ENVELOPE-FUNCTION METHOD FOR THE CONDUCTION-BAND IN GRADED HETEROSTRUCTURES

The Kohn-Luttinger representation and canonical transformation of the all-band kp Hamiltonian have been used to derive an envelope-function equation with position-dependent effective mass for the conduction ban d of a structure with a graded heterojunction between related lattice- matched zinc-blende symmetry semiconductors. This equation should also include non-parabolicity correction terms and an interface spin-split -off term. Several forms of the effective-mass equation have been obta ined that are at first sight different, but equivalent to one another. The boundary conditions for an envelope function at the heterointerfa ce (in the case when the heterojunction might be treated as an abrupt one) are shown to depend on how the envelope functions are defined. At tention has also been paid to the problem of the influence of the posi tion-dependent effective mass on the coefficient of optical absorption for transitions between conduction subbands in a quantum well. The ab sorption is shown to be negligibly small for the case of normal incide nce of light on the quantum well.