Probability density function of the rate of energy transfer from luminescent ions to a random distribution of traps in the static limit

Abstract

The transfer of excitation of luminescent ions to a random distribution of traps is revisited in the static limit, with the emphasis on the probability density function (PDF) of the decay rate. Knowledge of the PDF is advantageous for situations when the time evolution of an individual ion’s excited state differs from an exponential decay or when no closed-form solution for the ensemble average exists, because it allows one to reconstruct an ensemble average from the knowledge of the behavior of a single class of ions. A model with dipole-dipole interactions with no minimum distance leads, in the continuum limit, to an inverse gamma (IG) PDF with shape parameter α=1/2, which has infinite moments. With a minimum nearest trap distance, closed-form solutions of the moments of the actual PDF are well matched with those of a smoothly truncated IG distribution.