Scaling of current-voltage characteristics of bulk heterojunction solar cells

The transport in the mixture of p-type and n-type materials of a bulk heterojunction solar cell is modeled as an effective discretized resistor and diode network. Within this model the current and potential profile is solved using a relaxation method for systems of 100,000 sites. Both an ordered structure, where the p-type and n-type materials form pillars, and a random mixture are considered. Motivated by an analytic approximate solution for the ordered case, scaling relations are developed, where the current-voltage (I-V) characteristics for all sample thicknesses for a given sample composition collapse onto a single curve. The thickness dependence of the I-V characteristics including the optimal thickness for power output is governed by a new length scale which depends on the conductivities of the p- and n-regions and the derivative of the diode I-V characteristic used for transport between regions.