Band structure of n - and p -doped core-shell nanowires

We investigate the electronic band structure of modulation-doped GaAs/AlGaAs core-shell nanowires for both n and p doping. We developed an 8-band Burt-Foreman k·p Hamiltonian approach to describe coupled conduction and valence bands in heterostructured nanowires of arbitrary composition, growth directions, and doping. Coulomb interactions with the electron/hole gas are taken into account within a mean-field self-consistent approach. We map the ensuing multiband envelope function and Poisson equations to optimized, nonuniform real-space grids by the finite element method. Self-consistent charge-density, single-particle subbands, density of states, and absorption spectra are obtained at different doping regimes. For n-doped samples, the large restructuring of the electron gas for increasing doping results in the formation of quasi-one-dimensional electron channels at the core-shell interface. Strong heavy-hole (HH)/light-hole (LH) coupling of hole states leads to nonparabolic dispersions with mass inversion, similarly to planar structures, which persist at large dopings, giving rise to direct LH and indirect HH gaps. In p-doped samples the hole gas forms an almost isotropic, ringlike cloud for a large range of doping. Here as a result of the increasing localization, HH and LH states uncouple, and mass inversion takes place at a threshold density. A similar evolution is obtained at fixed doping as a function of temperature. We show that signatures of the evolution of the band structure can be singled out in the anisotropy of linearly polarized optical absorption.