Estimation of exciton diffusion lengths of organic semiconductors in random domains

Exciton diffusion length plays a vital role in the function of opto-electronic devices. In many experiments, photoluminescence in a regular domain is measured as the observation data to estimate this length parameter in an inverse manner. However, the domain occupied by the organic semiconductor is often subject to surface measurement error. The result is sometimes sensitive to the surface geometry of the domain and the estimations based on 1D or 2D models are found to be inconsistent due to the uncertainty in the domain boundary. In this paper, we employ a random function representation to address this uncertainty. Our forward model is a diffusion-type equation over the domain whose geometric boundary is subject to small random perturbations. We propose an asymptotic-based method as an approximate forward solver which only needs to solve several deterministic problems over a fixed domain. For the same accuracy requirements we tested here, the running time of our approach is more than one order of magnitude smaller than that of directly solving the original stochastic problem by the stochastic collocation method. From numerical results, we find that the correlation length of randomness is important to determine whether a 1D reduced model is a good surrogate for the 2D model. This discovery suggests that for some materials where both small molecules and polymers can form crystal structures, exciton diffusion can be well described by the 1D model, but for other organic materials with low crystalline order, the reduced 1D model is not sufficiently accurate for diffusion length estimation.