Numerical simulations of stress generation and evolution in Volmer–Weber thin films

Abstract

We present a detailed model of the stresses and shape changes that occur in polycrystalline thin films during Volmer–Weber growth. Our model tracks the shape of an array of islands as they grow and coalesce into a continuous film. The islands change shape as a result of the deposition flux, as well as surface and grain boundary diffusion. Stress is generated in the film as a result of forces exerted between neighboring islands as they meet to form a grain boundary. The internal stresses in the islands and the diffusive changes on their surfaces and grain boundaries are computed using a coupled finite element scheme. Interactions between neighboring islands are modeled using a cohesive zone law. Our model predicts stress-thickness vs. thickness behavior that is in excellent agreement with experiments. Specifically, we observe a three-stage growth process consisting of a stress-free pre-coalescence stage, a rapid tensile rise at coalescence, and an eventual transition to a steady-state. The steady-state stress may be tensile or compressive, depending on the deposition rate, the grain size, and the properties of the film. Detailed parametric studies are conducted to establish the influence of material properties and growth conditions on the stress history, and the results are compared with experimental observations and previous models.