A physical model of quantum cascade lasers: Application to GaAs, GaN and SiGe devices

The philosophy behind this work has been to build a predictive bottom up physical model of quantum cascade lasers (QCLs) for use as a design tool, to interpret experimental results and hence improve understanding of the physical processes occurring inside working devices and as a simulator for developing new material systems. The standard model uses the envelope function and effective mass approximations to solve two complete periods of the QCL under an applied bias. Other models, such as k·p and empirical pseudopotential, have been employed in p-type systems where the more complex band structure requires it. The resulting wave functions are then used to evaluate all relevant carrier-phonon, carrier-carrier and alloy scattering rates from each quantised state to all others within the same and the neighbouring period. This information is then used to construct a rate equation for the equilibrium carrier density in each subband and this set of coupled rate equations are solved self-consistently to obtain the carrier density in each eigenstate. The latter is a fundamental description of the device and can be used to calculate the current density and gain as a function of the applied bias and temperature, which in turn yields the threshold current and expected temperature dependence of the device characteristics. A recent extension which includes a further iteration of an energy balance equation also yields the average electron (or hole) temperature over the subbands. This paper will review the method and describe its application to mid-infrared and terahertz, GaAs, GaN, SiGe cascade laser designs.