Atomistic simulations combining a Monte Carlo algorithm and molecular static relaxations were carried out to predict the alloying profile in pyramid and dome shaped Ge(Si)/Si(001) islands. The results show that the composition profile is dominated by the surface segregation of Ge and segregation of Si to the substrate island interface. Within the interior of the island the composition profile is found to be uniform. An analysis of the energetics of the alloying shows that at typical growth temperatures, the lowering of the energy achievable through the formation of a nonuniform alloying profile would be too small to overcome the tendency towards randomization driven by the entropy of mixing of the system. The shape transformation from the pyramid to the dome shape is shown to be predicted accurately by the modeling.
