Electron spectrum in a quantum superlattice with cylindrical symmetry

Abstract

A quantum superlattice with axial symmetry, a heterostructure in which two semiconductor materials in the form of coaxial wires with a nanosize cross section are in contact with one another and form a periodic structure in the radial direction, is studied. It is shown that the electron energy spectrum consists of alternating allowed and forbidden bands. The electron dispersion law is studied for different values of the period of the potential, thicknesses of the semiconductor layers, and radius of the inner crystal of the system. It is shown that the coherent electron effective mass of the quantum superlattice is a tensor: The longitudinal component is close in value to the electron effective mass of the semiconductor material characterizing the quantum well of the superlattice and the radial component depends strongly on the period of the potential, the thicknesses of the coaxial semiconductor layers, and the core radius of the heterosystem, taking on positive or negative values in different allowed bands.