Modeling distributed kinetics in isolated semiconductor quantum dots

Abstract

A detailed modeling of recently observed nonexponential fluorescence intermittency in colloidal semiconductor quantum dots (QDs) is presented. In particular, experiments have shown that both ``on''-time and ``off''-time probability densities generated from single-QD fluorescence trajectories follow an inverse power law, $P({\ensuremath{\tau}}_{\mathrm{o}\mathrm{n}/\mathrm{o}\mathrm{f}\mathrm{f}})\ensuremath{\propto}1/{\ensuremath{\tau}}_{\mathrm{o}\mathrm{n}/\mathrm{o}\mathrm{f}\mathrm{f}}^{1+\ensuremath{\alpha}},$ over multiple decades in time, where the exponent $1+\ensuremath{\alpha}$ can, in general, differ for ``on'' versus ``off'' episodes. Several models are considered and tested against their ability to predict inverse power law behavior in both $P({\ensuremath{\tau}}_{\mathrm{on}})$ and $P({\ensuremath{\tau}}_{\mathrm{off}}).$ A physical picture involving electron tunneling to, and return from, traps located several nanometers away from the QD is found to be consistent with the observed $P({\ensuremath{\tau}}_{\mathrm{off}})$ but does not yield the inverse power-law behavior seen in $P({\ensuremath{\tau}}_{\mathrm{on}}).$ However, a simple phenomenological model based on exponentially distributed and randomly switched on and off decay rates is analyzed in detail and shown to yield an inverse power-law behavior in both $P({\ensuremath{\tau}}_{\mathrm{on}})$ and $P({\ensuremath{\tau}}_{\mathrm{off}}).$ Monte Carlo calculations are used to simulate the resulting blinking behavior, and are subsequently compared with experimental observations. Most relevantly, these comparisons indicate that the experimental $\mathrm{o}\stackrel{\ensuremath{\rightarrow}}{n}\mathrm{off}$ blinking kinetics are independent of excitation intensity, in contradiction with previous multiphoton models of on/off intermittency based on an Auger-assisted ionization of the QD by recombination of a second electron-hole pair.