Strain-modified effective two-band model for calculating the conduction band structure of strain-compensated quantum cascade lasers: effect of strain and remote band on the electron effective mass and nonparabolicity parameter

Abstract

We propose a strain-modified effective two-band model to calculate the conduction band (CB) structure of strain-compensated quantum cascade lasers (QCLs). The proposed model can consider the effect of strain and remote band (RB) on the band-edge energy, electron effective mass, and nonparabolicity parameter although the currently used empirical two-band model can be applicable to only the unstrained QCLs. Based on the three-band second-order k·p Hamiltonian along with the Pikus-Bir Hamiltonian, analytical formula for the electron effective mass and nonparabolicity parameter are derived at the zone center, where the effects of strain and RB interaction are included. Then, the three-band first-order k·p Hamiltonian is reduced to the strain-modified effective two-band Hamiltonian, where the effective Kane energy, determined by the electron effective mass and nonparabolicity parameter, is used to include the nonparabolicity of the CB. By numerically solving the proposed strain-modified effective two-band model based on the finite difference method, we calculate the CB structure of several strain-compensated or unstrained QCLs in the mid-IR and terahertz range and predict their lasing wavelengths, which are well matched with the measured values in the literatures.