Screening effects during late stage phase separation

Abstract

Late stage phase separation is an important non-equilibrium thermodynamics process with a range of implications for applied systems such as thin film growth. A number of studies describe quantitatively Ostwald ripening, the dominant process under mass conservation. In these models the concept of a screening length occurs in different context, for three-dimensional systems to accommodate finite volume fractions of the minority phase, and for two-dimensional systems to circumvent the diverging steady state solution to the diffusion equation. We present a comprehensive review of this concept and show that the screening length in two- and three-dimensional systems has the same form if the average cluster radius and the average cluster cluster distance are used as parameters. In the experimental section, examples for two- and three-dimensional systems are given, showing that the screening length shields the interaction between clustering systems across a concentration step. This leads to sharper than expected interfaces between neighbouring ripening systems on a surface, and explains the resistance of sub-surface silicide clusters to dissolve into a uniform, buried film during annealing.