Role of Thermally Occupied Hole States in Room‐Temperature Broadband Gain in CdSe/CdS Giant‐Shell Nanocrystals

Growing CdSe/CdS nanocrystals from a large CdSe core, and employing a giant CdS shell, a continuous, broadband gain spectrum, covering the spectral range between the CdSe and the CdS band edge, is induced. As revealed by k·p calculations, this feature is enabled by a set of closely spaced S-, P- and, for larger CdSe cores, D-state hole levels, which are thermally occupied at room temperature, combined with a sparse density of electron states. This leads to a range of bleach signals in the transient absorption spectra that persist up to a microsecond. By extending a state-filling model including relevant higher-energy states and a Fermi–Dirac distribution of holes at finite temperature, it is shown that thermal occupancy can lower the gain threshold for excited states. Inclusion of Gaussian broadening of discrete transitions also leads to a smoothening of the gain threshold spectrum. Next to a direct measurement of the gain threshold, a method is also developed to extract this from the gain lifetime, taking advantage that population inversion is limited by Auger recombination and recombination rates scale with the exciton density as 〈N〉·(〈N〉 − 1). The results should be readily extendable to other systems, such as perovskite or III–V colloidal nanocrystals.