Simulations of Carbon Containing Semiconductor Alloys: Bonding, Strain Compensation, and Surface Structure

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Abstract
This paper reviews recent Monte Carlo simulations within the empirical potential approach, which give insights into fundamental aspects of the bulk and surface structure of group-IV semiconductor alloys containing carbon. We focus on the binary Si 1-x C x and ternary Si 1-x-y Ge x C y alloys strained on silicon substrates. The statistical treatment of these highly strained alloys is made possible by using the semigrand canonical ensemble. We describe here improvements in the algorithm which considerably speed up the method. We show that the identity switches, which are the basic ingredients in this statistical ensemble, must be accompanied by appropriate relaxations of nearest neighbors in order to reach "quasiequilibrium" in metastable systems with large size mismatch between the constituent atoms. This effectively lowers the high formation energies and large barriers for diffusion which make molecular dynamics methods impractical for this problem. The most important findings of our studies are: (a) The prediction of a repulsive Ge–C interaction and of a preferential C–C interaction in the lattice. (b) The prediction for significant deviations of the structural parameters and of the elastic constants from linearly interpolated values (Vegard's law). As a result, for a given amount of carbon, strain compensation is shown to be more drastic than previously thought. (c) Investigation of the surface problem shows that the competition between the reconstruction strain field and the preferential arrangement of carbon atoms leads to new complicated structural patterns.