Microscopic structure of the discommensurate phases in Ge(111)/Ga. I. Atomic structure within domains.

Abstract

The atomic structure within domains of three different discommensurate phases that appear in Ge(111)/Ga is determined by means of x-ray standing waves together with first-principles total-energy calculations. The global structure of these phases consists of a superstructure of domains separated by elementary discommensurations (domain walls). The interior of the domains essentially preserves the symmetry of the ideal Ge(111) surface except for an expansive strain of the lattice. The structure of such phases is determined by shape, size, and disposition of the domains, by the number of gallium atoms per unit cell in the interior of the domains, and the adsorption site and chemical bonding of these gallium atoms, as well as strain within the domains. The two lower coverage phases \ensuremath{\gamma} and \ensuremath{\beta} have one single Ga atom per 1\ifmmode\times\else\texttimes\fi{}1 surface unit cell. In the lowest coverage phase \ensuremath{\gamma}, the Ga atom substitutes for the Ge atom of the ideal Ge(111) surface layer giving rise to a hexagonal superstructure of equivalent domains. The domain superstructure in the \ensuremath{\beta} phase shows two different types of domains, both of them triangular, that tile the surface: Ga substitutes for the surface Ge atom in both domain types. They differ by the presence of a stacking fault of the Ga layer with respect to the underlying bulk Ge in one type of domain, whereas the other one shows the correct stacking. At higher coverages a second layer of Ga atoms begins to cover the \ensuremath{\beta} phase in ${\mathit{H}}_{3}$ positions. This structure, called ${\mathrm{\ensuremath{\beta}}}_{\mathit{H}3}$ is possibly an intermediate state towards the formation of bulk Ga clusters. It is speculated that Ga atoms at ${\mathit{H}}_{3}$ positions can facilitate the \ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\beta} phase transition.