Quantum confinement phenomena in nanowire superlattice structures

Nanowire superlattices (NWSLs) are objects with a wide range of potential applications in nanoscale electronics and photonics. These objects are already grown experimentally in laboratories and studies of their properties represent an important task in nanotechnology research. Tools of mathematical modelling provide a powerful means for studying these fascinating structures with an ultimate goal of predicting their properties and understanding their limits. In this paper, we analyse finite nanowire GaAs/Al0.3Ga0.7As superlattice structures with a cylindrical cross-section and determine their electronic eigenstates and energy eigenvalues. We analyse in detail the qualitative differences, in terms of wavefunctions and energy eigenvalues, between structures containing the same number of barriers and wells (asymmetrical) and structures where the number of barrier layers is one above the number of well layers (symmetrical). We demonstrate that asymmetrical NWSL structures have well-pronounced qualitative and quantitative differences as compared to both symmetrical NWSL structures and infinite periodic NWSL structures. We show also that there exists a critical radius Rc for quantum confinement, that is the NWSL ground state is confined in GaAs (Al0.3Ga0.7As) for a nanowire of radius R above (below) Rc. In the specific case where R=Rc, the ground state is smeared out over the entire NWSL structure.