Date of Award

2014

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Applied Mathematics

First Advisor

Charles L. Epstein

Abstract

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.

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