Mean-field theory of heteroepitaxial thin metal film morphologies

We develop a mean-field statistical mechanical theory to examine the growth mechanisms and structures of fee (face-centered cubic) metal thin films grown on fc&O) metal substrates. Eleven hetero-interfaces with bulk cohesive energy differences as large as 4 eV and lattice mismatches ranging from 21% to 16% are examined in order to develop an understanding of how these intrinsic properties of the interface may determine film morphology. For small (up to 5%) mismatched interfaces, pseudomorphic Stranski-Krastanov growth is predicted to be competitive with pseudomorphic layer-by-layer growth. When the lattice mismatch is 10% or greater, the growth mechanism is invariably incommensurate three-dimensional growth, where (111) cluster formation is energetically competitive with (100) cluster growth. The overlayer structures and growth modes correlate most closely with only one property: the lattice strain between the substrate and the adlayer. By contrast, the trends in the bulk cohesive energies do not allow even any qualitative prediction of the overlayer structures. However, surface energies can dictate minor changes in the growth modes of the films. Finally, no dependence of the film morphology on temperature is found over the temperature range 300-800 K for the cases we examined, although the film morphologies can be markedly different from those predicted at lower temperatures.