Estimation of parameters in a distributed parameter model for thin film layered organic photovoltaic cells

We develop a stochastic finite element based scheme for constructing a likelihood function for the Bayesian estimation of parameters in a distributed parameter model for thin film layered organic photovoltaic cells. The scheme is based on a distributed parameter model for the propagation of the optical wave through the various layers of the cell and its conversion to an electrical current in the active layers of the device. The model consists of three components: a frequency domain wave equation based propagation model for the optical wave through the various transparent and active layers, a diffusion equation describing the dynamics of exciton density in the active layers of the device, and an output equation that describes the external quantum efficiency (EQE) of the cell. There are two parameters in the diffusion equation that have to be estimated based on measurements of EQE: the exciton diffusion length and half-life or lifetime. In this paper, a stochastic finite element based scheme that yields a probability density function (pdf) for EQE as a function of the uncertainty in exciton diffusion length and lifetime are developed. The ultimate goal is to use this pdf to construct a likelihood function as part of a Bayesian estimation scheme for the exciton diffusion length and half-life.. Numerical results involving data from an actual device are presented and discussed.