Elastic Scattering in Kane Type Semiconductor Circular Dots

In this paper we have investigated the scattering of electrons by a circular narrow penetrable δ-type potential barrier in $A^{3}B^{5}$ type semiconductors by using three-band Kane model. By using the Kane equations with the continuous conditions of the wave functions and flux discontinuous at the interface of two circular dots, we have analytically calculated the total cross-section and the Boltzmann conductivity for the semiconductor quantum rings with delta potential barrier. It has been shown that the quasi-bound states appear as peaks in the cross-section.