Geometrical Study Of Two-dimensional Adatom Islands On Crystal Surface

Since the quantum effects of nanostructures are keen to the sizes and geometric structures, predicting and preparing desired nanostructures on solid surfaces become very important at present for many advanced material technologies. At present, there are four theoretical methods studying shape of atomic islands on crystal surface which are the Wulff construction based on free energy established in 1901, the lowest energy structure optimizing method with genetic algorithm, the molecular dynamics including kinetic Monte Carlo method and the mean field kinetics with rate equations. There are still some problems for these existed theoretical methods. Although the most widely used Wulff construction could be easily processed with first principle calculations, it can not reproduce all the shapes of the compact atomic islands observed in experiments. For instance, the Wulff construction predicts that the homoepitaxial compact atomic islands on Pt(111) are nearly hexagons, while it takes on triangular shape at 400K. The rest three methods could not be applied with the ab initio calculations but calculations by the empirical potentials. Even with the empirical potential calculations, the genetic algorithm could only deal with atomic islands of tens of atoms and the molecular dynamic simulations would face tremendous calculations as the number of the atoms increases, while the mean field method with rate equations needs initial input of rate parameters which could not be given precisely by calculations with empirical potentials.With problems mentioned above, this work builds a concise physical model by proposing the condensing potential (CP) conception to predict the geometric shape of the two-dimensional atomic island on crystal surface which could be processed by ab initio calculations easily. Its basic idea is that the growth speed of an atomic island step is closely related to the CP which an adatom feels near the island step, and thus once the CP value is calculated, the island shape is predicted. For the growth speed of an atomic island step is decided by its ability of trapping adatoms, it is first demonstrated in the work that the CP of an atomic island step strongly affects its ability of trapping adatoms. Then the CP model is applied in homoepitaxial systems of Ag and Cu by calculations with empirical potentials, and results show that homoepitaxial atomic islands on Ag(111) and Cu(111) surface are hexagonal and the ones on'Ag(100) and Cu(100) have square shapes. These predictions are all in agreement with relevant experiments. We then focus on the Pt/Pt(111) epitaxial system, with calculations by either first principle method or semi-empirical potentials, the same result is obtained that the compact island on Pt(111) during homoepitaxy is not near hexagon which is the prediction of the Wulff construction, but the exact triangle given by the CP model. This theoretical result accords well with the experimental observations given in 1998's PRL.