  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.
