Vacancy-driven stress relaxation in layers

The role of vacancies together with their generally non-ideal sources and sinks has been investigated previously in the context of multi-component diffusion. This concept is applied to a thin layer on a substrate subjected to an initial eigenstress state. The surface of the layer is assumed to act as an ideal source and sink for vacancies. The interface may act either as an ideal or as no source and sink for vacancies. Non-ideal sources and sinks are supposed in the bulk. The formation of a vacancy site fraction profile across the layer due to active sources and sinks and due to diffusion is studied, provoking a relaxation of the residual eigenstress state. A set of two nonlinear partial differential equations for both the vacancy site fraction and the eigenstress distributions is developed. The problem is reformulated in dimension-free quantities. The relation between the diffusivity and the activity of sources and sinks for vacancies in the bulk is characterized by a vacancy intensity parameter k. Numerical solutions are presented, and the influence of nonlinear terms in the evolution equations is evaluated. The simulations provide the evolution of the vacancy site fraction and of the hydrostatic stress profiles in the layer. The development of a film of newly deposited or removed atoms at the layer surface and of the total thickness of the layer is also calculated. The results of simulations are discussed.