Determining the Internal Quantum Efficiency of PbSe Nanocrystal Solar Cells with the Aid of an Optical Model

We determine the internal quantum efficiency (IQE) of the active layer of PbSe nanocrystal (NC) back-contact Schottky solar cells by combining external quantum efficiency (EQE) and total reflectance measurements with an optical model of the device stack. The model is parametrized with the complex index of refraction of each layer in the stack as calculated from ellipsometry data. Good agreement between the experimental and modeled reflectance spectra permits a quantitative estimate of the fraction of incident light absorbed by the NC films at each wavelength, thereby yielding well-constrained QE spectra for photons absorbed only by the NCs. Using a series of devices fabricated from 5.1 +/- 0.4 nm diameter PbSe NCs, we show that thin NC cells achieve an EQE and an active layer IQE as high as 60 +/- 5% and 80 +/- 7%, respectively, while the QE of devices with NC layers thicker than about 150 nm falls, particularly in the blue, because of progressively greater light absorption in the field-free region of the films and enhanced recombination overall. Our results demonstrate that interference effects must be taken into account in order to calculate accurate optical generation profiles and IQE spectra for these thin film solar cells. The mixed modeling/experimental approach described here is a rigorous and powerful way to determine if multiple exciton generation (MEG) photocurrent is collected by devices with EQE < 100%. On the basis of the magnitudes and shapes of the IQE spectra, we conclude that the 1,2-ethanedithiol treated NC devices studied here do not produce appreciable MEG photocurrent.