One-band effective-mass approximation for smooth heterojunctions

We used Kohn-Luttinger representation and canonical transformation of all-band k·p Hamiltonian to derive an effective-mass equation for conduction band of a smooth heterojunction of related lattice-matched zinc-blende symmetry semiconductors. All terms proportional to 1/E¯_g were accounted for, here E¯ _g is the typical interband separation. The derived equation naturally included the weak non-parabolicity correction terms as well as a position-dependent correction term to the conduction band edge effective mass and an interface spin-split-off term. We obtained several at first sight different, but equivalent to each other forms of the effective-mass equation. It was shown that boundary conditions for envelope functions (in case when the heterojunction might be treated as an abrupt one) depend on the manner of the envelope function definition. Also, we showed the smallness of the coefficient of optical interconduction-subband absorption for the in-plane polarized light as compared even to additional terms (because of taking into account weak non-parabolicity and position dependence of the effective mass) to the coefficient of absorption caused by the normal-to-plane polarized light