Diffusion of excitons in systems with non-planar geometry: theory

Hypothetical experiments are described in which excitons diffuse in systems that exhibit cylindrical or spherical symmetry. A line source of excitation will be assumed at the axis of the cylinder, and a point source at the center of the sphere. Diffusion equations that are appropriate for these geometries are set up and solved in closed form for the boundary conditions of complete quenching of excitons or complete reflection of excitons. Steady state and transient conditions are treated. Based upon assumed values of the diffusion lengths, plots are constructed of the spatial distribution of excitons. For a wide range of assumed values of the diffusion lengths, these values can be recovered from an analysis of the resultant diffusion currents and their absorption coefficient dependence to within a few percent. (C) 2002 Elsevier Science B.V. All rights reserved.