Theory of InP nanocrystals under pressure

Abstract

An empirical tight-binding theory which includes the effects of lattice relaxation is employed to investigate the optoelectronic properties of InP nanocrystals under external hydrostatic pressure. For bulk InP, our model accurately describes the evolution of the lowest conduction-band edges with pressure and predicts the ${\ensuremath{\Gamma}}_{1c}\text{\ensuremath{-}}{X}_{1c}$ crossover at the same lattice contraction as measured in experiment. For small InP nanocrystals, the lattice-relaxed tight-binding model is compared with a tight-binding model which assumes a scaled bulklike arrangement for the atoms in the nanocrystal. Atomistic bond-length-scaling models predict that a direct-to-indirect band gap (the ${\ensuremath{\Gamma}}_{1c}\text{\ensuremath{-}}{X}_{1c}$ crossing) produces the redshift observed experimentally in nanocrystals at high pressure. However, the scaling models are not able to describe quantitatively the band-gap evolution with pressure. When lattice relaxation effects are included, the band-gap dependence on pressure agrees quantitatively with the experimental results. The agreement in the band-gap variation with pressure is due to the stronger mixture between ${\ensuremath{\Gamma}}_{1c}$ and ${L}_{1c}$ minima and the more localized character of hole states. Moreover, in the lattice-relaxed model, the experimental redshift results as a transition of the lowest states from bound states localized inside the dot to surfacelike states on the dot exterior, rather than as the direct-to-indirect band gap crossover.