We investigate the bulk and surface structure of ${\mathrm{Ge}}_{1-x}{\mathrm{C}}_x$ alloys using Monte Carlo simulations in the semigrand canonical ensemble, within the empirical potential formalism. We consider free-floating alloys as well as epitaxial alloys on Si and Ge substrates. The lattice constants as a function of carbon content are calculated and fitted to quadratic expressions for easy reference. Large deviations (negative bowing) from Vegard’s law are found. We confirm the presence of Ge–C bonds and thus of substitutional carbon in the bulk of the material, for both epitaxial conditions. The most probable bulk carbon-carbon configurations are in a third-nearest-neighbor arrangement. The surface structure of alloys strained on Ge is characterized by strong segregation of carbon to the top layers. Segregation is less effective in alloys strained on Si. Most probable dimer configurations are both C–C and Ge–C dimers, for low carbon contents and Ge-substrate conditions, and Ge–C dimers for higher carbon contents and both epitaxial conditions.

• Received 27 January 1999

DOI:https://doi.org/10.1103/PhysRevB.60.10837