A generalized plane-wave formulation of formalism and continuum-elasticity approach to elastic and electronic properties of semiconductor nanostructures

We present a generalized and flexible plane-wave based implementation of the multiband k · p formalism to study the electronic properties of semiconductor nanostructures. All ingredients of the modeling process, namely the Hamiltonian, the nanostructure’s geometry and the required material parameters, are defined in human-readable input files that can be easily generated and modified. The generalized k · p model can contain an arbitrary number of directly treated bands as well as strain, piezoelectric, and external potentials. All calculations can be performed for arbitrary crystal structures. The nanostructure is described in terms of a real-space composition map that may contain an arbitrary number of base compounds and alloys. We demonstrate the applicability and flexibility of our implementation for the example of (111)-oriented, site-controlled InGaAs quantum dots, where a rotated eight-band k · p Hamiltonian is employed. As a second example, a 14-band k · p model that captures the bulk inversion asymmetry of the zinc-blende lattice is applied for the case of a pyramidal (0 0 1)-oriented InAs/GaAs quantum dot. Here we show that the explicit treatment of 14 bands removes the well known shortcoming of eight-band k · p models for (0 0 1)-oriented zinc-blende quantum dots which leads to artificially degenerate p-like electron states.