Current-Voltage Characteristics of Superconductive Heterostructure Arrays

A systematic approach is presented to calculate the I-V characteristic of a general superconductive multilayer heterostructure, consisting of superconductors(S), normal metals(N), semiconductors(Sm) and insulators(I), with finite transparency and effective mass mismatch at the junctions. The transfer matrix method is used to obtain the scattering probability amplitudes of quasiparticles for the Andreev and ordinary reflection as well as the transmission with and without branch-crossing based on the solutions of the Bogoliubov-de Gennes equation. The method is then applied to study a niobium NSNSN structure with variable thickness of layers.