Dynamical screening of excitons by free carriers

The Bethe‐Salpeter equation for the electron‐hole polarization function is treated in the screened ladder approximation. The dynamically screened Coulomb potential is taken into account in the plasmon pole approximation. An iterative procedure leads to an effective Bethe‐Salpeter equation in which the screening is described by a virtual exchange of plasmons between the electron and hole. The resulting exciton binding energy is considerably larger than that obtained by the statically screened Coulomb potential approximation. Results of the numerical calculation of the binding energy as a function of the free carrier density are given. The calculated binding energy vanishes only asymptotically in the limit of high free‐carrier densities.