Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

and excited QD core states to fluctuate in a random walk. The minimumhopping time of the surrounding charge environment gives the minimumtimescale for each step of the random walk to occur. This simple 1D discretetimerandom walk model for blinking immediately gives the characteristicpower-law probability distribution of on and off times with a power-lawexponent of 1.5 [33]. The intrinsic hopping time is most likely orders ofmagnitude faster than our experimental binning resolution (100 ms). Althoughthe hopping mechanism is probably temperature dependent, thistemperature dependence would only be reflected in experiments that couldprobe timescales on the order of the hopping times, before power-lawstatistics set in and beyond the reach of our experimental time resolution.Although this simple random walk model may require further development,it nevertheless explain the general properties observed. The off-timestatistics are temperature and intensity independent because although thehopping rate of the random walker changes, the statistics of returning toresonance between the trap and excited state does not. In addition, size andsurface morphology do not play a significant role in this model as long as atrap state is energetically accessible to the intrinsic excited state. Figure 11arepresents a Monte Carlo simulation of the histogram of return times to theorigin in a one-dimensional, discrete-time random walk. The open circles representa histogram with a slower hopping rate than the filled circlesanalogous to thermally activated motion at 10 K and 300 K. The experimentallyaccessible region of the statisticals simulation is suggested as thearea inside the dotted lines in Fig. 11a. Further experimental and theoreticalwork should go toward completing this model. For example, temperatureandstate-dependent hopping rates as well as a higher-dimension randomwalk phase space and multiple transition states may be necessary.The magnitude of truncation of the on-time power-law distributiondepends on which QD is observed, as shown in Figs. 9a and 9b. In Fig. 9b, theFigure 11 (a) Histogram of return times to the origin in a 1D discrete-time randomwalk simulation. The boxed region of the histogram represents the accessible timeregime (>100 ms and