Carrier-carrier scattering in the gain dynamics of ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{y}}$As diode lasers

Ultrafast optical nonlinearities in semiconductors play a central role in determining transient amplification and pulse-dependent gain saturation in diode lasers. Both carrier-phonon and carrier-carrier scattering are expected to determine the gain dynamics in these systems. We present a relaxation-time approximation model for carrier-carrier scattering in strained-layer lasers. The carrier-carrier scattering rates are determined using the quasiequilibrium distribution functions for a given background carrier density. The distribution function to which the photoexcited distribution relaxes is a Fermi-Dirac function where the chemical potential and temperature are self-consistently chosen so that both particle number and energy are conserved in the carrier-carrier scattering process. The relaxation approximation makes the problem an effective one-dimensional problem which can then be solved directly for the carrier distributions using an adaptive Runge-Kutta routine. This procedure is less computationally intensive than a full Monte Carlo simulation. The results show that the inclusion of carrier-carrier scattering improves previous results where only carrier-phonon scattering was included and that carrier-carrier scattering is necessary to produce heating of the carriers in the high-energy tails. © 1996 The American Physical Society.