Analytical validation of the Young–Dupré law for epitaxially-strained thin films

Davoli, Elisa; Piovano, Paolo

doi:10.1142/s0218202519500441

Cited by 17 publications

(18 citation statements)

References 38 publications

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“…Recently the analysis of [11] has been extended to three dimensions in [12]. A complete analysis of the regularity of optimal profiles, as well as of contact angle conditions will be the subject of the companion paper [8].…”

Section: Introductionmentioning

confidence: 99%

Derivation of a heteroepitaxial thin-film model

Davoli

Piovano

2020

Interfaces Free Bound.

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A variational model for epitaxially-strained thin films on rigid substrates is derived both by Γ-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for regular configurations. The model is characterized by a configurational energy that accounts for both the competing mechanisms responsible for the film shape. On the one hand, the lattice mismatch between the film and the substrate generate large stresses, and corrugations may be present because film atoms move to release the elastic energy. On the other hand, flatter profiles may be preferable to minimize the surface energy. Some first regularity results are presented for energetically-optimal film profiles.

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Section: Introductionmentioning

confidence: 99%

Derivation of a heteroepitaxial thin-film model

Davoli

Piovano

2020

Interfaces Free Bound.

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“…where γ f , γ s , and γ f s denote the surface tensions of the film-vapor, substrate-vapor, and film-substrate interfaces, respectively. The energy F coincides (apart from the presence of delamination) with the thin-film energy in [22,23]…”

Section: Resultsmentioning

confidence: 70%

“…As a byproduct of our analysis, we extend previous results for the existence of minimal configurations to anisotropic surface and elastic energies, and we relax constraints previously assumed on admissible configurations in the thin-film and crystal-cavity settings. For thin films we avoid the reduction considered in [22,23,31] to only film profiles parametrizable by thickness functions, and for crystal cavities the restriction in [30] to cavity sets consisting of only one connected starshaped void.…”

Section: Introductionmentioning

confidence: 99%

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A Unified Model for Stress-Driven Rearrangement Instabilities

Kholmatov

Piovano

2020

Arch Rational Mech Anal

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A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is characterized by an energy displaying both elastic and surface terms, and allows for a unified treatment of a wide range of settings, from epitaxially-strained thin films to crystalline cavities, and from capillarity problems to fracture models. The existence of minimizing configurations is established by adopting the direct method of the Calculus of Variations. The compactness of energy-equibounded sequences and energy lower semicontinuity are shown with respect to a proper selected topology in a class of admissible configurations that extends the classes previously considered in the literature. In particular, graph-like constraints previously considered for the setting of thin films and crystalline cavities are substituted by the more general assumption that the free crystalline interface is the boundary, consisting of an at most fixed finite number m of connected components, of sets of finite perimeter. Finally, it is shown that, as m → ∞, the energy of minimal admissible configurations tends to the minimum energy in the general class of configurations without the bound on the number of connected components for the free interface. Contents

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“…They are very well studied in the physical and numerical literature, see for instance [26,29,40,41,42]. Concerning rigorous mathematical analysis, we refer to [6,8,10,17,21,25,28] for some existence, regularity and stability results 1 related to a variational model describing the equilibrium configurations of two-dimensional epitaxially strained elastic films, and to [9,16] for results in three-dimensions. A hierarchy of variational principles to describe equilibrium shapes in the aforementioned contexts has been introduced in [30].…”

Section: Introductionmentioning

confidence: 99%