4.6
A complete MUPPETS data set on an excitonic system has been analyzed for the first time. Accomplishing this analysis required progress in several directions. The first was systematizing the treatment of complex data. MUPPETS data is inherently complex, and complex transient-grating data was collected to assist in the analysis. An external standard was used to determine the absolute phase of the absorbances. Expressions for both transient-grating and MUPPETS data in terms of practical parameters allowed systematic fitting of the complex data and transfer of parameters between the two
experiments. Assumptions that the solute absorbance is real or that all transitions have the same phase or magnitude were avoided and clearly do not apply to this system.
A second direction was making a detailed comparison of 2D and 1D data. Along the τ1 = 0 cut, the MUPPETS data should be almost entirely determined by quantities measurable by 1D methods. Using the heterodyned transient-grating data, the MUPPETS results, including its time-dependent phase, were explained. The only adjustable
parameter was the ratio of ground-to-exciton and exciton-to-biexciton absorption cross- sections. The fit value is exactly what is expected from an uncorrelated-electron model, which is widely used for CdSe nanoparticles.43 Overall, this fit verifies the theory and execution of the MUPPETS experiment and shows that the simple spectroscopic model used here captures all relevant species and transitions.
The complex τ1 = 0 data provide a more rigorous test of the conclusions of our earlier letter.22 We confirmed the original conclusion that the biexciton decay is highly disperse. This finding challenges existing theories for the biexciton decay and the standard methods of extracting biexciton decays from fluence-induced experiments. Biexciton decay has been explained by extending the theory of Auger recombination in bulk semiconductors to nanoparticles.43, 52, 54, 69 This theory predicts a single exponential decay, in contrast to the dispersed decay found here. Previously, dispersed decays were attributed solely to the involvement of higher excitons. In fact, the assumption of exponential decay has been used to decompose such data into components due to different numbers of excitons.52, 54 Photoproducts have also been implicated as mimicking biexciton decay.44, 62 The concerted analysis of fluence-induced transient- grating and MUPPETS data has shown that the observed dispersion is not due to higher
excitons or photoproducts, but rather is inherent to the biexciton decay. This finding joins several recent challenges to the existing theory of decay by Auger recombination.56- 58 The ability of the surface to modify the biexciton decay has been documented and may
provide a route to resolving the current discrepancies.59, 107
Reference 66 showed that MUPPETS in excitonic systems should involve a cross- relaxation term (Figure 4.2B) in addition to pure exciton and biexciton dynamics. This paper showed that it is experimentally feasible to gather sufficient information to
calculate these terms and included them in a quantitative analysis. In the current system, these terms are quite small.
Going beyond the τ1 = 0 cut provided information on dispersion in the exciton decay and correlations between the exciton and biexciton decays. The extent of nonradiative decay is large: 40% within 2 ns was observed directly, and 64% was extrapolated from fitting. The nonradiative component is highly dispersed; it fits a stretched exponential with β = 0.3. Similar results have been seen by others.55, 64, 94, 102 The most obvious interpretation is that the surface passivation is still incomplete. Thus, the decay should be heterogeneous due to particle-to-particle variation in the number and activity of the remaining passivation defects. Surprisingly, the MUPPETS measurements contradict this explanation. They find a homogeneous relaxation, that is, one driven by a relaxation initiated by the creation of the exciton.
Given this conclusion, we can speculate about the mechanism. There are various charged species at the surface of the particle: lattice defects, charged surfactants, and counterions. Thermal fluctuations in the properties of nanoparticles seen in single-
polarizable.50, 63, 72 The exciton is also more polarizable than the ground state. Upon excitation, the exciton and surface should relax to a mutually polarized state. The Stokes shift of the exciton is small, so the resulting change in transition energies must be small.43 However, the polarized exciton would also have a reduced electron–hole overlap, which would reduce the absorption cross-section. Thus, surface polarization would cause a loss of signal, but not population decay. Both a large signal decay and a high quantum yield would occur. This mechanism provides at least one physically plausible explanation for the MUPPETS result.
The biexciton decay was found to have substantial dispersion, but to be uncorrelated with the exciton decay. The fact that the biexciton decay is much faster than the exciton already suggests a different decay process, so the lack of correlation is not surprising. Current ideas about biexciton decay are focused on Auger recombination, but with an influence from the surface.59, 107 Thus, the dispersion in the biexciton could reflect surface heterogeneity. The MUPPETS experiments discussed here do not directly comment on the heterogeneity of the biexciton decay. (The possibility of addressing this question is discussed in chapter 5.79) However, a homogeneous exciton relaxation and a heterogeneous biexciton decay would be consistent with the lack of correlation found by MUPPETS.
Overall, the data in this paper have shown the features of MUPPETS in excitonic systems that were predicted in ref 66. Chapter 5 of this paper79 will discuss potential interferences that are encountered in real experiments, but that go beyond the basic theory of MUPPETS, as developed in ref 66 and used here. It will confirm that the conclusions of this paper are sound, even when these effects are considered.