On the choice of proper average lifetime formula for an ensemble of emitters showing non-single exponential photoluminescence decay

Abstract

In this paper, we investigate non-single exponential photoluminescence decays in various disordered condensed-matter systems. For such materials, two formulas for the average lifetime of system’s excited state are commonly used in the analysis of experimental data. In many cases, the choice of formula is arbitrary and lacks a clear physical justification. For this reason, our main goal is to show that the choice of correct mathematical formula should be based on the interpretation of measured photoluminescence decay curve. It is shown that depending on the investigated system, after appropriate normalization, photoluminescence decay curve can represent either a survival probability function or a probability density function of lifetime and for this reason two different formulas for the average lifetime are required. It is also shown that, depending on luminescence quantum yield, some information on the probability density function of lifetime can be lost in the process of measurement, which results in underestimated values of average lifetime. Finally, we provide an interpretation of total decay rate distributions which are frequently obtained by phenomenological modeling of non-single exponential photoluminescence decays.

Electron Transfer Going the Distance: Mn-Doped ZnSe as a Model Photocatalytic System

“…In contrast, the doped Mn:ZnSe nanocrystals exhibit a dramatically longer excited lifetime that is typical of similar Mn-doped nanocrystalline systems. ,, A time-resolved PL decay measurement out to a millisecond time delay on a linear scale appears in Figure S3 for reference. The time-resolved PL decay trace was fitted over this time range using a stretched exponential (Kohlrausch–Williams–Watts) function (black), which is commonly used to model NCs with non-single exponential PL decays − and doped NCs . The form of the stretched exponential function permits calculation of an average time constant ⟨τ⟩ from the time constant τ 0 and the stretching exponent β according to the expression , The best fit of the time-resolved PL decay trace of the doped Mn:ZnSe nanocrystals in chloroform revealed an average time constant of 270 ± 20 μs.…”

Site Occupancies, Electron–Vibration Interaction and Energy Transfer of CaMgSi2O6: Eu2+, Mn2+ Phosphors for Potential Temperature‐Sensing and Anti‐counterfeiting Applications

“…Here, we chose Equation ( 5) as an appropriate formula to calculate the average lifetime according to ref. [37]. Where I(0) Chemistry-A European Journal and I(t) represent the initial intensity and that at time t, respectively.…”

Optical Stability of Thick‐Shell CdSe@ZnS/ZnS Quantum Dots Dissolved in n‐Octane in Wide Range of Mass Concentration: Photoluminescence Decay Study

“…As shown in our previous paper, this equation correctly describes the average lifetime of excited state for an ensemble of emitters showing non-exponential decays due to distribution of radiative lifetimes. [23] Moreover, it is well known that doubleexponential fits can be sensitive to different numerical factors, and for this reason, accurate determination of small changes of τ 1 and τ 2 is often difficult. From this perspective, the average lifetime is a more reliable quantity as its value depends only on the general shape of the PL decay curve.…”