Effective-mass theory for carriers in graded mixed semiconductors

The applicability of the effective-mass method and of the concept of the position-dependent band parameters to the description of the motion of carriers in graded mixed semiconductors (i.e., quasiheterojunctions) is examined. Within the framework of the virtual-crystal approximation the effective-mass Hamiltonian is found and discussed for graded mixed crystals whose components have a degenerate band with several nonspherical extrema. The case in which the locations of the band extrema within the Brillouin zone are different in the single-component crystals is considered. It is shown that in the case of low lattice symmetry the knowledge of the effective-mass tensor and of the energy of the band edge for homogeneous mixed crystals is insufficient to describe the dynamics of carriers in graded mixed semiconductors.