R. Due to the increase in circuit resistance, charge extraction from the device takes longer. The consequence of this is illustrated in Fig. 1c, which shows the changes in Q_e/CU₀ and t_1/2 for each resistance as the light intensity is increased. The extracted charge Q_e saturates at high excitation densities due to bimolecular recombination while t_1/2 begins to increase when Q_e = CU₀, the charge stored on the electrodes (as shown by the dashed lines in Fig. 1c). Both observations have been seen in previous work on regioregular and/or annealed P3HT:PCBM, another non-Langevin system.⁹ As observed from Fig. 1b and 1c, the extraction time t_e (the difference in t_1/2 at high and low excitation densities) increases significantly with increasing resistance. Furthermore, the quantity of charge extracted (relative to the capacitive charge) decreases with increasing resistance: the slower timescale of extraction allows more recombination to take place. The combination of these effects leads to an overall reduction in β/β_L as the resistance is increased (Table 1); that is, the recombination behaviour appears to become even more strongly non-Langevin. At 10 kΩ, for example, the recombination coefficient is reduced by over two orders of magnitude compared to Langevin recombination, while at 50 Ω the reduction is a factor of 25. Experimentally, this decrease in β/β_L with increasing resistance is attributed to a stronger increase in extraction time that is not fully compensated for by a proportional decrease in extracted charge. In turn this produces a β that decreases from 2.4 × 10⁻¹² cm³ s⁻¹ to 6.0 × 10⁻¹³ cm³ s⁻¹ as the resistance is increased from 50 Ω to 10 kΩ. The possibilities are therefore that the β is decreasing as a function of time, t, or charge density, n.

Table 1 The results of the TOF analysis as a function of resistance

R (Ω)	t e (s)	Q e /CU0	β/βL	β (cm^3 s^−1)
50	2.3 × 10^−6	7.7	0.04	2.4 × 10^−12
1000	8.8 × 10^−6	3.8	0.02	1.2 × 10^−12
10000	3.9 × 10^−5	1.9	0.01	6.0 × 10^−13

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Independently of the origin of the decreasing β, this result is important as it indicates that the extraction timescale (resistance) is a significant parameter for TOF that should be clearly defined. In order to investigate this more thoroughly, we have utilised a time-resolved charge extraction technique that provides information on the kinetics of charge density decay over time in the device active layer. As such, β can also be determined via this method. This charge extraction technique involves photogenerating charges with a nanosecond laser pulse in a photovoltaic device held at open circuit, followed by extraction of these charges under the built-in field by switching to short circuit after an adjustable delay time. This technique is similar to that employed by Shuttle et al.,²³ except that the charge extraction technique performed here is accomplished as a function of delay time as well as light intensity. In this way we are able to establish if β decreases as a function of n (varying the light intensity) or t (varying the delay time).

The charge extraction results for KP115:PCBM solar cells are presented in Fig. 2. Integration of the extracted charge over time provides the charge density at each delay time (between the laser pulse and switch) measured. It is clear from Fig. 2 that KP115:PCBM exhibits biphasic recombination kinetics, with a fast excitation density-dependent phase from 200 ns to 20 μs and a slower power law phase until 1 ms. Such biphasic behaviour has previously been observed in TAS experiments on a number of different polymer/PCBM systems.^24,25 The slow phase has typically been assigned to bimolecular recombination of dissociated charges in the presence of an exponential distribution of localised (trapped) states. Conversely, the fast phase, which is observed most clearly at high excitation densities, is usually assigned to bimolecular recombination of free charge carriers generated when the density of photogenerated charges exceeds the density of localised states. Furthermore, non-uniform charge distribution, such as charges located at the interfaces and/or contacts, may also influence these decay dynamics.

Fig. 2 Charge density decay with time as a function of laser excitation intensity (λ_exc = 532 nm) for KP115 : PCBM (1 : 2) photovoltaic devices, with an active layer thickness of 140 nm. Inset: the charge extraction curves as a function of delay time between the laser and the switch at one excitation intensity, the integration of which provides the charge density under those conditions.

