A unified description of current-voltage characteristics in organic and hybrid photovoltaics under low light intensity

We develop a simple model that can explain the current-voltage ( J- V) curves of excitonic photovoltaic solar cells, spanning polymer:polymer, polymer:fullerene, and polymer:nanocrystal devices. We show that by subtracting out the dark current, we can explain apparent intensity-dependent characteristics and thus identify geminate recombination as the dominant loss mechanism and establish its electric field dependence. We present an analytic fit to the J- V curves of all measured devices based on a single fitted parameter, the electric field required to split 50% of geminate charge pairs, which we term the critical field. Devices of different material combinations and morphologies can all be described by this method and yield critical fields varying between >1 x 10(8) V/m for blends of poly(9,9'-dioctylfluorene- co-bis- N, N'-(4-butylphenyl)-bis- N, N'-phenyl-1,4-phenylenediamine) (PFB) and poly(9,9'-dioctylfluorene- co-benzothiadiazole) (F8BT) and 8 x 10 (5) V/m for slow-grown blends of poly(3-hexylthiophene-2,5-diyl) (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM). A comparison with material properties reveals that the primary route to improved photovoltaic materials is enhanced charge delocalization.