Efficient strain-modified improved nonparabolic-band energy dispersion model that considers the effect of conduction band nonparabolicity in mid-infrared quantum cascade lasers

Abstract

Intersubband polar-optical-phonon (POP) scattering plays an important role in determining the population inversion and optical gain of mid-infrared (mid-IR) quantum cascade lasers (QCLs). In particular, the nonparabolicity of the conduction band (CB) significantly affects the energy dispersion relation and intersubband POP scattering time. However, the currently used parabolic-band (PB) and nonparabolic-band (NPB) energy dispersion models are not appropriate for mid-IR QCLs because they are unsuitable for high electron wave vectors and do not consider the effect of applied strain on the energy dispersion relation of the CB. The eight-band k·p method can provide a relatively accurate nonparabolic energy dispersion relation for high electron wave vectors but has the disadvantages of high computational complexity and spurious solutions to be discarded. Consequently, we propose a strain-modified improved nonparabolic-band (INPB) energy dispersion model that has no spurious solution and acceptable accuracy, compared to the eight-band k·p method. To demonstrate the accuracy and efficiency of our proposed INPB model compared with those of the PB, NPB, and eight-band k·p models, we calculate the energy dispersion relations and intersubband POP scattering times in a strain-compensated QCL with a lasing wavelength of 3.58 µm. Calculation results reveal that our proposed model is almost as accurate as the eight-band k·p model; however, it enables much faster calculations and is free from spurious solutions.