A Criterion for Exciton Binding in Dense Electron—Hole Systems—Application to Line Narrowing Observed in GaAs

Abstract

When classical statistics apply, exciton binding is expected to cease when the concentration increases to the point that the Debye shielding length becomes less than the exciton radius which obtains in the absence of shielding. The statement is made more accurate by employment of Hulthén and Laurikainen's variational solutions of the Schrödinger equation for a particle acted on by an attractive central potential of the form, const×exp(−r)/r. The result is applied to recent experiments with GaAs injection lasers. It is concluded that excitons (either free or bound to impurities) do not play a role in the recombination process at high current levels. A similar criterion for binding is derived for low temperatures and applied to proposed experiments to observe line narrowing due to a Bose—Einstein condensation of excitons in CdS and CdSe. Finally, it is concluded that heavy holes do not contribute effectively to the shielding when their thermal (or Fermi) velocity is considerably less than the orbital velocity of the bound electron which obtains in the absence of shielding.