  The new contribution of this paper is to develop a cylindrical representation
of an already known multiphysics model for embedded nanowire superlattices
(NWSLs) of wurtzite structure that includes a coupled, strain dependent 8-band
$\mathbf{k\cdot p}$ Hamiltonian in cylindrical coordinates and investigate the
influence of coupled piezo-electromechanical effects on the barrier
localization and critical radius in such NWSLs. The coupled
piezo-electromechanical model for semiconductor materials takes into account
the strain, piezoelectric effects and spontaneous polarization. Based on the
developed 3D model, the band structures of electrons (holes) obtained from
results of modeling in Cartesian coordinates are in good agreement with those
values obtained from our earlier developed 2D model in cylindrical coordinates.
Several parameters such as lattice mismatch, piezo-electric fields, valence and
conduction band offsets at the heterojunction of $\mathrm{Al_xGa_{1-x}N/GaN}$
supperlattice can be varied as a function of the Al mole fraction. When the
band offsets at the heterojunction of $\mathrm{Al_xGa_{1-x}N/GaN}$ are very
small and the influence of the piezo-electromechanical effects can be
minimized, then the barrier material can no longer be treated as an infinite
potential well. In this situation, it is possible to visualize the penetration
of the Bloch wave function into the barrier material that provides an
estimation of critical radii of NWSLs. In this case, the NWSLs can act as
inversion layers. Finally, we investigate the influence of symmetry of the
square and cylindrical NWSLs on the band structures of electrons in the
conduction band.

Mesoscale and Nanoscale Physics