Numerically efficient density-matrix technique for modeling electronic transport in mid-infrared quantum cascade lasers

Abstract

We present a numerically efficient density-matrix model applicable to mid-infrared quantum cascade lasers. The model is based on a Markovian master equation for the density matrix that includes in-plane dynamics, preserves positivity of the density matrix and does not rely on phenomenologically introduced dephasing times. Nonparabolicity in the band structure is accounted for with a three-band $${\bf k}\cdot {\bf p}$$ model, which includes the conduction, light-hole, and spin-orbit split-off bands. We compare the model to experimental results for QCLs based on lattice-matched as well as strain-balanced InGaAs/InAlAs heterostructures grown on InP. We find that our density-matrix model is in quantitative agreement with experiment up to threshold and is capable of reproducing results obtained using the more computationally expensive nonequilibrium Green’s function formalism. We compare our density-matrix model to a semiclassical model where off-diagonal elements of the density matrix are ignored. We find that the semiclassical model overestimates the threshold current density by 29% for a 8.5- $$\upmu $$ m-QCL based on a lattice-matched heterostructure and 40% for a 4.6- $$\upmu $$ m-QCL based on a strain-balanced heterostructure, demonstrating the need to include off-diagonal density-matrix elements for accurate description of mid-infrared QCLs.