Islands grown during semiconductor heteroepitaxy are in a thermodynamically metastable state. Experiments show that diffusion at the surface region, including the interior of the islands, is fast enough to establish local equilibrium. I review here applications of a Monte Carlo method which takes advantage of the quasi-equilibrium nature of quantum dots and is able to address the issue of intermixing and island composition. Both Ge islands grown on the bare Si(100) surface and C-induced Ge islands grown on Si(100) precovered with C are discussed. In the bare case, the interlinking of the stress field with the composition is revealed. Both are strongly inhomogeneous. In the C-induced case, the interplay of strain and chemical effects is the dominant key factor. Islands do not contain C under any conditions of coverage and temperature.