Boundary conditions for envelope functions in heterostructures

In this paper a detailed derivation of the boundary conditions for envelope functions is carried out making use of the kp method. The resulting conditions are different from those of Harrison by an extra term originating from a surface energy. This term removes the difference between expressions for the transmission coefficient obtained with the help of microscopical calculations and the envelope-function method. In the case of a simple band structure the resulting boundary conditions contain two independent parameters. It is shown that the general boundary conditions suggested by Ando and Mori contain a term which has to be neglected in the frame of the effective-mass method. The form of the boundary conditions for degenerate bands and for the case of different degrees of degeneracy in the interfacing materials is considered.