Efficient Inverse Auger Recombination at Threshold in CdSe Nanocrystals

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We apply the semiempirical nonlocal pseudopotential method to the investigation of prospects for direct carrier multiplication (DCM) in neutral and negatively charged CdSe nanocrystals. In this process, known in the bulk as impact ionization, a highly excited carrier transfers, upon relaxation to the band edge, its excess energy Δ to a valence electron, promoting it across the band gap and thus creating two excitons from one. For excess energies just a few meV above the energy gap Eg (the DCM threshold), we find the following: (i) DCM is much more efficient in quantum dots than in bulk materials, with rates of the order of 1010 s-1. In conventional bulk solids, comparable rates are obtained only for excess energies about 1 eV above Eg. (ii) Unlike the case in the bulk, in both neutral and charged nanocrystals the DCM rate is not an increasing function of the excess energy but oscillates as Δ moves in and out of resonance with the energy of the discrete spectrum of these 0D systems. (iii) The main contribution to the DCM rates is found to come from the dot surface, as in the case of Auger multiexciton recombination rates. (iv) Direct radiative recombination of excited electron−hole pairs and phonon-assisted decay are slower than DCM, but (v) the rate of Auger cooling (where the relaxation energy of an excited electron is used to excite a hole into deeper levels) can be of the same order of magnitude as that of the DCM process. Furthermore, for excess energies well above the DCM threshold, the presence of an energy gap within the hole manifold considerably slows DCM compared to Auger cooling (AC), which is not affected by it. Achieving competitive DCM processes will, therefore, require the suppression of Auger cooling, for example, by removing the hole from the dot or by trapping it at the surface.