2007
Statistical analysis of timeresolved emission from ensembles of semiconductor quantum dots: interpretation of exponential decay models
Publication
Publication
Phys. Rev. B , Volume 75  Issue Article number: 35329 p. 1 8
We present a statistical analysis of timeresolved spontaneous emission decay curves from ensembles of emitters, such as semiconductor quantum dots, with the aim of interpreting ubiquitous nonsingleexponential decay. Contrary to what is widely assumed, the density of excited emitters and the intensity in an emission decay curve are not proportional, but the density is a time integral of the intensity. The integral relation is crucial to correctly interpret nonsingleexponential decay. We derive the proper normalization for both a discrete and a continuous distribution of rates, where every decay component is multiplied by its radiative decay rate. A central result of our paper is the derivation of the emission decay curve when both radiative and nonradiative decays are independently distributed. In this case, the wellknown emission quantum efficiency can no longer be expressed by a single number, but is also distributed. We derive a practical description of nonsingleexponential emission decay curves in terms of a single distribution of decay rates; the resulting distribution is identified as the distribution of total decay rates weighted with the radiative rates. We apply our analysis to recent examples of colloidal quantum dot emission in suspensions and in photonic crystals, and we find that this important class of emitters is well described by a lognormal distribution of decay rates with a narrow and a broad distribution, respectively. Finally, we briefly discuss the Kohlrausch stretchedexponential model, and find that its normalization is ill defined for emitters with a realistic quantum efficiency of less than 100%.
Additional Metadata  

dx.doi.org/10.1103/physrevb.75.035329  
Phys. Rev. B  
van Driel, A. F, Nikolaev, I. S, Vergeer, P, Lodahl, P, Vanmaekelbergh, Daniël A, & Vos, W.L. (2007). Statistical analysis of timeresolved emission from ensembles of semiconductor quantum dots: interpretation of exponential decay models. Phys. Rev. B, 75(Article number: 35329), 1–8. doi:10.1103/physrevb.75.035329
