Model-independent determination of the carrier multiplication time constant in CdSe nanocrystals

The experimental determination of the carrier multiplication (CM) time constant is complicated by the fact that this process occurs within the initial few hundreds of femtoseconds after excitation and, in transient-absorption experiments, cannot be separated from the buildup time of the 1p-state population. This work provides an accurate theoretical determination of the electron relaxation lifetime during the last stage of the p-state buildup, in CdSe nanocrystals, in the presence of a single photogenerated hole (no CM) and of a hole plus an additional electron-hole pair (following CM). From the invariance of the 1p buildup time observed experimentally for excitations above and below the CM threshold producing hot carriers with the same average per-exciton excess energy, and the calculated corresponding variations in the electron decay time in the two cases, an estimate is obtained for the carrier multiplication time constant. Unlike previous estimates reported in the literature so far, this result is model-independent, i.e., is obtained without making any assumption on the nature of the mechanism governing carrier multiplication. It is then compared with the time constant calculated, as a function of the excitation energy, assuming an impact-ionization-like process for carrier multiplication (DCM). The two results are in good agreement and show that carrier multiplication can occur on timescales of the order of tens of femtoseconds at energies close to the observed onset. These findings, which are compatible with the fastest lifetime estimated experimentally, confirm the suitability of the impact-ionization model to explain carrier multiplication in CdSe nanocrystals.