Excitons in Double Quantum Wells-beyond the single-subband limit

Calculations of the exciton binding energy in quantum well systems carried out in the single sub-band limit where only the lowest electron and hole states contribute to the exciton have been widely reported.(1,2) This limit is valid when the confined electron and hole energy levels in the well are widely separated in energy compared to the exciton binding energy. At the other extreme would be the case of a superlattice in which the electron and hole subband bandwidths are much larger than the exciton binding energy and the exciton would be made from a linear combination of a number of subband states.(3) In this paper we wish to treat an intermediate case, namely a double quantum well system consisting of two identical wells of width Lw separated by a barrier of width Lb. When Lb is large the two lowest lying states ( i.e. the first symmetric and anti-symmetric electron and hole states ) arc almost degenerate. This near-degeneracy is progressively lifted as the barrier thickness, decreases. This means that for thick barriers in order to correctly calculate the exciton binding energy one must account for the mixing caused by the Coulomb potential between the two pairs of states.