Structure of dimers at the C(100), Si(100) and Ge(100) surfaces

We have performed density functional calculations using cluster models of t he C(100), Si(100) and Ge(100) surfaces, We find that the ground-state geom etry is strongly dependent upon the constraints imposed during geometry opt imization and also can be affected significantly by the cluster size in the range of cluster sizes typically used for such calculations. Our calculati ons show that the ground state has a symmetric dimer geometry for the carbo n surface and an asymmetric diner geometry for the silicon and germanium su rfaces. This is in agreement with the latest first-principles slab calculat ions and, for silicon, is also consistent with experimental results. Severa l previous cluster calculations favour a symmetric dimer on the silicon sur face. Our results show that inappropriate geometry constraints or inadequat e cluster size may have led to a symmetric ground state in these calculatio ns. The change in energy of the cluster as a function of the dimer buckling angle is also investigated for all three surfaces, We find that dimer buck ing is driven by a lowering of the kinetic energy of the electrons, We also observed that the dimer electron density is qualitatively different betwee n the carbon surface on the one hand and the silicon and germanium surfaces on the other. We rationalize this in terms of the small core size of the c arbon atom and relate it to the different groundstate dimer symmetry found for the C(100) surface as opposed to Si(100) and Ge(100) surfaces. Copyrigh t (C) 1999 John Wiley & Sons, Ltd.