Quantum cascade lasers (QCLs) are compact sources that have demonstrated high output powers at terahertz (THz) frequencies. To date, all THz QCLs have been realized in III-V materials. Results are presented from Si _1-x Ge _x quantum cascade superlattice designs emitting at around 3 THz which have been grown in two different chemical vapor deposition systems. The key to achieving successful electroluminescence at THz frequencies in a p -type system has been to strain the light-hole states to energies well above the radiative subband states. To accurately model the emission wavelengths, a 6-band k ∙ p tool which includes the effects of nonabrupt heterointerfaces has been used to predict the characteristics of the emitters. X-ray diffraction and transmission electron microscopy have been used along with Fourier transform infrared spectroscopy to fully characterize the samples. A number of methods to improve the gain from the designs are suggested.