A first principles study of sub-monolayer Ge on Si(001)
  Experimental observations of heteroepitaxial growth of Ge on Si(001) show a (2xn) reconstruction for sub-monolayer coverages, with dimer rows crossed by missing-dimer trenches. We present first-principles density-functional calculations designed to elucidate the energetics and relaxed geometries associated with this reconstruction. We also address the problem of how the formation energies of reconstructions having different stoichiometries should be compared. The calculations reveal a strong dependence of the formation energy of the missing-dimer trenches on spacing n, and demonstrate that this dependence stems almost entirely from elastic relaxation. The results provide a natural explanation for the experimentally observed spacings in the region of n \~ 8. 
J.Oviedo, D.R.Bowler and M.J.Gillan