CONNECTION RULES AND ELECTRON TRANSMISSIVITY AT AN INTERFACE BETWEEN MATERIALS WITH DIFFERENT ELECTRONIC-PROPERTIES

We derive approximate connection rules for conduction-electron waves at an abrupt interface between two materials with different electronic properties. We avoid the arbitrariness in the connection rules for effective-mass wave functions by taking the Bloch functions into account in an approximate way that is appropriate for the non-epitaxial interfaces that we wish to study. The result is particularly relevant for the physics of superconductor-semiconductor heterostructures because the basic property governing their behaviour is the transmissivity of the interface. The application of the result to measurements on niobium-silicon heterostructures shows that the situation has been reached in which the transmissivity is mainly limited by the large Fermi wave vector mismatch of metal and semiconductor.