Thickness Dependence of Current and Power in Bulk Heterojunction Solar Cells

We model the the transport in the mixture of p-type and n-type materials of a bulk heterojunction solar cell as a discretized resistor and diode network. Each external electrode only allows one type of carrier to flow, either electrons or holes. Within this simplified model we can solve for the current and potential profile 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, we develop a scaling where the IV 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 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.