Exciton dispersion in multiple quantum wells and superlattices: An additional contribution to the linewidth

The exciton dispersion in multiple quantum wells (MQW’s) and superlattices is studied with use of a tight-binding model. The Coulomb interaction between the exciton states in different wells induces an effective dipole-dipole interaction, even when tunneling is neglected. A distinctive feature of the exciton dispersion relation is that when the wave vector approaches zero from different directions (perpendicular or parallel to the growth direction), the limiting energy has different values. This makes a remarkable intrinsic contribution to the linewidth of the exciton, which is of the order of meV for GaAs-${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As MQW’s.