The feasibility of population inversion is studied for the SiGe/Si system and compared with that of GaAs/AlGaAs. Because of the absence of strong polar optical phonon scattering in SiGe/Si, the lifetime difference of the upper and lower lasing levels, to which the population inversion and laser gain are proportional, is consistently an order of magnitude larger than that of GaAs/AlGaAs; nor does it show the sudden drop to zero or negative values when the lasing energy exceeds the optical phonon energy. Both systems studied are superlattices, each period of which consists of three coupled quantum wells and barriers.