Multimillion-atom modeling of InAs/GaAs quantum dots: interplay of geometry, quantization, atomicity, strain, and linear and quadratic polarization fields

摘要

Electronic structure and optical properties of self-assembled quantum dots strongly depend on an intricate interplay of the quantum mechanical size quantization and the atomistic built-in/internal electrostatic fields in the underlying material system. Specifically, built-in fields in zincblende quantum dots originate mainly from: (1) fundamental crystal atomicity and the interfaces between two dissimilar materials, (2) microscopic distribution of strain, and (3) the piezoelectric polarization. In this paper, we first study the origin and nature of these internal fields in InAs/GaAs quantum dots having three different geometries, namely, box, dome, and pyramid. We then quantify and delineate the impact of these internal fields on the one-particle electronic states in terms of symmetry-lowering and localization in the wavefunctions, shift in the energy states and bandgap, anisotropy and non-degeneracy in the level, and formation of mixed excited bound states near the Brillouin zone center. Finally, we study the geometry and size-dependence of interband optical transitions in the XY and XZ planes treating the quantum size quantization and the internal fields as parameters. The computational framework employs a combination of fully atomistic valence force-field molecular mechanics, 20-band nearest-neighbor tight-binding electronic bandstructure models, and appropriate post-processing tools to obtain the interband optical transition rates. In particular, to model piezoelectricity, four different polarization models (based on the experimental and ab initio coefficients accounting for both linear and non-linear effects) have been considered in increased order of accuracy. With the non-linear piezoelectricity generally opposing the linear counterpart, the net piezoelectric field is found to be negligible in smaller dots but exhibits non-vanishing effects as the dot height is increased.