Lifetime determination of materials that exhibit a stretched exponential luminescent decay

We report frequency- and time-domain luminescent lifetime measurements for materials that exhibit a broad spectrum of lifetimes, specifically, those for which the observed decay dynamics can be described by a stretched exponential function. The spectrum of lifetimes of such materials can be characterized by an average lifetime, and in principle this average can be extracted from either time- or frequency-domain measurements. In practice, this requires some care, because the extent to which the various states are excited depends on how long their lifetime is relative to the excitation pulse width or period. For the complex luminescent materials ZnS:Cu,Al and CdS quantum dots we compare the average lifetime obtained from frequency-domain data and from time-domain data under both pulsed laser excitation and steady-state, dc excitation. The agreement between the average measured lifetimes is good, but not perfect, showing that quoted average lifetimes for complex materials can be dependent on the measurement technique. Finally, a spectrum of lifetimes is given that gives rise to stretched exponential relaxation and this spectrum is used to compute frequency-domain data for a stretched exponential material.