On the Differences between Dark and Light Ideality Factor in Polymer

Jul 3, 2013 - We find that both the dark and light ideality factors are sensitive to bulk recombination mechanisms at the internal donor:acceptor inte...
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Letter pubs.acs.org/JPCL

On the Differences between Dark and Light Ideality Factor in Polymer:Fullerene Solar Cells Thomas Kirchartz,*,† Florent Deledalle,‡ Pabitra Shakya Tuladhar,‡ James R. Durrant,‡ and Jenny Nelson† †

Department of Physics and Centre for Plastic Electronics and ‡Department of Chemistry and Centre for Plastic Electronic, Imperial College London, South Kensington Campus SW7 2AZ, United Kingdom S Supporting Information *

ABSTRACT: Ideality factors are derived from either the slope of the dark current/voltage curve or the light intensity dependence of the open-circuit voltage in solar cells and are often a valuable method to characterize the type of recombination. In the case of polymer:fullerene solar cells, the ideality factors derived by the two methods usually differ substantially. Here we investigate the reasons for the discrepancies by determining both ideality factors differentially as a function of voltage and by comparing them with simulations. We find that both the dark and light ideality factors are sensitive to bulk recombination mechanisms at the internal donor:acceptor interface, as is often assumed in the literature. While the interpretation of the dark ideality factor is difficult due to resistive effects, determining the light ideality factor dif ferentially indicates that the open-circuit voltage of many polymer:fullerene solar cells is limited by surface recombination, which leads to light ideality factors decreasing below one at high voltage. SECTION: Energy Conversion and Storage; Energy and Charge Transport

T

he main performance-limiting mechanism in many efficient organic bulk-heterojunction solar cells is nongeminate recombination of separated charge carriers.1−10 Thus, the understanding of the recombination mechanisms of separated charge carriers is crucial to design strategies to reduce nongeminate recombination.11−13 However, recent publications on the question of the dominant mechanism for nongeminate recombination disagree with each other.2,5,14−17 In particular, the question of whether recombination is typically affected by localized states in the band gap or rather involves the recombination of free carriers is highly debated.2,5,14−17 Part of this disagreement is due to the challenge of correctly interpreting electrical measurements to analyze the recombination mechanism. A particularly important indicator of the effect of traps on recombination is the so-called ideality factor that describes the slope of the exponential dependence of recombination rate R on voltage.18−23 As with related parameters like the order of recombination,20,24−26 there is a discrepancy between the conceptual understanding of what the ideality factor should mean and the meaning of the actually measurable ideality factor. The exponential dependence of the local recombination rate R(x) on the local splitting of the quasi-Fermi levels ΔEf(x) can be written as ⎛ ΔE (x) ⎞ f ⎟⎟ R(x) = R 0(x) exp⎜⎜ n ( ⎝ id,C x)kT ⎠

n id,C =

(2)

The conceptual ideality factor nid,C in this definition would now provide information on the local recombination mechanism at position x. If we assume for simplicity that we have as many free electrons nf as free holes pf (nf = pf ∝ exp(ΔEf(x)/2kT))) at position x, a midgap trap with equal capture cross sections for electrons and holes would be filled with a probability of nf/ (nf + pf) = 0.5 with electrons, and this occupation probability would be independent of the quasi-Fermi level splitting. Thus, recombination of say a free hole with a trapped electron scales as R(x) ∝ pf ∝ exp(ΔEf(x)/2kT) and nid,C would approach 2. In contrast, in the case of recombination of free electrons and holes the recombination rate would scale with R(x) ∝ nfpf ∝ exp(ΔEf(x)/kT) and the ideality factor would be one. More complicated trap distributions will lead to a range of ideality factors 1 < nid,C < 2.27 On first approximation, the closer the ideality factor is to 2, the closer to midgap the states that dominate recombination will be.20,27 In addition, we can argue that nid,C > 1 implies that traps are involved in recombination. The conceptual definition of the ideality factor would thus be a very useful tool that could be combined with complementary techniques to analyze recombination and traps. However, neither the local recombination rate nor the local quasi-Fermi level splitting are easily accessible quantities; therefore, the definition in eq 2 is never used in practice. Instead, the ideality

