Modeling Nongeminate Recombination in P3HT:PCBM Solar Cells

By introducing tail states into a continuum drift diffusion model, we are able to self-consistently reproduce the experimental voltage-dependent carrier concentration, the current voltage curve, and the nongerninate recombination prefactor as measured by transient photovoltage (TPV) measurements of poly-3-hexylthiophene:phenyl-C61-butyric acid methyl ester (P3HT:PCBM). A mobility edge is introduced into the density of states (DoS) for both electrons and holes thus separating each population into mobile and trapped carriers. The effective mobility for each charge type is calculated from the ratio of free to trapped carriers within the DoS and is thus carrier density dependent. By introducing this effective mobility into Langevin's formula for charge recombination, we are able to reproduce the experimentally observed quasi-third-order recombination rates. Furthermore, we evaluate three possible DoS shapes, a pure Gaussian, a Gaussian with an exponential superimposed, and a pure exponential. It is found that an exponential DoS is essential to reproduce the experimental data.