Theoretical studies of isolated silicon and germanium clusters, and silicon clusters on Si(111)-7x7 surface

We have performed a systematic search for the ground state geometry of Si+n and Si-n in the size range 3 ≤ n ≤ 20 within the framework of density functional theory (DFT) with the local density approximation (LDA) and generalized gradient approximation (GGA). Various properties such as ionization potentials for neutral clusters, vertical detachment energies and photoelectron spectra for anions, fragmentation pathways and dissociation energies for cations, and mobilities for both anions and cations, are calculated and compared with experiments. The structures for medium-sized clusters (10 ≤ n ≤ 20) generally follow the prolate stacked Si9 tricapped trigonal prism (TTP) pattern. Both bulk silicon and bulk germanium pack in a tetrahedral diamond lattice. Small silicon and germanium clusters with n ≤ 10 also have identical geometries. We performed a systematic ground state search for Gen and Ge+n up to 16 atoms. Like silicon clusters, medium-sized germanium clusters build up by stacking TTP subunits but the global minima for sizes starting from n = 13 differ in details indicating that the growth patterns of silicon and germanium clusters diverge after n = 12. Global minima search for silicon clusters (n = 6--14) on the Si(111)7 x 7 surface were also carried out using both simulated annealing and a genetic algorithm. For n = 6 and n = 7, cluster atoms are anchored to the surfaces to saturate the dangling bonds of the surfaces but the cluster atoms are not bonded together directly. Starting from n = 8, cluster atoms bond together and the clusters begin to grow in three dimensions for n ≥ 13