Data-driven electronic structure calculations in semiconductor nanostructures — beyond the eight-band k · p formalism

In this work, we present a scheme to extract electronic structure parameters for multi-band k · p models beyond the well-established eight-band approach using up-to-date ab initio band structures. Our scheme allows us to identify parameters for k · p models with Hamiltonian matrices of arbitrary complexity and level of sophistication. The computational effort of our approach is very small and increases only slightly with the number of parameters that need to be fitted. We can furthermore apply priorities to specific bands or high-symmetry points of the Brillouin zone and can incorporate routines that help to increase the numerical stability of electronic structure simulations of semiconductor nanostructures using the obtained parameter sets.