To study the growth conditions for substitutional incorporation of carbon into Si layers a series of pseudomorphic Si1-yCy/Si superlattices was grown by molecular beam epitaxy (MBE) with absolute carbon concentrations between 0.3% and 2% and growth temperatures varying between 400 and 650 degrees C. All layers showed well behaved Si1-yCy band gap photoluminescence, which shifts linearly to lower energies with increasing carbon content at a slope of 70 meV per atomic percent of substitutional carbon. We employed a novel technique for an unambiguous determination of the substitutional carbon concentrations, which is based on comparative x-ray rocking analyses of Si1-yCy/Si superlattices grown with constant and step-graded temperature profiles. In addition, the surface morphology was assessed by a combination of in situ reflection high energy electron diffraction experiments and postgrowth atomic force microscopy investigations on Single layers and superlattices. At MBE-typical growth rates around 1 Angstrom/s, we find complete substitutional incorporation of carbon up to growth temperatures of 550 degrees C and carbon concentrations of 1.2%. At higher growth temperatures and/or higher carbon fluxes, the percentage of substitutionally incorporated carbon drops drastically, concomitant with a morphological transition from two-dimensional to three-dimensional growth.