We study the thermodynamics of C incorporation on Si(100), a system where strain and chemical effects are both important. Our analysis is based on first-principles atomistic calculations to obtain the important lowest energy structures, and a classical effective Hamiltonian which is employed to represent the long-range strain effects and incorporate the thermodynamic aspects. We determine the equilibrium phase diagram in temperature and C chemical potential, which allows us to predict the mesoscopic structure of the system that should be observed under experimentally relevant conditions.PACS numbers: 61.66. Dk, 68.35.Rh, 68.35.Bs Carbon-enriched silicon systems are the focus of current interest as candidates for a material with tailored electronic properties, which is compatible with wellestablished silicon technology. The tetravalent nature and large band gap in the diamond structure make carbon an ideal candidate for incorporation in Si. However, the solubility of C in Si under thermodynamic equilibrium is extremely low (≈ 10 −5 ) due to the huge mismatch in bond length (35%) and bond energy (60%) between C and Si. Non-equilibrium methods, such as molecular beam epitaxy (MBE), that exploit the higher atomic mobility on surfaces, can be used to overcome this obstacle and enhance solubility [1]. As predicted theoretically by Tersoff[2], C solubility is enhanced by several orders of magnitude near the Si(100) surface, especially in subsurface layers. Osten et al.[3] confirmed experimentally this prediction and observed that C atoms diffuse to subsurface layers above a certain temperature. This finding opened new possibilities for growth of C-rich metastable structures.The enhanced solubility near the surface has important consequences. The large tensile strain associated with C incorporation in Si has proven a very powerful tool in device engineering: a small amount of C can compensate the Ge-induced tension in pseudomorphic SiGe layers [4,5,6] , and can also suppress dopant outdiffusion. This idea was recently implemented in a novel heterojunction bipolar transistor [7]. Another interesting effect [8,9] produced by C incorporation on the Si(100) surface is an unusual change of the surface periodicity after deposition of even a small amount of C (≈ 1 8 of a mono-layer (ML)): the well-known c(2 × 4) or p(2 × 2) reconstructions of the pure Si surface change to a c(4 × 4) pattern. This is clearly visible in several LEED experiments after ethylene exposure [10,11], or MBE [8].The microscopic features of C incorporation in Si are rather well understood. Previous work by the authors [12,13,14] revealed an oscillatory C profile driven by the competition between two factors: the tendency of C atoms to occupy favorable sites which are determined by the reconstruction strain field, and the preferential arrangement of C atoms at certain distances which minimizes the lattice elastic energy. The profile is characterized by enhancement of C content in the first and third layer, depletion in the second and an exponential red...