Critical nucleus phase diagram for theCu(100)surface

Abstract

An experimental exploration of island nucleation dynamics during epitaxial film growth on the $\mathrm{Cu}(100)$ surface is presented that connects previous results from other groups at low temperatures with the room temperature regime. The steady-state balance of various atomistic processes during island nucleation has direct impact on the physical properties of epitaxial films, e.g., larger nuclei densities allow layer-by-layer growth to be achieved at lower temperatures. Within many theoretical frameworks, the critical nuclei size $i$ (the largest assembly of atoms with a higher probability for decay than growth) plays a major role in determining island nuclei densities, and, by extension, the physics of film growth. This paper presents island density and island size distributions from recent STM studies and analysis that allows for accurate determination of the critical nuclei size at various deposition rates and temperatures near room temperature and the $i=1$ to $i=3$ boundary (dimer to tetramer stable island). This is accomplished by using the scaling behavior of coarsening to develop statistical weight by rescaling individual distributions and summing them. The rescaled island size distributions are then compared with analytical models that allow unambiguous assignment of the critical island size. The results of this study are then combined with previously published results from other researchers to determine empirically the structure of the phase boundary from $i=1$ to $i=3$ as a function of temperature and deposition rate. At low temperatures and fluxes, the observed position of the phase boundary agrees with predictions when only adatom mobility is considered. Deviations at higher temperatures suggest that the mobility of dimers and other small islands may be important in determining the effective critical nucleus near room temperature.