Design and simulation of losses in Ge/SiGe terahertz quantum cascade laser waveguides

The waveguide losses from a range of surface plasmon and double metal waveguides for Ge/Si_1-xGe_x THz quantum cascade laser gain media are investigated at 4.79 THz (62.6 μm wavelength). Double metal waveguides demonstrate lower losses than surface plasmonic guiding with minimum losses for a 10 μm thick active gain region with silver metal of 21 cm^-1 at 300 K reducing to 14.5 cm^-1 at 10 K. Losses for silicon foundry compatible metals including Al and Cu are also provided for comparison and to provide a guide for gain requirements to enable lasers to be fabricated in commercial silicon foundries. To allow these losses to be calculated for a range of designs, the complex refractive index of a range of nominally undoped Si_1-xGe_x with x = 0.7, 0.8 and 0.9 and doped Ge heterolayers were extracted from Fourier transform infrared spectroscopy measurements between 0.1 and 10 THz and from 300 K down to 10 K. The results demonstrate losses comparable to similar designs of GaAs/AlGaAs quantum cascade laser plasmon waveguides indicating that a gain threshold of 15.1 cm^-1 and 23.8 cm^-1 are required to produce a 4.79 THz Ge/SiGe THz laser at 10 K and 300 K, respectively, for 2 mm long double metal waveguide quantum cascade lasers with facet coatings.