Quantifying charge carrier density in organic solar cells by differential charging techniques

Ion-induced electron emission reduction via complex surface ABSTRACT Accurate determination of charge carrier density in organic solar cells under light irradiation is essential because charge carrier density is directly related to the bimolecular recombination rate and open-circuit voltage of the cells. We investigate the robustness of transient photovoltage/current (TPV/C) and impedance spectroscopy (IS) to interference from the geometric capacitance of the cells ( C geo ) during quantification of the charge carrier density. TPV/C and IS accurately quantify the charge carrier density of bulk heterojunction cells with small C geo . For planar heterojunction cells with a larger C geo contribution, IS fails to separate the charge carriers in the organic layer from those in the electrodes. In contrast, TPV/C eliminates the effect of C geo and gives a reasonable estimation of the charge carrier density in the organic layer with the planar heterojunction, demonstrating that TPV/C is more robust than IS to interference from C geo of the cells. Power conversion efficiency of organic solar cells (OSCs) has been improved up to 16%, 1 mainly driven by the development of new organic semiconductor materials. Although the short-circuit current density ( SC this we examine the suitability of TPV/C and IS techniques for evaluating the charge carrier density in with bulk heterojunction and planar heterojunction structures. differences between BHJs and PHJs are the donor/acceptor (D/A) interface area the film thickness. BHJs a larger D/A interface area larger film thickness small C geo contribution to the apparent charge, PHJs larger C separate evaluations reliability of

Power conversion efficiency of organic solar cells (OSCs) has been improved up to 16%, 1 mainly driven by the development of new organic semiconductor materials. Although the short-circuit current density (J SC ) and fill factor (FF) 2,3 of OSCs are now comparable with those of inorganic and perovskite solar cells, 4 the opencircuit voltage (V OC ) of OSCs could be improved. The electronic energy levels of the materials should be tuned appropriately 5 to increase V OC while maintaining a sufficient energy difference for efficient charge generation. 6,7 Furthermore, suppressing bimolecular recombination produces a higher charge carrier density under light irradiation, increasing V OC . 8,9 The bimolecular recombination depends on the square of the charge carrier density; however, in contrast to inorganic solar cells, the recombination rates in OSCs are much lower than those expected from the Langevin recombination model. 10,11 This discrepancy has been explained by the involvement of the interfacial charge transfer state, 12 but the details of the recombination mechanism in OSCs are still unclear. Therefore, to relate the interfacial structures to the recombination kinetics of the charge carriers in OSCs, it is vital to obtain accurate information about the charge carrier density in the organic layers.
Charge extraction (CEX) is widely used to evaluate the charge carrier density. [13][14][15] In this technique, OSCs are initially kept under open-circuit conditions with steady light irradiation, and then, short-circuit conditions are rapidly applied (within ∼100 ns) while simultaneously turning off the light. The integration of the transient current over time gives the electric charges stored in both the organic layer and the electrodes. In OSCs, there is a thin (approximately 100 nm) organic layer between two electrodes, resulting in a large geometric capacitance (Cgeo). Consequently, many charge carriers are stored in the electrodes, which makes quantifying the charge carriers in the organic layer by CEX difficult in some cases. [16][17][18] Instead of counting all the charge carriers by CEX, differential charging techniques, such as transient photovoltage/current (TPV/C) and impedance spectroscopy (IS), can quantify the charge carrier density indirectly by using the differential capacitance (C diff ). 13,19 C diff is the voltage-dependent capacitance, defined as the ratio between small changes in the charge and voltage (ΔQ/ΔV), and it is measured by applying a small charge density perturbation to the cell. The integration of C diff from 0 V to V OC gives the number of total charge carriers in OSCs under irradiation. Differential charging methods have the advantage that they can evaluate the number of charge carriers in the organic layer separately from those stored in the electrodes. OSCs have been analyzed by TPV/C and IS; however, the accuracy and the robustness to the cell geometric capacitance of these methods for determining the charge carrier density in OSCs need careful assessment.

