Identifying the forces responsible for self-organization of nanostructuresat crystal surfaces

The spontaneous formation of organized surface structures at nanometre scal es(1,2) has the potential to augment or surpass standard materials patterni ng technologies. Many observations of self-organization of nanoscale cluste rs at surfaces have been reported(1-10), but the fundamental mechanisms und erlying such behaviour-and in particular, the nature of the forces leading to and stabilizing self-organization-are not well understood. The forces be tween the many-atom units in these structures, with characteristic dimensio ns of one to tens of nanometres, must extend far beyond the range of typica l interatomic interactions. One commonly accepted source of such mesoscale forces is the stress field in the substrate around each unit(1,11-13). This , however, has not been confirmed, nor have such interactions been measured directly. Here we identify and measure the ordering forces in a nearly per fect triangular lattice of nanometre-sized vacancy islands that forms when a single monolayer of silver on the ruthenium (0001) surface is exposed to sulphur at room temperature. By using time-resolved scanning tunnelling mic roscopy to monitor the thermal fluctuations of the centres of mass of the v acancy islands around their final positions in the self-organized lattice, we obtain the elastic constants of the lattice and show that the weak force s responsible for its stability can be quantified. Our results are consiste nt with general theories of strain-mediated interactions between surface de fects in strained films.