### Abstract

We present a statistical analysis of time-resolved spontaneous emission decay curves from ensembles of
emitters, such as semiconductor quantum dots, with the aim of interpreting ubiquitous non-single-exponential
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 non-single-exponential 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 well-known emission quantum efficiency
can no longer be expressed by a single number, but is also distributed. We derive a practical description of
non-single-exponential 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 log-normal distribution of decay rates with a
narrow and a broad distribution, respectively. Finally, we briefly discuss the Kohlrausch stretched-exponential
model, and find that its normalization is ill defined for emitters with a realistic quantum efficiency of less than
100%.

Original language | English |
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Journal | Physical Review B Condensed Matter |

Volume | 75 |

Issue number | 3 |

Pages (from-to) | 035329 |

ISSN | 0163-1829 |

DOIs | |

Publication status | Published - 2007 |

### Bibliographical note

Copyright 2007 American Physical Society### Keywords

- RELAXATION
- PHOTONIC CRYSTALS
- RECOVERY
- MAXIMUM-ENTROPY
- STATE
- TRANSIENT ABSORPTION
- EFFICIENCY
- DYNAMICS
- FLUORESCENCE LIFETIMES
- UNDERLYING DISTRIBUTIONS

## Cite this

Van Driel, A. F., Nikolaev, I. S., Vergeer, P., Lodahl, P., Vanmaelkelbergh, D., & Vos, W. L. (2007). Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: Interpretation of exponential decay models.

*Physical Review B Condensed Matter*,*75*(3), 035329. https://doi.org/10.1103/PhysRevB.75.035329