EVALUATION OF VARIOUS APPROXIMATIONS USED IN THE ENVELOPE-FUNCTION METHOD

We investigate a number of issues related to the application of the en velope-function method to calculate confined-state energies and subban d structure in quantum-well structures. We first consider zone-center confined-state energies and show how the explicit elimination of spuri ous solutions from the envelope-function band structure leads to a sli ghtly modified form of the standard result through which the conductio n-band confined-state energies are calculated using a one-band model a nd an energy-dependent effective mass. We show that the effects of non parabolicity can be predicted directly from the bulk band structure in an infinitely deep quantum well, and demonstrate how the bulk band st ructure can also be used to predict the errors in calculated confineme nt energies in wells of finite depth. The correct choice of boundary c onditions still remains controversial for the calculation of valence-s ubband structure using the Luttinger-Kohn Hamiltonian. We compare the valence-band structure calculated with the lowest conduction band incl uded either explicitly or treated as a remote band, using perturbation theory. We demonstrate that the boundary conditions recently derived by Burt and Foreman are correct. Finally, we compare the valence-band structure calculated using the 4X4 and 6X6 Luttinger-Kohn Hamiltonians . We show how the warping of the highest valence band is markedly diff erent at both intermediate and large wave vectors when the spin-split- off band is included. The use of the axial model to calculate valence- band density of states is therefore questionable with the 6X6 Hamilton ian. The calculated warping is very sensitive to the values of the Lut tinger gamma parameters used, indicating the importance of investing m ore effort to determine these parameters accurately.