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<p>A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the infimal energy is proven. The results quantify the expectation that in certain parameter regimes, island formation or topological defects are favorable. This generalizes results in the purely elastic setting from [<CitationRef CitationID="CR23">23</CitationRef>]. To handle dislocations in the lower bound, a new variant of a ball-construction combined with thorough local estimates is presented.</p>

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A scaling law for a model of epitaxially strained elastic films with dislocations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月13日

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  • J. Ginster,
  • L. Neubauer,
  • B. Zwicknagl

摘要

A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the infimal energy is proven. The results quantify the expectation that in certain parameter regimes, island formation or topological defects are favorable. This generalizes results in the purely elastic setting from [23]. To handle dislocations in the lower bound, a new variant of a ball-construction combined with thorough local estimates is presented.