Nonlinear gain coefficients in semiconductor quantum-well lasers: effects of carrier diffusion, capture, and escape

Effective nonlinear gain coefficients due to the effects of carrier diffusion, capture, and escape are derived from the carrier transport equations. The quantum capture and escape processes between the confined states and the unconfined states are calculated from first principles by evaluating the carrier-polar longitudinal optical phonon interactions. The dc and ac capture times and escape times are derived from evaluating the net capture current of carriers. The differences in capture and escape times between dc and ac operating conditions are numerically investigated. We find that both dc and ac escape times are strongly dependent on the quantum well structure. This differs from the dc and ac capture times that are not sensitive to the quantum well structure. We also find that the dc escape time predicted by the classical thermionic emission theory will no longer be valid for narrow or shallow quantum wells. We show that both dc and ac capture and escape time ratios will increase as the carrier temperature and the carrier density in the quantum well increase. Therefore, we suggest that the possible cause of the resonant frequency degradation and dramatic increase in the damping rate results from the increase of the ac capture to escape time ratio by the effects of carrier heating. Two theoretical models (2N and 3N models) were used to study the effects of carrier diffusion-capture-escape on the modulation response of quantum-well lasers and a distributed model of carrier transport in quantum-well lasers is proposed. Their implications in designing high-speed quantum-well lasers are discussed