A single semiconductor quantum dot under continuous laser excitation does not fluoresce steadily — it randomly switches ("blinks") between a bright, radiative ON state and a dark, non-radiative OFF state. In the OFF state an Auger process ejects a charge carrier into the surrounding matrix (or a surface trap), leaving the dot charged; a trion then recombines non-radiatively via Auger recombination instead of emitting a photon, until the trap carrier returns.
The defining, and initially surprising, experimental fact (Nirmal et al. 1996; Kuno et al. 2000) is that both the ON-time and OFF-time durations are not exponentially distributed (as ordinary two-state kinetics would predict) but follow a power law, often truncated at long times:
P_on(t) ∝ t^(-α_on) · exp(-t/τ_c)
P_off(t) ∝ t^(-α_off) · exp(-t/τ_c)
typical range: 1.0 < α < 2.5 (Efros–Rosen diffusion-controlled
tunneling / trap-distance model)
Because a power law has no characteristic timescale, blinking looks "the same" whether you zoom into milliseconds or zoom out to minutes — a hallmark of 1/f-type intermittency very different from simple Poisson blinking. The exponential factor exp(-t/τc) is a physical cutoff: at very long times the probability of the trapped charge returning eventually saturates (finite tunneling range / diffusion), so real dots don't stay dark forever.
- αon / αoff — steeper exponents (higher α) bias the dot toward many short flickers; shallower exponents (α near 1) allow occasional very long ON or OFF excursions.
- τc — the truncation timescale; larger τc lets rare long dark periods survive longer before being cut off.
- Durations are drawn here by rejection sampling from a pure power law weighted by exp(-t/τc) — the standard way to generate a truncated power-law random variable, and the same statistical model used to fit real single-dot blinking traces.
Real-world relevance: blinking is a major practical obstacle for quantum dots used as single-photon sources, biological fluorescent labels, and display emitters — "blinking-suppressed" core/thick-shell dots (e.g. CdSe/CdS with a thick shell) are engineered specifically to push α up and shorten OFF excursions.