Exchange effects on excitons in quantum wells

Exchange splitting of quasi-two-dimensional excitons confined in quantum wells is studied theoretically by performing a simplified calculation with a scaling argument. Both the exchange energy and the longitudinal-transverse splitting are found to be enhanced drastically when the confinement of the exciton increases. Taking into account the difference of the enchange interaction between the heavy-hole and the light-hole exciton, the intrinsic splittings of the exciton ground states are calculated for GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As quantum wells within the envelope-function approximation.