Calculus of Variations and Geometric Measure Theory

P. Piovano - F. Sapio

Evolution of crystalline thin films by evaporation and condensation in three dimensions

created by piovano on 23 Jun 2023
modified on 03 Nov 2024

[BibTeX]

Submitted Paper

Inserted: 23 jun 2023
Last Updated: 3 nov 2024

Year: 2023

ArXiv: 2306.13432 PDF

Abstract:

The morphology of crystalline thin films evolving on flat rigid substrates by condensation of extra film atoms or by evaporation of their own atoms in the surrounding vapor is studied in the framework of the theory of Stress Driven Rearrangement Instabilities (SDRI). By following the literature both the elastic contributions due to the mismatch between the film and the substrate lattices at their theoretical (free-standing) elastic equilibrium, and a curvature perturbative regularization preventing the problem to be ill-posed due to the otherwise exhibited backward parabolicity, are added in the evolution equation. The resulting Cauchy problem under investigation consists in an anisotropic mean-curvature type flow of the fourth order on the film profiles, which are assumed to be parametrizable as graphs of functions measuring the film thicknesses, coupled with a quasistatic elastic problem in the film bulks. The existence of a regular solution for a finite period of time is established under periodic boundary conditions by means of employing minimizing movements to exploit the gradient-flow structure of the evolution equation.

Keywords: existence, regularity, minimizing movements, gradient-flow, Thin films, evaporation, condensation , 3 dimensions, mismatch strain, curvature regularization


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