An empirical tight-binding theory which includes the effects of lattice relaxation is employed to investigate the opto-electronic properties of InP nanocrystals under an external hydrostatic pressure. For bulk InP, our model describes accurately the evolution of the lowest conduction band-edges with pressure and predicts the $\Gamma_1c}-X_1c}$ crossover at the same lattice contraction as measured in the experiment. For small InP nanocrystals, the lattice-relaxed TB model is compared with a tight-binding model which assumes a scaled bulk-like arrangement for the atoms in the nanocrystal. Atomistic bond-length-scaling models predict that a $\Gamma_1c}-X_1c}$ crossing is the mechanism for the red-shift 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 with the experimental results due to the stronger mixture between the $\Gamma_1c}-$ and $L_1c}-$ minima and the more localized character of hole states. Moreover, in the lattice-relaxed model the experimental red-shift is explained as a transition from bound states localized inside the dot to surface-like states on the dot exterior, rather than simply as a direct-to-indirect band gap crossover. In addition, the evolution of the near-band-edge optical spectra as a function of pressure has been analyzed for different nanocrystal sizes, geometries and degrees of surface passivation with both the simple scaling and lattice-relaxed tight-binding approaches.
Physical Review B (Condensed Matter and Materials Physics)