The kinetics of the fast phase can be fitted to a simple bimolecular equation:

Where n(t) is the charge density at time t, n₀ is the initial charge density, and β is the bimolecular recombination coefficient. The bimolecular recombination coefficient β acquired by this fitting technique is ∼(2.2 ± 0.2) × 10⁻¹² cm³ s⁻¹ at the highest excitation density, which is very close to the β value obtained using TOF at 50 Ω. In order to assess the n dependence of β independently of time, the kinetics at different excitation densities (and thus differing n₀) were examined. As expected for a bimolecular process, the effective bimolecular recombination lifetime (τ = 1/βn₀) decreases as the excitation density increases. Furthermore, β does change slightly with excitation density in this fast time regime, indicating a possible n dependence during this timescale, but this is difficult to examine fully as the slow power law phase begins to dominate at low excitation densities and saturation behaviour is observed at higher excitation densities. However, it is clear that β is independent of excitation density and thus n during the slow power law phase.

This slow phase, however, has previously been correlated with a time dependent bimolecular recombination coefficient in polymer:PCBM solar cells.^17,26 This was therefore examined here for KP115:PCBM using an alternative method for obtaining β: by calculating the derivative dn/dt at each delay time, assuming pure bimolecular recombination:

At early times (300 ns to 5 μs, see Fig. 3), the bimolecular recombination coefficient is independent of time, with a value of β ∼ 2.2 × 10⁻¹² cm⁻³ s⁻¹. This value is similar to that provided by the bimolecular equation fitting, as expected given that the same timescale was used, and also the TOF result at 50 Ω. At later times (from 5 μs), β shows a significant time dependence and decreases by an order of magnitude. This same behaviour in β as a function of time is observed irrespective of excitation density.

Fig. 3 The bimolecular recombination coefficient β(t) of KP115 : PCBM (1 : 2) obtained from the charge extraction results at the highest excitation density using the derivative method (eqn 3), compared to the β values (and corresponding extraction times, marked with crosses) estimated from TOF at each resistance.

These time-dependent β values estimated using charge extraction can now be compared to the resistance-dependent β values obtained using TOF; this is illustrated in Fig. 3. The observation of a resistance-dependent β is therefore a result of the timescale over which the charge is extracted in the TOF measurements, combined with biphasic bimolecular recombination decay kinetics that produces a time-dependent β. As the extraction timescale increases with R, more of the slow power law phase, which has a significantly – and increasingly – smaller β, is involved within that time period, thereby reducing the estimated β. In other words, the TOF provides an averaged β value for any given R, as it assumes only a single bimolecular recombination mechanism, rather than the more complex behaviour that is observed here. This averaged β value therefore includes both recombination phases, as has been previously noted for photo-CELIV measurements.²⁷ This is an important result, implying that TOF may be limited in its ability to accurately describe bimolecular recombination in biphasic systems such as KP115:PCBM and, potentially, P3HT:PCBM.¹⁷ This is further illustrated in Fig. 4, which shows the simulated decay curves based on the single bimolecular recombination coefficients estimated using TOF. Not only do these curves fail to replicate the biphasic decay behaviour of KP115:PCBM, but the wider time range over which the single-mechanism recombination occurs is also evident for the higher resistances.

Fig. 4 Simulated bimolecular recombination (BR) curves using the β values estimated from TOF at each resistance, compared to the measured decay in charge density over time of KP115:PCBM (1 : 2).

In conclusion, therefore, it has been observed that resistance is a vital parameter in TOF measurements that primarily affects the extraction time, giving a time-averaged bimolecular recombination coefficient. This has been exemplified by the KP115:PCBM system, which exhibits rare but highly desirable non-Langevin recombination behaviour. Furthermore, TOF may not be an appropriate technique to investigate the bimolecular recombination of polymer blend systems that exhibit biphasic decay dynamics and a time-dependent β. In this case, TOF should be used in conjunction with other charge extraction techniques to ensure a full description of the system in question is obtained.

Acknowledgements

The authors thank Russell Gaudiana and Andrew Nattestad for discussions, and Shogo Mori for providing the switch instrument. This research was supported under the Australian Research Council's Linkage and Discovery Projects funding scheme. AJM acknowledges the ARC for providing equipment support through LIEF, as well as supporting AJM and TMC with an Australian Research Fellowship and Australian Postdoctoral Fellowship Industry, respectively.

Notes and references

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