Non-uniform distributions of misfit dislocations in thin films were considered with regard to a 3-element reaction-diffusion model for the kinetics of gliding, climbing and misfit dislocations, and the resultant patterns. The non-local integral expression for the effective stress field at the film surface, which was the main driving force for misfit-dislocation patterning, was approximated by a gradient expression in the misfit-dislocation density. The corresponding gradient coefficients had an explicit dependence upon the film thickness which thus defined a characteristic length for the pattern. Analytical solutions to the model were obtained which described transient spatially uniform dislocation distributions, as well as steady-state spatially periodic dislocation distributions. Linear stability analysis around a uniform steady-state solution demonstrated the formation of misfit-dislocation patches as a result of a dynamic spatial instability. This instability was governed by a competition between spatial coupling which was provided by the misfit-dislocation stress field and a diffusion-like term which entered the dynamics of the gliding dislocations. A stochastic argument for the corresponding diffusion coefficient, which depended upon the average spacing between misfit-dislocations, provided an explanation for the lack of observation of misfit-dislocations at film thicknesses of less than 1µ.

Misfit Dislocation Patterning in Thin Films. K.Cholevas, N.Liosatos, A.E.Romanov, M.Zaiser, E.C.Aifantis: Physica Status Solidi B, 1998, 209[2], 295-304