Simultaneous determination of carrier lifetime and electron density-of-states in P3HT:PCBM organic solar cells under illumination by impedance spectroscopy

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Abstract

We report new insights into recombination kinetics in poly(3-hexylthiophene):methanofullerene (P3HT:PCBM) bulk heterojunction (BHJ) solar cells, based on simultaneous determination of the density of states (DOS), internal recombination resistance, and carrier lifetime, at different steady states, by impedance spectroscopy. A set of measurements at open circuit under illumination was performed aiming to better understand the limitations to the photovoltage, which in this class of solar cells remains far below the theoretical limit which is the difference between the LUMO level of PCBM and the HOMO of P3HT (∼1.1 eV). Recombination kinetics follows a bimolecular law, being the recombination time (lifetime) inversely proportional to the density of photogenerated charges and the recombination coefficient γ=6×10−13 cm3 s−1. We find that the open-circuit photovoltage is governed by the carrier ability of occupying the DOS, which results in Gaussian shape and spreads in energy σ≈125–140 meV. The energy position of the Gaussian DOS center (EL=0.75–0.80 eV), which corresponds to half occupation of the electron DOS, approximates LUMO(PCBM)–HOMO(P3HT) difference. But the recombination rate is strongly enhanced at high illumination levels, what produces the photogenerated charge to remain in the tail of the DOS. Consequently, the electron and hole Fermi levels are unable to reach the center of the DOS, then substantially limiting the photovoltage. Detailed theoretical analysis of the lifetime dependence on photovoltage is provided.

Introduction

Bulk heterojunctions (BHJ) formed by an interpenetrating blend of an optically active polymer and electron accepting molecules constitute a very promising route towards cheap and versatile solar cells [1], [2], as recently demonstrated in progress of automated roll-to-roll processing and solar-cell stability [3], [4]. The photovoltaic performance of the combination of poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl C61-butyric acid methyl ester (PCBM) in organic blends has recently increased rapidly, approaching 6% energy-conversion efficiency [5], and 6.1% efficiency was achieved using poly[N-9”-hepta-decanyl-2,7-carbazole-alt-5,5-(4’,7’-di-2-thienyl-2’,1’,3’-benzothiadiazole) (PCDTBT) and fullerene derivative [6,6]-phenyl C70-butyric acid methyl ester (PC70BM) blends [2]. Further improvements of BHJs based on rational design of materials and interfaces require characterization methods that provide elementary electronic parameters in the working conditions of the solar cell. In particular it is very important to ascertain (i) factors affecting open-circuit photovoltage Voc [6], [7], and closely related to this, (ii) the mechanism governing recombination kinetics of photogenerated charge.

Impedance Spectroscopy (IS) has provided enormous success for the determination of energetic and kinetic factors governing the operation of dye-sensitized solar cells (DSC) [8], [9]. While IS measurement is quite straightforward, interpretation of the results requires an appropriate conceptual framework adapted to the specific features of a kind of devices. IS is a small perturbation method that resolves the capacitances and resistances in the system at a particular steady state. For solar-cell characterization, the most significant range of steady-state conditions is between open-circuit voltage (Voc) and short circuit under illumination. Close to zero bias voltage, the operation of reasonably efficient solar cells (with a high collection efficiency [2]) is usually determined by charge generation. On another hand, in the maximum power point and close to Voc, recombination kinetics plays a major role in the current density/potential (JV) curve, and hence on the device efficiency [10]. Therefore a quantitative interpretation and modeling of the IS results in this bias region provides essential information on device characteristics.

In the case of DSCs, determination of electron lifetimes by IS at voltages close to Voc has been validated with independent methods of measurement, such as open-circuit voltage decay [9], [11], [12]. In inorganic solar cells, it is possible to apply contactless methods to determine minority carrier lifetime [13], and IS results are in agreement with these methods too [14], [15]. The convergence of different experimental methods provides great confidence on the significance of the results obtained by IS. We report in this paper for the first time the application of IS to determine simultaneously the charging characteristics (capacitance) and recombination kinetics of BHJ solar cells in working conditions, under illumination. The results show that energy disorder in the electron and hole conducting materials plays a major role to determine detailed features of carrier lifetime, and models appropriate to interpret the experimental results are derived below.

