Effects of scatterings on the gain broadening of type-I quantum-cascade lasers

The gain bandwidth of a quantum-cascade (QC) laser is important for determining the magnitude of the optical gain, the refractive index change, and the linewidth enhancement factor. We investigate the effects of the scattering mechanisms on the gain linewidth of a type-I QC laser and compare our theoretical results with experimental data. The bandwidth of the gain spectrum of a QC laser is related to the electron relaxation rate, which is determined by scatterings that change the electron momentum or energy in the same subband (intrasubband) or different subbands (intersubband). Polar optical phonon scattering, impurity scattering, and electron-electron scattering are the important mechanisms. In this paper, we investigate the magnitude of the linewidth of the optical gain spectrum due to these scattering mechanisms in type-I mid-IR QC laser structures. In particular, the dependence of the scattering rate on the doping position will be shown in the case of the impurity scattering. We also present calculated optical gain, refractive index change, and linewidth enhancement factor spectra. Our theoretical results agree well with the experimental data.