MISFIT DISLOCATION PATTERNING IN THIN-FILMS

The emergence of non-uniform distributions of misfit dislocations (MDs ) in thin films is discussed. A three-element reaction-diffusion model for the kinetics of gliding, climbing and misfit dislocations as prop osed by Romanov and Aifantis (R-A model) is used to describe the corre sponding pattern. The non-local integral expression for the effective stress field at the film surface, which is the main driving force for MD patterning, is approximated by a gradient expression in the MD dens ity. The corresponding gradient coefficients have an explicit dependen ce on the film thickness which, thus, defines a characteristic length for the pattern. Analytical solutions of the model are obtained which describe transient spatially uniform dislocation distributions, as wel l as steady-state spatially periodic dislocation distributions. Linear stability analysis around a uniform steady-state solution demonstrate s the formation of MD patches as a result of a dynamical spatial insta bility. This instability is governed by the competition of the spatial coupling provided by the MD stress field and a diffusion-like term en tering the dynamics of the gliding dislocations. A stochastic argument for the corresponding diffusion coefficient, which depends on the ave rage spacing between MDs (thus providing a second characteristic lengt h scale), yields an explanation for not observing MD patterns for film thicknesses below 1 mu m.