Influence of Crystal Structure and Shape Anisotropies on Valence-Band States of InP Colloidal Nanocrystals: Application of the xyz Algorithm

We demonstrate that traditional classification of electronic states in semiconductor nanocrystals based on the quantum numbers of angular momenta becomes inappropriate and even misleading in nanocrystals with strong crystalline anisotropy, such as InP. We propose an alternative classification based on irreducible representations of the symmetry group fully taking into account symmetry aspects of both the underlying crystal lattice and the overall nanocrystal shape. Furthermore, we present a new tool for modeling semiconductor nanocrystals within the effective mass approximation by adapting the xyz algorithm widely used to find eigenfrequencies for vibrational modes of both macroscopic elastic objects and nanoparticles and based on the Rayleigh–Ritz variational principle. We demonstrate its extreme efficiency and versatility by studying the influence of crystal structure and shape anisotropies on valence-band states of InP colloidal nanocrystals destined to replace highly toxic cadmium and lead containing quantum dots in numerous applications.