(1)

where R0(x) is the equilibrium recombination rate, kT is the thermal energy, and nid,C we will call the conceptual ideality factor. Thus, this ideality factor is calculated via © XXXX American Chemical Society

1 d ΔEf kT d ln(R )

Received: June 11, 2013 Accepted: July 3, 2013

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factor is defined using easily measurable analogues for recombination rate and quasi-Fermi level splitting. The most common method to determine an experimental ideality factor, which is an approximation but not necessarily identical to the conceptual ideality factor, is to use the dark current/voltage (J/V) curve. The dark current Jd replaces the recombination rate in eq 2, and the external voltage Ve is taken to represent the local quasi-Fermi level splitting ΔEf(x). Thus, the ideality factor nid,d from the dark J/V curve is defined as

n id,d =

q dVe kT d ln(Jd )

(3)

where q is the elementary charge. The definition in eq 3 has the advantage that the dark current−voltage curve is typically measured routinely anyway. The disadvantage is that the series and parallel resistances influence the dependence of Jd on V and therefore make it difficult to attribute changes in the measured ideality factor to changes in shunt or series resistance on one hand and recombination on the other hand. In addition to the external series resistance of the contacts, the finite mobilities in the active layer of the organic solar cell will cause the quasiFermi level splitting ΔEf(x) to be a strong function of position x within the active layer, which will have a similar influence on the current/voltage curve and the ideality factor nid,d as the external series resistance. An alternative way to determine the ideality factor is to use the light intensity and voltage Voc at open circuit instead of the current and the external voltage in the dark. At open circuit, the integrated generation and recombination rates must be identical to ensure zero net current flow. Because the generation rate is proportional to the light intensity ϕ, a useful definition for the ideality factor nid,l under illumination is n id,l =

q dVoc kT d ln(ϕ)

Figure 1. Ideality factors as a function of voltage of (a) a P3HT:PC61BM solar cell and (b) a DPP-TT-T:PC71BM solar cell. The solid lines are the ideality factors nid,d derived from the dark current/voltage curve and the symbols are the ideality factors nid,l from a light-intensity-dependent measurement of the open-circuit voltage. Especially in case b there are substantial differences between the light and the dark ideality factor.

dark ideality factor nid,d > 1 in all materials including P3HT:PC61BM. We present a series of experimental data comparing the light and dark ideality factor measured on the same device over a range of materials. Unlike in previous studies,14,17,28 we measure the light-intensity-dependent Voc with a sufficient number of closely spaced data points, so we are able to calculate the nid,l as a function of open-circuit voltage. This enables us to compare the voltage dependence of light and dark ideality factors, which allows us to explain the differences between them. In addition, we use drift-diffusion simulations to understand the effects of variations in thickness, built-in voltage, mobility, and shunt resistance on light and dark ideality factors. Figure 1b shows a typical case that can be frequently encountered when comparing light and dark ideality factors of polymer:fullerene solar cells. The polymer used is (poly[[2,5bis(2-octyldodecyl)-2,3,5,6-tetrahydro-3,6-dioxopyrrolo[3,4-c]pyrrole-1,4-diyl]-alt-[[2,2′-(2,5-thiophene)bis-thieno[3,2-b]thiophen]-5,5′-diyl]]) (DPP-TT-T),29 and the device has an active layer thickness of around 100 nm and a power conversion efficiency of 6.5%. The dark ideality factor is proportional to the inverse slope of ln(dark current) versus voltage. Thus, only in the voltage range where the exponential increase in current density is dominant is the dark ideality factor. In the voltage range where shunt or series resistance dominates, the ideality factor increases dramatically relative to the value in the exponential voltage region. We see from Figure 1b that the shunt and series resistance dominates the ideality factor in the whole voltage region with the exception of the minimum of the nid,d at around 0.55 V. Here it is unclear whether the ideality factor is already saturated to the value given by the quasi-Fermi level dependence of the recombination current or whether nid,d is still dominated by shunt and series resistance. The light ideality factor is slightly lower than

(4)

