Matching conditions for effective-mass functions at an abrupt heterojunction, tested on an exactly solvable model

In the effective-mass treatment of heterostructures different matching cond itions at an abrupt interface have been proposed in the literature. In a re cent derivation by Einevoll and Sham, in which the periodic potentials are assumed weak and cell symmetric, the symmetry of the band-edge Bloch functi ons of the matching materials is emphasized. These Bloch functions either h ave vanishing gradient at cell boundary (dass I), or vanish themselves (cla ss II). For the three different types of interfaces (I-I, II-II or I-II) th ey predict matching conditions with the much-used BenDaniel-Duke boundary c onditions valid for I-I interfaces only. We test the three different Einevo ll-Sham matching conditions through exact calculations on model quantum wel ls. We verify the Einevoll-Sham matching conditions for I-I and II-II inter faces, but not those for I-II interfaces.