Ekenberg U., Altarelli M.
The binding energy of excitons belonging to the different subbands in a quantum well has been calculated for different well widths and barrier heights. The degeneracy of the valence band, the non-parabolicity of the conduction band and the matching of the wave function at the interfaces are taken into account. The zeroth order wave function is taken to be the product of the envelope functions in the z-direction (perpendicular to the layers) for the electron and the hole and a purely two-dimensional (2D) exciton wave function. The difference between the 2D and 3D interaction between the electron and the hole is included in a variational- perturbation approach. The effect of the valence band degeneracy on the properties of the holes is described with the use of the 4*4 Luttinger Hamiltonian. Most previous authors have only considered the diagonal elements of this matrix, which are included in our Zeroth order Hamiltonian. The present authors include the off-diagonal elements in perturbation theory up to second order. This involves summations over bound exciton states and integrals over the continuum states, which are found to be important. These off-diagonal elements in some cases modify the results considerably and improve the agreement with recent experimental results.
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