While nid,l is still affected by parallel resistances, it is measured at open circuit; therefore, the voltage drop over the series resistance is zero and allows a better analysis of the recombination mechanism at higher voltages. In practice, the difference between nid,l and nid,d in organic solar cells has been measured14 to be often drastic, leading to completely different conclusions when interpreted in terms of the influence of traps on recombination. Figure 1a shows the voltage-dependent light and dark ideality factors of a poly(3hexylthiophene) (P3HT):1-(3-methoxycarbonyl)propyl-1-phenyl-[6,6]-methano fullerene (PC61BM) solar cell with an active layer thickness of 150 nm. While the light ideality factor is reasonably constant and has a value of around nid,l = 1.6, the dark ideality factor increases strongly with voltage due to the influence of the series resistance. As shown in Figure 1a, the light and dark ideality factors are similar and substantially higher than 1, indicating that localized states in the interfacial band gap participate in the recombination process. This is consistent with other reports in literature that present similar findings of nid,l > 1 on P3HT:PC61BM solar cells.14,17 However, it has to be mentioned that there is also one report28 about P3HT:PC61BM devices with a light ideality factor nid,l = 1 indicating that the ideality factor may be influenced by processing or thickness variations. Most reports14,17,28 on other polymer:fullerene blends, however, present evidence of nid,l ≈ 1 (or equivalently for the fact that Voc scales with kT/q ln(ϕ)), while usually the 2372

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consistent. While there would be a trend in the dark ideality factor if only the minimum of the curves was taken for comparison, from the voltage dependent data, it becomes apparent that the changes in ideality factor are most likely due to the trends in shunt and series resistances. The thicker the cell, the higher the shunt resistance and the lower its influence. Thus, for voltages below the minimum of nid,d, the thinnest cell has the highest apparent nid,d. The contrary is true for higher voltages. Here the thicker cells have a higher series resistance caused by majority carrier transport in the active layer. Thus, the thickest cell is most affected by the series resistance and has the highest apparent nid,d for voltages above the minimum of nid,d. Because the effect of the series resistance in this example is slightly stronger, it creates an apparent trend of min(nid,d) increasing with thickness that is most likely unrelated to any changes in recombination dynamics. To test whether our explanation of the data so far is plausible, we performed drift-diffusion simulations as explained in refs 20 and 25. The drift-diffusion simulations are performed with the software ASA,30 which solves the Poisson equation as well as the continuity equations for electrons and holes and allows for Shockley−Read−Hall recombination via distributions of localized states. In addition, the model allows for surface recombination of electrons at the anode and holes at the cathode and for external circuit elements like shunt and series resistances. The results of these simulations for the PCDTBT:PCBM thickness series are shown in Figure 2b. While we have to change the parallel resistance manually as a function of thickness to reproduce the data, the general trend for higher voltages is reproduced without having to assume a thickness-dependent series resistance. Instead, we can neglect all external series resistances and just change the thickness of our active layer. For the thicker active layers, the internal series resistance due to charge transport in the active layer leads to similar shifts in the dark ideality factor, as are observed in the experiment. A remarkable feature of both the experiment in Figure 2a and the simulation in Figure 2b is the fact that the light ideality factor falls considerably below unity at higher voltages. This effect can again be explained by surface recombination at the electrodes31−36 in the limit when Voc approaches the built-in voltage Vbi.26 In this case, the minority carrier concentrations at the contacts continue to increase with illumination, but the voltage cannot increase anymore because the selectivity of the device has nearly or completely vanished at Vbi.37 Around V = Vbi there is no concentration or electric field gradient left that forces additional electrons to be extracted at the cathode rather than at the anode and vice versa for holes. Thus, the opencircuit voltage does not increase anymore at higher light intensities, leading to a light ideality factor that drops below one. Figure 3a provides further evidence that the lower-than-one ideality factors are caused by surface recombination at the electrodes. Light and dark ideality factors of two PCDTBT:PC71BM solar cells are shown that differ from each other by the choice of cathode. In the case of the Ca/Al cathode, the built-in voltage is expected to be higher relative to the Al cathode due to the lower workfunction of Ca relative to Al. In both cases, the light ideality factors are steeply decreasing below one but are shifted relative to each other on the voltage axis. The higher Vbi of the device with Ca/Al cathode leads to the higher V o c , indicating that the V o c of these PCDTBT:PC71BM solar cells is limited by the electrodes at