ARTICLE scitation.org/journal/adv
In this study, we examine the suitability of TPV/C and IS techniques for evaluating the charge carrier density in OSCs with bulk heterojunction (BHJ) and planar heterojunction (PHJ) structures. The major differences between BHJs and PHJs are the donor/acceptor (D/A) interface area and the film thickness. BHJs have a larger D/A interface area and larger film thickness and thus have a small Cgeo contribution to the apparent charge, whereas PHJs have a larger Cgeo contribution. We discuss separate evaluations of the charge carriers stored in the organic layer and the electrodes, and the reliability of the experimentally obtained charge carrier density. Figure 1(a) shows the molecular structures of poly(3hexylthiophene) (P3HT) and [6,6]-phenyl-C 61 -butyric acid methyl ester (PC 61 BM) used as the donor and the acceptor, respectively. We prepared the PHJ by transferring a P3HT film onto a PC 61 BM film by using the contact film transfer method. 20,21 The BHJ was prepared as a randomly mixed thin film by spin-coating a mixed solution of P3HT and PC 61 BM (1:1 by weight). The electrodes were polyethylenimine ethoxylated (PEIE)-modified ITO and MoOx/Ag. The film thicknesses of the BHJ and PHJ were 183 and 45 nm, respectively.
The average photovoltaic performances under AM1.5 100 mW/cm 2 simulated sunlight irradiation were J SC , V OC , FF, and PCE of 1.0 mA/cm 2 , 0.50 V, 0.56, and 0.28%, respectively, for the PHJ and 9.6 mA/cm 2 , 0.61 V, 0.72, and 4.2%, respectively, for the BHJ. The limited D/A interface area of PHJs resulted in a J SC one order of magnitude lower than that of BHJs. Figure S1 shows the current density-voltage characteristics.
TPV/C measurements were performed under steady light irradiation with a white light-emitting diode (LED) and neutral-density filters to tune the light intensity. Irradiation with a 0.4 ns pulsed laser with a wavelength of 520 nm perturbed the charge density in the devices under open-circuit and short-circuit conditions for the transient photovoltage and photocurrent, respectively. IS measurements were performed using the same LED. An external DC voltage equal to V OC was applied to the sample during the measurement to keep the sample under nearly open-circuit conditions with superimposing a 5.0 mV AC voltage. We analyzed the impedance response by equivalent circuit fitting and extracted the values of the resistive and capacitive components. Details of the materials, device fabrication, and measurements are given in the supplementary material. Figure 2 shows the results of the TPV/C and IS measurements for the P3HT:PC 61 BM BHJ device. The equivalent circuit used for IS analysis 22,23 is shown in the inset of Fig. 2(c), where Rs is the series resistance of the electrodes, R bulk is the resistance of the organic layer, Cgeo is the geometric capacitance, and Cμ and Rrec are the chemical capacitance 24 and the recombination resistance at the D/A interface, respectively. 25,26 Figure S2 shows the fitting results of the impedance response. Figure 2(a) shows the capacitance values measured by TPV/C and IS plotted against V OC . V OC depended on the background white light intensity. We calculated the differential capacitance, C diff , in TPV/C technique by where ΔQ is the amount of charge generated by a single pulsed laser shot in the TPV/C measurement, evaluated by the integral of the transient photocurrent signal over time. 14,19 ΔV OC is the maximum perturbation of V OC by the single pulsed laser shot, which was below 10 mV. C diff of TPV/C should include both chemical capacitance Cμ and geometric capacitance Cgeo. IS can evaluate these capacitances separately if their time constants are different enough. C diff in TPV/C and Cμ in IS depend exponentially on V OC , whereas Cgeo is almost constant [solid lines in Fig. 2(a)]. As expected for BHJs, Cgeo was smaller than Cμ due to the large D/A interface area and thick film thickness.
We calculated charge carrier density n by integrating the capacitance over voltage from 0 V to V OC , where q is the elemental charge, A is the electrode area, and d is the film thickness. The integration of Cμ over V OC is the charge carrier density in the device. For TPV/C, the number of charges stored in the electrodes was subtracted, where C diff (0) is the differential capacitance at 0 V, which represents the geometrical capacitance. 27 Thus, C diff (0) × V OC is the amount of charge stored in the electrodes. Figure 2(b) shows the calculated charge carrier densities. TPV/C and IS gave similar charge densities, in agreement with previously reported values. 8,28 The difference in charge carrier density measured by two these methods was less than 20% within the experimental range of the irradiation intensity.
