A structure for ordered silicon-tin systems on a silicon substrate, based on the known structure of a monolayer of tin on the (111) face of silicon, is proposed. The corresponding electronic structure of this system is modelled using the local density approximation to the density functional theory of the electron gas in the Kohn-Sham formulation with ab initio pseudopotentials taken for the electron-ion interaction. The total energy is minimized including relaxation of all the ionic positions, and the single electron states then evaluated. It is found that the overall energy gap in the band structure decreases rapidly with increasing tin concentration, and the direct gap is only 0.6 eV larger than the indirect gap for a tin concentration of 0.17 (a silicon concentration of 0.83). Effective masses of the electrons and the holes are evaluated at a tin concentration of 0.17. The lighter holes and electrons are found to be of similar mass to those in silicon. However, heavy electrons and holes are also found in the layer structure.