Several techniques have been applied to extract recombination time [16] (lifetimes) in BHJ devices, including modulated photoinduced absorption [17], transient absorption [18] photo-CELIV [19], [20], double-injection currents [21], and time-of-flight methods [22]. However many of these methods do not operate in open-circuit conditions under continuous irradiation what makes it difficult to relate them to the cell operation. Recently, two papers have determined the capacitance and lifetime by small-amplitude perturbation of a steady state, using transient photovoltage [23] and impedance spectroscopy [24]. In these works, it was observed that when the Fermi level of electrons, EFn, increases, then (i) the lifetime decreases and (ii) the capacitance increases [23], [24]. These results indicate that it is possible to separate in BHJs the carrier density and kinetic terms in the time constant for recombination, provided that the chemical capacitance [25], Cμ, can be measured, which provides access to the density-of-states (DOS) of the electron transporting phase [26], [27]. However, in Ref. [23] capacitance and lifetime are measured in different conditions, and in Ref. [24] only the dark values have been estimated, and the capacitance was found to decrease at strong forward bias. In the present work, the capacitance and recombination resistance of a state-of-art P3HT:PCBM BHJ device, with 3.1% energy conversion efficiency, are simultaneously monitored under illumination as a function of Voc.

These results allow us to address important questions concerning BHJ operation. First, in contrast to Ref. [23] we obtain that the lifetime is inversely proportional to steady-state carrier density, which indicates that recombination probability is proportional to both electron and hole concentration. In addition, based on thermodynamic principles, the open-circuit voltage is directly related to the separation between EFn, and the Fermi level of holes in the P3HT, EFp[28]-qVoc=EFn-EFpbeing q the elementary charge. One upper limit to Voc in this kind of devices is the difference of energies between the donor highest occupied molecular orbital, EHOMO, and the acceptor lowest unoccupied molecular orbital, ELUMO. Since at these energy levels the density of states is very high and no further split of Fermi levels is possible, we should obtain VocEg/q, where Eg=EHOMOELUMO, which can be interpreted as the effective (electrical) band gap of the blend. However, such limit is not reached in practice, instead a linear correlation between Voc and the Eg/q is obtained, with an average shift of ∼0.3 V [29].

Since molecular orbitals in disordered media spread in energy, the shape of the DOS corresponding to electronic levels should play a significant role in establishing Voc values. In fact EFnEFp difference must be governed both by the shape of the DOS around the effective EHOMO and ELUMO values, and by the extent of filling of available states which is established by the recombination rate. Therefore, we conclude in this paper that both issues, the Voc origin and charge-carrier recombination are closely related: the DOS occupancy (carrier density) is limited by recombination losses at high (∼1 sun) illumination levels, which in turn establishes the reachable Voc value.

Section snippets

Experimental

Solar cells of structure ITO/PEDOT:PSS/P3HT:PCBM/LiF/Al were built following the procedure explained elsewhere [30]. The thickness of the P3HT:PCBM blend layers was approximately equal to 115 nm. The impedance measurements, both in the dark and under illumination up to simulated air mass 1.5 global (AM1.5 G) conditions, were carried out in an electrically shielded box, that was integrated in an inert atmosphere (<0.1 ppm O2 and H2O) glovebox. The impedance measurements were performed with an

Results and discussion

The impedance results at different illumination intensities are shown in Fig. 1. As mentioned before, the applied bias voltage compensates the effect of the photovoltage so that effectively the cell is measured at open-circuit conditions, i.e., photocurrent is cancelled by the recombination flow and jdc=0. The spectra are characterized by a major RC arc plus additional minor features at high frequency. The high-frequency part of the spectra may contain information of transport and series

Conclusion

To conclude, we have shown in this study how impedance spectroscopy is able to reliably determine recombination kinetics and charge–carrier density in organic photovoltaic devices under conditions of continuous irradiation. Recombination rate is enhanced at high illumination levels, and this is viewed as the limiting mechanism for the photogenerated charge accumulation, which finally states the reachable Voc value.

Acknowledgements

We are very grateful to Dr. Martijn Lenes for helpful discussions, Dr. Alejandra Soriano for device preparation and characterization, Dr. Antoni Munar for his collaboration in experimental set-up and Jorge Ferrando for his assistance with the design in the temperature control of the measurement cell. We thank financial support from Ministerio de Ciencia e Innovación under projects HOPE CSD2007-00007, CSD2007-00010, MAT2006-28187-E, Generalitat Valenciana project PROMETEO/2009/058, Universitat

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