We also evaluated the small-perturbation lifetime (τ Δn ) of charge carriers at the D/A interface by using TPV/C 11,19 and IS 29 [ Fig. 2(c)]. The TPV/C measurement provides τ Δn as the singleexponential decay rate of small perturbed V OC , In the IS measurements, the time constant of the D/A interfacial component, Cμ × Rrec, is defined as τ Δn . This is because the single exponential decay in the time domain in TPV/C is equivalent in Fourier transformation to the impedance response of the RC parallel circuit in the frequency domain in IS. τ Δn of BHJ cells evaluated by TPV/C and IS matched well as previously reported, 30,31 indicating the high reliability of these measurements [ Fig. 2(c)]. The difference in τ Δn determined by TPV/C and IS was about 20%.
For the P3HT:PC 61 BM BHJ solar cell, TPV/C and IS provided similar charge carrier densities and lifetimes. The small differences may originate from the error in the equivalent circuit fitting of IS, which is improved as difference increases between the time constants of the components from the bulk and the D/A interface in the frequency domain. Because the charge carrier density and lifetime are typically measured over several orders of magnitude and plotted on a logarithmic scale, the difference of about 20% is acceptable for discussing the recombination.
The same experimental and analytical procedures were applied to the P3HT/PC 61 BM PHJ, and the results are shown in Fig. 3. The differential capacitance of the PHJ depended weakly on voltage  Fig. 3(a)]. For the TPV/C data, however, C diff was fitted with an exponential curve, as for the BHJ, and the contribution of chemical capacitance in the cell was derived from the differential capacitance. In contrast, Cμ in IS did not show the expected exponential dependence on voltage. The unexpected behavior of Cμ in IS may arise from the comparable Cμ and Cgeo in the PHJ, which makes the separation of these components in the frequency domain difficult owing to the similar time constants. We observed only one semicircle in the Cole-Cole plot, indicating that the impedance response was dominated by one RC component (Fig. S3). Cgeo calculated by IS was similar to C diff (0) of TPV/C, indicating that the dominant impedance response was from the geometric capacitance. Therefore, we did not obtain an accurate value for the charge carrier density in the organic layer by IS. Consequently, the calculated charge carrier density [ Fig. 3(b)] and small perturbation lifetime [ Fig. 3(c)] evaluated by TPV/C and IS did not match.
We also evaluated the charge carrier density by CEX, in which all the charge carriers stored at the electrodes and D/A interface were directly counted via the integral of the transient current over time. The amount of collected charge in the CEX measurements depended linearly on the voltage for the PHJ [ Fig. S4(a)], whereas it depended exponentially on the voltage for the BHJ [ Fig. S4(b)]. The linear voltage dependence in the PHJ implies that most of the collected charge came from the electrodes (geometric capacitance contribution), not from the D/A interface.
The dependence of the small-perturbation lifetime on charge carrier density differed between the BHJ and the PHJ (Fig. S5). The reaction order of the recombination in the BHJ was estimated as 2.8 using the slope parameter of the τ Δn -n plot 11 [ Fig. S5(a)], whereas the PHJ showed a steeper slope with a reaction order of 6.5. The slope parameter of the PHJ in the n-V OC plot was bigger than that of the BHJ, meaning that in the PHJ, a smaller change in the charge carrier density caused a large change in V OC [ Fig. S5(b)]. This is because of the inhomogeneous charge carrier distribution in PHJs; 32,33 the local charge carrier density at the D/A interface determines V OC rather than the averaged (integrated) charge carrier density we experimentally measured. 34 Therefore, for more detailed analysis of the recombination kinetics, we need not only the charge carrier density but also the charge carrier density distribution. A numerical simulation based on the experimental density of states of the donor and acceptor materials 35 may be an excellent tool for obtaining information about the charge carrier distribution in devices.
In summary, when the geometric capacitance contribution was large, only TPV/C was able to estimate the charge carrier density in the cell, implying that the differential charging used in TPV/C is more robust than IS for quantifying the charge carrier density. The accurate estimation of the charge carrier density, lifetime, and distribution in PHJ structures with well-defined interfaces will contribute to revealing the link between the D/A interfacial structure and charge carrier recombination kinetics. Once guidelines are established for an ideal D/A structure that suppresses the recombination without decreasing charge carrier generation, the structure will improve the performance of OSCs.
See the supplementary material for the experimental setup procedure and supplementary material figures.