Auger recombination is the central non-radiative relaxation process affecting all aspects of carrier dynamics in semiconductor nanocrystals. Auger processes, being significantly enhanced in quantum-confined structures, can dominate the decay of multiexcitons, facilitate fluorescence intermittency, induce the efficiency droop in nanocrystal light-emitting diodes, and limit the performance of nanocrystal lasing applications. The mechanism of the Auger rate acceleration is connected with the combined effect of spatial confinement of carriers and the presence of abrupt interfaces in the nanocrystals. These two effects admix high-momentum components into the ground state wavefunctions of the carriers, thereby relaxing the strict momentum conservation rule during the Auger recombination. Based on the experimental data, the existence of a universal material-independent scaling law of the multiexcitonic Auger recombination rate with the nanocrystal size has been proposed. Similar size-dependence of the trion Auger recombination has been measured in CdSe quantum dots. Theoretically, however, this universal scaling has not been explained yet. Previous calculations of the Auger rates in CdS quantum dots predicted a stronger dependence on the nanocrystal size. This previous model incorporated a simplified version of the boundary conditions which enforced continuity of envelope functions across the nanocrystal surface. This, in turn, precluded generation of a sufficient amount of the high-momentum components in the wavefunctions. Here we calculate the rates of the Auger recombination of negatively charged trions in CdSe nanocrystals in the framework of the 8-bandk.p model. We apply the most general form of the boundary conditions, which permit discontinuity of the envelope functions across the nanocrystal interface, thereby enhancing the generation of the high-momentum components in the carriers' wavefunctions. This allows us to explain the experimental size-dependence of the Auger recombination rate. In addition, our calculations demonstrate orders-of-magnitude oscillations of the Auger rate with size caused by a cyclic switching between constructive and destructive interference of the wavefunctions of carriers participating in the Auger process.
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