A PDE-based Method for Optimizing Solar Cell Performance

In this paper, we address the optimal design problem for organic solar cells (OSC). In particular, our focus is to enhance short-curcuit photocurrent by optimizing the donor-acceptor interface. To that end, we propose two drift-diffusion models for organic solar cells, both of which account for the physics of OSC's that charge carriers are mostly generated in the region near the donor-acceptor interface. For the first drift-diffusion model, the generation of charge carriers is translated into a boundary condition across the donor-acceptor interface. We apply the theory of shape optimization to compute the shape gradient functional of the photocurrent. In particular, shape differential calculus is extensively applied in the computation. For the second drfit-diffusion model, we parameterize the donor-acceptor interface as a leve set of a function, i.e. the "phase field function". The dependence of the second drift-diffusion model on the geometry is therefore transformed into its dependence on the phase field function. Such transformation greatly simplifies the sensitivity analysis and leads to an easy-to-implement numerical optimization algorithm. In numerical examples, it is shown that the maximum output power of the optimized solar cell can be increased by a factor of 3. Our analysis and examples in this paper are in two dimensions, but the generelization of both the analysis and numerical optimization to three dimensions is straightforward.