Theory of excitons in semiconductor quantum wells containing degenerate electrons or holes

A variational theory is presented for the binding energy and optical strength of the quasi-two-dimensional excitons created optically at low temperature in a quantum well containing degenerate carriers of one type (electrons or holes). Both screening and the exclusion principle are taken into account. Radiative recombination is also considered, and it is shown that either no exciton is involved in the radiation, or the radiation is from an exciton identical to the one created optically. It is shown that when the exclusion principle applies, binding is not obtained for arbitrarily large carrier density. It is shown that the binding energy can be very small while the optical strength is still significant. Calculations are presented showing the binding energy and optical strength versus density for GaAs wells of various widths and electron and hole densities 0<N<2×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$.