We use molecular-dynamics simulations to study the growth of pure Si, Si0.5Ge0.5, and pure Ge on the 2 × 1 reconstructed surface of Si(100) in a way appropriate to the fabrication of thin films by the method of molecular-beam epitaxy (MBE), namely sequential deposition of energetic atoms. The atoms interact with one another via effective potentials of the Stillinger–Weber form, with parameters adjusted such as to describe all possible types of triplet interactions. Motivated by numerous experimental studies of MBE-grown films, we investigate in particular the structure of the deposits as a function of substrate temperature. We find in all three cases that at low substrate temperatures, poorly ordered structures form, while at high substrate temperatures, epitaxial growth takes place. The presence of Ge limits the number of crystalline overlayers that form, even though it appears to favor a more-ordered structure in the initial stages of growth. For pure Ge epitaxy, in particular, only the first three layers are crystalline, after which growth appears to proceed by the formation of islands, reminiscent of the Stranski–Krastanow growth scheme, and in qualitative agreement with recent experimental and theoretical work. In all samples, annealing improves the quality of the films—at least when grown at sufficiently high substrate temperatures. The interdiffusion of the species at the substrate-deposit interface is also examined.