Figure 1.

(a) A bulk semiconductor has continuous conduction and valence energy bands separated by a fixed bandgap E_g,0. A semiconductor QD features discrete atomic-like states whose energies are dependent on QD radius, R, due to the quantum-size effect. The three lowest energy levels of a spherical QD are usually labeled as 1S, 1P, and 1D. They correspond to states with the orbital momentum of the envelope wave function L = 0, 1, and 2, respectively. The QD bandgap is defined by the energy separation between the 1S electron and hole states and is given by the sum of the bulk bandgap and the confinement energy (ΔE_conf), which scales approximately as 1/R². Adapted with permission from ref (32). Copyright 2021 Springer Nature Limited. (b) Size-dependent emission energies of QDs of IV-VI (PbS,⁷²⁻⁷⁴ PbSe⁷⁵), III-V (InP^76,77), and II-VI (CdE, E = Te,^78,79 Se,^42,80 S^78,81) semiconductors (colored symbols). The respective bulk-semiconductor bandgaps are shown by color-matched horizontal lines. Reproduced with permission from ref (15). Copyright 2021 Springer Nature Limited.