Title: Understanding Quasi-random Nanostructures of the Bulkheterojunctions(BHJ) in Organic Solar Cell Active Layers with Spectral Density Function (SDF)

Bulkheterojunctions in organic photovoltaic solar cell (OPVC) active layers are believed to be determining the performance of the OPVCs. The domain features measured in the active layer exhibits quasi-random nanostructures. Though it is believed that the quasi-random nanostructures in the BHJ play a decisive role on determining the performance, it is unclear how to quantify this quasi-random nanostructures into a quantity that could be used to guide the synthesis. In this work, we will present mathematical description of SDF for two dimensional images followed by a simplified fitting equation for general SDF analysis. The simplified fitting equation will extract the information of domain sizes (average and deviation), and domain distances (average and deviation). Validation of this equation is tested by simulated model data. After testing with the simulated data, this equation is applied to two dimensional cross-sectional scanning tunneling microscopy and spectroscopy (XSTM/S) data and small angle X-ray diffraction data measured on the active layer made of poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl C61 butyric acid methyl ester (PCBM). It will be argued that this method could be applied to various types of data exhibit similar two-domain quasi-random features.