Diffusion and relaxation of energy in disordered organic and inorganic materials

In this paper we examine the following problem: Given a band of localized states randomly distributed in space and obeying a distribution function for energies, how does an excitation diffuse as a function of time and initial energy? This question is encountered in luminescence, photoconductivity, and transport work in organic and inorganic semiconductors and in novel quantum-well structures. We also allow random processes which do not conserve excitation number (radiative and nonradiative recombination). We present analytic solutions and exact Monte Carlo simulations and discuss the validity of approximation procedures focusing in this paper on Gaussian energy distributions appropriate to organic materials.