As an alternative to wet chemical treatments and hydrogen termination, we propose the sulphur-termination of silicon surfaces in order to obtain favourable starting conditions for epitaxial growth of chalcopyrite semiconductors. We show that a high-temperature treatment of Si(0 0 1) and Si(1 1 1) in ultra-high vacuum under continuous exposure to a reactive sulphur molecular beam from a cracker source leads to new well-defined ordered surfaces. We identify the ideal sulphur termination of Si(0 0 1) with (1 x 1) structure and a quasi-ideal termination of Si(1 1 1) with a (4 x 4) surface structure. We propose structural models and discuss three surfaces also in the light of former experimental effort and theoretical predictions. Furthermore, we elucidate the implications of sulphur termination for epitaxial growth of the CIS compound.