Boundary conditions in the Kane two-band theory of semiconductors

A quantum theory of semiconductor heterostructures is presented. Attention is focused on the interface between two intrinsic direct-gap semiconductors, especially when the gap is narrow. The motion of electrons in the semiconductors is analyzed in the framework of the Kane two-band theory. Conditions are formulated for the envelope wave functions of the electrons on the contact plane. They generalize the Ben Daniel-Duke boundary condition which was formerly derived in a different manner. (Ben Daniel and Duke used the standard Schr & ouml;dinger equation as an equation of the second order while our conditions can concern an equation of the n-th order, with the possibility that n tends to infinity.)