the dark ideality factor at equal voltage but then decreases drastically toward higher voltages and even decreasing slightly below one around V = 0.62 V. The depiction of the dark and light ideality factors as a function of voltage here allows us to come to a substantially different conclusion than a single value for the fit of light and dark ideality factor would provide. If the light ideality factor was determined by a simple fit to the data (thereby averaging over the whole voltage range), then a value nid,l ≈ 1.08 would be obtained (see Supporting Information), and from the dark ideality factor a value nid,d ≈ 1.35. This has usually been interpreted in terms of free to free recombination for nid,l ≈ 1 and recombination via traps, for instance, in exponential band tails for nid,d ≈ 1.35. The voltage-dependent depiction of the ideality factors shows that the ideality factors at V ≈ 0.55 V are not too dissimilar, while at higher voltages, the dark ideality factor is limited by the series resistance. The light ideality factor is linearly decreasing, which hints at a transition between two recombination mechanisms. While at lower voltages, either the shunt or some trap-assisted recombination leads to nid,l > 1; at higher voltages, a recombination mechanism with a steeper voltage dependence takes over. In this particular example, it is unclear what this mechanism is. It could indeed be nongeminate recombination of free charges or alternatively recombination at the electrodes.20 Figure 2a shows light and dark ideality factors of Poly[N-9″hepta-decanyl-2,7-carbazole-alt-5,5-(4′,7′-di-2-thienyl-2′,1′,3′-

Figure 2. Comparison of (a) measured light and dark ideality factors of three PCDTBT:PC71BM solar cells with different thicknesses and (b) the corresponding simulations. Because thicker cells usually have higher shunt and series resistances, the dark ideality factor is directly affected in shape and magnitude at a given voltage. The light ideality factor is hardly affected by this, but it decreases below one at high forward bias both in experiment and simulation. This effect is due to surface recombination in the simulation and likely also in the experiment. The cathode is made from LiF (10 nm) and Al (150 nm).

benzothiadiazole)] (PCDTBT):PC71BM solar cells with different active layer thicknesses. Again, in the voltage range where the light ideality factor can be determined the dark ideality factor is limited by the series resistance of the device. Thus, taking into account a transition between different recombination mechanisms, the light and dark ideality factor seem to be 2373

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Figure 3. Comparison of (a) experimental and (b) simulated light and dark ideality factors for PCDTBT:PC71BM solar cells with two different cathodes. In one case (circles), the cathode is made from 25 nm Ca and 150 nm Al, while in the other case (squares) the Ca is missing. The Ca layer leads to a higher built-in voltage that causes a reduction of surface recombination at the cathode and therefore an increased open-circuit voltage. The active layer thickness is around 80 nm for both devices.

Figure 4. Effect of changing the slope of the exponential density of states (assumed to be the same for the conduction and valence band tail) on the ideality factors in an idealized case (perfect contacts, no external series, and parallel resistances) and in a case where the same contacts and resistances are assumed as in Figure 3b. While in the idealized case, the ideality factor basically depends only on the tail slope and agrees well between light and dark; in the more realistic case, the influence of the tail slope is obvious and substantial but very difficult to quantify and discriminate from other effects.

high light intensities. Although the light ideality factor is around one on average over the whole voltage range, it is considerably above one for low voltages and considerably below one for high voltages. Thus, the light ideality factor is still consistent with trap-assisted recombination, playing an important role in these devices, as suggested by Street et al.5 and Beiley et al.38 To study whether any information about the recombination mechanism in the bulk of the device could be still derived from the data, we performed some additional simulations where we changed the energetic distribution of trap states and studied whether that would have an impact on the simulated ideality factors. First, we modified the traps for the case of perfect contacts and negligible influence of external circuit elements like shunt and series resistances. In this case, we obtain the dark and light ideality factors shown in Figure 4a for two different slopes of the exponential tail. We note that the ideality factors are now only weakly voltage-dependent. The biggest voltage dependence can be seen in the dark ideality factor that is still affected by the finite mobility in the active layer. However, the absence of a shunt makes the data flatten out for low voltages. The light ideality factors are nearly constant, as expected in the absence of shunt effects and surface recombination effects. For both tail slopes, the light and dark ideality factors are reasonably similar, and the tail slope itself remains the main factor that controls the value. The analytical approximations20,25−27 (nid,tails = 2/(1 + kT/Ech)) for the ideality factor expected for the two tail slopes are indicated as thin dashed lines and fit well to the simulated light ideality factor. If we compare this idealized situation with the case where contacts and external circuit elements are assumed to have the values used to fit the real device with the Ca/Al contact, we see in Figure 4b that a change in tail slope will still have a major impact on the ideality factors, especially on the dark ideality factor. However because of their voltage dependence and the

