Energy minibands and analytical wave functions in semiconductor heterostructures

Abstract

We bring back the basic analytical results of our study of the electronic properties of semiconductor heterostructures. The one particle hamiltonian, the effective mass approximation, the Kroning-Penney potential and the method of the transfer matrix have been used to calculate the normalized analytical wave and functions and the minibands energy. The analytically current density calculated starting from the exact structure of minibands is the same as the one associated with the analytical wave functions. We also discuss the effect of the non-porabolicity of the superlattice conduction band on electronic properties and how to obtain the width of minibands in the tight binding approximation. Energy minibands and wave functions reproduce and consequently generalize those of the different limiting cases. The effective masses of the particle in the wells and barriers can be either different or equal. Our results can be directly used in the calculations of energies and functions specific to heterostructures where perpendicular and parallel movements are uncoupled and when there are no magnetic and an arbitrary magnetic fields in the direction of the deposit layers.