Modeling distributed kinetics in isolated semiconductor quantum dots

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, $P\left({\tau }_{\mathrm{o}\mathrm{n}/\mathrm{o}\mathrm{f}\mathrm{f}}\right)\propto 1/{\tau }_{\mathrm{o}\mathrm{n}/\mathrm{o}\mathrm{f}\mathrm{f}}^{1+\alpha },$ over multiple decades in time, where the exponent $1+\alpha$ 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 $P\left({\tau }_{\mathrm{on}}\right)$ and $P\left({\tau }_{\mathrm{off}}\right).\mathrm{}$ 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 $P\left({\tau }_{\mathrm{off}}\right)$ but does not yield the inverse power-law behavior seen in $P\left({\tau }_{\mathrm{on}}\right).\mathrm{}$ 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 $P\left({\tau }_{\mathrm{on}}\right)$ and $P\left({\tau }_{\mathrm{off}}\right).\mathrm{}$ 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 $\mathrm{o}\overrightarrow{n}\mathrm{off}$ 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.