Proceedings of 6th International Conference on Hybrid and Organic Photovoltaics (HOPV14)
Publication date: 1st March 2014
Highly efficient polymer:fullerene solar cells have internal quantum efficiencies approaching 100%, which sometimes leads to the dangerous conclusion that charge carrier collection is efficient in these kind of devices. In reality high internal quantum efficiencies are achieved by using sufficiently thin absorber layers that minimize non-geminate recombination at least at short circuit. This implies that substantial losses in absorption are the price paid for low mobility-lifetime products [1]. In order to minimize non-geminate recombination, it is crucial to be able to interpret measurements of non-geminate recombination and to determine which type of recombination is dominant. We compare two frequently used ways of identifying the dominant recombination mechanism, namely the ideality factor [2] and the reaction order [3] and show what issues arise with the interpretation of these values.
The ideality factor is derived either from the slope of the dark current/voltage curve or from the slope of the open-circuit voltage as a function of light intensity. Therefore, it is relatively easy to measure but unfortunately in organic solar cells also challenging to explain. We explain the different reasons why the ideality factor measured in the two different situations discussed before (dark JV-curve and open-circuit voltage vs. light intensity) deviate from each other by calculating the differential ideality as a function of voltage. This allows us to better understand apparent inconsistencies between light and dark ideality factor discussed in the literature and to draw more detailed conclusions from the ideality factor. In particular, we show by experiment and simulation that differential ideality factors below unity are possible and indicative of recombination of charge carriers at the opposite electrode (electrons at the anode and holes at the cathode).
The reaction order is related to the ideality factor and defines the carrier concentration dependence of the recombination rate. Within the framework of multiple trapping models, the reaction order should provide information about e.g. the influence of traps on the recombination rate. In experiment, reaction orders that are substantially higher than 2 have often been observed. Here we discuss why these cannot be understood with simple rate equation models of recombination at one spatial position. Instead, high reaction orders can be explained by the large charge concentration gradient in devices with low absorber thicknesses (< 100 nm) or high unintentional doping concentrations [4]. Thus, reaction orders are prone to misinterpretation and the ideality factor should be the preferred way of analyzing recombination mechanisms.
Comparison of light and dark ideality factors of two PCDTBT:PCBM solar cells with different electrodes. (a) shows experimental data and (b) shows the simulation of that data assuming different workfunctions of the contact. At high voltages, the ideality factor derived from the light intensity dependent Voc decreases below one indicating surface recombination at the cathode is limiting the open circuit voltage.
[1] Kirchartz, T.; Agostinelli, T.; Campoy-Quiles, M.; Gong, W.; Nelson, J. Understanding the Thickness-Dependent Performance of Organic Bulk Heterojunction Solar Cells: The Influence of Mobility, Lifetime, and Space Charge, J. Phys. Chem. Lett. 2012, 3, 3470 - 3475 [2] Kirchartz, T.; Deledalle, F.; Tuladhar, P. S.; Durrant, J. R.; Nelson, J. On the Differences between Dark and Light Ideality Factor in Polymer:Fullerene Solar Cells. J. Phys. Chem. Lett. 2013, 4, 2371 - 2376 [3] Kirchartz, T.; Nelson, J. Meaning of reaction orders in polymer:fullerene solar cells. Phys. Rev. B 2012, 86, 165201 [4] Deledalle, F.; Tuladhar, P. S.; Nelson, J.; Durrant, J. R.; Kirchartz, T. Understanding the apparent charge density dependence of mobility and lifetime in organic bulk heterojunction solar cells. to be submitted
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