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arXiv · 1809.09991

Analytical validation of the Yound-Dupr\'e law for epitaxially-strained thin films

Elisa Davoli·Paolo Piovano
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Abstract

We present here an analysis of the regularity of minimizers of a variational model for epitaxially strained thin-films identified by the authors in the companion paper [Davoli E., Piovano P., Derivation of a heteroepitaxial thin-film model. Submitted 2018]. The regularity of energetically-optimal film profiles is studied by extending previous methods and by developing new ideas based on transmission problems. The achieved regularity results relate to both the Stranski-Krastanow and the Volmer-Weber modes, the possibility of different elastic properties between the film and the substrate, and the presence of the surface tensions of all three involved interfaces: film/gas, substrate/gas, and film/substrate. Finally, geometrical conditions are provided for the optimal wetting angle, i.e., the angle formed at the contact point of films with the substrate. In particular, the Young-Dupr\'e law is shown to hold, yielding what appears to be the first analytical validation of such law for a thin-film model in the context of Continuum Mechanics.

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Elisa Davoli, Paolo Piovano. 2018-09-26. Analytical validation of the Yound-Dupr\'e law for epitaxially-strained thin films. https://arxiv.org/abs/1809.09991

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