Electron temperature and mechanisms of hot carrier generation in quantum cascade lasers

A technique for calculating the temperature of the nonequilibrium electron distribution functions in general quantum well intersubband devices is presented. Two recent GaAs/Ga1−xAl𝑥As quantum cascade laser designs are considered as illustrative examples of the kinetic energy balance method. It is shown that at low current densities the electron temperature recovers the expected physical limit of the lattice temperature, and that it is also a function of current density and the quantised energy level structure of the device. The results of the calculations show that the electron temperature 𝑇𝑒 can be approximated as a linear function of the lattice temperature 𝑇𝑙 and current density J, of the form 𝑇𝑒=T𝑙+αe−lJ, where 𝛼e−l is a coupling constant (∼6–7 K/kA cm−2 for the devices studied here) which is fixed for a particular device.