Exciton binding energy in a quantum well with inclusion of valence-band coupling and nonparabolicity

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Abstract
Binding energies of excitons associated with several transitions between different subbands in undoped quantum wells are calculated for different well widths using a novel perturbational approach. The degeneracy of the valence band, the nonparabolicity 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-perturbational 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. We include the off-diagonal elements of this matrix in perturbation theory up to second order. This involves summations over the 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.