n-type Ge/SiGe terahertz quantum cascade laser are investigated using non-equilibrium Green's functions calculations. We compare the temperature dependence of the terahertz gain properties with an equivalent GaAs/AlGaAs QCL design. In the Ge/SiGe case, the gain is found to be much more robust to temperature increase, enabling operation up to room temperature. The better temperature robustness with respect to III-V is attributed to the much weaker interaction with optical phonons. The effect of lower interface quality is investigated and can be partly overcome by engineering smoother quantum confinement via multiple barrier heights.Terahertz (THz) quantum cascade lasers (QCLs) have been demonstrated with different III-V materials including GaAs/AlGaAs 1 , InGaAs/AlInAs 2,3 , InGaAs/GaAsSb 4 and InAs/AlAsSb 5 .In the past decade however, relatively small progress has been reported to increase the maximum operating temperature (presently 200 K) despite substantial efforts of design optimization 6-8 . The rationale for the quenching of THz laser emission above this temperature is due to the very effective electron-phonon (e-phonon) interaction, typical of III-V materials. Indeed in polar lattices the longitudinal optical (LO) phonons induce a long-range polarization field which strongly couples to the charge carriers (Fröhlich interaction). The THz transitions are typically designed to be well below the optical phonon energy (30-36 meV), so that at low temperature the upper laser state is protected against scattering by emission of LO-phonons. With increasing temperature however, the thermally activated electrons in the subband of the upper lasing state gain enough in-plane kinetic energy to access this scattering channel 9 . This non-radiative relaxation of carriers reduces the population inversion and is responsible for quenching of the laser emission with increasing temperature as the gain drops below the cavity losses. This fast non-radiative channel cannot easily be overcome by design engineering, as there is a necessary trade-off between selectivity and speed of the carrier injection in such closely spaced energy levels.To overcome this limitation, QCLs based on crystals having large optical phonon energy such as GaN or ZnO have recently been proposed 10 . As an alternative strategy, non-polar material systems are attractive because of their weaker e-phonon interaction. Indeed in these crystals the e-phonon coupling is controlled by the deformation potential which due to its short range is much less effective than the Fröhlich interaction. SiGe alloys fulfill this requirement and also have the great advantage of being non-toxic materials fully compatible with silicon technology. Among different configurations (electron or hole based, Si or Ge rich regimes) 11-14 , theoretical studies have indicated n-type Ge/SiGe heterostructures where charge transport is associated to L electrons, as the most promising architecture 15-17 . Experimentally, sharp THz absorption peaks, related to intersubband transitions in n-typ...