Frenkel-Kontorova Model of the Dimerized Overlayer System with Vacancies

The reconstruction of the dimerized overlayer system with vacancies is studied via a diatomic chain Frenkel-Kontorova model. We present the details of the exactly solvable model and the analytical solution of the atomic displacements in the ground state. Our calculations explain the 2 x N reconstruction observed in Ge/Si(100) and Ga/Si(112).