Extended density-matrix model applied to silicon-based terahertz quantum cascade lasers

Silicon-based terahertz quantum cascade lasers (QCLs) offer potential advantages over existing III-V devices. Although coherent electron transport effects are known to be important in QCLs, they have never been considered in Si-based device designs. We describe a density-matrix transport model that is designed to be more general than those in previous studies and to require less a priori knowledge of electronic band structure, allowing its use in semiautomated design procedures. The basis of the model includes all states involved in interperiod transport, and our steady-state solution extends beyond the rotating-wave approximation by including dc and counterpropagating terms. We simulate the potential performance of bound-to-continuum Ge/SiGe QCLs and find that devices with 4\char21{}5-nm-thick barriers give the highest simulated optical gain. We also examine the effects of interdiffusion between Ge and SiGe layers; we show that if it is taken into account in the design, interdiffusion lengths of up to 1.5 nm do not significantly affect the simulated device performance.