Microscopic structure of the discommensurate phases in Ge(111)/Ga. II. Domain superstructure and discommensurations.

We present atomically resolved scanning tunneling microscope (STM) images of two of the discommensurate phases---\ensuremath{\gamma} and \ensuremath{\beta}---occurring in the system Ge(111)/Ga. In both phases Ga atoms substitute the Ge atoms of the substrate surface layer, resulting in a local (1\ifmmode\times\else\texttimes\fi{}1) structure within domains. In the \ensuremath{\beta} phase, which occurs at slightly higher Ga coverages than the \ensuremath{\gamma} phase, a stacking fault is visible in half of the domains. The domains are separated by elementary discommensurations, so-called domain walls. In the present study we focus on the microscopic structure of these walls---a problem that is hard to access with methods other than STM. From the STM data we deduce a microscopic model of the walls of the \ensuremath{\beta} phase, where virtually all dangling bonds are saturated---in contrast to the situation in the \ensuremath{\gamma} phase. This energetically favorable situation is enabled by the presence of the stacking fault. We propose that the gain in energy due to the removal of all dangling bonds in the walls of the \ensuremath{\beta} phase exceeds the loss in energy associated with the stacking fault, driving the transition from the \ensuremath{\gamma} to the \ensuremath{\beta} phase.