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

Abstract

We have performed density functional calculations using cluster models of the C(100), Si(100) and Ge(100) surfaces. We find that the ground-state geometry is strongly dependent upon the constraints imposed during geometry optimization and also can be affected significantly by the cluster size in the range of cluster sizes typically used for such calculations. Our calculations show that the ground state has a symmetric dimer geometry for the carbon surface and an asymmetric dimer geometry for the silicon and germanium surfaces. This is in agreement with the latest first-principles slab calculations and, for silicon, is also consistent with experimental results. Several previous cluster calculations favour a symmetric dimer on the silicon surface. Our results show that inappropriate geometry constraints or inadequate cluster size may have led to a symmetric ground state in these calculations. 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 buckling is driven by a lowering of the kinetic energy of the electrons. We also observed that the dimer electron density is qualitatively different between 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 carbon atom and relate it to the different ground-state dimer symmetry found for the C(100) surface as opposed to Si(100) and Ge(100) surfaces.