Room‐temperature luminescence decay of colloidal semiconductor quantum dots: Nonexponentiality revisited

Abstract

While time-resolved luminescence spectroscopy is commonly used as a quantitative tool for the analysis of the dynamics of photoexcitation in colloidal semiconductor quantum dots, the interpretation of the virtually ubiquitous nonexponential decay profiles is frequently ambiguous, because the assumption of multiple discrete exponential components with distinct lifetimes for resolving the decays is often arbitrary. Here, an interpretation of the roomtemperature luminescence decay of CdSe/ZnS semiconductor quantum dots in colloidal solutions is presented based on the Kohlrausch relaxation function. It is proposed that the decay can be understood by using the concept of Förster resonance energy transfer (FRET) assuming that the role of acceptors of photoexcitation energy is played by highfrequency anharmonic molecular vibrations in the environment of the quantum dots. The term EVFRET (ElectronicVibrational Förster Resonance Energy Transfer) is introduced in order to unequivocally refer to this energy transfer process.Since the seminal works reporting a quantum size effect in semiconductor nanocrystals in 1981 [1] and luminescence from semiconductor colloidal solutions in 1982 [2,3] colloidal semiconductor quantum dots have become the subject of intensive experimental and theoretical research due to their wide range of size-tunable properties, notably optical properties [4-6] which make them potential candidates for applications in areas such as biolabeling, bioimaging, bio-and chemo-sensing, theranostics, lasing, photovoltaic energy conversion, photodetection, and light-emitting diodes among others [7][8][9][10][11][12][13][14][15].The understanding of the principles governing luminescence in colloidal quantum dot systems is necessary in order to envisage ways of controlling their properties. At the same time, the room-temperature luminescence decays of quantum dots are typically nonexponential, [7,[16][17][18] which may lead to ambiguity in their interpretation as the assumption of multiple discrete exponential components with distinct lifetimes for resolving the decays is often arbitrary. Indeed, pre-exponential factors and decay times in nonexponential luminescence decays have clear physical meaning only in the simplest cases [19]. On the other hand, while the intrinsic exciton dynamics of CdSe colloidal semiconductor quantum dots, by far the most extensively investigated quantum dot system, is generally understood [20,21], the same cannot be said about the effects of extrinsic factors, such as capping layer or colloidal solution environment, which are expected to play a prominent role in the photophysical processes in those systems [22].The Kohlrausch or stretched exponential relaxation function, exp [−(t/τ ) β ], where 0 < β ࣘ 1 and τ has the dimensions of time, has been in use for over 150 years to describe relaxation processes in electronic and molecular systems [23], including luminescence decay in condensed matter, most remarkably by Alfred Werner in 1907 and Theodor Förster in 1949 [24]. The stretching p...

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“…Therefore, this parameter is expected to increase as ν max lowers with an increase of the NC size. In accordance with this expectation, the TOPO‐capped CdSe NCs showed an increase of α from 0.20 to 0.33 as the average NC size increased from 2.5 nm to 5.0 nm . We should note that the a values derived in the present work for aqueous AIS NCs are much higher than those reported for CdSe‐TOPO NCs even at the lowest T studied.…”

“…We found that the PL decay curves of colloidal AIS NCs detected at different temperatures can be perfectly fitted with the Kohlrausch stretched exponential function (SI, Figure S9a). As in the case of TOPO‐capped CdSe NCs we found that the parameter β varies in the range of 0.5–0.6 with the temperature changes (SI, Figure S9b) indicating the same energy transfer mechanism as discussed in Ref. [42].…”

“…It allows the average PL lifetime to be evaluated and the representative values of rate constants of radiative and non‐radiative recombination (provided the PL QY values are known) to be calculated without any assumptions on the exact emission mechanism. The second model is based on less conventional Kohlrausch‐type stretched exponential model describing the PL emission as a purely radiative process perturbed by non‐radiative energy transfer processes with the participation of the vibrational states of the surface ligands . This model appears to be less favourable for the qualitative description of the PL decay dynamics because of high error margins of the fitting parameters but its allows the contribution of the interactions between the colloidal NCs, their ligand “shell”, and the surrounding dispersive medium to the dynamics of the radiative recombination to be evaluated.…”

“…Alternatively to the well‐reported examples of fitting the PL decay curves of metal‐chalcogenide NCs with linear combinations of two or three monoexponential functions, the PL decay can be described as a purely radiative process competing with a channel of electronic energy transfer to vibrational states using a Kohlrausch‐type stretched exponential function , where τ b is a lifetime of the “bright” state (purely radiative lifetime), and α and β are constants characterizing the energy transfer mechanism and the strength of interactions between the energy donor and acceptor …”

“…In particular, this model was applied to fit the PL decay curves of a series of size‐selected CdSe NCs capped with trioctylphosphine oxide (TOPO) molecules . The authors of this report assumed that the deviation of the PL decay curves of CdSe NCs from the single‐exponential character arises from the energy transfer between the electronically excited donor (CdSe NCs) and vibrational states of acceptor (anharmonic C−H vibrations of TOPO ligands).…”