Methods based on the measurement of impedance or admittance of an organic solar cell are widely used to understand electronic properties such as charge carrier lifetime, mobility, and charge carrier density. Here, I will first briefly review the different methods and then explain the challenges in understanding and interpreting these methods. The first approach is based on measuring the real and imaginary part of the impedance and analyzing the data by fitting equivalent circuit models to the data. This approach usually leads to characteristic time-constants that are affected by recombination but do not directly provide the actual charge carrier lifetimes because of the position dependence of the charge carrier density. A second approach is based on the determination of the charge-carrier density from an integration of the chemical capacitance.¹ In this case, the key challenge is to isolate the chemical capacitance of the active layer (that can be used to estimate the carrier concentration in the active layer) from the capacitance of the electrodes. One way of achieving this is to compare high and low frequency capacitances and to assume that the high frequency capacitance is due to the electrode and the additional capacitance at lower frequencies is due to the active layer. This approach has the advantage of providing a charge carrier density over the whole voltage range from reverse bias to forward bias.² However, the approach is not able to correctly take into account the voltage dependence of the electrode capacitance that is affected by charge redistribution in the active layer itself. A possible solution is to compare the capacitance under illumination vs. the capacitance in the dark and analyze the difference. This gives a rather precise estimate of the charge carrier density at low forward and reverse bias and thereby allows us to determine recombination parameters at these voltages. An obvious disadvantage is however that it doesn’t work at larger forward bias, where charge injection becomes substantial.³ Finally, we explain how the photogenerated excess capacitance at reverse bias can also be used to determine the charge carrier mobility.⁴

References

   (1)    Brus, V. V.; Proctor, C. M.; Ran, N. A.; Nguyen, T. Q. Capacitance Spectroscopy for Quantifying Recombination Losses in Nonfullerene Small-Molecule Bulk Heterojunction Solar Cells. Adv. Energy Mater. 2016, 6, 1502250.

   (2)    Heiber, M. C.; Okubo, T.; Ko, S. J.; Luginbuhl, B. R.; Ran, N. A.; Wang, M.; Wang, H.; Uddin, M. A.; Woo, H. Y.; Bazan, G. C. et al. Measuring the Competition Between Bimolecular Charge Recombination and Charge Transport in Organic Solar Cells Under Operating Conditions. Energ. Environ. Sci. 2018, 11, 3019-3032.

   (3)    Zonno, I.; Zayani, H.; Grzeslo, M.; Krogmeier, B.; Kirchartz, T. Extracting Recombination Parameters From Impedance Measurements on Organic Solar Cells. Phys. Rev. Applied 2019, 11, 054024.

   (4)    Zonno, I.; Martinez-Otero, A.; Hebig, J. C.; Kirchartz, T. Understanding Mott-Schottky Measurements Under Illumination in Organic Bulk Heterojunction Solar Cells. Phys. Rev. Applied 2017, 7, 034018.