influence of resistances and surface recombination, it is impossible to quantitatively analyze the data in terms of a density of trap states. We therefore conclude that a correct interpretation of ideality factors is only possible if the voltage dependence of light and dark ideality factors is taken into account and ideally if the obtained values are compared with information obtained from alternative measurements. Light ideality factors determined by fitting a straight line to a Voc versus ln(ϕ) plot may appear to be around one and are still consistent with trapassisted recombination being dominant because the fitting will average over different recombination mechanisms. At the same time, ideality factors much larger than one in the dark are no proof of trap-assisted recombination but can be caused by resistive effects. If, however, the light ideality factor is determined differentially as a function of open-circuit voltage, then more detailed conclusions can be drawn. In particular, we concluded from the voltage dependence of the ideality factor that PCDTBT:PC71BM solar cells made in our lab are limited by trap-assisted recombination at lower voltages and surface recombination at higher voltages. Studying the intensity dependence of the open-circuit voltage might be an easy way to detect situations, where surface recombination affects the achievable open-circuit voltage and therefore identifies the cases where electrode optimization would be beneficial.

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EXPERIMENTAL DETAILS The preparation of the devices is as follows: We make devices with the layer stack ITO/PEDOT:PSS/PCDTBT:PC71BM/X/ Al with X being nothing, LiF, or Ca. The active layers of these solar cells were prepared using a solution of 1:2%w in chloroform at a concentration of 13 mg/mL and left overnight under dark/stirring conditions. The solution was then 2374

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deposited using spin coating on plasma-treated ITO on 1 cm2 glass substrate. The thickness series was obtained by spin coating the solution at 3000, 2000, and 500 rpm, which resulted in active layers 65, 85, and 158 nm thick, respectively, assuming 30 nm of PEDOT:PSS. For the thickness series, the cathode was prepared by vacuum deposition of LiF (10 nm) and Al (150 nm). The PCDTBT Ca/Al series was made by spin coating a similar solution with a total concentration of 15 mg/ mL at 3000 rpm, resulting in thickness of around 80 nm. The cathode was prepared by vacuum deposition of either Ca (25 nm) and Al (150 nm) or just Al (150 nm) In the same manner, ITO/PEDOT:PSS/DPP-TT-T:PC71BM/Ca/Al was prepared using the same protocol, with a solution of DPP-TT-T:PC71BM in 1:2 wt % blend ratio in a binary solvent (chloroform:dichlorobenzene in 4:1) with a final concentration of 15 mg/mL. The thickness of the active layer resulting from spin-casting the solution was estimated to be around 100 nm. Prior to electrode vacuum deposition the device was thermally annealed at 120° C for 10 min. The measurement of the open-circuit voltage at different light intensities was conducted using an array of focusing 12 cool white 1W LEDs (Lumileds Luxeon III/start O). The illumination equivalent to 1 sun is found when matching the Jsc and Voc recorded beforehand under an AM1.5 solar simulator. A Si photodiode is used to measure the relative light intensity. The switch from open-circuit to short-circuit conditions is ensured using a fast switching MOSFET. Then, the electrical input power of the LEDs is tuned by a GPIB-controlled power supply to recreate illuminations ranging from a few fractions of percent of a sun to 5 to 6 suns. The device during this measurement is held under nitrogen in a sample chamber. During the whole scan for different light levels, one data point is taken in typically >100 ms to allow reaching steady-state conditions, while the whole scan is done in