Nonmonotonic size dependence of the dark/bright exciton splitting in GaAs nanocrystals

Abstract

The dark/bright exciton splitting {Delta}{sub x} in semiconductor nanocrystals is usually caused by electron-hole exchange interactions. Since the electron-hole wave-function overlap is enhanced by quantum confinement, it is generally assumed that {Delta}{sub x} increases monotonically as the quantum-dot size decreases. Using atomistic pseudopotential calculations, we show that in GaAs nanocrystals {Delta}{sub x} scales nonmonotonically with the nanocrystal size. By analyzing the nanocrystal wave functions in terms of contributions from different k points in the bulk Brillouin zone, we identify the origin of such nonmonotonic behavior in a transition of the lowest conduction-band wave function from {lambda} like to X like as the nanocrystal radius decreases below 19{angstrom}. The nonmonotonicity arises because the long-range component of the electron-hole exchange interaction all but vanishes when the electron wave function becomes X like. We also show that the direct/indirect transition induced in GaAs nanocrystals by external pressure results in a sudden reduction in {Delta}{sub x}.