Influence of injected charge carriers on photocurrents in polymer solar cells

Abstract

We determine and analyze the photocurrent ${J}_{\mathrm{ph}}$ in polymer solar cells under conditions where, no, one, or two different charge carriers can be injected by choosing appropriate electrodes and compare the experimental results to simulations based on a drift-diffusion device model that accounts for photogeneration and Langevin recombination of electrons and holes. We demonstrate that accounting for the series resistance of the device is essential to determine ${J}_{\mathrm{ph}}$. Without such correction, the results are, even qualitatively, incorrect. We show that in solar cells with forward bias applied ${J}_{\mathrm{ph}}$ is reduced by recombination of photogenerated charge carriers with injected charge carriers. Self-selective contacts or band bending are not necessary to explain the effects. Without injecting contacts ${J}_{\mathrm{ph}}$ is symmetric around the compensation voltage. A simple analytical model shows that under high forward bias ${J}_{\mathrm{ph}}$ scales inversely with 1 $+$ $\ensuremath{\xi}{\ensuremath{\gamma}}_{\mathrm{pre}}$, in which ${\ensuremath{\gamma}}_{\mathrm{pre}}$ represents the extent of Langevin recombination and \ensuremath{\xi} is a positive constant. Under conditions where Langevin recombination is very low or when electron and hole mobility are a very different, photogenerated charge carriers can affect the space-charge field and modify the injection of charge carriers. We show by simulations and experimentally that under such conditions the photocurrent can exceed that charge generation such that, effectively, photocurrent multiplication occurs.