Modeling of Sb-based type-II quantum cascade lasers

Abstract

The interband Sb-based quantum cascade lasers at mid-IR range are studied. A self-consistent method that solves the Schr\odinger's equation and Poisson's equation simultaneously to obtain the band structure and calculate the optical gain for type-II quantum cascade lasers is presented for the first time to the best of our knowledge. We start with the formulation of band structure based on the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ method with the inclusion of the conduction-band--valence-band coupling effect. The 8\ifmmode\times\else\texttimes\fi{}8 Hamiltonian for the k\ensuremath{\cdot}p method is block diagonalized into two 4\ifmmode\times\else\texttimes\fi{}4 blocks under the axial approximation. Explicit expressions for momentum-matrix elements for interband transitions are given. The optical gain formulation including many-body effects is then presented. The carrier accumulation in different layers and its screening effects are shown. For the lasers of our study, the carrier screening affects the peak gain wavelength by about 0.3 \ensuremath{\mu}m and the peak gain magnitude by 10%. The self-consistent model is shown to be important to give a good agreement with experimental data. The temperature dependence of the optical gain is also examined for the regular and the W-shaped type-II quantum-well structures. The optical gain for the W-shaped type-II quantum well is found to have a 50% enhancement over the regular type-II quantum well. Our model is important for designing high-power, high-efficiency, and high-temperature type-II interband cascade lasers.