Coupled multiphysics, barrier localization, and critical radius effects in embedded nanowire superlattices

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.