Figure 9.

(a) The illustration of a concept of single-exciton optical gain in QDs that feature strong exciton–exciton repulsion. In the absence of exciton–exciton Coulomb interactions, the single exciton state corresponds to optical transparency as the probability of photon absorption is equal to the probability of stimulated emission and both the “absorbing” and the “emitting” transitions have the same energy (left). In the presence of exciton–exciton repulsion, the “absorbing” transition in a QD containing an exciton is shifted up in energy. This shift is defined by the energy of exciton–exciton interaction (Δ_XX). If Δ_XX is greater than the QD ensemble line width, stimulated emission occurs without interference from the absorbing transition which leads to “single-exciton gain”. Adapted with permission from ref (112). Copyright 2007 Nature Publishing Group. (b) The repulsive exciton–exciton interaction can be realized using type-II heterostructures wherein electrons and holes are separated between different parts of the QD (e.g., the core and the shell, as shown in the picture). The blue and green curves depict electron and holes wave functions, respectively. Adapted with permission from ref (115). Copyright 2007 American Chemical Society. (c) Pump-fluence-dependent emission from a film of type-II CdS/ZnSe QDs shows the emergence of two ASE bands. The lower-energy feature, which develops at the center of the single-exciton spontaneous PL band, is due to single-exciton gain (labeled as ‘X’; red lines). The higher-energy feature is due to the standard biexciton gain mechanism (labeled as ‘XX’; blue line). (d) The amplitudes of the X and XX emission bands measured as a function of pump fluence indicate that the threshold of the single-exciton ASE (2 mJ cm^–2) is appreciably lower than the threshold of the biexciton ASE (6 mJ cm^–2). Panels (c) and (d) adapted with permission from ref (112). Copyright 2007 Nature Publishing Group.