Accounting for Interference, Scattering, and Electrode Absorption to Make Accurate Internal Quantum Efficiency Measurements in Organic and Other Thin Solar Cells

In solar cells, internal quantum effi ciency (IQE) is the ratio of the number of charge carriers extracted from the cell to the number of photons absorbed in the active layer. Because IQE measurements normalize the current generation effi ciency by the light absorption effi ciency, they separate electronic properties from optical properties and provide useful information about the electrical properties of cells that external quantum effi ciency measurements alone cannot. The magnitude of the IQE is inversely related to the amount of recombination that is occurring in the cell, while the spectral shape of the curve can provide information about the effi ciency of harvesting excitons in the cell or spatial dependence of charge recombination. [ 1 , 2 ] Effects like multiple exciton generation [ 3‐5 ] and singlet exciton fi ssion [ 6 ] as well as bias-dependent photoconductivity [ 7 ] can lead to interesting spectral shapes and be detected by measuring IQEs greater than 100%. Despite its usefulness as a characterization tool, IQE is rarely reported. When IQE is reported, absorption is frequently not measured in actual devices; this can lead to errors since refl ective electrodes induce strong interference effects that substantially affect absorption. When absorption is measured in actual devices, parasitic absorptions are almost never taken into account. We hope that by demonstrating a straightforward method of measuring IQE, it will become a standard measurement and the community may benefi t from a better understanding of how the best performing cells work. Organic photovoltaics (OPVs) and other ultra-thin solar cells [ 8‐11 ] are made as a stack of materials including an active semiconducting layer, electrodes, and in some cases modifi er layers such as charge blocking layers and optical spacers. [ 12‐15 ] The active layer is responsible for all charge generation in the cell. Typically 5‐10% of the incident light is absorbed in the electrodes. In many solar cells, the IQE should not vary with wavelength. Since parasitic absorption does vary with wavelength, one must account for it to observe the correct spectral shape. [ 1 ] Consequently in the general case, it is critically important to take this parasitic absorption into account when calculating internal quantum effi ciency. Determining the active layer’s contribution to the total absorption can be a challenge, as it generally requires optical modeling to relate the experimentally measurable total absorption to the absorption in each layer. The absorption of each layer cannot independently be measured because, due to interference effects, the optical density of the stack is not simply the sum of the optical densities of each layer. The most accurate commonly used model uses a transfer matrix formalism to calculate the interference of coherent refl ected and transmitted waves at each interface in the stack. [ 16 , 17 ] This calculation requires knowledge of the wavelengthdependent complex index of refraction of each material. The imaginary part, k , is related to the extinction coeffi cient and is responsible for absorption in a medium. The real part, n , determines the wavelength of light of a given energy in a material and is important for calculating where areas of constructive and destructive interference occur. Typically the optical constants are measured using variable angle spectroscopic ellipsometry (VASE). [ 18‐22 ] The data produced by this technique when measuring anisotropic organic materials are diffi cult to interpret and require complicated modeling not available to many research groups. In blended donor-acceptor fi lms, the optical properties depend strongly on morphology and therefore on processing conditions. Thus fi lms of different thicknesses, cast from different solvents, or dried for different amounts of time have different optical constants. [ 23 , 24 ] In such composite materials, morphology is also a function of depth due to vertical phase segregation. [ 24 , 25 ] In these cases the optical constants are spatially dependent and the data gathered by these methods are approximations themselves. It is not always feasible to use VASE to measure n and k for each fi lm, so a simpler method of determining active layer absorption is desirable. In this article we show that for typical OPVs, precise knowledge of the real part of the complex index of refraction of the active layer is not required for making the measurements of the active layer absorption necessary for calculating IQE. We have investigated several methods to calculate the active layer absorption using published values of the optical constants. [ 18‐22 ] We propose a method that minimizes error by using an optical model to calculate the parasitic absorption (the absorption by the layers that do not contribute to photocurrent) and subtracting this from the experimentally measured total absorption.