Electronic and hole minibands in quantum wire arrays of different crystallographic structure

We consider semiconductor heterostructures consisting of GaAs rods embedded in Al_xGa_1 − xAs and disposed in sites of a square or triangular lattice. The electronic and hole spectra around the conduction band bottom and the valence band top are examined for electrons and holes propagating in plane of periodicity, versus geometry of the lattice formed by the rods, concentration of Al in the matrix material, and structural parameters including the filling fraction and the lattice constant. Our calculations use the envelope function and are based on the effective-mass approximation. We show that the electronic and hole spectra resulting from the periodicity of the heterostructure, depend on the factors considered and that the effect of lattice geometry varies substantially with lattice constant. For low lattice constant values the minigaps are significantly wider in the case of triangular lattice, while for high lattice constant values only slightly thiner minigaps occur in the square lattice-based arrays. We discuss the consequences of our findings for the efficiency of solar cells.