Estimation of exciton diffusion lengths of organic semiconductors in random domains

TL;DR

This paper introduces an efficient asymptotic-based method to estimate exciton diffusion lengths in organic semiconductors, accounting for surface measurement uncertainties, and demonstrates significant computational advantages over traditional stochastic methods.

Contribution

The paper develops a novel asymptotic approximation for stochastic boundary problems, reducing computational cost and improving robustness in exciton diffusion length estimation.

Findings

The asymptotic method is over ten times faster than stochastic collocation.

Surface randomness significantly affects diffusion length estimates.

Correlation length influences the validity of reduced models.

Abstract

Exciton diffusion length plays a vital role in the function of opto-electronic devices. Oftentimes, the domain occupied by an organic semiconductor is subject to surface measurement error. In many experiments, photoluminescence over the domain is measured and used as the observation data to estimate this length parameter in an inverse manner based on the least square method. However, the result is sometimes found to be sensitive to the surface geometry of the domain. In this paper, we employ a random function representation for the uncertain surface of the domain. After non-dimensionalization, the forward model becomes 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 whose accuracy is justified both theoretically and numerically. It only requires solving several deterministic problems over a fixed domain. Therefore, 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 boundary-value problem by the stochastic collocation method. In addition, 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.