Dependence of Threshold Current Density on the Waveguide Ridge Width in Quantum-Cascade Lasers

We make a systematic study to find the dependence of the threshold current density of a mid-infrared quantum-cascade laser on the waveguide ridge width. The optical and thermal parameters of the waveguide are calculated with a finite-element method, and gain is found from a self-consistent rate equation model with energy-balance. The results show the existence of an optimal ridge width that minimizes the threshold current density of the laser. The influence of the interface roughness parameters on laser performance is also discussed.