Terahertz quantum cascade lasers (THz QCLs) have many potential applications, including detection of skin tumours, and of illicit drugs and explosives. To date, all THz QCLs use III–V compound semiconductors, but silicon (Si)-based devices could offer significant benefits. The high thermal conductivity of Si may allow higher operating temperatures, removing the need for large and costly cryogenic coolers, and the non-polar nature of Si may allow a wider range of emission frequencies. The mature Si processing technology may reduce fabrication costs and ultimately allow integration of THz QCLs with mainstream semiconductor electronics. This work investigates the suitability of a range of Si-based material configurations for THz QCL design. An effective mass/envelope function model of the electronic bandstructure is developed, taking into account the effects of strain and crystal orientation. Scattering models for Coulombic interactions, structural imperfections and interactions with phonons (lattice vibrations) are developed and used to predict the electron distribution, current density and gain in a range of device designs. The effect of nonabrupt interface geometries is investigated and the effect of intervalley mixing upon the emission spectrum is considered. It is shown that germanium/germanium–silicon heterostructures offer much better prospects for THz QCL development than silicon/silicon–germanium systems and can yield sufficient optical gain to overcome the threshold for copper–copper waveguides.