Coulomb Interaction in Semiconductor Lasers

Recent evidence suggests that the excitation density in semiconductor lasers exceeds the realm where exciton-based descriptions of the optical-gain process are valid. A treatment is presented based on the random-phase approximation from electron-gas theory in which the effects of the long-wavelength components of the Coulomb potential are included. In addition to the usual exchange term, a term derivable from electron-plasmon coupling modifies the electron self-energy (and gives an apparent "band-gap shift") in the range of density parameter $1\le r_s\le 5$ which appears to characterize semiconductor lasers. Agreement of prediction with experimental wavelength shifts for stimulated emission in an external magnetic field for GaAs and CdSn${\mathrm{P}}_2$ is excellent. The average electron self-energy shift from the long-wavelength part of the Coulomb interaction may be simply interpreted as arising from the plasma zero-point energy.