Apparent stretched-exponential luminescence decay in crystalline solids

The relaxation of different physical systems has been found to follow the stretched-exponential law, exp[-(t/τ)^β] with 0<β<1. In particular, the photoluminescence from porous silicon, nm size silicon in SiO₂, glassy materials and other solids have been reported in the literature to behave this way. It has been pointed out that the key role for this behavior is played by some kind of disorder in the system. The time constants τ reported were between 10^-12 and 10^-2s. In the present work, it is shown using numerical simulation relevant to the case of trapping controlled luminescence, that the decay from a single crystal with a single trapping state and a single kind of recombination center yields results which agree very well with the stretched-exponential function. Taking trapping parameters in the ranges known in luminescent materials for the stimulation of the decay curves yield different values of the parameter β between 0 and 1, and different values of the time constant τ, typically in the micro- to milli-second range. Thus, the stretched-exponential function has been shown to be even more ubiquitous than thought so far, being able to describe the decay of luminescence in an ordered crystal.