Fig. 1. Discovery order of biexciton phenomena in semiconductors and physical models of biexciton photoluminescence. (a) Discovery order of biexciton phenomena in semiconductors; (b) luminescence models of biexcitons and excitons and relationships between their luminescence intensities and excitation intensity

Fig. 2. Fundamental properties of biexciton PL spectra in quantum dots. (a) Schematic of biexciton energy level and binding energy; (b) schematic of biexciton luminescence peak (ΕXX) and exciton luminescence peak (ΕX); (c) biexciton emission intensity and exciton emission intensity versus excitation intensity; (d) influence of carrier spatial distribution on Coulomb interaction of biexcitons

Fig. 3. PL spectra of biexcitons in self-assembled QDs and colloidal QDs. (a) PL spectra of biexcitons in GaAs/AlGaAs QDs^[12]; (b) PL intensity of biexcitons versus laser power in GaAs/AlGaAs QDs^[12]; (c) biexciton PL spectra and (d) biexciton PL intensity versus excitation intensity in CdSe colloidal QDs at room temperature^[17]; (e) biexciton PL spectra and (f) biexciton PL intensity versus excitation intensity in CdSe colloidal QDs at 2 K^[18]

Fig. 4. Radiative recombination models of biexcitons at different temperatures. (a) Radiative recombination model of biexcitons at low temperature; (b) radiative recombination model of biexcitons at room temperature;(c) time-resolved PL decay spectra of biexciton and exciton in InGaAs self-assembled QDs at low temperature^[27]; (d) time-resolved PL decay spectra of CdSe colloidal QDs at room temperature^[29]

Fig. 5. Quantum confinement in QDs and quantum-dot-based entanglement. (a) Schematic of discrete energy levels in QDs^[36]; (b) size-dependent absorption and PL spectra of QDs^[36]; (c) schematic of biexciton-exciton cascade radiation process of QDs^[40]; (d) schematic of HOM effect in which two indistinguishable single photons (solid arrows) always exit at same output port through 50/50 beam splitter^[40]; (e) second order cross correlation curves of biexciton with exciton photons under different polarization conditions^[38]; (f) photon indistinguishability versus emission time separation^[46]

Fig. 6. Biexciton Auger recombination process in QDs. (a) Schematic of biexciton Auger recombination process in bulk material; (b) biexciton Auger recombination process (negative trions or positive trions) in QDs; (c) calculation result of negative trion Auger recombination rates versus radius for CdS QDs^[50]; (d) summary of biexciton lifetimes for various QDs^[60]; (e) calculation result of biexciton Auger recombination lifetime versus size using correlated (interacting) and uncorrelated (noninteracting) spin wave functions for CdSe QDs^[59]

Fig. 7. Optical gain in QDs. (a) Schematic of optical gain process; (b) difference between optical gain in QDs and optical gain in quantum wells; (c) pump-dependent absorption spectra for GaAs/AlGaAs quantum well^[61]; (d) pump-dependent absorption spectra for CdSe colloidal QDs^[63]; (e) optical gain in thick shell CdSe/CdS colloidal QDs under continuous-wave laser as pump source^[71]; (f) optical gain in CdSe/Cd_xZn_1-xSe/ZnSe_0.5S_0.5 colloidal QDs under electrical pumping^[72]