Electronic bands and gaps in two-dimensional semiconductor heterostructures: Square lattice systems of cylindrical quantum wells and barriers

We use the single band effective-mass approximation to calculate the energy spectrum of two-dimensional (2D) semiconductor heterostructures consisting of a square lattice-based system of cylindrical rods embedded in matrix. The electronic spectrum is studied versus the filling fraction; we also examine the role of material parameters, including the effective mass and the energy gap width in each component material, in the discretization of conduction bands. Referring to the case of 2D heterostructures, the results of our calculations allow to determine parameter values corresponding to electronic band structure with bands and gaps of desired width. An intuitive explanation of the obtained relations suggests similar ones in regular three-dimensional lattices of quantum dots, systems applied in photovoltaic and thermoelectric cells.