Fig. 1: Ordinary versus hybrid biexcitons.

a, In a conventional QD with colocalized electrons and holes (type-I QD), the optical gain is due to biexciton states. Their Auger recombination can be represented as a superposition of two negative-trion and two positive-trion pathways (rates r_A,X– and r_A,X+ per pathway, respectively). CB and VB are the conduction and valence bands, respectively. b, In the proposed scheme, the optical gain is due to a hybrid biexciton consisting of a spatially direct and a spatially indirect exciton. Such biexcitons can be realized in the so-called type-(I + II) QDs. These structures contain an additional, indirect compartment in the conduction band, which captures an electron from the primary (direct) QD compartment, allowing the electron to reduce its energy. However, the energy difference (Δ_d,i) driving electron transfer should be small enough to prevent the transfer of the second electron, which should remain in the primary compartment. This would lead to the creation of a hybrid direct/indirect biexciton. The Auger decay of such a biexciton occurs via a single positive-trion pathway. As a result, it is slower than that of a conventional biexciton. c, Practical implementation of type-(I + II) QDs. Top: schematic of the type-(I + II) CdSe/ZnSe/CdS/ZnS QD; r, l, h and d are the radius of the CdSe core, the thickness of the ZnSe barrier, the thickness of CdS interlayer and the thickness of the outer ZnS shell, respectively. Bottom: radial profiles of the electron and hole confinement potentials in the type-(I + II) QD. It features spatially direct (type I) and spatially indirect (type II) transitions (X_d and X_i excitons, respectively).