LIGHT-HOLE NONPARABOLICITY IN THE SINGLE BAND APPROXIMATION

In the envelope function treatment of quantum wells and superlattices, an effective mass Hamiltonian including corrections to the quadratic dispersion relation is commonly employed to describe non-parabolicity and other complications of the band structure. A careful definition of the boundary conditions used to connect the envelope functions at the interfaces is required to consistently take such higher order effects into account to a given order of approximation. It is possible to develop a single band scheme to describe the light-hole non-parabolicity implicitly accounting for the coupling to other bands. With respect to the conduction electron case, the coupling between the split-off and light-hole bands brings about qualitative changes in the boundary conditions. Model calculations show how the non-parabolicity affects the energy levels not only through the modified (i.e. non-quadratic) dispersion relation, but also through the consistently modified boundary conditions. The present simple theory compares favorably with experimental data and more refined theoretical treatments.