Understanding the Apparent Charge Density Dependence of Mobility and Lifetime in Organic Bulk Heterojunction Solar Cells

Energetic disorder in organic semiconductors leads to strong dependence of recombination kinetics and mobility on charge density. However, observed mobilities and reaction orders are normally interpreted assuming uniform charge carrier distributions. In this paper, we explore the effect of the spatial distribution of charge on the determination of mobility and recombination rate as a function of average charge density. Since the spatial gradient changes when the thickness of a device is varied, we study thickness series of two different polymer:fullerene systems and measure the charge density dependence of mobility and lifetime. Using simulations, we can show that the high apparent reaction orders frequently observed in the literature result from the spatial gradient of charge density at open circuit. However, the mobilities, measured at short circuit, are less affected by the gradients and therefore may show substantially different apparent charge density dependence than the recombination constants, especially for small device thicknesses.